Mathematics High School

A rectangle has a length of 4 feet and a perimeter of 14 feet. what is the perimeter of a similar rectangle with a width of 9 feet?
a. 36 ft
b. 108 ft
c. 42 ft
d. 126 ft

Answers

Answer 1
First Rectangle: P= 14; L= 4, W= ?
Second Rectangle: P= ?, L= ?, W= 9


STEP 1:
solve for the width in the first rectangle using perimeter formula

Perimeter= 2L + 2W
14= 2(4) + 2W

14= 8 + 2W
subtract 8 from both sides

6= 2W
divide both sides by 2

3= W


STEP 2:
Since the two rectangles are similar, they may be different sizes, but they have corresponding angles. We can set up a ratio to compare width and length.

First Rectangle: P= 14, L= 4, W= 3
Second Rectangle: L= ?, W= 9

length/width= length/width
4/3= L/9

cross multiply
4 * 9= 3 * L

36= 3L
divide both sides by 3

12= L


STEP 3:
find perimeter of second rectangle; use length from step 2

Perimeter= 2L + 2W
=2(12) + 2(9)
=24 + 18
=42 feet


ANSWER: (C) 42 feet

Hope this helps! :)

Related Questions

What is an equation for a sine curve with amplitude 2, and period 4pi symbolradians?

Answers

F(x)=2sin(1/2x) is the answer

A dilation produces a smaller figure. Which is a possible scale factor?
–2
1/3
1
4

Answers

we know that
if a dilation produces a smaller figure
then
 0< scale factor <1
so
case A) -2------> the scale factor must be a positive number
case B) 1/3----> 0< 1/3 <1---> is a possible scale factor
case C) 1------> this scale factor does not not produce a smaller figure, it produces the same figure
case D) 4----> this scale factor produces a larger figure

the answer is
1/3

Answer:

B

Step-by-step explanation:

Im assuming.

Helppp how do u do 34

Answers

We'll call area of entire circle 100%.
The 100 degree angle is (100 / 360) of the circle.
100 / 360 = 5 / 18


The answer is:  " [tex] \frac{5}{18} [/tex] " .
_________________________________________________________
The fraction of the "shaded area" of the circle is:  " [tex] \frac{5}{18} [/tex] " .
_________________________________________________________
Explanation:
_________________________________________________________
Given the following circle :
_________________________________________________________

your recipe calls for 1/2 a pound of potatoes. You use 1/6 of the bag of potatoes. whats the number of pounds per bag

Answers

I you use 1/6 of the bag for 1/2 a pound then you need to set up a proportion.

1/6 bag / 1 bag = 1/2 pound / x pounds      Cross Multiply
(1/6)*x = 1/2 pounds * 1 bag Divide by 1/6

Remember: in a 4 level fraction, the denominator inverts and multiplies.


x = [tex] {x = }\frac{ \frac{1}{2} }{ \frac{1}{6} } \\ \\ {x =} \frac{1}{2} * \frac{6}{1} \\ \\{x = } \frac{6}{2} = 3 [/tex]

3 pounds <<<< answer

A dog chases a squirrel. The dog is originally 200 feet away from the squirrel. The dog’s speed is 150 feet per minute. The squirrel’s speed is 100 feet per minute. How long will it take for the dog to get the squirrel?

Answers

Set up the equation as follows:

[tex]150x = 100x + 200[/tex]

150x represents the dog's speed, 100x represents the squirrel's speed, and 200 represents the distance the squirrel has on the dog. x is the amount of minutes that elapse.

Subtract 100x from both sides.

[tex]50x = 200[/tex]

Divide both sides by 50.

[tex]x = 4[/tex]

It will take the dog 4 minutes to catch up with the squirrel.

roger gets $40 per day as wages and $4.50 as commission for every pair of shoes he sells in a day. His daily earnings goal is $112.
Write an equation to determine how many pairs of shoes, ppp, Roger must sell in a day to meet his daily earnings goal.
Find the number of pairs of shoes he must sell to meet his daily earnings goal.

Answers

Basic Pay = $40

Commission for 1 pair of shoes = $4.50

Let x be the number of shoes he needs to sell.

40 + 4.5x ≥ 112
4.5x ≥ 72
x ≥ 16

Answer: He must sell at least 16 pairs of shoes.


Answer:

112=4.5p+40

16

Step-by-step explanation:

If a circle has a radius of 18 feet what's the closest approximation for circumference

Answers

Well, [tex]C = 2 \pi r[/tex], so that would be [tex]2 \pi 18[/tex] = 113.0973... Round that to 113.1 and there's your answer. Hoped this helped :)

Length of side AB???

Answers

[tex]\cos(\theta) = \dfrac{adj}{hyp} [/tex]

[tex]\cos(62) = \dfrac{AB}{12} [/tex]

[tex]AB = 12 \cos (62)[/tex]

[tex]AB = 5.6 \text { cm}[/tex]

When n is small (less than 30), how does the shape of the t distribution compare to the normal distribution?​
a. ​it is taller and narrower than the normal distribution.
b. ​there is no consistent relationship between the t distribution and the normal distribution.
c. ​it is almost perfectly normal.
d. ​it is flatter and more spread out than the normal distribution?

Answers

b is the answer it i think

The equation of the linear regression line represents the relationship between the number of cars washed for charity, x, and the amount earned for charity, y. yˆ=10x+20 How much money can the charity expect to earn if 50 cars come in for a wash?
a $3
b $20
c $720
d $520

Answers

$520.
y=10x+20 
Where x is the amount of cars.
y=10(50)+20
y=500+20
y=$520
Answer option D

By substituting 50 for x in the given linear regression equation, we find that the charity can expect to earn $520 if 50 cars come in for a wash.

The equation of the linear regression line given is y=10x+20, which represents the relationship between the number of cars washed for charity (x) and the amount earned for charity (y). To find how much money the charity can expect to earn if 50 cars come in for a wash, we substitute x with 50 in the equation: y = 10(50) + 20 = 500 + 20 = 520. Therefore, the charity can expect to earn $520 if 50 cars come in for a wash.

alyssa wants to build a fence around her garden to keep deer and rabbits out. the length of the fence must be at least 50 ft, but she only has 140 ft for entire perimeter

Answers

The perimeter of a rectangle is twice the sum of the length and width:
P = 2(L + W)
Since we are given L >= 50 ft and P = 140 ft:
140 >= 2(50 + W)
70 >= 50 + W
20 >= W
Therefore, the width is less than or equal to 20 ft.

(The maximum area is 50 x 20 = 1000 ft^2.)

Alyssa must design a fence within a 140 ft perimeter to keep out deer and rabbits, requiring heights and depths appropriate for each animal. She may use a combination of high electric fencing for deer and buried hardware cloth for rabbits, being mindful of her perimeter constraint.

The student, Alyssa, needs to build a fence around her garden and requires the length to be at least 50 ft with a total available perimeter of 140 ft. To keep deer and rabbits out, she might consider different fence designs.

For preventing deer from entering, it's suggested to use electric fencing at least 8-10 feet tall or two parallel fences that are about 4 feet high and spaced 3 feet apart.

For rabbits, a two-foot high fence made of hardware cloth or chicken wire should be used, extended at least five inches below the ground. This will discourage rabbits from digging under the fence and protect the garden effectively.

Since Alyssa has a limited amount of fencing material, she will need to calculate the perimeter carefully to maximize the enclosed area while keeping within the 140 ft limitation. She might use lengths of sides that meet her minimum requirement and stay within her total available perimeter.

Which number replaces the box to make this a true sentence? 3 × (6 – 2) = (? × 6) – (3 × 2)

Answers

3(6-2) = (?*6) - (3*2)
? would be equal to 3

3

Applying Distribution Law, we multiply 3 with 6 and 2.

So, 3 * ( 6 -2 ) = ( 3* 6 ) - ( 3 * 2)

so, '?' = 3

The point, (-4, 1) is located in which quadrant?

Answers

It is located at quadrant 2. Quadrant one is the top right side. Quadrant three is the bottom left side. Quadrant four is the bottom right side.

Answer:

B its is B that is the most ansewrablea .

Step-by-step explanation:

A set of data has 12 pieces of data. Which of the following statements is NOT TRUE?
A.) There are 3 pieces of data in the first quartile.
B.) There are 6 pieces of data between the first quartile and the third quartile.
C.) There are 9 pieces of data that are greater than the median.
D.) There are 3 pieces of data in the upper quartile.
Please help!!

Answers

To help you understand this, it is helpful to create a sample set of data:

__,__,__,(Q1 is here)__,__,__,(median is here)__, __,__,(Q3is here)__,__,__

A. The first 3 lines are 3 pieces of data in the first quartile.

B. here are 6 pieces of data between the 1st and 3rd quartiles.

D. There are 3 pieces of data in the upper quartile.
                                 

The correct answer is C.) There are 9 pieces of data that are greater than the median. The statement that is NOT TRUE is C.) There are 9 pieces of data that are greater than the median.

To understand why option C is not true, let's review some basic concepts about quartiles and the median in a set of data:

- 3 pieces of data are less than Q1.

- 3 pieces of data are in the first quartile (Q1).

- 6 pieces of data are between Q1 and Q3 (the interquartile range, IQR).

- 3 pieces of data are in the third quartile (Q3).

- Including the median itself, 4 pieces of data are greater than or equal to the median.

This breakdown correctly accounts for all 12 pieces of data. As a result, the statement that is NOT TRUE is indeed option C:

C.) There are 9 pieces of data that are greater than the median.

Since there are 4 pieces of data that are greater than or equal to the median, option C, which asserts there are 9 such pieces, is false. The correct understanding aligns with your analysis of quartiles and the median in this dataset.

How do you find zeros when given a quadratic relation in vertex form

Answers

In order to find the zeros in a quadratic in vertex form, you need to follow a number of steps. They have been outlined for you along with a sample problem.

y = (x - 2)^2 - 16

After getting the original form, you can place a 0 in for y. In is where the graph will cross the x-axis, so it is where you will find both of your zeros.

0 = (x - 2)^2 - 16

Now take the constant and add it to both sides. In this equation, -16 is your constant. So, we'll add 16 to both sides to begin to solve.

16= (x - 2)^2

Now we can take the square root of both sides. After we do so, we take both the positive and negative version of what we get. This is because both 4 and -4 squared is equal to 16.

+/-4 = x - 2

Now we add 2 to both sides to get us what is left of x.

2 +/- 4 = x

Now that we have a final form such as this, we can separate and get two answers for our two zeros.

2 + 4 = 6

2 - 4 = -2

When p is divided by 12, the quotient is q with a remainder of 5, where p and q are positive integers. what is the remainder when p is divided by 6?

Answers

p/12 = q+5

p/6=q/2+5/2

The remainder will be 5/2 or 2.5

turn 11/40 into a decimal

Answers

.275
Divide 11 by 40

Answer:  0.275

To get 11/40 converted to decimal, you simply divide 11 by 40. Then you get 0.275

An event that is made up of two or more outcomes is called.....

Answers

An event that is made up of two or more outcomes is called a compound event.
Hope this helps!

Charlie walk 9 blocks to school after school he walked 3 blocks to soccer practice he walks 7 blocks back home how many total blocks did Charlie walk in one day

Answers

9 + 3 +7 =19 blocks each day

Answer:

19 blocks

Step-by-step explanation:

9+7=16

16+3=19

For f(x) = 2x + 1 and g(x) = x2 – 7, find (f – g)(x).

A. –x^2 + 2x – 6
B. –x^2 + 2x + 8
C. x^2 – 2x – 8
D. 2x^2 – 15

Answers

f(x) = 2x + 1; g(x) = x² - 7

(f - g)(x) = (2x + 1) - (x² - 7) = 2x + 1 - x² + 7 = -x² + 2x + 8

Answer: B. -x² + 2x + 8

The width of a rectangle is half the length. the perimeter of the rectangle is 54 in. what is the length of the rectangle?

Answers

2(x +1/2x) = 54
3x = 54
x = 18
Length: 18

What are the coordinates of the point that corresponds to -7x/4 on the unit circle

Answers

This is a problem of intersection. So, we have two equations, first of all we have a straight line and the second equation is a circle with ratio equal to 1. Therefore, in a mathematical language this is established as follows:

(1)[tex]y = \frac{-7x}{4}[/tex]
(2)[tex]x^{2}+y^{2}=1[/tex]

We introduce (1) into (2):

[tex]x^{2}+(\frac{-7x}{4})^{2}=1[/tex]
[tex]x^{2}+\frac{49x}{16}^{2}=1[/tex]
[tex]65x^{2}=16[/tex]

There are two values, namely:

[tex]\left \{ {{x_{1} = +0.4961 } \atop {x_{2} = -0.4961 }} \right.[/tex]

Then, substituing these values in the first (1) equation, we find:

[tex]\left \{ {{y_{1} = -0.8681 } \atop {y_{2} = +0.8681 }} \right.[/tex]

Finally, the points are two:

[tex]P_{1}=(0.4961,-0.8681)[/tex]
[tex]P_{2}=(-0.4961,0.8681)[/tex]

a___ is a solid consisting of a polygon, a point not in the same plane as the polygon, and all points between them.

Answers

Pyramid is correct answer.

Pyramid is a solid it consisting to a polygon, a point it does not have a same plane as the polygon, and all points from between them.'

Hope it helped you.

-Charlie

Thanks!

Have a great day!

A pyramid is the correct answer


The dimensions of a rectangle has aa width of three more than three times its lenght.Find the dimensions if the area of the rectangle is 36m to the second power.

Answers

A) width = length * 3
B) width * length = 36

Substituting equation A) into B)
length * 3 * length = 36
3 * length^2 -36 = 0
length ^2 -12 = 0
length = 3.4641
width = 3 * 3.4641 = 10.3923

****************************************
Double-check

area = 3.4641 * 10.3923
area = 36



It would take an hour for plane A to meet plane B which is flying towards it. If the distance between them will be 200 miles after 45 minutes, how far apart are they now?

Answers

Let a = speed of the plane A, and b = speed of plane B.
(Assume that the net effect of the wind is negligible.)
From the first sentence, the distance between A and B after each travels for 1 hour is a + b miles. From the second sentence, after 45 minutes, or 0.75 hour, the distance between A and B is 200 miles. Plane a has traveled 0.75a, while plane B has traveled 0.75b.
Hence a + b = 0.75a + 0.75b +200
==> 0.25(a + b) = 200.
==> a + b = 800.
Therefore planes A and B are 800 miles apart now.

Answer:

800 miles apart

Step-by-step explanation:

0.75a+0.75b=200

0.25(a+b)=200

a+b=800 miles apart

Angles a and b are the two acute angles in a right triangle. Use the relationship between sine and cosine to find the value of b if b < α. sin(7x − 15) = cos(3x + 5)

Answers

The value of b is 5 by combining like terms.

In order for the sine and cosine to be equal, the angles must be complementary

sin (7x-15) = cos (3x+5)

7x-15+3x+5 =90 (because sum of both angles a and b must be 90)

10x -10 = 90

10x = 100

x =10

One angle = 7x-15= 7*10-15 = 70-15 =55

Other angle = 3x +5 = 3*10+5 = 30+5 = 35

Since B is less than A, A = 55 degrees and B = 35 degrees

Since we need B, B = 35 degrees

The surface inside the circles will be painted green. The surface outside the circles will be painted white. What is the ratio of green paint to white paint?

A. π : (4 - π)
B. (4 - π) : π
C. π : (π - 4)
D. π^2 : (4 - π^2)

Answers

b / a right .?????/////.

Answer:

The ratio of green paint to white paint is A. [tex]\pi:(4-\pi)[/tex]

Step-by-step explanation:

To find the ratio of green paint to white paint we need to divide the surface that will be painted green by the surface that will be painted white.

In the graph we can see 4 equal circles. Let be ''R'' the radius of the circles.

We can also see a square. The side of the square is 4R (because the length of the side is 4 times the radius of any circle).

The surface of a circle which radius is ''R'' is equal to :

[tex]\pi .R^{2}[/tex]

The surface inside this 4 circles is equal to :

[tex]4.\pi .R^{2}[/tex]

The surface [tex]4.\pi .R^{2}[/tex] will be painted green.

The surface outside the circles is equal to [tex]4.\pi .R^{2}[/tex] subtracted to the area of the square.

The area of the square is :

[tex](4R)^{2}=16R^{2}[/tex] ⇒

[tex]16R^{2}-4.\pi.R^{2}[/tex] is the surface that will be painted white.

If we make the division between the surfaces :

[tex]\frac{GreenSurface}{WhiteSurface}[/tex] ⇒

[tex]\frac{4.\pi .R^{2}}{16R^{2}-4.\pi .R^{2}}[/tex]

[tex]\frac{(4R^{2}).\pi}{(4R^{2}).(4-\pi)}=\frac{\pi}{4-\pi}[/tex]

We find that the ratio of green paint to white paint is [tex]\pi:(4-\pi)[/tex]

i need help!!!!!!!!!!!!!!?!!!

Answers

Here's the thing, just as squaring a number "un-does" its square root, sin "un-does" [tex] sin^{-1} [/tex].  So if you're taking the sin of its inverse, what you get back is what you started with.  The sin of the inverse sin of sqrt(3)/2 is sqrt(3)/2, choice b.

15 Points!

Find f(x) and g(x) so that the function can be described as y = f(g(x)).

Answers

[tex]f(x)=\dfrac{3}{\sqrt{x}}\\\\g(x)=3x+4\\\\\\y=f(g(x))=f(3x+4)=\dfrac{3}{\sqrt{3x+4}}[/tex]

let f(x)=x*2+2x-1 and g(x)=2x-4 find 2f(x)-3g(x)

Answers

f(x)=x²+2x-1 and g(x)=2x-4           2f(x)-3g(x)=?

2f(x)=2*(x²+2x-1)=2x²+4x-2
3g(x)=3(2x-4)=6x-12
2f(x)-3g(x)=(2x²+4x-2) - (6x-12)= 2x²+4x-2 - 6x+12 =2x²-2x +10

2f(x)-3g(x) = 2x²-2x +10

Composite functions involve combining more than one functions

The value of 2f(x) - 3g(x) is [tex]2x^2 -2x-+ 10[/tex]

We have:

[tex]f(x) = x^2 + 2x - 1[/tex]

[tex]g(x) =2x - 4[/tex]

The value of 2f(x) - 3g(x) is calculated as follows:

[tex]2f(x) - 3g(x) = 2 \times f(x) -3 \times g(x)[/tex]

Substitute the values of f(x) and g(x)

[tex]2f(x) - 3g(x) = 2 \times (x^2 + 2x -1) -3 \times (2x - 4)[/tex]

Open brackets

[tex]2f(x) - 3g(x) = 2x^2 + 4x -2 -6x + 12[/tex]

Collect like terms

[tex]2f(x) - 3g(x) = 2x^2 + 4x -6x-2 + 12[/tex]

[tex]2f(x) - 3g(x) = 2x^2 -2x-+ 10[/tex]

Hence, the value of 2f(x) - 3g(x) is [tex]2x^2 -2x-+ 10[/tex]

Read more about composite functions at:

https://brainly.com/question/19695569

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