Using the commutative property we can get an equation that depends on the sum of the two variables:
(M + N) = (62 - 2N)/29
How to apply the commutative property?The commutative property of the multiplication and sum means that we can permutate the variables:
A*B = B*A
A + B = B + A
In this case, we have the equation:
29*M = 31*(N + 2)
We can distribute the product to get:
29*M = 31*N + 31*2
29*M = 31*N + 62
Now we want to find the value of the sum of the variables, because we have only one equation we can't do that (two variables means that we need two equations) But we can write an expression that depends on the sum of the two variables.
29M + 31N = 62
And now use the commutative property to write:
(29M + 29N) + 2N = 62
(M + N) = (62 - 2N)/29
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7. N.CN.7 Determine the zeroes for the equation below. Select all that apply.
x² - 6x +13=0
A. 1
B. 5
C. 13
D. -3 + 2i
E. 3+2i
F. 3+4i
G. 6 + 4i
H. 3-21
I .6-41
Answer:
D. -3 + 2i and E. 3+2i are the zeroes for the equation.
Step-by-step explanation:
7. Tristan is in grade 12 and has worked at a local fast food chain for just over two years.
He earns $1500 per month. Tristan deposits $750 at the end of each month into an account that pays 3.25% per year, compounded monthly.
a) How much was in Tristan's account at the end of
one year?
b) How much was in Tristan's account at the end of
two years?
c) Compare your answers to parts a) and b). Explain why the answer to part b) is not double the answer to part a.
The compound interest is solved and answer to part b) is not double the answer to part a) because the interest is compounded monthly, not annually.
Given data ,
To calculate how much was in Tristan's account at the end of one year, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the amount at the end of the time period, P is the principal (the initial deposit), 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 time in years.
In this case, P = $750, r = 0.0325, n = 12 (since the interest is compounded monthly), and t = 1. Plugging in these values, we get:
A = $750(1 + 0.0325/12)⁽¹²ˣ¹⁾ = $8,086.43
Therefore, there was $8,086.43 in Tristan's account at the end of one year.
b)
To calculate how much was in Tristan's account at the end of two years,
t = 2,
A = $750(1 + 0.0325/12)⁽¹²ˣ²⁾ = $16,575.29
Hence , there was $16,575.29 in Tristan's account at the end of two years
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quadrilateral a'b'c'd' is the image of quadrilateral abcd under a rotation about the origin (0 0) A) -45 degrees B) -15 degrees C) 15 degrees D) 45 degrees
The rotation's angle is -45 degrees.
Quadrilateral A'B'C'D' is the representation of quadrilateral ABCD rotated around (0,0).
Consider D and D's coordinates.
D(2,3) and D'(-2,-3)
Now, Join D and D' then
<DOD = 45
Here, the actual rotation is -45 degree rotation can be visualized as a reflection across the y-axis followed by a 45 degree rotation in the clockwise direction.
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The expression πr2h represents the volume of a right circular cylinder with radius r and height h. Why is this expression a monomial? What is its degree?
I NEED ASAP
Answer:
The expression πr2h is a monomial because it is a single term that is the product of three variables: π, r2, and h. The term "mono" means "one," and "monomial" refers to a single term in algebraic expressions.
The degree of a monomial is the sum of the exponents of its variables. In this case, the degree of the monomial is 3, because the variables π, r, and h have exponents of 1, 2, and 1 respectively. Therefore, the degree of the monomial is 1 + 2 + 1 = 3.
Using the graphing function on your calculator, find the solution to the system
of equations shown below.
A. More than 1 solution
B. No solution
C. x = 3, y=-3
D. x = 4, y = -4
3y-3x = -9
4y-4x=-12
SUBMIT
The number of solutions the system of equations have is (a) more than one solutions
How to deterine the number of solutions the system of equations have?From the question, we have the following parameters that can be used in our computation:
3y-3x = -9
4y-4x=-12
Simplify the equations
So, we have
y - x = -3
y - x = -3
Subtract the equations
0 = 0
The above equation is true for all values of x and y
This means that the number of solutions in the equation is many i.e. more than one solutions
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Fondue pot
Regular price: $92
Discount: 45%
Sales tax: 6%
Final price:
The cost of the fondue pot after the 45% discount and 6% sales tax is calculated using the following equations:
$92 × 0.45 = $41.40 $41.40 × 0.06 = $2.48$41.40 + $2.48 = $43.88In this example, the original price of the fondue pot is $92 and the discount is 45%, which would make the discount amount $41.40. The sales tax is 6%, which would be $2.48
Therefore, the final price of the fondue pot would be $43.88
Hope this helps! Have a great day. :)The formula for glue says to add 45 of hardener to each container of resin. How much hardener should be added to 14 containers of resin?
Write your answer in liters.
630 Liters of hardener will be added to 14 container of resins.
Given,
To add 45 of hardener to each container of resin.
Now,
Total number of containers = 14
Each container will have 45 hardener.
Let the amount of hardener to be added be x,
Then according to unitary method,
1 container = 45 hardener
14 container = x hardener
x = 630 liters.
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How many cubic meters are in 2.11 yd3? I want to see the work and I am stuck.
Doing a change of units, we can see that 2.11 yd³ is equivalent to 1.7513 m³
How many cubic meters are in 2.11 yd³?We know that the relation between one yard and one meter is:
1yd = 0.91m
Then the relation between one cubic yard and one cubic meter is:
(1yd)³ = (0.91m)³
1 yd³ = 0.83 m³
Now we can perform a change of units between the volume in yards and the volume in meters, we will get:
2.11 yd³ = 2.11*(0.83 m³) = 1.7513 m³
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I need help………………………………………
The side length x and y of the right triangle are [tex]\frac{8\sqrt{3} }{3}[/tex] and [tex]\frac{16\sqrt{3} }{3}[/tex] respectively.
What are the value of side length x and y ?The figure in the image is a right triangle.
Angle θ = 60°
Opposite to angle θ = 8
Adjacent to angle θ = x
Hypotenuse = y
To solve for side lengths x and y, we use the trigonometric ratio.
Note that:
sine = opposite / hypotenuse
cosine = adjacent / hypotenuse
tangent = opposite / adjacent
First, we determine the value of x.
tanθ = opposite / adjacent
tan( 60 ) = 8/x
x = 8/tan( 60 )
x = [tex]\frac{8\sqrt{3} }{3}[/tex]
Next, solve for y:
sinθ = opposite / hypotenuse
sin( 60 ) = 8/y
y = 8/sin( 60 )
y = [tex]\frac{16\sqrt{3} }{3}[/tex]
Therefore, the value of x is [tex]\frac{8\sqrt{3} }{3}[/tex] and the value of y is [tex]\frac{16\sqrt{3} }{3}[/tex].
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a dilation has center (0,0). Find the image of the point L(-4,0) for the scale factor 7.
The image of the point L(-4,0) after a dilation with a center of (0,0) and a scale factor of 7 is the point L'(-28,0).
A dilation with a center of (0,0) and a scale factor of 7 means that every point in the plane will be multiplied by a factor of 7 from the origin.
To find the image of the point L(-4,0) after a dilation with a center of (0,0) and a scale factor of 7, we can simply multiply the coordinates of L by the scale factor.
The coordinates of the image point L' will be:
L' = (-4 × 7, 0 × 7) = (-28, 0)
Therefore, the image of the point L(-4,0) after a dilation with a center of (0,0) and a scale factor of 7 is the point L'(-28,0).
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HELP! Whoever answers first to get marked as brainliest!
Pick the first option.
f(x) is dependent on x.
the 2nd option is wrong; the dependent variable is the output, the independent variable is the input.
3rd option is wrong, dependent determines the range.
4th is wrong, x is independent variable.
A square pyramid has a slant height of 3 inches and a surface area of 40 inches. What is the length of a side of the base, in inches. PLEASE HELP
Check the picture below.
so notice, the area of the pyramid is really just the area of the four triangles with an altitude of 3 and a base of "s", and a square that s² in area, and we happen to know that's 40 inches.
[tex]\stackrel{ \textit{\LARGE Areas} }{\stackrel{ \textit{four triangles} }{4\left[\cfrac{1}{2}(\underset{b}{s})(\underset{h}{3}) \right]}~~ + ~~\stackrel{ square }{(s)(s)}}~~ = ~~40\implies 6b+s^2=40\implies s^2+6b-40=0 \\\\\\ (s+10)(s-4)=0\implies s= \begin{cases} -10\\ ~~ ~~ 4 ~in~~ \textit{\LARGE \checkmark} \end{cases}[/tex]
now, let's notice, we can't use the negative value, because the sides are never negative.
A random sample of 16 ATM transactions shows the mean transaction time of 2.8 minutes with a standard deviation of 1.2 minutes. Can you show the width of the 90 percent confidence interval for the true mean transaction time?
The width of the confidence interval is 1.2786.
From the question we are told that
The sample size is n = 16
The mean time is x = 2.8 minutes
The standard deviation is = 1.2 minutes
Generally, the degree of freedom is mathematically represented as
df = n-1
df = 15
From the question we are told the confidence level is 95%, hence the level of significance is =
α = 100-95
α = 0.05
Generally, the margin of error is mathematically represented as =
[tex]E = t_{\alpha/2}, 15 \times \sigma/\sqrt{n}[/tex]
E = 2.131 × 1.6 / √16
E = 0.6393
Generally, the width the confidence 95% confidence interval
W = 2E
W = 1.2786
Hence the width of the confidence interval is 1.2786.
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5. A shopkeeper sold a pen for Rs.13.20 to make a profit of 10 percent. In order to earn a profit
of 15 percent, he should have sold it for.
a. Rs.13.53
b. Rs.13.73
c. Rs.13.80
d. Rs.13.86
The shopkeeper should have sold the pen for Rs. 13.80 in order to earn a profit of 15%. Option C
To determine the selling price of the pen in order to earn a 15% profit, we can use the concept of a profit margin.
Let's start by finding the cost price of the pen. Since the shopkeeper wants to make a 10% profit when selling the pen for Rs. 13.20, we can set up the equation:
Cost price + 10% profit = Selling price
Let's assume the cost price of the pen is C. Then, we can write theequation as:
C + 0.1C = 13.20
Simplifying the equation, we have:
1.1C = 13.20
Dividing both sides by 1.1, we find:
C = 12
So, the cost price of the pen is Rs. 12.
Now, to determine the selling price that will yield a 15% profit, we can use the formula:
Selling price = Cost price + Profit
Profit is calculated as a percentage of the cost price. In this case, the profit percentage is 15%. Substituting the values, we have:
Selling price = 12 + 15% of 12
Selling price = 12 + (0.15 * 12)
Selling price = 12 + 1.8
Selling price = 13.8
Therefore, the shopkeeper should have sold the pen for Rs. 13.80 in order to earn a profit of 15%.
The correct answer is option c. Rs. 13.80. Option C
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Marisol designed a spinner for a game. The spinner is fair if there is an equal chance for the
pointer to land on each letter. The spinner has 6 equal sized sections. Two sections are labeled
A
a. What is the probability of the pointer landing on A?
b. What is the probability of the pointer landing on C, D or E?
C.
Is the spinner a fair spinner?
a. Probability of landing on A = 2/6 = 1/3. b. Probability of landing on C, D, or E = 3/6 = 1/2. c. The probabilities are not equal, the spinner is not fair.
a. Since there are 6 equal-sized sections on the spinner and only 2 sections labeled A, the probability of the pointer landing on A is given by:
Probability of landing on A = Number of favorable outcomes / Total number of possible outcomes
Number of favorable outcomes = 2 (since there are 2 sections labeled A)
Total number of possible outcomes = 6 (since there are 6 equal-sized sections on the spinner)
Probability of landing on A = 2/6 = 1/3
b. To find the probability of the pointer landing on C, D, or E, we need to determine the number of favorable outcomes (sections labeled C, D, or E) and the total number of possible outcomes.
Number of favorable outcomes = 3 (since there are 3 sections labeled C, D, or E)
Total number of possible outcomes = 6 (since there are 6 equal-sized sections on the spinner)
Probability of landing on C, D, or E = Number of favorable outcomes / Total number of possible outcomes
Probability of landing on C, D, or E = 3/6 = 1/2
c. To determine if the spinner is fair, we need to check if the probabilities of landing on each letter are equal. From the previous calculations, we found that the probability of landing on A is 1/3 and the probability of landing on C, D, or E is 1/2.
Since the probabilities are not equal, the spinner is not fair.
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To pay for a home improvement project that totals $20,000, a homeowner is choosing between two different credit card loans with an interest rate of 6%. The first credit card compounds interest semi-annually, while the second credit card compounds quarterly. The homeowner plans to pay off the loan in 10 years.
Part A: Determine the total value of the loan with the semi-annually compounded interest. Show all work and round your answer to the nearest hundredth.
Part B: Determine the total value of the loan with the quarterly compounded interest. Show all work and round your answer to the nearest hundredth.
Part C: What is the difference between the total interest accrued on each loan? Explain your answer in complete sentences.
Part A: The total value of the loan with semi-annual compounding is $36,351.74.
Part B: The total value of the loan with quarterly compounding is $36,645.80.
Part C: The difference between the total interest accrued on each loan is $294.06, with the loan that compounds quarterly accruing more interest due to the more frequent compounding periods, which results in a higher effective interest rate over the same time period.
Part A:
To find the total value of the loan with semi-annually compounded interest, we can use the formula for compound interest:
[tex]A = P(1 + r/n)^{ (nt) }[/tex]
Where:
A = the total amount paid
P = the principal amount borrowed
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this case, P = $20,000, r = 0.06 (6%), n = 2 (semi-annually compounded), and t = 10 years.
[tex]A = 20000(1 + 0.06/2)^{(2*10) } = $36,109.13[/tex]
Therefore, the total value of the loan with semi-annually compounded interest is $36,109.13.
Part B:
To find the total value of the loan with quarterly compounded interest, we use the same formula but with n = 4 (quarterly compounded):
[tex]A = 20000(1 + 0.06/4)^{(4*10)} = $36,533.71[/tex]
Therefore, the total value of the loan with quarterly compounded interest is $36,533.71.
Part C:
The difference between the total interest accrued on each loan is the difference between the total amount paid for each loan minus the principal borrowed:
For the semi-annually compounded loan:
Total interest = $36,109.13 - $20,000 = $16,109.13
For the quarterly compounded loan:
Total interest = $36,533.71 - $20,000 = $16,533.71
The difference in total interest accrued between the two loans is:
$16,533.71 - $16,109.13 = $424.58
The loan with quarterly compounded interest accrues more interest due to the higher compounding frequency.
The difference in total interest accrued between the two loans is relatively small, but over time it can add up.
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A study was commissioned to find the mean weight of the residents in certain town. The study found the mean weight to be 189 pounds with a margin of error of 8 pounds. Which of the following is not a reasonable value for the true mean weight of the residents of the town?
180.6 is not a reasonable value for the true mean weight of the residents of the town.
Given that the mean weight to be 189 pounds with a margin of error of 8 pounds.
So, the range of the mean weight is =
(189 + 8, 189 - 8)
(197, 181)
Therefore the range will lie between 197 and 181.
Hence 180.6 is not a reasonable value for the true mean weight of the residents of the town.
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Problem 1-26
Jerrod and Sonia were working with their team on
problem 1-2 to put the function machines in order.
These functions are reprinted for you below.
f(x) = √x
g(x) = (x - 2)²
h(x) = 2*-7
k(x) = − − 1
Jerrod first put an input of 6 into the function g(x) and
got an output of -16. He wanted to try f(x) as his next
function in the order, but he thinks there might be a
problem using -16 as an input. Is there a problem?
Explain.
There is a problem with the input -16 in the function f(x) = √x
How to determine if there is a problem with the inputFrom the question, we have the following parameters that can be used in our computation:
f(x) = √x
g(x) = (x - 2)²
h(x) = 2x - 7
k(x) = -x -1
Also, we understand that
He puts the functions in the machine in order
So, we have
f(x) = √x
The input is -16
So, we have
f(-16) = √-16
The square root of -16 is not a real number
Hence, there is a problem with the input
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Graph the function -40x^2 + 640x. Label the vertex.
The graph is given below.
The vertex for the function is located at (8, 1280).
We have,
The given function is a quadratic function of form f(x) = ax² + bx + c, where a = -40, b = 640, and c = 0.
To find the vertex, we need to use the formula:
x = -b/2a
where a = -40 and b = 640.
So,
x = -b/2a = -640/(2(-40)) = 8
Now, we can find the y-coordinate of the vertex by plugging x = 8 into the function:
y = -40(8)^2 + 640(8) = 1280
Therefore,
The vertex for the function is located at (8, 1280).
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Which of the following functions is graphed below? HELP
The equation of the functions represented on the graph are (b)
Which of the functions is represented on the graph?From the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have the following intervals:
Interval 1: Closed circle that stops at 1Interval 2: Open circle that starts at 1When the intervals are represented as inequalities, we have the following:
Interval 1: x ≤ 1
Interval 2: x > 1
This means that the intervals of the graphs are x ≤ 1 and x > 1
From the list of options, we have the graph to be option (b
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The dot plot shows the ages of employees at a summer camp. Ages of Employees 00 16 0000 17 ● 00 18 Age (years) Each means 1 employee. 19 20 21 years. Choose the correct answer from each drop-down menu to complete the statements. The range is The median is years.
The range is 5 years.The median is 18 years.
To determine the range and median from the given dot plot of ages, we need to analyze the distribution of the data points.
The range represents the difference between the maximum and minimum values in a dataset. Looking at the dot plot, the minimum age appears to be 16, while the maximum age is 21. Therefore, the range can be calculated as:
Range = Maximum age - Minimum age = 21 - 16 = 5 years.
Thus, the range of the ages of employees at the summer camp is 5 years.
The median represents the middle value in a dataset when it is arranged in ascending or descending order. To determine the median, we need to organize the ages in order from least to greatest:
16, 17, 18, 19, 20, 21
Since there are six data points, the median would be the value in the middle. In this case, the median would be the third value, which is 18.
Therefore, the median of the ages of employees at the summer camp is 18 years.
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What is the percentage equivalent to 16 over 40?
Answer:
16/40 = 40%
Step-by-step explanation:
I divided 16/40 and got 0.4,
To turn a decimal into a percentage, either multiply by 100 or move the decimal to the right 2 times.
A group of adults were asked how many children they have in their families. The bar graph below
shows the number of adults who indicated each number of children.
a) The number of families that were surveyed is given as follows: 17.
b) The percentage of families with exactly one children is given as follows: 29.4%.
What does a bar graph show?A bar graph shows the output considering a given input.
In this problem, the input is the number of children, while the output is the number of families that have the given number of children.
Hence:
4 families have zero children.5 families have one children.5 families have two children.2 families have three children.One family has five children.Hence, for item a, the total number of families is given as follows:
4 + 5 + 5 + 2 + 1 = 17.
Out of the 17 families, 5 have exactly one children, hence the percentage is given as follows:
5/17 x 100% = 29.4%.
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100 POINTS!!
Select the correct answer.
The function g(x)=x² is transformed to obtain function :
h(x) = g(x) + 1.
Which statement describes how the graph of his different from the graph of g?
A. The graph of h is the graph of g horizontally shifted left 1 unit.
B. The graph of h is the graph of g vertically shifted down 1 unit.
C. The graph of h is the graph of g horizontally shifted right 1 unit.
D. The graph of h is the graph of g vertically shifted up 1 unit.
A statement that describes how the graph of his different from the graph of g include the following: D. The graph of h is the graph of g vertically shifted up 1 unit.
What is a translation?In Mathematics and Geometry, the translation of a graph to the left simply means subtracting a digit from the numerical value on the x-coordinate of the pre-image;
g(x) = f(x + N)
Conversely, the translation a geometric figure or graph upward simply means adding a digit to the numerical value on the positive y-coordinate (y-axis) of the pre-image; g(x) = f(x) + N.
Based on the information provided, we have:
(x, y) → (x, y + 1)
g(x) = x²
h(x) = g(x) + 1 → h(x) = x² + 1
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Please help with this 1-3
Answer:
1 is a
2 is c
3 is b
Step-by-step explanation:
Which of the following statements is NOT true?
The blues is often in a 12-bar format
The roots of the blues were in New York City.
The blues influenced music that came later.
Lyrics are important to the blues.
‘
The statement "The roots of the blues were in New York City" is NOT true.
among the late 19th and early 20th centuries, the blues first appeared among African American communities in the southern United States, particularly Mississippi.
African American musical traditions such field hollers, work songs, and spirituals were among those that influenced the development of the blues. African Americans utilised it to express their joys and achievements as well as their struggles and tribulations.
Even though the blues eventually spread to other parts of the United States and the world, its roots are firmly planted in the rural South.
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Given that X U(1, 12), calculate P(x < 4).
Round your answer to three decimal places.
0.273
0.333
0.727
0.250
The probability P(x < 4) will be 0.273. The correct option is A.
Probability is a branch of mathematics that deals with the measurement and analysis of uncertainty. In other words, probability is the measure of the likelihood or chance that a particular event will occur.
Since X is a continuous uniform distribution between 1 and 12, the probability density function (PDF) is given by:
f(x) = 1/11 for 1 ≤ x ≤ 12
= 0 otherwise
The probability P(X < 4) can be calculated as follows:
P(X < 4) = ∫[from 1 to 4] f(x) dx
= ∫[from 1 to 4] 1/11 dx
= [1/11 * x] (from 1 to 4)
= (4/11) - (1/11)
= 3/11
Rounding this to three decimal places, we get:
P(X < 4) ≈ 0.273
Therefore, the answer is 0.273.
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2. Consider this dilation.
Pre-image
9 cm
Image
3 cm B
(a) Find the scale factor. Show your work. (5 points)
(2-a.) Scale factor Image length
Pre-image length
The scale factor is 1/3
How to determine the scale factorThe formula for calculating scale factor is expressed as;
SF = IL/PL
Such that the parameters are expressed as;
SF is the scale factorIL is the image lengthPL is the pre- imageFrom the information given, we have that;
IL = 3cm
PL =9cm
Substitute the values, we have;
Scale factor = 3/9
Divide the values, we have;
Scale factor = 1/3
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Note: Picture is not drawn to scale.
Triangle A is a scaled version of triangle B. The dimensions of triangle A are twice the dimensions of triangle B. The area of triangle B is 24.5 sq cm.
What is the area of triangle A?
A.
343 sq cm
B.
98 sq cm
C.
49 sq cm
The area of triangle A is 98 sq cm. Option B is correct.
Since triangle A is a scaled version of triangle B, the ratio of their areas is equal to the square of the ratio of their corresponding side lengths.
If the dimensions of triangle A are twice the dimensions of triangle B, then the ratio of their side lengths is 2:1.
The ratio of their areas, therefore, is (2:1)² = 4:1.
Given that the area of triangle B is 24.5 sq cm, we can find the area of triangle A by multiplying 24.5 by the ratio of their areas:
Area of triangle A = 24.5 × 4 = 98 sq cm
Therefore, the area of triangle A is 98 sq cm.
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A group decides to go white rafting on the river map of the river has a scale in which 1.5 inches represents 5 miles on the map distance between the starting point in the ending point of their trip is 12 inches. What is the actual distance from the starting point to the ending point.
The actual distance from the starting point to the ending point is 39.96 miles.
Understanding How to Scale DistanceFor someone working with the map or scaled drawing, we can define the scale factor as the ratio between a distance on the drawing or map and the corresponding actual distance in the real world.
From the question,
1.5 inches on the map = 5 miles in actual distance
1 inch on the map = x miles
Perform cross multiplication
1 inch on the map = (5 x 1) / 1.5 = 3.33 miles/inch (scale factor)
The scale factor can then be expressed as ratio:
5/1.5 = 1:0.3
0r
5/1.5 = 10:3
So, the actual distance between the starting point and the ending point can be found by multiplying the length on the map by the scale factor:
Actual distance = Map distance x Scale factor
Actual distance = 12 inches x 3.33 miles/inch = 39.96 miles
Therefore, the actual distance from the starting point to the ending point is approximately 39.96 miles.
Learn more about scale factor here:
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