Answers
option D is correct answer As we can see, the graph is a parabola for x <= 0 and an exponential curve for x > 0. The function is continuous, but not differentiable at x = 0
what is exponential curve?
An exponential curve is a mathematical curve that rises or falls at an increasing rate as its values get larger. The curve is defined by an exponential function
In the given question,
To graph this function, we can start by plotting the points for different values of x. Since the function behaves differently for x <= 0 and x > 0, we will plot the points separately for each region.
For x <= 0:
x g(x)
-2 4
-1 1
0 0
For x > 0:
x g(x)
0.5 e⁰⁵ = 1.65
1 e = 2.72
2 e²= 7.39
x <= 0 x > 0
As you can see, the graph is a parabola for x <= 0 and an exponential curve for x > 0. The function is continuous, but not differentiable at x = 0 because the derivative from the left and the derivative from the right do not match.
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Related Questions
A cannon on a 1m raised platform fires a cannonball at a speed of 200m/s. It lands in a field of equal elevation 2km away.
At what angle did the cannon fire the shot, and when did it land? Disregard air resistance.
For an easier problem, eliminate the raised platform
Note: Please show all work!
Answers
The cannonball will land approximately 20.4 seconds after it was fired.
What is the name of a cannon ball?A round shot is a solid, spherical projectile fired from a gun that is also known as a decent shot or simply a ball. Its diameter is just a little bit smaller than the diameter of the barrel that it is fired from.
A cannon ball's composition.An iron anti-personnel bullet having a hollow internal cavity filled with leads or iron round pellets and a tiny explosive charge that explodes with just enough power to crack open the iron projectile's thin walls. A time fuse was put into a receptacle at the projectile's outer edge after a powder trains in a tiny iron sleeve.
We can use the equations of motion for projectile motion to solve this problem. Let's assume that the cannonball is fired at an angle θ above the horizontal and lands at a distance of x = 2000 meters from the cannon. We also know that the initial speed of the cannonball is 200 m/s.
The horizontal and vertical components of the velocity can be expressed as:
vₓ = v₀ cos(θ)
vₐ = v₀ sin(θ) - gt
where v₀ is the initial velocity (200 m/s), g is the acceleration due to gravity (9.8 m/s²), and t is the time taken for the cannonball to land.
Using the equation for the horizontal motion, we can find the time taken for the cannonball to travel a distance of 2000 meters:
x = v₀ cos(θ) * t
t = x / (v₀ cos(θ))
Using the equation for the vertical motion, we can find the time taken for the cannonball to reach the ground:
y = v₀ sin(θ) * t - (1/2) * g * t²
0 = v₀ sin(θ) * t - (1/2) * g * t²
Solving for t in the second equation gives:
t = 2 * v₀ sin(θ) / g
Substituting this expression for t into the first equation gives:
x = (v₀² / g) * sin(2θ)
We can now solve for θ:
sin(2θ) = (g * x) / v₀²
θ = 0.5 * arcsin((g * x) / v₀²)
Plugging in the given values for g, x, and v0, we get:
θ = 0.5 * arcsin((9.8 m/s² * 2000 m) / (200 m/s)²) ≈ 20.3 degrees
Therefore, the cannon fired the shot at an angle of approximately 20.3 degrees above the horizontal.
To find the time taken for the cannonball to land, we can use the expression for t derived earlier:
t = 2 * v₀ sin(θ) / g
t = 2 * 200 m/s * sin(20.3°) / 9.8 m/s² ≈ 20.4 seconds
Therefore, the cannonball will land approximately 20.4 seconds after it was fired.
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on the July 7 billing date, Marvin had a balance due of $216.71 on his credit card. the transactions during the following month were
July 14 office supplies $52.04 July 17 scarf $15.66
July 21 payment of $100
July 24 charge: toy truck $44.03
the interest rate on the card is 1.25% per month. using the previous balance method find the finance charge on August 7 then find the new balance of August 7.
simple interest formula i=prt
Answers
Answer:
The first step is to calculate the average daily balance for the billing cycle. This is done by adding up the daily balances for each day of the billing cycle and then dividing by the number of days in the billing cycle. In this case, the billing cycle is from July 7 to August 6, so there are 31 days in the billing cycle.
The daily balances are as follows:
* July 7: $216.71
* July 14: $268.75
* July 17: $284.37
* July 21: $116.71
* July 24: $260.74
The average daily balance is therefore $226.81.
The next step is to calculate the finance charge. This is done by multiplying the average daily balance by the interest rate and then by the number of days in the billing cycle. In this case, the interest rate is 1.25% and the number of days in the billing cycle is 31 days.
The finance charge is therefore $7.43.
The final step is to calculate the new balance. This is done by adding the finance charge to the previous balance. In this case, the previous balance is $216.71 and the finance charge is $7.43. The new balance is therefore $224.14.
Here is the solution in mathematical form:
* Average daily balance = (216.71 + 268.75 + 284.37 + 116.71 + 260.74) / 31 = 226.81
* Finance charge = 226.81 * 0.0125 * 31 = 7.43
* New balance = 216.71 + 7.43 = 224.14
Step-by-step explanation:
HELP!!!
The graph represents a relation where x represents the independent variable and y represents the dependent variable. a coordinate plane with points at negative 5 comma 1, negative 2 comma 0, 0 comma 2, 1 comma negative 2, 3 comma 3, and 5 comma 1 What is the domain of the relation?
Answers
The domain of the relation is the set {-5, -2, 0, 1, 3, 5}.
The domain of a relation is the set of all possible input values (independent variable) that correspond to an output (dependent variable).
The domain of a function or relation is the set of all possible input values (independent variable) that correspond to an output (dependent variable). It represents the values for which the function or relation is defined.
Looking at the given points, we can see that the x-coordinates of the points are -5, -2, 0, 1, 3, and 5. Therefore, the possible input values for this relation (i.e., the domain) are:
Domain: {-5, -2, 0, 1, 3, 5}
So the domain of the relation is the set {-5, -2, 0, 1, 3, 5}.
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Suppose you have $50 in a savings account and deposit an additional $10 each week.
a) Write a recursive formula to represent the sequence.
b) Write an explicit formula to represent the sequence.
c) How much money do you have in savings after 26
weeks? Show all work.
Answers
a. The recursive formula to represent the sequence is aₓ = aₓ₋₁ + 10.
b. The explicit formula to represent the sequence is aₓ = 50 + 10x.
c. We have $310 in savings after 26 weeks.
What is sequence?
A progression or sequence of numbers known as an arithmetic sequence keeps the difference between any subsequent term and its preceding term constant throughout the entire sequence. In that arithmetic progression, the constant difference is known as the common difference.
We are given that there are $50 in a savings account and each week additional $10 are deposited.
a. Let x be the number of weeks
a₀ = $50
aₓ = aₓ₋₁ + 10
So, the recursive formula to represent the sequence is aₓ = aₓ₋₁ + 10.
b. Let x be the number of weeks.
So, the explicit formula is given by
aₓ = 50 + 10x
c. Now, we are given x = 26.
So, by substituting this, we get
⇒ a₂₆ = 50 + 10 * 26
⇒ a₂₆ = 50 + 260
⇒ a₂₆ = $310
Hence, the required solutions have been obtained.
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A ladder forms the hypotenuse of a right triangle with a building and the ground, as shown. The ladder reaches to a height of 30 feet on the building, while the base of the ladder is 6 feet from the bottom of the building. What is the length of the ladder?
Answers
The length of the ladder is approximately 30.6 feet. The height of the building is 90 degrees.
Let "θ" be the angle between the ladder and the ground. Then, we have:
sin(θ) = 30 ÷ x
Solving for "x", we get:
x = 30 ÷ sin(θ)
Since the ladder is the hypotenuse, we know that the angle opposite the height of the building is 90 degrees. Therefore, the angle between the ladder and the ground is the complement of this angle, which is:
θ = 90 - arcsin(30 ÷ x)
Substituting this expression for "θ" into the equation for "x", we get:
x = 30 ÷ sin(90 - arcsin(30 ÷ x))
Using the identity sin(90 - θ) = cos(θ), we can simplify this to:
x = 30 / cos(arcsin(30 ÷ x))
Using the identity cos(arcsin(x)) = [tex]\sqrt[] 1-x^{2}[/tex] , we can simplify this further to:
x = [tex]\frac{30}{\sqrt{(1-(30/x^{2}))\\} }[/tex]
Squaring both sides and simplifying, we get:
x² = 30² + 6²
x² = 900 + 36
x² = 936
x = [tex]\sqrt{936}[/tex]
x = 30.6 feet is height of ladder
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you ride a bike to campus a distance of 5 miles and return home on the same route. Going to campus, you ride mostly downhill and average 9 miles per hour faster than on your return trip home. If the round trip one hour and ten minutes that is 7/6 hours; what is your average velocity on your return trip
Answers
We know that the distance to campus and back is a total of 5 miles in each direction, so the total distance traveled is 10 miles.
We also know that the total time it takes is 7/6 hours.
Using the formula:
Total distance = (average speed) x (total time)
we can set up two equations:
5 = x(t1) (distance to campus)
5 = (x - 9)(t2) (distance back home)
where t1 is the time it takes to get to campus and t2 is the time it takes to get back home.
We also know that t1 + t2 = 7/6, since the total time is 7/6 hours.
We can solve for t1 in terms of t2:
t1 = (7/6 - t2)
Now we can substitute this value for t1 in the first equation:
5 = x(7/6 - t2)
Solving for x, we get:
x = 30/(7 - 6t2)
We want to find the speed on the way back home, which is x - 9.
x - 9 = 30/(7 - 6t2) - 9
Simplifying:
x - 9 = (30 - 9(7 - 6t2))/(7 - 6t2)
x - 9 = (3t2 - 3)/(-6t2 + 7)
Now we can use the fact that t1 + t2 = 7/6 to solve for t2:
t1 + t2 = 7/6
(7/6 - t2) + t2 = 7/6
Solving for t2:
t2 = 1/2
Now we can plug in t2 = 1/2 into the expression we found for x - 9:
x - 9 = (3(1/2) - 3)/(-6(1/2) + 7)
x - 9 = 3/5
x = 42/5
So the speed on the way back home is x - 9 = (42/5) - 9 = 3/5, which is approximately 0.6 miles per minute.
If an answer for this question is not a whole number, enter it as a decimal.
Students collected a random sample of data on how many seconds 7th grade boys and 7th grade girls could maintain a handstand
The data collected from the sample is shown below.
7th grade boys: 19, 17, 19, 20, 19, 18, 19, 24
7th grade girls: 16, 21, 17, 16, 18, 19, 21, 18
The difference between the boys' mean time and the girls' mean time is
second(s)
second(s)
The difference between the boys' median time and the girls' median time is
Based on the sample data, which population of students, the 7th grade boys or the 7th grade girls, would be more likely to hold a
handstand for about 19 seconds or more? the 7th grade
Answers
Based on the sample data, 7th grade boys, would be more likely to hold a handstand for about 19 seconds or more.
The difference between the boys' mean time and the girls' mean time is 1 second.
The difference between the boys' median time and the girls' median time is 1.5 seconds.
What is sample data?A subset of data collected from a larger population. It is typically used to represent the larger population and is used for testing and analysis.
In this data set, the mean time of the 7th grade boys= 19.375 seconds, while the mean time of the 7th grade girls = 17.875 seconds.
This means that the 7th grade boys have a higher mean time than the 7th grade girls.
The difference is 1.5 seconds.
The median time of the 7th grade boys = 19 seconds, and the median time of the 7th grade girls = 18 seconds.
This also indicates that the 7th grade boys have a higher median time than the 7th grade girls.
The difference is 1 second.
Given this data, the 7th grade boys are more likely to hold a handstand for about 19 seconds or more than the 7th grade girls.
This is because the mean and median times for the 7th grade boys are higher than the mean and median times for the 7th grade girls.
This indicates that the 7th grade boys have a higher average time than the 7th grade girls, and thus, are more likely to hold a handstand for a longer period of time.
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PLEASE HELP ILLL MAKE BRAINLY
Answers
By looking at the 0 and 1 column, 200 people own less than two smartphones
You can get 52 to point if you answer every single answer hurry up this a test
Determine the number of units a given figure would be translated using the given notation.
Answers
The number of units a given figure would be translated using the given notation are shown below.
What is a translation?In Mathematics, the translation of a graph to the left is a type of transformation that simply means subtracting a digit from the value on the x-coordinate of the pre-image while the translation of a graph to the right is a type of transformation that simply means adding a digit to the value on the x-coordinate of the pre-image.
Based on each of the transformation rule, the number of units a given figure would be translated using the given notation include the following:
(x, y) → (x + 7, y - 6)
7 units right.
6 units down.
(x, y) → (x - 9, y + 2)
9 units left.
2 units up.
(x, y) → (x - 11, y)
11 units left.
0 units up/down.
(x, y) → (x - 8, y - 5)
8 units left.
5 units down.
(x, y) → (x + 13, y + 3)
7 units right.
3 units up.
(x, y) → (x, y + 9)
0 units right/left.
9 units up.
(x, y) → (x - 14, y + 12)
14 units left.
12 units up.
(x, y) → (x, y - 4)
0 units right/left.
4 units down.
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there are several possible heights at which the higher end of the bridge can be attached to the higher end of the mountain. Fill in the table below to use 5 possible values for y, and calculate the resulting values for r
Answers
The resulting values for r will be sqrt(140).
Let's assume that the bridge is a straight line segment that connects the top of the mountain (point A) to a point on the ground (point B).
Let's also assume that the distance from the top of the mountain to point B is a fixed value d.
If we attach the higher end of the bridge to the top of the mountain at a height y, the distance between point A and the attachment point can be calculated using the Pythagorean theorem as:
x = sqrt([tex]d^2[/tex] - [tex]y^2[/tex])
The length of the bridge, which is also the hypotenuse of the right triangle formed by points A, B, and the attachment point, can then be calculated as:
r = sqrt([tex]x^2[/tex] + [tex](d-y)^2[/tex])
To find the values of r for different heights y, we can simply substitute different values of y into these equations and calculate the resulting values of r.
For example, if we use the values d=10 and y=3, we get:
To calculate the values for "r" given 5 possible values for "y," we need to use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the bridge is the hypotenuse, and we know the height of the mountain (x) and the distance from the mountain to the lower end of the bridge (d). So we can write:
r^2 = [tex]x^2[/tex] + [tex](d + y)^2[/tex]
x = sqrt([tex]10^2[/tex] - [tex]3^2[/tex])
x = sqrt(91)
r = sqrt((sqrt([tex]91))^2[/tex] + [tex](10-3)^2[/tex])
r = sqrt(91 + 49)
r = sqrt(140)
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Which is a solution for the following system of inequalities?
Answers
Text → Graphing Exponential Functions: Mastery Test
2
Select the correct answer.
Which statement correctly compares the graph of function g with the graph of function f?
f(x) = e - 4
g(x) =
- 4
OA.
OB.
O C.
O D.
The graph of function g is a horizontal shift of the graph of function f to the left.
The graph of function g is a vertical stretch of the graph of function f.
The graph of function g is a horizontal shift of the graph of function f to the right.
The graph of function g is a vertical compression of the graph of function f.
Answers
Answer:
x=2
Step-by-step explanation:
4 x1,2 =2
The correct statement which compares the graph of function g with the graph of function f is,
⇒ The graph of function g is a vertical compression of the graph of function f.
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
Functions are,
f (x) = eˣ - 4
g (x) = 1/2eˣ - 4
Now, We have to find that;
The graph of function g is a vertical compression of the graph of function f.
Hence, The correct statement which compares the graph of function g with the graph of function f is,
⇒ The graph of function g is a vertical compression of the graph of function f.
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Ariel checked the prices of 9 dog training programs. The prices were: $78.00$78.00$80.00$77.00$78.00$77.00$78.00$77.00$79.00 What was the median price charged?
Answers
The median price charged is $78.00
The median of the data:
The median of a set of data is the middle value when the data is arranged in numerical order.
In other words, it is the value that separates the data into two halves, with half of the values being less than the median and half being greater than the median. If there is an even number of data points, the median is the average of the two middle values.
Here we have
The prices of 9 dog training programs were:
$ 78.00, $ 78.00, $80.00, $77.00, $78.00, $77.00, $78.00, $77.00, $79.00
To find the median price, we need to arrange the prices in order from least to greatest:
$77.00, $77.00, $77.00, $78.00, $78.00, $78.00, $78.00, $79.00, $80.00
There are nine prices, which is an odd number,
So the median is the middle number.
In this case, the middle number is the fifth number, which is $78.00
Therefore,
The median price charged is $78.00
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find x if 2x+3x+3x-4x=32x^2
Answers
Answer: x=0, x=1/8
Step-by-step explanation:
Simplifying the equation give us: 4x=32x^2
Subtract 4x from both sides: 32x^2-4x=0
Factor:4x(8x-1)=0
Using the Zero Product Property, x=0, x=1/8
Answer:
x equals 0 it wont only let me put answer so i am typing more
Recursive Rules from Word Problems
1) Sally started a new job. After depositing her 1st paycheck into her bank account she had
$225. Every week she was paid the same amount. After her 8th paycheck she had $1275 in her
bank account.
Complete the table
Answers
after her 2nd paycheck, Sally had $375 in her bank account, after her 3rd paycheck she had $525, after her 4th paycheck she had $675, after her 5th paycheck she had $825, after her 6th paycheck she had $975, and after her 7th paycheck she had $1125.
How to solve the problem?
Let's call the amount that Sally gets paid every week "x". We know that after her 1st paycheck, she had $225, so we can write:
1st paycheck: $225
2nd paycheck: $225 + x
3rd paycheck: $225 + 2x
4th paycheck: $225 + 3x
5th paycheck: $225 + 4x
6th paycheck: $225 + 5x
7th paycheck: $225 + 6x
8th paycheck: $225 + 7x = $1275
To solve for "x", we can start by subtracting $225 from both sides of the equation for the 8th paycheck:
$225 + 7x = $1275
7x = $1050
x = $150
So Sally gets paid $150 every week.
To find the amount of money she had in her account after each paycheck, we can substitute "x" into the equations above:
1st paycheck: $225
2nd paycheck: $225 + $150 = $375
3rd paycheck: $225 + 2($150) = $525
4th paycheck: $225 + 3($150) = $675
5th paycheck: $225 + 4($150) = $825
6th paycheck: $225 + 5($150) = $975
7th paycheck: $225 + 6($150) = $1125
8th paycheck: $225 + 7($150) = $1275
Therefore, after her 2nd paycheck, Sally had $375 in her bank account, after her 3rd paycheck she had $525, after her 4th paycheck she had $675, after her 5th paycheck she had $825, after her 6th paycheck she had $975, and after her 7th paycheck she had $1125.
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which of the following describes a move away from capitalism
Answers
The nationalization of major industries in Hugo Chavez's Venezuela describes a move away from capitalism. Thus, option C is correct.
What is capitalism?
Capitalism is an economic system characterized by private ownership of the means of production and the creation of goods or services for profit in a competitive market. In capitalism, individuals and businesses are free to invest and produce goods and services that they can sell for a profit.
A move away from capitalism would entail a shift in economic system from one that is primarily driven by profit and private ownership to one that prioritizes social welfare and collective ownership.
Chavez, a clοse ally οf Cuba’s cοmmunist leaders, has steadily increased the rοle οf the state in Venezuela with a slew οf natiοnalizatiοns and tοugh cοntrοls οn prices and fοreign exchange.
Despite an ecοnοmy weakened by lοwer οil incοme, Chavez has sοlid apprοval ratings and is nοw pοwering ahead with his plan tο regulate and reduce the private sectοr in the OPEC cοuntry
Therefore, The nationalization of major industries in Hugo Chavez's Venezuela describes a move away from capitalism. Thus, option C is correct.
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Complete question:
Which of the following describes a move away from capitalism?
O A. Sweden's 1980s cutback on social programs
O B. the transformation of the former Soviet Union to today's Russia
O C. the nationalization of major industries in Hugo Chavez's Venezuela
O D. economic reforms following the Great Depression in the United States
PLEASE SHOW WORK FOR BRAINLIST!!!
In circle A what is angle DAR?
Answers
Answer:
68°
Step-by-step explanation:
because the inscribed angle (at B) is half of the arc angle (at A).
angle B = 1/2 × angle A
34 = 1/2 × angle A
angle A = 34×2 = 68°
3/2=4x what is x
Solve the equation.
3
2
=
4
�
2
3
=4xstart fraction, 3, divided by, 2, end fraction, equals, 4, x
�
=
x=x, equals
Answers
Answer:
x = 3/8
Step-by-step explanation:
You want the solution to 3/2 = 4x.
One-step equationYou solve this one-step linear equation by multiplying both sides by the inverse of the x-coefficient:
[tex]\dfrac{3}{2}=4x\qquad\text{given}\\\\\\\dfrac{1}{4}\times\dfrac{3}{2}=\dfrac{1}{4}\times4x\\\\\\\dfrac{3}{8}=\dfrac{4}{4}x\\\\\\\boxed{x=\dfrac{3}{8}}[/tex]
__
Additional comment
The "one step" is multiplying both sides by 1/4. The rest is simplifying the result.
Of course, this is the same as dividing both sides by 4. The result is x = (3/2)÷4 = 3/(2·4) = 3/8.
A speaker claimed that if the number of factories in the country increases by 3% per annum, then even if they all immediately reduced the amount of pollution they produce by 80%, the total annual pollution will be back to its present level in about 50 years. (Hint use Logarithms)
Answers
Actual time is much longer than the 50-year timeframe suggested by the speaker.
How to verify the statement?
This claim is based on the assumption that the rate of pollution reduction from each factory remains constant at 80%, and the number of factories increases by 3% per annum.
To verify this claim, we can use the following formula to calculate the expected total pollution after n years:
Total pollution after n years = [tex]Present \: pollution \: level x (1 + 0.03)^n \times (1 - 0.8)^n[/tex]
Here, the first factor represents the increase in pollution due to the growth in the number of factories, and the second factor represents the reduction in pollution due to the 80% reduction in pollution from each factory.
We can set the expected total pollution after n years equal to the present pollution level and solve for n:
[tex]Present \: pollution \: level = Present \: pollution \: level \times (1 + 0.03)^n \times (1 - 0.8)^n[/tex]
Simplifying this equation, we get:
[tex]1 = 1.03^n \times 0.2^n[/tex]
Taking the logarithm of both sides of the equation, we get,
[tex]n \times log(1.03) + n \times log(0.2) = 0 \\ n \times (log(1.03) + log(0.2)) = 0 \\ n = \frac{0} { (log(1.03) + log(0.2))} \\ n = 271.56[/tex]
Therefore, according to this calculation, it would take approximately 272 years for the total annual pollution to return to its present level if the number of factories in the country increases by 3% per annum, and they all immediately reduce the amount of pollution they produce by 80%. This is much longer than the 50-year timeframe suggested by the speaker.
It is important to note that this calculation assumes that the pollution reduction from each factory remains constant at 80% and does not take into account any other factors that may affect pollution levels, such as changes in technology or regulations. Therefore, this should be considered as a rough estimate and not as an exact prediction.
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Correct question is "A speaker claimed that if the number of factories in the country increases by 3% per annum, then even if they all immediately reduced the amount of pollution they produce by 80%, the total annual pollution will be back to its present level in about 50 years. Verify the statement. (use logarithm)"
Pls help me
How long is the side CD? (Hint: opposite sides are equal. Put the expressions equal to each other and solve for x. Then, plug back into the expression for CD to find CD).
Answers
the side CD will be 27 units.
What is parallelogram?
A unique variety of quadrilateral made up of parallel lines is known as a parallelogram. A parallelogram can have any angle between its adjacent sides as long as its opposite sides are parallel. If two opposite sides of a quadrilateral are parallel and congruent, it will be a parallelogram. Consequently, a quadrilateral in which both pairs of opposite sides are parallel and equal is known as a parallelogram.
Here CD=AB
2x+13=5x-8
3x = 13+8
x= 21/3
x=7
CD= 2*7+13=14+13=27
Hence the side CD will be 27 units.
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Amanda was watching her little brother Mike play on a swing
set. She decided that she would like to find his distance above
the ground using a sine or cosine curve. She starts timing and
finds that at t-2 seconds Mike is at his highest point. He
reachers his lowest point exactly 1.5 seconds later. Amanda
also records the highest Mike gets as 9 feet whle the lowest
point occurs at 1 foot. Write an equation that will find Mike's
height after t seconds.
Answers
Putting all these values together, we get the equation: h(t) = 4 cos(2π/3 (t - 2)) + 1 with Mike's height above the ground as a function of time t in seconds, where h(t) is measured in feet.
What is equation?An equation is a mathematical statement that shows that two expressions are equal. It contains an equals sign (=) and at least two expressions on either side of the equals sign. The expressions on either side of the equals sign can be numbers, variables, or a combination of both, and the equation represents a relationship between them. Equations are used in mathematics to solve problems and find unknown values by manipulating the expressions within the equation while keeping the equality true.
Here,
Assuming that Mike's motion on the swing set follows a periodic pattern, we can model his height above the ground using a sinusoidal function. Let's use the cosine function, since it reaches its maximum value when the input is 0 and decreases to its minimum value at π or 180°.
The general form of a cosine function is:
y = A cos(Bx + C) + D
where:
A = amplitude (half the distance between the maximum and minimum values)
B = frequency (the number of cycles per unit of x)
C = phase shift (horizontal shift of the graph)
D = vertical shift (vertical shift of the graph)
We are given that Mike's highest point is at 9 feet and his lowest point is at 1 foot. Therefore, the amplitude A = (9 - 1) / 2 = 4.
The frequency is determined by the time it takes for Mike to complete one cycle. We know that it takes him 1.5 seconds to go from his highest point to his lowest point and back up again. Therefore, the period of the function is 3 seconds (2 x 1.5), and the frequency is 1/3 cycles per second. Hence, B = 2π/3.
The phase shift is the horizontal displacement of the graph from the origin. We know that at t = 2 seconds, Mike is at his highest point. Therefore, we need to shift the cosine curve 2 seconds to the right to match this point. Thus, C = -2.
Finally, the vertical shift D is the position of the center of the curve. Since Mike's lowest point is at 1 foot, we need to shift the entire curve up by 1 foot. Thus, D = 1.
Putting all these values together, we get the equation:
h(t) = 4 cos(2π/3 (t - 2)) + 1
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if the volume of a cube can be represented by a polynomial of degree 9, what is the degree of the polynomial that represents each side lenght
Answers
Answer:
Each side length of the cube will be a polynomial of degree 3.
HELP I NEED THIS ASAP PLS HELP
Answers
Answer:
A
Step-by-step explanation:
I added a photo of my notes (the angles I've marked as equal are cross angles)
[tex]w = 180° - 30° - x°[/tex]
[tex]w = 150° - x°[/tex]
Find the trigonometric ratios as simplified fractions and as decimals to the nearest thousandths (as necessary).
Sin X: Fraction ______ Decimal _______
Cos X: Fraction ______ Decimal ______
Tan X: Fraction _______ Decimal ______
(30 points)
Answers
By answering the presented question, we may conclude that tan(X): trigonometry Fraction 3/4, Decimal 0.750
what is trigonometry?The study of the connection between triangle side lengths and angles is known as trigonometry. The concept first originated in the Hellenistic era, during the third century BC, due to the application of geometry in astronomical investigations. The subject of mathematics known as exact techniques deals with certain trigonometric functions and their possible applications in calculations. There are six commonly used trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their separate names and acronyms (csc). The study of triangle characteristics, particularly those of right triangles, is known as trigonometry. As a result, geometry is the study of the properties of all geometric forms.
Using the Pythagorean theorem,
hypotenuse² = opposite² + adjacent²
hypotenuse² = 4² + 3²
hypotenuse² = 16 + 9
hypotenuse² = 25
hypotenuse = √25
hypotenuse = 5
Now we can find the trigonometric ratios:
sin(X) = opposite / hypotenuse = 3/5
sin(X) = 0.600 (rounded to the nearest thousandth)
cos(X) = adjacent / hypotenuse = 4/5
cos(X) = 0.800 (rounded to the nearest thousandth)
tan(X) = opposite / adjacent = 3/4
tan(X) = 0.750 (rounded to the nearest thousandth)
Therefore, the trigonometric ratios for angle X are:
sin(X): Fraction 3/5, Decimal 0.600
cos(X): Fraction 4/5, Decimal 0.800
tan(X): Fraction 3/4, Decimal 0.750
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Tammy ran 4 2
5 miles on Saturday.
On Sunday she ran for 1
2 of the distance
she ran on Saturday. Write and solve an
equation that will help you figure out how
far Tammy ran on Sunday. Explain the
steps you took to solve the problem
Answers
Tammy ran 2.25 miles on Sunday.
What is Linear Equation?A linear equation is a mathematical expression that describes a straight line on a graph. It is of the form y = mx + b, where "m" is the slope of the line and "b" is the y-intercept.
Let's start by figuring out how far Tammy ran on Sunday. We know that she ran for 1/2 of the distance she ran on Saturday. Therefore, if we let "x" be the distance Tammy ran on Sunday, we can set up the following equation:
x = 1/2(4.5)
Here, we used the fact that Tammy ran 4.5 miles on Saturday.
To solve for "x", we simply need to simplify the right-hand side of the equation:
x = 1/2(4.5)
x = 2.25
Therefore, Tammy ran 2.25 miles on Sunday.
In summary, we used the equation x = 1/2(4.5) to represent the distance Tammy ran on Sunday, where "x" is the unknown distance. We then solved for "x" by simplifying the equation and found that Tammy ran 2.25 miles on Sunday.
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A side of a inner circle trapezium is a diameter of the circle. The non-parallel sides are equal to the radius of a circle. If the radius of the circle is 2 units, the area of the trapezium can be written as n√n. What is the value of n?
Answers
The value of n = 12, and the area of the trapezium can be written as 12√12.
How to determine the the value of nLet's call the diameter of the circle (and one of the parallel sides of the trapezium) "AB", and let's call the non-parallel sides "CD" and "EF". We know that CD and EF are both equal to the radius of the circle, which is 2 units.
We know that AB is a diameter of the circle, which means that its length is twice the radius, or 4 units.
We also know that CD and EF are each 2 units long.
To find the height of the trapezium, we can draw a perpendicular line from point C to line AB:
We can see that the height of the trapezium is the distance from point H to line AB. Since point H is directly above the center of the circle (point O), we can use the Pythagorean theorem to find its distance from point A (or point B, since AB is a diameter):
The length of the hypotenuse (OB) is 2 units (the radius of the circle), and the length of one of the legs (OA) is 2 units (half of AB). To find the length of the other leg (HB), we can use the Pythagorean theorem:
HB^2 + OA^2 = OB^2
HB^2 + 2^2 = 2^2
HB^2 = 0
This tells us that HB (and therefore the height of the trapezium) is 0 units.
Since the height is 0, the area of the trapezium is simply the average of the two parallel sides (AB and CD) multiplied by the distance between them (which is also AB).
Area = (AB + CD) / 2 * AB
= (4 + 2) / 2 * 4
= 3 * 4
= 12
Therefore, n = 12, and the area of the trapezium can be written as 12√12.
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Solve 9+5x-x^2 by completing the square
Answers
Explanation:
1. Rearrange
x^2+5x-9
2. Divide the coefficient of x by 2 squared.
[x^2+5x+(5/2)^2-(5/2)^2-9]
4. Put the first terms into ( )^2
(x+5/2)^2-64/1
5. Rearrange
61/4-(x-5/2)^2
A survey is taken at a movie theater in Winterville. The first 150 people who entered the theater were asked about their favorite type of movie. What is true about this situation?
The population is the first 150 people at the theater, and the sample is the total number of people who go to the movie theater.
The population is the number of people who go to the movie theater, and the sample is the number of people in the town of Winterville.
The population is the total number of people who go to the movie theater, and the sample is the first 150 people at the theater.
The population is the number of people in the town of Winterville, and the sample is the number of people who go to the movie theater.
Answers
Answer:
The population is the total number of people who go to the movie theater, and the sample is the first 150 people at the theater.
Step-by-step explanation:
The population is the potential people that could be sampled, and the sample is the people who are being asked the question.
Answer:ccccccccccccccccccccccccccc
Step-by-step explanation:
helpppppppppppppppppppppppppppp
Answers
Answer: 9+3z<-12
Step-by-step explanation: because first -3(2-z)= -6+3z
then 15-6=9
so then it is 9+3z for the left side and we didn't touch the right side so it would be the same
Adzo says the graph is of the function y = 2-¹x - √25.
Ben says it is y- 5 = 0.5x. Who is correct? Explain your answer.
Answers
Based on the information provided, I think that Ben is correct.
Let's analyze and compare the given expressions:
Adzo says the graph is of the function y = 2-¹x - √25.
In this expression, y is equal to 2 raised to the power of -1 multiplied by x, minus the square root of 25. This can also be written as y = (1/2)x - 5.
Ben says it is y - 5 = 0.5x.
In this expression, y - 5 is equal to 0.5 times x.
How do we compare the expressions?Comparing the two expressions, we can see that Ben's expression, y - 5 = 0.5x, is a linear equation in slope-intercept form, where the slope is 0.5 and the y-intercept is -5, representing a straight line on a graph.
On the other hand, Adzo's expression, y = (1/2)x - 5 or y = 2-¹x - √25, also represents a straight line on a graph with a slope of 1/2, but it is shifted vertically downward by 5 units due to the subtraction of 5 in the expression.
Thus, both expressions represent straight lines on a graph, however Ben's expression is in the standard slope-intercept form.
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