Note that in the proof stated above, there is no incorrect statement.
How is this so?The evidence is that when four lines are drawn starting from a point and making two right angles, the two angles between those lines are equal.
The proof begins by stating that when you have a right angle, the two angles that add up to produce the correct angle are referred to as complementary angles.
The Congruent Complements Theorem is then used to demonstrate that the two angles in the centre are equal.
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What is the value of sine at 330
What is the definition of perpendicular lines?
1.two lines that intersect in a way that forms right angles
2.two lines that intersect in a way that cuts both lines in half
3.two lines that intersect in a way that they share more than one common point
4.two lines that intersect in a way that forms two congruent angles
Answer:
Step-by-step explanation:
The correct definition of perpendicular lines is option 1: "Two lines that intersect in a way that forms right angles."
When two lines intersect to form four right angles (90-degree angles), they are said to be perpendicular to each other. The point at which the lines intersect is called the point of intersection.
Therefore, option 1 is the correct definitation of perpendicular lines.
Answer: 1. Two lines that intersect in a way that forms right angles.
Step-by-step explanation:
Hope this helped! :)
1 Complete the steps to find 253 X 34.
253 X 34= 253(30+4)=(x 30) + X 4)
+
253
X 30
90 (30 X 3)
(30 X
11
______X
253 X 34= 7,590 + 1,012 =
253
Answer:
8602
Step-by-step explanation:
To complete the steps to find 253 X 34, you can follow these steps:
Break down 34 into 30 + 4
Multiply 253 by 30 and 4 separately
Add the two products together
So, 253 X 34 = 253(30+4) = (253 X 30) + (253 X 4) = 7590 + 1012 = 8602
To reach escape velocity, a rocket must travel at the rate of 2.2×106 feet per minute. Express this number in standard notation.
The rocket must travel at a rate of 2,200,000 feet per minute to reach escape velocity.
Expressing this number in standard notation.2.2×10^6 feet per minute is in its scientific notation.
In scientific notation, a number is written as the product of a coefficient and a power of 10.
So, 2.2×10^6 is already in scientific notation, where the coefficient is 2.2 and the power of 10 is 6.
If you want to convert it to standard notation, you can multiply the coefficient by the power of 10:
2.2×10^6 = 2.2 x 1,000,000 = 2,200,000
Therefore, the rocket must travel at a rate of 2,200,000 feet per minute to reach escape velocity.
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Beth pulls a slinky a distance of 24 inches from its equilibrium position and then releases it. The time for one oscillation is 2 seconds. Step 2 of 2 : Find the function in terms of t for the displacement of the slinky. Assume that the slinky is at its maximum displacement at t=0 . Also assume that the function includes no horizontal or vertical shifts.
The final function for slinky displacement is: 24 sin(t/2 - /2) d(t). This offers the displacement in inches as a function of time in seconds.
How to Solve the Problem?A sinusoidal function of the form: can be used to describe the slinky's displacement.
A sin(t + ) = d(t).
where A is the greatest displacement, is the angular frequency (2 divided by the period), and is the phase angle (starting phase).
We know the slinky's greatest displacement (amplitude) occurs at t=0, thus we have:
24 inches = d(0) = A sin()
We also know that the period is T=2 seconds because the time for one oscillation (i.e., one complete cycle) is 2 seconds. As a result, the angular frequency is:
ω = 2π / T = π radians/second
The phase angle can be calculated using the fact that the slinky is at its equilibrium position at t=T/4=0.5 seconds. At this time, the sine function's argument is:
= 2 / T = radians per second
The phase angle can be calculated using the fact that the slinky is at its equilibrium position (zero displacement) at t=T/4=0.5 seconds. At this time, the sine function's argument is:
ωt + φ = π/2
When we substitute the known values, we get:
π/2 + φ = 0.5π
φ = -π/2
As a result, the slinky's displacement function is:
A sin(t/2 - /2) = d(t).
We may utilize the information that the amplitude is 24 inches to calculate A:
A = |24| = 24
As a result, the final function for slinky displacement is:
24 sin(t/2 - /2) d(t)
This offers the displacement in inches as a function of time in seconds.
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Graphing Geometry. Show work
A graph of the reflection of line segment AB is shown on the coordinate plane below.
What is a reflection across the x-axis?In Mathematics, a reflection across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate changes from positive to negative.
Furthermore, a reflection across the line y = x would interchange (switch) the x-coordinate and y-coordinate and this is represented by the following transformation rule:
(x, y) → (y, x)
Ordered pair A = (4, -1) → Ordered pair A' = (-1, 4).
Ordered pair B = (4, 5) → Ordered pair B' = (5, 4).
In this exercise, we would use an online graphing calculator to plot the image of line segment AB after a reflection about the line y = x.
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What is the area of this figure?
8 m
6 m
5 m
2 m
13 m
8 m
Answer:
It's not clear what figure is being referred to. The provided numbers could be dimensions of a shape, but without additional information or context, it's impossible to determine the area of the figure. Can you please provide more details or a diagram?
Step-by-step explanation:
Kelly bought a new SUV for $28,000. She made a down payment of $11,000 and has monthly payments of $332.63 for 5 years. She is able to pay off her loan at the end of 36 months. Using the actuarial method, find the unearned interest and payoff amount.
The unearned interest and the payoff amount is $11,022.12 and $18,784.87 respectively
Given data ,
Kelly bought a new SUV for $28,000. She made a down payment of $11,000 and has monthly payments of $332.63 for 5 years.
She is able to pay off her loan at the end of 36 months.
Now , Total interest = (monthly payment x number of months) - loan amount
Total interest = ($332.63 x 60) - $17,000
Total interest = $19,957.80
Next, we need to calculate the interest that has already been paid over the first 36 months of the loan. We can use the formula:
Interest paid = (monthly payment x number of months) - (loan amount - down payment)
Interest paid = ($332.63 x 36) - ($28,000 - $11,000)
Interest paid = $8,935.68
The unearned interest is the difference between the total interest and the interest paid so far:
Unearned interest = total interest - interest paid
Unearned interest = $19,957.80 - $8,935.68
Unearned interest = $11,022.12
To find the payoff amount, we need to add the remaining principal balance to the unearned interest:
Payoff amount = remaining balance + unearned interest
To calculate the remaining balance, we can use the formula for the present value of an annuity:
Remaining balance = monthly payment x (1 - (1 + r)^-n) / r
Where r is the monthly interest rate and n is the number of remaining months. We can solve for r by using the total interest calculated earlier:
r = (Total interest / loan amount) / 12
r = ($19,957.80 / $17,000) / 12
r = 0.0986%
Using this interest rate and n = 24 (the remaining 24 months of the loan), we can calculate the remaining balance:
Remaining balance = $332.63 x (1 - (1 + 0.0986%)^-24) / 0.0986%
Remaining balance = $7,762.75
Payoff amount = $7,762.75 + $11,022.12
Payoff amount = $18,784.87
Hence , the interest is solved
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what is the graphed line of the equation 2x + 3y = -6
The graphed line of the equation is attached 2x + 3y = -6
What is linear equation?A linear equation is an expression that consists of a single power of the variable(s) in which it contains. This formulation can be impeccably illustrated in the following way:
ax + b = 0
The given equation 2x + 3y = -6 can be rearranged to get
y = -2/3x - 2
The x variables is plugged in to solve for y and used for the table of values for the graph
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Bob wants to break the school record of scoring 30 points in his basketball game. He scored 13 points in the first half. How many two point baskets must Bob make in the second half to break the school record?
Bob needs to make at least 9 two-point baskets in the second half to break the school record of scoring 30 points in his basketball game.
To break the school record of scoring 30 points, Bob needs to score more than 30 points in his basketball game. Since he scored 13 points in the first half, he needs to score at least 17 points in the second half to break the record.
Let's assume that Bob makes x two-point baskets in the second half. Since each two-point basket contributes 2 points to his score, his total score from two-point baskets would be 2x.
Therefore, to break the school record, we need to solve the following inequality:
2x + 13 > 30
Subtracting 13 from both sides, we get:
2x > 17
Dividing both sides by 2, we get:
x > 8.5
Since Bob cannot make a fractional number of baskets, he needs to make at least 9 two-point baskets in the second half to break the school record.
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What are the x-intercepts of the function f(x)= 4x^2-36 over x-9?
Therefore , the solution of the given problem of function comes out to be f(x) = (4x² - 36)/(x - 9) has -3 and 3 as its x-intercepts.
Describe function.On the midterm exam, there will be a variety of inquiries in each subject, including inquiries concerning both hypothetical and actual places as well as inquiries relating the creation of numerical variables. a diagram showing the relationships between different elements that cooperate to generate the same result. A service is composed of numerous distinctive components that cooperate to create distinctive results for each input.
Here,
Setting the y-value (or output) of a function to zero and then solving for the corresponding x-values will allow us to determine the x-intercepts of the function.
The function in this instance is f(x) = (4x² - 36)/(x - 9)
=> 4x² - 36 = 0
To make the equation simpler, we can factor out a 4:
=> 4(x² - 9) = 0
We can factor further based on the difference of squares we now have:
=> 4(x + 3)(x - 3) = 0
We may determine the x-values where the function crosses the x-axis by setting each element to zero:
=> x + 3 = 0 or x - 3 = 0
To find x, solve for:
=> x = -3 or x = 3
The function f(x) = (4x² - 36)/(x - 9) has -3 and 3 as its x-intercepts.
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Find the missing side lengths. Leave your answers as radicals in simplest form.
Answer:
In a 30°-60°-90° triangle, the length of the longer leg is √3 times the length of the shorter leg, and the length of the hypotenuse is twice the length of the shorter leg.
[tex]n = \frac{2}{ \sqrt{3} } = \frac{2 \sqrt{3} }{3} [/tex]
[tex]m = \frac{4 \sqrt{3} }{3} [/tex]
Correct answer gets brainliest!!!!
Answer:
it is a zero dimensional point
Step-by-step explanation:
points are an exact location represented by a dot.
points do not have dimension (length, width, or height)
Diane is a camp counselor she designs a new obstacle course in testicles with three friends. The plot data shows the time it takes them to complete the obstacle course. What is the mean of time
To find the mean time it takes for Diane and her friends to complete the obstacle course, we added up the time taken by each person and divided by the total number of people. The mean time is 13.0 minutes.
Add up the time taken by each person
Diane: 12
Friend 1: 14
Friend 2: 10
Friend 3: 16
Total time = 12 + 14 + 10 + 16 = 52 minutes
Count the total number of people:
Diane and three friends, so the total number of people = 4
Divide the total time by the total number of people to find the mean time
Mean time = Total time / Total number of people
Mean time = 52 / 4
Mean time = 13.0 minutes
Therefore, the mean time it takes for Diane and her three friends to complete the obstacle course is 13.0 minutes.
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--The given question is incomplete, the complete question is given
" Diane is a camp counselor she designs a new obstacle course in testicles with three friends. The plot data shows the time it takes them to complete the obstacle course. What is the mean of time
the plot data for the time taken by each person in minutes is as follows
Diane: 12
Friend 1: 14
Friend 2: 10
Friend 3: 16 "--
5 years ago i was 5 times older then my son. in 8 years time i will be 3 times older then my son. how old am i today?
Answer:
70 , 18
Step-by-step explanation:
Keeping x as Father and y as son;
5 years ago Person X was 5 times older than Person y , so the equation will be:
x - 5= 5(y-5)
x = 5y - 20
simularily after 8 years , x will be 3 times older than y , so
x + 8 = 3(y + 8.)
I will now try to find y by equating value of x into y:
5y - 20 + 8 = 3y + 24
5y - 3y = 24 + 20 - 8
2y = 44 - 8 = 36
y = 18
so x will be = 5 (18) - 20.
x = 90-20 = 70 years.
therefore father is 70 years , and son is 18 years old.
Someone help i really need help with this
The cost of each admission tickets is 37.5 dollars.
How to find the cost in dollars of each admission ticket?Ms Boi spent a total of 175 dollars for 4 admission ticket and for parking at a baseball game. The cost of each admission ticket was the same amount, including tax. The cost of the parking was 25 dollars.
Therefore, the equation that can be use to determine the cost, i of each admission ticket can be represented as follows:
Therefore,
175 = 4i + 25
subtract 25 from both sides of the equation
175 = 4i + 25
175 - 25 = 4i + 25 - 25
150 = 4i
divide both sides by 4
i = 150 / 4
i = 37.5 dollars
Therefore,
cost of each admission ticket = 37.5 dollars
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what is the volume of this triangular prism?
The volume of the triangular prism is 36 in³.
What is a triangular prism?A triangular prism is a polyhedron made up of two triangular bases and three rectangular sides.
To calculate the volume of the triangular prism, we use the formula below
Formula:
V = bhH/2.................... Equation 1Where:
b = Base of the triangleh = Height of the triangleH = Height of the prismFrom the question,
Given:
b = 3 inh = 4 inH = 6 inSubstitute these values into equation 1
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find 15x2 2/3 using the distributive property
is 1 over 16 the same as 16 A: Yes B.NO
Answer:
1 over 16 is not the same as 16.
1 over 16 is a fraction, which means that it represents a part of a whole. It can be written as 1/16, which means one part out of a total of sixteen equal parts.
On the other hand, 16 is a whole number, which represents a quantity of sixteen units.
So, 1/16 is not equal to 16.
Step-by-step explanation:
please find the SA and can you please explain?
Please hurry if you can.
Answer:
Rounding to the nearest hundredth, the surface area of the regular hexagonal pyramid is approximately 663.2 square centimeters.
Step by Step Explanation:
The surface area of a regular hexagonal pyramid can be calculated using the formula:
Surface area = (1/2) x Perimeter of base x Slant height + Base area
To find the perimeter of the hexagonal base, we can use the formula:
Perimeter of hexagon = 6 x Length of one side
Since the base edge length is 8 centimeters, the length of one side of the hexagon is also 8 centimeters. Therefore, the perimeter of the hexagonal base is:
Perimeter of base = 6 x Length of one side = 6 x 8 = 48 centimeters
To find the base area of the pyramid, we can use the formula:
Base area = (3/2) x (Square root of 3) x (Length of one side)^2
Substituting the values, we get:
Base area = (3/2) x (Square root of 3) x (8)^2 = 96(sqrt(3)) square centimeters
Now we can substitute the values into the surface area formula:
Surface area = (1/2) x Perimeter of base x Slant height + Base area
Surface area = (1/2) x 48 x 15 + 96(sqrt(3))
Surface area = 360 + 96(sqrt(3)) square centimeters
A coach asked her athletes if they enjoy running. Fifty-five percent of the team do not like to run. Of those, 70% enjoy cycling, while 80% of those who enjoy running also enjoy cycling. The tree diagram shows how the athletes are divided into subgroups.
The tree diagram shows athletes branching off into two categories, enjoys running and does not enjoy running. Enjoys running branches off into two sub-categories, enjoys cycling and does not enjoy cycling. Does not enjoy running branches off into two subcategories, enjoys cycling and does not enjoy cycling.
What is the total percentage of the athletes who enjoy cycling?
9%
25.5%
55%
74.5%
Answer:
75%
Step-by-step explanation:
To determine the total percentage of athletes who enjoy cycling, we need to consider the percentages given in the problem.
According to the information provided:
55% of the team does not like to run.
Of those who do not like to run, 70% enjoy cycling.
Of those who enjoy running, 80% also enjoy cycling.
To calculate the total percentage of athletes who enjoy cycling, we need to consider the percentages from both branches of the tree diagram.
Percentage of athletes who do not like to run and enjoy cycling:
= (Percentage of athletes who do not like to run) * (Percentage of those who enjoy cycling within that group)
= 55% * 70% = 38.5%
Percentage of athletes who enjoy running and enjoy cycling:
= (Percentage of athletes who enjoy running) * (Percentage of those who enjoy cycling within that group)
= (100% - 55%) * 80% = 45% * 80% = 36%
Total percentage of athletes who enjoy cycling:
= Percentage of athletes who do not like to run and enjoy cycling + Percentage of athletes who enjoy running and enjoy cycling
= 38.5% + 36% = 74.5%
Therefore, the correct answer is:
74.5%
PLEASE HELP ME QUICK!!!!
Answer:
B. $7.50
Step-by-step explanation:
We know profit or P-----P(n) where n is the quantity/number of the item) is the difference of the revenue-----R(n)-----and the cost-----C(n)
P(n) = R(n) - C(n)
Revenue is
the product of price (p) of the item and, number/quantity (n) of the item:R(n) = pn
Cost is a combination of
fixed costs (represented by a constant (c), as the business or Indvidual making a profit must pay a certain cost, even if they don't make any of their items) and, variable costs (this costs changes depending on the number/quantity of the item and is the product of the marginal cost (m) and the number/quantity (n) of the item)The cost function resembles a linear equation:
C(n) = mn + c
Since we're shown that P = 7.5n - (2.25n + 15), we know that R(n) must be R(n) = 7.5n and C(n) must be C(n) = 2.25n + 15
Thus, we know she charges $7.5 per necklace sold.
If Melisha can pay for her vehicle with a 4-year loan or with a lease with the same down payment and same interest rate, why will the loan have a higher monthly payment?
A. Because the lease is riskier to the financing company.
B. Because the loan is riskler to the financing company.
C. Because Melisha will own her vehicle at the end of the loan.
D. Because Melisha will own her vehicle at the end of the lease.
The loan have a higher monthly payment Because the lease is riskier to the financing company.
To Determine the costs of buying versus leasing a motor vehicle, we need to consider the total costs associated with each option. For buying, the total cost is the sum of the down payment, loan payments, and the estimated value at the end of the loan, minus the resale value of the car.
On the other hand, for leasing, the total cost can be calculated as the sum of the security deposit, lease payments, and end-of-lease charges. We also need to consider the opportunity cost of investing the down payment and the security deposit.
We know that Melisha can pay for her vehicle with a 4-year loan or with a lease with the same down payment and same interest rate.
Therefore, the loan have a higher monthly payment Because the lease is riskier to the financing company.
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Sarah uses a square and two semicircular7 inches regions to design a heart shaped poster find the area of the heart then find the approximate area by using 3.14radius
The poster has an area equal to 192.423 square inches.
How to determine the area of a heart shaped poster
In this problem we must determine the area of a heart shaped poster, that is, the combination of the areas of a square and two semicircles, whose resulting formula is introduced below:
A = D² + (π / 4) · D²
Where:
A - Area of the heart shaped poster, in square inches.D - Side length of the square, in inches.If we know that π = 3.14 and D = 7 in, then the area of the poster is:
A = 7² + (π / 4) · 7²
A = (5π / 4) · 7²
A = 192.423 in²
The area of the poster is equal to 192.423 square inches.
Remark
The image is missing and the statement is not well explained. A correct statement is shown below:
Sarah uses a square with side length of 7 inches and two semicircles with diameter of 7 inches to design a heart shaped poster. Find the area of the heart. Then, find the approximate area by using 3.14.
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A fair number cube is rolled twice. After 500 trials of the experiment, the experimental probability of rolling two 3s is 11/50. What is the difference between the number of expected outcomes and the number of actual outcomes?
Write an inequality that matches the number line model. Then write
a situation that the inequality could represent.
25 is less than x
A specific radioactive substance follows a continuous exponential decay model. It has a half-life of 16 days. At the start of the experiment, 65.7 g is present.
(a) Lett be the time (in days) since the start of the experiment, and let
y be the amount of the substance at time t.
Write a formula relating y to t.
Use exact expressions to fill in the missing parts of the formula.
Do not use approximations.
y = ei
(b) How much will be present in 13 days?
Do not round any intermediate computations, and round your
answer to the nearest tenth.
08
X
Oina
3
Answer:
Step-by-step explanation:
(a) Lett be the time (in days) since the start of the experiment, and let
y be the amount of the substance at time t.
Write a formula relating y to t.
Use exact expressions to fill in the missing parts of the formula.
Do not use approximations.
y = ei
Answer: (a) The formula relating the amount of substance, y, to time, t, is given by:
y = y₀ * e^(-λ*t)
where y₀ is the initial amount of the substance, λ is the decay constant, and e is the mathematical constant approximately equal to 2.71828.
The half-life, T½, is related to the decay constant as:
T½ = ln(2)/λ
We are given that the half-life of the substance is 16 days, so we can solve for λ:
λ = ln(2)/T½ = ln(2)/16
Substituting this value of λ in the formula for y, we get:
y = 65.7 * e^(-ln(2)*t/16)
(b) To find the amount of substance present after 13 days, we substitute t = 13 in the formula for y:
y = 65.7 * e^(-ln(2)*13/16) ≈ 42.1
Rounding to the nearest tenth, we get y ≈ 42.1 g. Therefore, approximately 42.1 g of the substance will be present after 13 days.
Step-by-step explanation:
Use the unit circle to find the exact value of the trig function
cos(210°)
Answer:
-[tex]\sqrt{3}[/tex]/2
Step-by-step explanation:
cos is negative in quad II
cos(210)= -cos(30) = -[tex]\sqrt{3}[/tex]/2
A new television set was recently purchased for the common room in a Residence Hall for $451.50 including tax. If the tax rate is 5%, find the price of the television set before taxes.
Answer:
430
Step-by-step explanation:
Let's call the price of the television set before taxes "x".
The total cost including tax is $451.50, which is equal to x plus 5% of x (the tax). In other words:
x + 0.05x = $451.50
Simplifying the left side by factoring out x, we get:
1.05x = $451.50
Dividing both sides by 1.05, we get:
x = $430
Therefore, the price of the television set before taxes was $430.
What is the output for x = -1
Answer:
f(-1) = 16
Step-by-step explanation:
"output" and the f(x) setup just means to plug in -1 in place of x and calculate.
For the function f(x) = 12(3/4)ˣ you have to already know that once you put that -1 in place of x that the -1 power only goes to the 3/4, not the 12 and also what to do with a negative exponent.
Exponent rules are just shortcuts. The shortcut to know here is that the -1 exponent will flip the 3/4 over and make it 4/3 (there are math reasons for this, it's not random. But that's how it works)
So now you have
f(-1) = 12(3/4)⁻¹ which becomes
f(-1) = 12(4/3)
Now you need to know how to multiply with fractions. Here you have a whole, big number times a fraction, which is:
"big num×top all over bottom"
So multiply the 12 times the 4 and put it over the 3
f(-1) = 48/3 = 16
(or you can "cancel" the 12 with the 3 and get 4×4, which is 16, so it comes out the same)
[SKIP TO HERE IF YOU DON'T CARE WHY]
f(x) = 12(3/4)ˣ
f(-1) = 12(3/4)⁻¹
f(-1) = 12(4/3)
f(-1) = 16