Using the addition operation, the sum of 40 + 5 is 45.
What is the addition operation?The addition operation is one of the basic mathematical operations.
Other mathematical operations include subtraction, division, multiplication, exponentiation, and functions.
The addition operation involves two addends added using the addition operand (+) and the equal symbol (=) we show the result of the algebraic operation called the sum or total.
Thus, when five is added to forty (40 + 5), the result or sum is forty-five (45).
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Andrew is building a gate in his fence in the shape of a trapezoid.
What is the area of the gate?
ANSWER: 16FT
SOLUTION IN IMAGES
Use the figure below to answer the questions
Solve for X
The measure of angle x in the hexagon is 140 degree.
What is the measure of angle x?The formula for calculating the sum of interior angles of a polygon is ( n − 2 ) × 180 degree.
where is the number of sides
Since the number of sides of the polygon in the diagram is 6, we can find the sum of the interior angle.
Sum of interior angle = ( n − 2 ) × 180
Plug in n = 6
Sum of interior angle = ( 6 − 2 ) × 180
Sum of interior angle = ( 4 ) × 180
Sum of interior angle = 720°
Next, we sum up the interior angles given in the diagram equate to 720 degree and solve for x.
108 + 155 + 123 + 104 + 90 + x = 720
Collect and add like terms
580 + x = 720
Subtract 580 from both sides
580 - 580 + x = 720 - 580
x = 720 - 580
x = 140°
Therefore, the value of x is 140 degree.
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Please help, look at the photos for the question and write an explanation.
The correct answer is (C) the total number of rolls sold (small and large).
What are algebraic equations?
An algebraic equation is a mathematical expression that includes one or more variables and mathematical operations such as addition, subtraction, multiplication, and division. The equation asserts that two expressions are equal.
The goal in solving an algebraic equation is to determine the value(s) of the variable(s) that make the equation true. Algebraic equations are used to solve problems in various fields such as physics, engineering, economics, and finance.
In the equation 3s + 135 = 4.5(s + 10), the expression (s + 10) represents the total number of rolls sold (small and large).
To see why, let's break down the equation:
3s represents the total amount earned from selling small rolls (since the
club earns $3.00 for every small roll sold).
4.5(s + 10) represents the total amount earned from selling all the rolls (small and large). The (s + 10) part represents the total number of rolls sold, since the club sold 10 more large rolls than small rolls, which is represented by adding 10 to the number of small rolls sold (s).
Therefore, the correct answer is (C) the total number of rolls sold (small and large).
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What is the solution to the system of linear equations shown below?
A. (3, 1)
B. (3, 0)
C. (-1, 4)
D. (1, 3)
Answer:
D. (1, 3)
Step-by-step explanation:
The solution is the coordinates of the intersection of the 2 lines
can someone please help me and please show your work
also check your work before posting it
Answer:
Step-by-step explanation:
To determine if the graphs of two linear equations are parallel, we need to compare their slopes. If the slopes are equal, then the lines are parallel. If the slopes are not equal, then the lines are not parallel.
In case (a), the two equations are y = x + 3 and y = x + 6. Both equations have a slope of 1, which means the lines have the same steepness. However, the y-intercepts are different (3 and 6), which means the lines are shifted up or down relative to each other. Since the slopes are equal, but the y-intercepts are different, the lines are parallel.
In case (b), the two equations are y = 4x - 1 and y = 1 - 4x. Both equations have a slope of -4, which means the lines have the same steepness. However, the y-intercepts are different (-1 and 1), which means the lines are shifted up or down relative to each other. Since the slopes are equal, but the y-intercepts are different, the lines are not parallel.
In case (c), the two equations are y = 2x - 3 and y = -2x + 3. The slopes of the two equations are 2 and -2, which are negative reciprocals of each other. This means the lines are perpendicular, not parallel.
In case (d), the two equations are 3y = x - 12 and 6y = 2x + 12. We can rewrite these equations in slope-intercept form by solving for y. The first equation becomes y = (1/3)x - 4 and the second equation becomes y = (1/2)x + 2. The slopes of the two equations are 1/3 and 1/2, which are not equal. Therefore, the lines are not parallel.
Answer:
22. Parallel
23. Not parallel
24. Not parallel
25. Parallel
Step-by-step explanation:
The slope equation form of a line is
y = mx + b
where
m = slope
b = y-intercept
If two lines are parallel their slopes, the value of m will be the same, in slope-intercept form
Q22
y = x + 33 → slope = 1
y = x + 6 → slope = 1
Slopes are the same with = 1
Hence the lines are parallel
Q23
y = 2x - 3 → slope m = 2
y = -2x + 3 → slope m = -2
Slopes not equal hence not parallel
Q24
y = 4x - 1 → slope = 4
y = 1 --4x or y = - 4x + 1 → slope = - 4
Slopes are different, hence not parallel
Q25
3y = x - 12
6y = 2x + 12
Divide the first equation by 3
=> 3y/3 = x/3 - 12/3
=> y = x/3 -4 → slope = 1/3
Divide the second equation by 6
6y/6 = 2x/6 + 12/6
y = x/3 + 2 → slope = 1/3
Slopes are same, hence parallel
Can somone help me with this I lost all my brain cells Lol
The volume of this cylinder is 492,452.48 cubic meters. What is the height?
Use ≈ 3.14 for pi and round your answer to the nearest hundredth. No height is given, but the radius is 52?
[tex] \Large{\boxed{\sf Height = 58 \: m}} [/tex]
[tex] \\ [/tex]
Explanation:The volume of a cylinder can be calculated using the following formula:
[tex] \Large{\sf V = B \times h} [/tex]
Where:
V is the volume of the cylinder.B is the area of its base.h is the height of the cylinder.[tex] \\ [/tex]
Since we are not given the area of its base, which is a circle, we will have to calculate it applying the following formula:
[tex] \Large{\sf B = \pi \times r^2} [/tex]
Where:
B is the area of the circle (the base of the cylinder).r is its radius.[tex] \\ [/tex]
Combining these two formulas, we can express the volume of the cylinder as follows:
[tex] \Large{\sf V = \underbrace{\sf \pi \times r^2}_{B} \times h} [/tex]
[tex] \\ [/tex]
Now, rearrange the formula to isolate the height, h.
[tex] \sf V = \pi \times r^2 \times h \Longleftrightarrow \dfrac{V}{\pi \times \times r^2} = \dfrac{ \pi \times r^2 \times h}{\pi \times r^2 } \Longleftrightarrow h = \dfrac{V}{\pi \times r^2} [/tex]
[tex] \\ [/tex]
[tex] \Large{\boxed{\sf Given \text{:} } \begin{cases} \sf V &=\sf 492,452.48 \: m^3 \\ \sf r &=\sf 52 \: m \: \\ \sf \pi &= \sf 3.14 \: (approximately) \end{cases} } [/tex]
[tex] \\ [/tex]
Substitute these values into our formula:
[tex] \sf h = \dfrac{492,452.48 \: m^3}{(52 \: m)^2 \times 3.14 } = \dfrac{492,452.48 \: m^3}{8,490.56\: m^2 } \\ \\ \\ \\ \implies \boxed{\boxed{\sf h = 58 \: m}} [/tex]
13. Debra's backyard has a patio and a garden. Find the area of the garden.
(Sides meet at right angles.)
4 yd
2 yd
patio
4 yd
6 yd
garden
2 yd
6 yd
The area of the garden alone is 21 yd²
What is an equation?An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.
The total length of the patio and garden is 6 yards while the total width is 5 yard. Hence:
Area of garden and patio = length * width = 6 yards * 5 yards = 30 yd²
The length of patio is 3 yard and width of the patio is 3 yard, hence:
Area of Patio = length * width = 3 yd. * 3 yd. = 9 yd²
Therefore:
Area of garden = Area of garden and patio - Area of Patio = 30 yd² - 9 yd² = 21 yd²
The area of the garden is 21 yd²
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Ramiro is also a college student. He has a credit card balance of $500.00. The APR on his card is 18.24%. His minimum payment is $10.00. (do not use commas or dollar signs in the answers)
If Ramiro stops using his credit card, how long will it take him (in months) to pay off the $500.00 if he makes only the minimum payment?
Answer:
Using the formula for the number of months to pay off a credit card balance with minimum payments:
Number of months = (-1/30) * log(1 - (balance * monthly rate / payment))
where balance is the initial balance, monthly rate is the APR divided by 12, and payment is the minimum payment.
Plugging in the given values, we get:
Number of months = (-1/30) * log(1 - (500 * 0.01824/12 / 10))
Number of months = 46.05
Rounding up to the nearest whole number, it will take Ramiro 47 months to pay off his credit card balance with only minimum payments.
Step-by-step explanation:
What are the coordinates of each point after the quadrilateral RSTU is rotated 90 degrees about the origin?
After the rotation, the coordinates of each point will be:Point R: (x,y) = (-y,x)Point S: (x,y) = (-x,-y)Point T: (x,y) = (y,-x)Point U: (x,y) = (x,y)
What is coordinates?Coordinates are a set of two or more numbers or variables that indicate the position of a point, line, or object in space. Coordinates are used in many fields, from mathematics and science to navigation and cartography. Coordinates are essential for accurately mapping and measuring the location of objects on Earth and in the universe. Coordinates can also be used to calculate the area of a region or the volume of an object. Coordinates are one of the most important tools for understanding and manipulating the physical world.
Quadrilateral RSTU has a rotation of 90 degrees about the origin. After the rotation, the coordinates of each point will be:
Point R: (x,y) = (-y,x)
Point S: (x,y) = (-x,-y)
Point T: (x,y) = (y,-x)
Point U: (x,y) = (x,y)
This occurs because when rotating a point around the origin, the x-coordinates and y-coordinates change places. The sign also changes for the x-coordinate and the y-coordinate in order to preserve the direction of the rotation.
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Please help me, this question is so confusing and I tried almost every way to solve this and it’s still wrong. It wants me to find how much metal need to make the 16 cans and I tried multiplying 16 and it’s still wrong. Please help! Diameter is 8, height is 9. Please use 3 as pi to solve.
Answer:
[tex]4992 \text{ cm}^2[/tex]
Step-by-step explanation:
We can model the amount of metal, in square centimeters, that is needed to make a soup can with the expression:
[tex](2 \cdot \text{area of base}) + (\text{area of side})[/tex]
We can first solve for the surface area of a soup can, using the fact that its bases are circles.
[tex]A_{\text{circle}} = \pi r^2[/tex]
↓ substituting 3 for π
[tex]A_{\text{base}} = 3r^2[/tex]
↓ plugging in radius (which is 1/2 of diameter, given as 8)
[tex]A_{\text{base}} = 3(4)^2[/tex]
↓ simplifying
[tex]A_{\text{base}} = 48 \text{ cm}^2[/tex]
Then, we can solve for the area of its side, which we can think of as an elongated circumference (circumference multiplied by height).
[tex]A_{\text{circumference}} = \pi d[/tex]
[tex]A_{\text{side}} = h(\pi d)[/tex]
↓ substituting 3 for π
[tex]A_{\text{side}} = h(3d)[/tex]
↓ plugging in height and diameter
[tex]A_{\text{side}} = 9(3 \cdot 8)[/tex]
↓ simplifying
[tex]A_{\text{side}} = 216 \text{ cm}^2[/tex]
Next, we can solve for the surface area of one soup can.
[tex](2 \cdot \text{area of base}) + (\text{area of side})[/tex]
↓ plugging in solved values
[tex](2 \cdot 48 \text{ cm}^2) + 216 \text{ cm}^2[/tex]
↓ simplifying
[tex]96 \text{ cm}^2 + 216 \text{ cm}^2[/tex]
↓ performing addition
[tex]312 \text{ cm}^2[/tex]
Finally, we can solve for the amount of metal needed for 16 cans by multiplying the amount for 1 can by 16.
[tex]16 \cdot 312 \text{ cm}^2[/tex]
↓ performing multiplication
[tex]\boxed{4992 \text{ cm}^2}[/tex]
A man in a photograph is 1.5 inches in height. If the man is 6 feet tall, what is the scale?
SHOW YOUR WORK ON THE BOTTOM OF YOUR EQUATION!!!
PLEASE AND THANK YOU!!
Answer:
To find the scale of the photograph, we need to determine the ratio between the actual height of the man and the height of the man in the photograph.
First, we convert the height of the man from feet to inches:
6 feet = 6 x 12 = 72 inches
Next, we can set up a proportion:
actual height of man / height of man in photograph = scale factor
Substituting the given values, we get:
72 inches / 1.5 inches = scale factor
Simplifying, we get:
scale factor = 48
Therefore, the scale of the photograph is 1:48, which means that one inch in the photograph represents 48 inches (or 4 feet) in real life.
6. A normal distribution has a mean of 48 and a standard deviation of 7. Find the probability
sigerandomly selected x-value from the distribution is in the given interval.
a. Between 34 and 55
b. At most 41
c. At least 48
d. Between 62 and 76
13.5%
2.35%
0.15%
82
34%
34%
111
x 30
-20
13.5
x+ 20
The probability is approximately 0.8185 or 81.85%.
What is normal distribution?Normal distribution, also known as Gaussian distribution, is a probability distribution that is commonly used in statistics, mathematics, and the natural sciences to describe real-valued random variables whose distributions are not known.
To find the probability that a randomly selected x-value from a normal distribution with a mean of 48 and a standard deviation of 7 is between 34 and 55, we need to standardize the values using the z-score formula:
z = (x - μ) / σ
where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation.
For x = 34:
z = (34 - 48) / 7 = -2
For x = 55:
z = (55 - 48) / 7 = 1
We can use a standard normal distribution table or a calculator to find the area under the standard normal distribution curve between z = -2 and z = 1. This area represents the probability that a randomly selected x-value from the given normal distribution is between 34 and 55.
Using a standard normal distribution table, we can find the probabilities as follows:
P(z < -2) = 0.0228 (from the table)
P(z < 1) = 0.8413 (from the table)
Therefore, the probability that a randomly selected x-value from the given normal distribution is between 34 and 55 is:
P(-2 < z < 1) = P(z < 1) - P(z < -2) = 0.8413 - 0.0228 = 0.8185
So, the probability is approximately 0.8185 or 81.85%.
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Much of Ann's investments are in Cilla Shipping. Ten years ago, Ann bought seven bonds issued by Cilla Shipping, each with a par value of $500. The bonds had a market rate of 95.626. Ann also bought 125 shares of Cilla Shipping stock, which at the time sold for $28.00 per share. Today, Cilla Shipping bonds have a market rate of 106.384, and Cilla Shipping stock sells for $30.65 per share. Which of Ann's investments has increased in value more, and by how much?
Using basic arithmetic operation, Ann's stock investment has increased in value more, by $331.25, compared to her bond investment, which has increased in value by $378.66.
The current value of Ann's bond investment can be calculated using the following formula:
Current Value of Bonds = Par Value x Market Rate
Since Ann has 7 bonds with a par value of $500 each, the total par value of her bond investment is:
$500 x 7 = $3,500
Using the market rate of 106.384, we can calculate the current value of Ann's bond investment as:
Current Value of Bonds = $3,500 x 1.06384 = $3,725.44
The current value of Ann's stock investment can be calculated by multiplying the number of shares she owns by the current stock price:
Current Value of Stock = Number of Shares x Stock Price
Since Ann owns 125 shares of Cilla Shipping stock and the current stock price is $30.65, the current value of her stock investment is:
Current Value of Stock = 125 x $30.65 = $3,831.25
To determine which investment has increased in value more, we need to compare the difference between the current and original values of each investment. The original value of Ann's bond investment is:
Original Value of Bonds = Par Value x Market Rate = $500 x 7 x 0.95626 = $3,346.78
The difference between the current and original value of Ann's bond investment is:
$3,725.44 - $3,346.78 = $378.66
The original value of Ann's stock investment is:
Original Value of Stock = Number of Shares x Stock Price = 125 x $28.00 = $3,500
The difference between the current and original value of Ann's stock investment is:
$3,831.25 - $3,500 = $331.25
Hence, Ann's stock investment has increased in value more, by $331.25, compared to her bond investment, which has increased in value by $378.66.
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a mountain road rises 48 feet for a 290 foot run. What is its slope
Answer:
the slope is 24/145
Step-by-step explanation:
slope= rise/run
48/290
24/145
the slope is 24/145
A kite is shown below.
Find the size of angle BCD.
A
117°
B
55°
D
C
PLEASE DO IT
The value of x and y in the trapezium are 118 and 35 degrees respectively.
How to find angles in a trapezium?The diagram above is a trapezium. A trapezium is a quadrilateral with 4 sides. The sum of all the four angles of the trapezium is equal to 360°.
A trapezium has two parallel sides and two non-parallel sides.
Therefore, let's find x and y as follows:
x = 180 - 62(supplementary angles)
x = 118 degrees
y = 180 - 145(supplementary angles)
y = 35 degrees
Therefore,
x = 118 degrees
y = 35 degrees
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I just need the last 2. I don't understand what the last 2 r asking for
Answer:
Question 3
Equation for Malik:
y = 350 + 7x
Equation for Saraiah:
y = 400 + 4x
Question 4
Both of them will have the same amount of money after
50/3 years
or
16 2/3 years
or
16 years 8 months
Step-by-step explanation:
Malik's interest rate as decimal = 2/100 = 0.02Saraiah's interest rate as decimal = 1/100 = 0.01The formula for simple interest is given as#3
Amount in Malik's account after x years given 2% interest
y = 350(1 + 0.02x)
y = 350 + 7x
For Saraiah's account:
y = 400(1 + 0.01x)
y = 400 + 4x
#4
If both Malik and Saraiah have the same amount of money after x years, then the right side of both their equations must be equal
Therefore
[tex]350+7x = 400+4x\\\\\mathrm{Move}\:350\:\mathrm{to\:the\:right\:side \:by \:subtracting\: 350 \:from\:both\: sides}\\350+7x-350=400+4x-350\\\\\mathrm{Simplify}\\7x=4x+50\\\\[/tex]
[tex]\mathrm{Subtract\:}4x\mathrm{\:from\:both\:sides}\\\\7x-4x=4x+50-4x\\3x=50\\\\\mathrm{Divide\:both\:sides\:by\:}3\\\\\dfrac{3x}{3}=\dfrac{50}{3}\\\\x=\dfrac{50}{3}[/tex]
Therefore both of them will have the same amount of money after [tex]\dfrac{50}{3}[/tex] years which is [tex]{16\dfrac{2}{3}[/tex] years
2/3 year = 2/3 x 12 months = 8 months
So both of them will have the same amount of money after [tex]{16\dfrac{2}{3}[/tex] years or 16 years and 8 months
Help I’ve been struggling with math for a while, and I really need help on this. Please help.
ncluding zero) depending on your answer.
Match each system on the left with all words that describe the system
on the right. Choices on the right can be used more than once.
y=2x+3
x+y=-3
3y=9x-6
2y-6x=4
y=1/2x +2
x+2y=4
inconsistent
consistent
independent
dependent
By rewriting the 3 given systems, we will see that:
1) Independent and consistent.
2) Independent and inconsistent.
3) Dependent.
What is the system of equations?
A finite set of equations for which common solutions are sought is referred to as a set of simultaneous equations, often known as a system of equations or an equation system.
Let's look at the first one, we can rewrite it as:
y = 2x + 3
y = -x - 3
So, the slopes are different, meaning that we have one solution, so this system is consistent and independent.
Now let's look at the second system, we can rewrite it as:
y = 3x - 2
y = 3x + 2
Here both lines have the same slope, so the lines never do intersect, meaning that the system is inconsistent and independent.
For the final system, we have:
y = (-1/2)×x + 2
y = (-1/2)×x + 2
Hence, we have two equal lines, so this system is dependent.
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Sasha solved an equation. The last line of her solution is 0 = 13. Sasha says that the solution to her equation is 13. Is she correct? Why or why not?
Answer:
No, Sasha's conclusion is not correct. If her last line is 0 = 13, this means that 0 is equal to 13, which is not true. Therefore, there is no solution to the equation that Sasha solved.
It's possible that Sasha made an error in her algebraic manipulations that led to this incorrect conclusion. It's also possible that there is no solution to the equation. In either case, the fact that her last line is 0 = 13 indicates that there is an error in her solution or that the equation is inconsistent and has no solution.
Step-by-step explanation:
step-by-step explanation of why Sasha's conclusion is not correct:
Given: Sasha's last line of her solution is 0 = 13.
Recall that the goal of solving an equation is to find the value(s) of the variable that make the equation true.
If the equation is true, then both sides of the equation should be equal.
However, Sasha's last line states that 0 is equal to 13. This is not true, since 0 is not equal to 13.
Therefore, the conclusion that the solution to the equation is 13 is not correct.
It's possible that Sasha made an error in her algebraic manipulations, which led to this incorrect conclusion.
Alternatively, it's possible that the equation itself is inconsistent and has no solution.
In either case, the fact that Sasha's last line is 0 = 13 indicates that there is an error in her solution or that the equation is inconsistent and has no solution.
No, Sasha's conclusion is not correct. If her last line is 0 = 13, this means that 0 is equal to 13, which is not true. Therefore, there is no solution to the equation that Sasha solved.
Why is there no solution?It's possible that Sasha made an error in her algebraic manipulations that led to this incorrect conclusion. It's also possible that there is no solution to the equation. In either case, the fact that her last line is 0 = 13 indicates that there is an error in her solution or that the equation is inconsistent and has no solution.
Given: Sasha's last line of her solution is 0 = 13.
Recall that the goal of solving an equation is to find the value(s) of the variable that make the equation true.
If the equation is true, then both sides of the equation should be equal.
However, Sasha's last line states that 0 is equal to 13. This is not true, since 0 is not equal to 13.
Therefore, the conclusion that the solution to the equation is 13 is not correct.
It's possible that Sasha made an error in her algebraic manipulations, which led to this incorrect conclusion.
Alternatively, it's possible that the equation itself is inconsistent and has no solution.
In either case, the fact that Sasha's last line is 0 = 13 indicates that there is an error in her solution or that the equation is inconsistent and has no solution.
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In the diagram ABC is right angle triangle horizontal ground AD is a vertical tower < BAC = 90 5 82m the length of AC and BD = 100m. Find and correct to I decimal place Find the height Find Length of DC
The measure of the length DC would be 28.9 m.
What is a triangle?A triangle is a two - dimensional figure with three sides and three angles.
The sum of the angles of the triangle is equal to 180 degrees.
∠A + ∠B + ∠C = 180°
Given is that ABC is right angle triangle with horizontal ground AD.
We can write -
DC = 100 - 82 sin (60)
DC = 100 - 82 x √3/2
DC = 100 - 71.1
DC = 28.9 m
Therefore, the measure of the length DC would be 28.9 m.
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What is the solution to the equation log2 (5x - 2) = -2?
Step-by-step explanation:
We can solve for x using the properties of logarithms as follows:
log2 (5x - 2) = -2
2^(-2) = 5x - 2 (using the definition of logarithms)
1/4 = 5x - 2 (simplifying 2^(-2))
5x = 2 + 1/4 = 9/4
x = 9/20
Therefore, the solution to the equation log2 (5x - 2) = -2 is x = 9/20.
Can someone please help me with this math problem, ASAP?
The value of the given function for x=4 is 82.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The given function is y+√x=5x+(x+4)².
Here, y=5x+(x+4)²-√x
f(x)=5x+(x+4)²-√x
Substitute x=4 in the function, we get
f(4)=5(4)+(4+4)²-√4
= 20+64-2
= 82
Therefore, the value of function is 82.
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The principal represents an amount of money deposited in a savings account subject to compound interest at the given rate.
Principal $3000
Rate 2%
Compounded quarterly
Time 5 years
A. Find how much money there will be in the account after the given number of years.
B. Find the interest earned.
The required final amount and interest are 3311.05 and 311.05
What is Compound interest?When you make interest on both the money you've saved and the interest you've earned, this is known as compound interest.
According to question:A. To find the amount of money in the account after 5 years, we can use the formula for compound interest:
[tex]$$A = P \left(1 + \frac{r}{n}\right)^{nt}$$[/tex]
where A is the final amount, P is the principal, r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.
In this case, P = $3000, r = 0.02 (2%), n = 4 (compounded quarterly), and t = 5. Plugging in these values, we get:
[tex]$$A = 3000\left(1 + \frac{0.02}{4}\right)^{4\cdot5} \approx $3311.05$$[/tex]
Therefore, there will be approximately 3311.05 in the account after 5 years.
B. To find the interest earned, we can subtract the principal from the final amount:
[tex]$$I = A - P = $3311.05 - $3000 = $311.05$$[/tex]
Therefore, the interest earned is 311.05.
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NO LINKS!! URGENT HELP PLEASE!!!!
Please help me with #1 - 3
For each table, state if the model is linear or exponential and write an equation.
Answers:
Linear; equation is y = -5x+15Linear; equation is y = -x+4Exponential; equation is y = 80*2^x=====================================================
Explanation:
Problem 1
Each time x goes up by 1, y goes down by 5. This constant rate of change leads to the equation being linear. The slope is m = -5/1 = -5. You can use the slope formula for any two points in the table to confirm this is the correct slope.
The y intercept is b = 15 because we have x = 0 lead to y = 15.
Therefore, we go from y = mx+b to y = -5x+15
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Problem 2
Each time x goes up by 3, the y coordinate goes down by 3. Therefore, we have another linear equation here. The slope is m = -3/3 = -1.
The y intercept is b = 4 because x = 0 leads to y = 4.
y = mx+b turns into y = -x+4
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Problem 3
Each time x goes up by 1, y is NOT going up the same amount. The jump from 10 to 20 is +10. The jump from 20 to 40 is +20. And so on.
Therefore, this equation isn't linear. Instead it's exponential. Each y term doubles when x increases by 1, so that's why the b term is b = 2.
The initial term is a = 80 because x = 0 leads to y = 80.
We go from y = a*b^x to y = 80*2^x
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You can use a tool like Desmos or GeoGebra to visually confirm each of the answers. Both also offer support for function tables.
Answer:
1. y = -5x + 15.
2. y = -x + 4.
3. y = 80(2^(x/3))
Step-by-step explanation:
1.
From the given data, we can see that as x increases by 1, y decreases by a fixed amount of 5. This means that the relationship between x and y is linear, specifically a decreasing linear relationship.
To write the equation for a linear relationship, we need to find the slope (m) and y-intercept (b).
Using the formula for slope:
m = (change in y) / (change in x)
m = (0 - 30) / (3 - (-3))
m = -5
Using the point-slope form of a linear equation:
y - y1 = m(x - x1)
y - 30 = -5(x - (-3))
y - 30 = -5x - 15
y = -5x + 15
So the equation for this linear relationship is y = -5x + 15.
2.
From the given data, we can see that as x increases by 3, y decreases by a fixed amount of 3. This means that the relationship between x and y is linear, specifically a decreasing linear relationship.
To write the equation for a linear relationship, we need to find the slope (m) and y-intercept (b).
Using the formula for slope:
m = (change in y) / (change in x)
m = (-5 - 13) / (9 - (-9))
m = -18 / 18
m = -1
Using the point-slope form of a linear equation:
y - y1 = m(x - x1)
y - 13 = -1(x - (-9))
y - 13 = -1(x + 9)
y = -x + 4
So the equation for this linear relationship is y = -x + 4.
3.
From the given data, we can see that as x increases by 1, y doubles. This means that the relationship between x and y is exponential.
To write the equation for an exponential relationship, we can use the general form of an exponential function:
y = ab^x
where a is the initial value, b is the base, and x is the exponent.
To find a and b, we can use the first and fourth data points since they have the smallest and largest values of y, respectively.
When x = -3, y = 10, so we have:
10 = ab^(-3)
When x = 0, y = 80, so we have:
80 = ab^(0)
From the second equation, we can see that a = 80. Substituting this into the first equation, we get:
10 = 80b^(-3)
Simplifying, we get:
b = 2^(1/3)
So the equation for this exponential relationship is:
y = 80(2^(1/3))^x
Simplifying further:
y = 80(2^(x/3))
I need immediate help!!
Answer:
First: P, R. Second: 3.
Step-by-step explanation:
In this, you can see the first tree diagram with C,R C,B and C,W.
Then when you go to the other diagram it's P,R P,B and P,W.
Therefore the combination P,R is missing from the tree diagram and belongs to the box.
When you count the number of combinations:
1, P,R
2, P,B
3, P,W
Therefore they are a total of 3 combinations.
Match the correct units for the answer of each formula.
Step-by-step explanation:
Refer to pic............
Calculate the value of the expression-6(-5-4)-4(-3-2)=
Answer:
74
Step-by-step explanation:
-6(-5-4) - 4(-3-2)
30 + 24 + 12 + 8
= 54 + 12 + 8
= 66 + 8
= 74
Which equations are true for x = –2 and x = 2? Select two options x2 – 4 = 0 x2 = –4 3x2 + 12 = 0 4x2 = 16 2(x – 2)2 = 0
Answer:
The correct answer that you are looking for is the following equations make x = 2 correct: x2 - 4 = 0, 4x2 = 16, and 2(x-2)2 = 0
The following equations make x = -2 correct: x2 = -4, and 3x2+12=0
Step-by-step explanation:
When finding out if x fits a certain number, there are many things to keep in mind, such as making sure that both sides are equal, making that if x changes the equation is resolved correctly, and also having to solve all the equations, of course.
The strategy that I chose was replacing x with either 2, or -2, and whichever one matched the final result would mean that x does equal that term.
Another strategy that could be more beneficial is solving the equation with step-by-step ideas.
I replaced x as 2 in x2 - 4 = 0, 4x2 = 16, and 2(x-2)2 = 0 and they matched the result.
For the remaining equations that didn't match the result I replaced x with -2 and then they finally matched.
I replaced x as -2 in x2 = -4, and 3x2+12=0 and they matched the result.
If in any shape or form, I was incorrect please inform me and I'll attempt to resolve the issue and see my mistake, sorry if thi was wordy and long.
I hope this was helpful!
Simplify the expression. √8/81
The value of the given expression √8/81 = 2√2/81.
What is square root of a number?The opposite of squaring an integer is finding its square root. The result of multiplying a number by itself yields its square value, whereas the square root of a number may be found by looking for a number that, when squared, yields the original value. The equation a a = b is true if 'a' is the square root of 'b'. Every integer has two square roots, one of a positive value and one of a negative value, because the square of any number is always a positive number. For instance, the square roots of 4 are both 2 and -2.
Given that,
√8/81
We can write the value of √8 = √(2)(2)(2) = 2√2.
Thus, we have the value of √8/81 = 2√2/81.
Learn more about square root here:
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