Rectangular pyramid B is the image of rectangular pyramid A after
dilation by a scale factor of 3. If the surface area of rectangular
pyramid A is 87 cm², find the surface area of rectangular pyramid B,
the image.

The equation of the line that passes through the point (5, 4) and is perpendicular to the line whose equation 2x + y = 3 is y = 1/2x + 3/2

The given equation of the line is

2x + y = 3

y = 3 - 2x

y = -2x + 3

The slope of the line is -2

The slope of the original line will be negative inverse of -2

= - 1/-2

= 1/2

The line is passing through the point (5, 4)

The slope intercept form is

y = mx + b

Substitute the values in the equation

4 = 1/2(5) + b

4 = 5/2 + b

b = 4 - (5/2)

b = 3/2

Therefore, the equation of the line is y = 1/2x + 3/2

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The unknown angle of the right angle triangle is as follows:

A right angle triangle is a triangle that has one of its angles as 90 degrees.  The sides of a right angle triangle can be named base on the position of the angles. The sides includes hypotenuse side, opposite side and adjacent side.

The sum of angles in a right angle triangle is 180 degrees.  Therefore, let's find the ∠C in the triangle ABC.

Therefore,

180 = ∠A + ∠B + ∠C

m ∠B = y + 40

m ∠C = 3y - 10

m ∠A = 90°

Hence,

180 = 3y - 10 + y + 40 + 90

180 = 4y + 120

180 - 120 = 4y

y = 60 / 4

y = 15

Hence,

m ∠C = 3(15) - 10

m ∠C = 45 - 10

m ∠C = 35 degrees

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The consequence of the two functions f(x) = (1 / 6) · ∛x and g(x) = 6 · x³ by composition is f[g (x)] = (1 / 6) · ∛3 · x and g[f (x)] = (1 / 6) · x³, respectively.

In this question we must use the definition of composition between two functions f and g, where the independent variable of the function f is substituted by function g. That is to say:

f ° g (x) = f [g(x)]

If we know that f(x) = (1 / 6) · ∛x and g(x) = 6 · x³, then the result of each composition is:

f [g (x)] = (1 / 6) · ∛(6 · x³)

f[g (x)] = (1 / 6) · ∛3 · x

g[f (x)] = 6 · [(1 / 6) · ∛(6 · x³)]³

g[f (x)] = 6 · (1 / 216) · (6 · x³)

g[f (x)] = (1 / 6) · x³

The results of the compositions of the two functions f(x) = (1 / 6) · ∛x and g(x) = 6 · x³ are f[g (x)] = (1 / 6) · ∛3 · x and g[f (x)] = (1 / 6) · x³, respectively.

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The numerical  top and bottom limits for a d grade is 68 and 61 respectively

What can we learn from mean and standard deviation?

In statistics, the measurement of variability known as the standard deviation (SD) is frequently utilised. It demonstrates how different things are from the norm (mean). While a high SD shows that the data are dispersed throughout a wide range of values, a low SD suggests that the data points tend to be close to the mean.

Given,

Mean = 75.1

Standard Deviation = 9.1

For a D grade at / 6th Percentile and 78th Percentile critical

Z- Scores are -0.77 and -1.55 respectively

The Corresponding Top grade for d

x + z * σ

75.1 + (-0.77) * 9.1 =68

The Corresponding Bottom grade for d

x + z * σ

75.1 + (-1.55) * 9.1 =61

A d grade has numerical top and bottom limitations of 68 and 61, respectively.

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The annual rate of interest she is charging you is 12%.

Given that, you ask your best friend to lend you $200 to buy your favorite toy.

An interest rate tells you how high the cost of borrowing is, or high the rewards are for saving. So, if you're a borrower, the interest rate is the amount you are charged for borrowing money, shown as a percentage of the total amount of the loan.

Here,

Extra money per month =$2

Extra money per year = $2×12

Extra money per two year = 2×2×12 = 4×12 = $48

Money lend = $200

Money given after two years = $(200+48) = $248

Now, the rate of interest can be find using SI=(P×R×T)/100

48= (200×R×2)/100

⇒ 48= 4R

⇒ R=12%

Hence, the annual rate of interest she is charging you is 12%.

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"Your question is incomplete, probably the complete question/missing part is:"

You ask your best friend to lend you $200 to buy your favorite toy. She says she can lend you the money only if you give her an extra $2 for every month that passes before you return it. What is the total amount you must pay her if you return it after two years? rupees What is the annual rate of interest she is charging you?

Carlos points are 12

Let , Fabio points = x= 31

Carlos points = Y

Fabio had 7 points less than 2 times as many points as Carlos.

X = 2Y - 7

X = 2Y - 7

X + 7 = 2Y

Y = (x + 7)/2

X = (31 - 7)/2

x = 24/2

X = 12

Carlos points are 12

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x = 2 , y' = 70 , x' = 30 : by using the property of SAS(side angle side) in ΔKMN and ΔKLI as they were similar polygon.

The property of a triangle whose two sides and the angle between these sides are stated is "SAS," which stands for "Side, Angle, Side". The SAS formula can be used to determine the area of a given triangle ABC with two known sides and an included angle between these sides.

Assume that the triangle's three sides are a, b, and c.

A SAS Triangle's perimeter

The following formula can be used to determine a triangle's area using SAS:

When sides "b" and "c" are known, along with angle A, the triangle's area is equal to: 1/2 bc sin(A)

The area of the triangle is equal to 1/2 ab sin(C) when sides 'b' and 'a' as well as included angle B are known

when sides "a" and "c" were added using SAS in triangle 1ΔMKN ~ ΔJKL

So, MN/KN = JL/KL

(x+1)/12 = (3x-2)/32

∴ 5x = 10 ⇒ x = 2

Using same property (SAS) in triangle 2

J = 80

∴ 30 = <x'

∵ in a triangle sum of angles is equal to 180° so, y' + <

J + 30 = 180

∴ <J = 80

then, y' = 70 and x' = 30

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Answer: 100

Step-by-step explanation:

To solve this expression, we can start by performing the operations inside the parentheses first:

560 divided by 7 + 140 divided by 7

= 80 + 20

= 100

So the result of the expression is 100.

I hope this helps! Let me know if you have any questions.

There is no horizontal asymptote since n > m.

Find the place where the phrase x 2 x 2 x 15 x 2 x 12 is undefined.

x = 0

When n is the degree of the numerator and m is the degree of the denominator, the rational function R (x) = an x n b x m is used.

1. The x-axis, with y = 0, is the horizontal asymptote if n m.

2. If n = m, then the line y = a b is the horizontal asymptote.

3. There is no horizontal asymptote if n > m. (there is an oblique asymptote).

Identify n and m.

n= 4 m = 2

There is no horizontal asymptote since n > m.

Domain and Range

Domain: (−∞,0)∪(0,∞),{x|x≠0}

Range: (−∞,∞),{y|y∈R}

Oblique Asymptotes: y = x 2 x 3 x 12.

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The equation that matches this table is  X=Y*k,k=12,  Hence Given table is direct variation.

X=12,Y=1

X=24,Y=2

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A story that can be represented using the equation y=x+1/5x is "John has an apple and he cut another apple into 5 equal parts and took on part. What's the rural fraction of apple that he has?

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

In this case, if John has an apple and he cut another apple into 5 equal parts and took on part.

This can be illustrated as:

y = x + 1/5x

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Answer:

x = -3

Step-by-step explanation:

7x+10 = -4x-23

11x+10 = -23

11x = -33

x = -3

Answer:

x= -33/4

Step-by-step explanation:

area of triangle = (b × h) ÷ 2

where b is the base so (g - 8)m,

h is the height so (g - 11)m

and area is 35

35 = (g - 11) × (g - 8) /2

35 = g² - 19g + 88 / 2

35 = 1/2g² - 19/2g + 44

1/2g² - 19/2g + 9 = 0

use the quadratic formula to find the two values of g and you will get:

g = 18 and g = 1

if we use g as 1 we will get negative metres for the values for the base and height so we use g = 18 instead!

base = (18) - 8

= 10m

height = (18) - 11

= 7m

The list that shows all the possible outcomes for choosing two marbles at random is yy, oo, ro, yo, oy, ry, yr, or, rr

From the question, we have the following parameters that can be used in our computation:

Orange = o

Red = r

Yellow = y

From the question, we understand that the selection is with replacement

This means that it is possible to select a marble two times

So, we have the following representation

yy    oo     ro

yo    oy     ry

yr     or      rr

Hence, the list is yy, oo, ro, yo, oy, ry, yr, or, rr

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Answer:

4.5 as a fraction is 9/2.

Step-by-step explanation:

Please give the brainliest.

Answer:

y = 1.25x + 5

Step-by-step explanation:

I found the answer using linear regression.

By simplifying the expression we get [tex]4x^{\frac{3}{2} }y^{\frac{5}{2} }[/tex]

A number can be obtained by multiplying the square root of that integer by itself. The word "square root" is represented by the symbol [tex]\sqrt[2]{}[/tex] .The opposite of squaring an integer is finding its square root.

According to the given information

Given x > 0

          y > 0

we need to simply the following expression

[tex]\sqrt[4]{256x^{6}y^{10} }[/tex]

By simplifying

we get

= [tex](4^{4}x^{6} Y^{10}) ^{\frac{1}{4} }[/tex]

= [tex]4x^{\frac{6}{4} } y^{\frac{10}{4} }[/tex]

=  [tex]4x^{\frac{3}{2} }y^{\frac{5}{2} }[/tex]

Hence

By simplifying the expression we get [tex]4x^{\frac{3}{2} }y^{\frac{5}{2} }[/tex]

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Answer:

The distributions of the income of the 3 states are pretty similar. The highest income in Maine is 50s, in Indiana it is pretty evenly spread out and Connecticut is highest in 60/70 and has multiple stragglers in 170 - 200 and a few near 300. The main place where most of the plot points are is 10 - 150.

Not completely sure if this helps, but I hope it does.

Answer:

56

Step-by-step explanation:

When you subtract a negative number. Just consider it addition.

So, 40+16

It's very simple from there.

Answer:

56!

Step-by-step explanation:

The question is 40 minus negative 16.
When you subtract a negative, it's the same as adding.

So 40 - (-16) is the same as 40 + 16, which equals 56.

Example:

If you have 3 apples, and you remove negative 3 apples from 3, now you have 6.
So, 3 - (-3) = 6.

Answer:

F(x)= x +10 (Cus when x is 0, Function is 10)

Answer:

y=x+10

Step-by-step explanation:

You first need to find the y intercept using the coordinates where x equal 0. Then you can figure slope by solving for m when you plug in the other points.

Answer:

Step-by-step explanation:

hard

Answer:

28 feet long

Step-by-step explanation:

we find the area of the first lawn using recent angle formula (l)(w)=a

(7)(3)

21

Now we multiply this by 4 since the second lawn is four times it

21x4

84

Now we rearrange the rectangle area formula to where length is what we are trying to find

a=(l)(w)

/w. /w

a/w=l

Now we fill in this formula

84/3=a

28

Hopes this helps

The probability that a student is chosen randomly from the class has a cat or a dog is 26/29.

It is based on the probabilities that something could happen. The theory of probability primarily relies on the justification for probability. A coin is tossed, for instance, and the theoretical likelihood of randomly receiving a head is 1 in 2.

explanation:

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.

P(E) = Number of favorable outcomes / total number of outcomes

The total strength of the class is 29

The probability that a student is chosen randomly from the class has a cat or a dog =  Number of favorable outcomes / total number of outcomes

P(E) = 26/29

Hence, The probability that a student is chosen randomly from the class has a cat or a dog is 26/29.

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Step-by-step explanation:

angle bisector theorem :

the ratio of the 2 baseline segments is the same as the ratio of the 2 legs of the main triangle.

in our case :

44.8/56 = (x + 4)/35

x + 4 = 44.8×35/56 = 44.8×5/8 = 28 mm

x = 24

FYI : one way of explaining the theorem is : we could see this as 2 projections originating from E at the same angle but onto a tilted projection screen.

the length on the projection screen (HD or GD) is directly related to the distance from the projection point to the end of the tilted projection : ED or EG. and so the ratios of both projections must be equal (due to the equal angle).

so, in our case

35/56 = (x + 4)/44.8

which leads, of course, to the same result

44.8×35/56 = x + 4

Answer: x =4 , y =1

Step-by-step explanation:

Multiply the first equation by 4,and multiply the second equation by 3.

4(4x+3y=19)

3(3x−4y=8)

Becomes:

16x+12y=76

9x−12y=24

Add these equations to eliminate y:

25x=100

Then solve 25x=100 for x:

25x=100

(Divide both sides by 25)

x =4

Now that we've found x let's plug it back in to solve for y.

Write down an original equation:

4x+3y=19

Substitute4forxin4x+3y=19:

(4)(4)+3y=19

3y+16=19( Simplify both sides of the equation)

3y+16+−16 = 19+−16 (Add -16 to both sides)

3y=3

(Divide both sides by 3)

y=1

Pete is correct because the student used multiplication as the correct function operation to simplify the expression.

Answer:

Step-by-step explanation:

The number of trials needed to produce results similar to their predicted outcomes is likely to be higher for Kasey's experiment with 20 possible outcomes than for Gerald's experiment with 3 possible outcomes.

the equation of the straight line is y = -x-7

What is equation straight line?

Y = mx + c is the general equation for a straight line, where m denotes the line's slope and c the y-intercept. It is the version of the equation for a straight line that is used most frequently in geometry. There are numerous ways to express the equation of a straight line, including point-slope form, slope-intercept form, general form, standard form, etc. A straight line is a geometric object with two dimensions and infinite lengths at both ends. The formulas for the equation of a straight line that are most frequently employed are y = mx + c and axe + by = c. Other versions include point-slope, slope-intercept, standard, general, and others.

In the graph the slope m = -1

the y-intercept will be -7

Hence the equation of the st. line is y = -x-7

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