The length of a rectangle is six times its width.
If the perimeter of the rectangle is 84 ft, find its area.

Answer:

Step-by-step explanation:

See the steps

Answer:

x=5

x=−5

Step-by-step explanation:

5x^2+8 =133

Subtract 8 from both sides.

5x^2=133−8

Subtract 8 from 133 to get 125.

5x^2=125

Divide both sides by 5.

x^2=125/5

Divide 125 by 5 to get 25.

x^2=25

Take the square root of both sides of the equation.

x=5

x=−5

Answer:

5, 6

Step-by-step explanation :

Answer:

the answer is f(n)=14.5−1.4n

Step-by-step explanation:

Hope this helps

The function models the n term of the given sequence is f(n)=14.5+1.4(n-1). Therefore, option B is the correct answer.

An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same. The general form an arithmetic sequence is an=a+(n-1)d

The given arithmetic sequence is 14.5, 13.1, 11.7, 10.3,....

Here, a=14.5 and d=14.5-13.1=1.4

Substitute a=14.5 and d=1.4 in an=a+(n-1)d, we get

f(n)=14.5+1.4(n-1)

The function models the n term of the given sequence is f(n)=14.5+1.4(n-1). Therefore, option B is the correct answer.

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Answer:

65%

Step-by-step explanation:

so there were 20 total voters. 20-7 = 13 that did not vote for the tax

13/20= . 65 = 65%

Answer: Choice A.  (8, 4)

==========================================================

Explanation:

Because x = 2y, we can replace every copy of x with 2y

Let's do so in the second equation

3x - 4y = 8

3(x) - 4y = 8

3(2y) - 4y = 8 .... x replaced with 2y; now let's isolate y

6y - 4y = 8

2y = 8

y = 8/2 ..... divide both sides by 2

y = 4

Use this y value to find x

x = 2y

x = 2*4

x = 8

So we have x = 8 and y = 4 pair together to get the answer (x,y) = (8, 4) which is choice A.

Step-by-step explanation:

1)

a-13b

2) b

3) -3d+14e

4)12x-11y

5)-3rs

6)8xy-10cs

7)

[tex] - 2 {x}^{2} - 4x + 7[/tex]

8)

[tex]8 {y}^{2} - 7[/tex]

Answer:

1. 6a - 3b

2. b + 6c

3.- 3d - 2e

4. 12x + 5y

5. -3rs - 14bc

6. 8xy - 8cs

7. -2x^2 - 8x + 3

Step-by-step explanation:

Subtract polynomials

Answer:

14x² + 41x + 15

Step-by-step explanation:

............

Answer:

Possible dimensions are [tex]r=4\,\,cm\,,\,h=4\,\,cm[/tex] and [tex]h=16\,\,cm\,,\,r=2\,\,cm[/tex]

Step-by-step explanation:

Given:

Volume of a cylinder is [tex]64\pi\,\,cm^3[/tex]

To find: Dimensions of a cylinder

Solution:

Let [tex]r,h[/tex] denote height of a cylinder.

Volume of a cylinder = [tex]\pi r^2h[/tex]

Therefore,

[tex]64\pi=\pi r^2h\\64=r^2h\\4^2\,4=r^2h[/tex]

One possible dimension can be [tex]r=4\,\,cm\,,\,h=4\,\,cm[/tex].

Also, [tex]64=r^2h[/tex] can be written as [tex]16(2^2)=hr^2[/tex]

So, another possible dimension can be [tex]h=16\,\,cm\,,\,r=2\,\,cm[/tex]

Answer:

see below

Step-by-step explanation:

Answer in your own words:

Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape. Which can also be used to calculate the dimensions of the new figure or the original figure by simply substituting the values in the same formula.  

• The scale factor of a dilated figure is denoted by 'r' or 'k'.

• If the scale factor is more than 1 (k > 1), the image is enlarged.

• If the scale factor is less than 1 (0< k <1), the image is contracted.

• If the scale factor is 1 (k = 1), the image remains the same.

• The scale factor cannot be zero.

Scale factor = k

Pre-image lengths: a, b  

(perimeter = 2a + 2b)

Image lengths: ka, kb

(perimeter = 2ka + 2 kb or k (2a + 2b))

Marissa needs to say that the perimeter of the image is the perimeter of the pre-image times the same scale factor.

area of the pre-image = ab

area of the image = (ka)(kb) or k^2 (ab) (The area of the image is the area of the preimage times the square of the scale factor)

Scale factor 5 (then repeat it with scale factor 6)

length of the pre-image = 3 x 4  

(perimeter = 2 (3 + 4) = 2(7) = 14)

length of the image = (3x5) x (4x5) = 15 x 20= 300

(perimeter = 2 (15 + 20) = 2 (35) = 70 or 14 x 5 = 70  

area of the pre-image = 3 x 4 = 12

area of the image = 15 x 20 = 300

12 x (5^2) = 12 x 25 = 300  

Answer

The corresponding angles of the triangles are congruent

The image is a reduction of the pre-image

Neither the dilation nor the rotation change the shape of the triangle

Explanation:

For shapes to be similar:

1- there should be a ratio between the sides

2- angles in first shape should be congruent to angles in second shape

Now, a scale factor of 0.2 means that the sides of the image are 0.2 of the length of the original shape. However, angles are not changes

Let's check the choices:

1- The corresponding sides of the triangles are congruent:

This option is incorrect as dilation changes the lengths of the sides

2- The corresponding angles of the triangles are congruent:

This option is correct as neither dilation nor rotation alters the measures of the angles

3- The corresponding sides of the image are 5 times as long as those of the pre-image:

This option is incorrect as the sides of the image are only 0.2 times as long as those of the pre-image

4- The image is a reduction of the pre-image:

This option is correct as the sides of the image are 0.2 times those of the pre-image which means that the shape is reduced

5- Neither the dilation nor the rotation change the shape of the triangle:

This option is correct as both dilation and rotation are rigid transformations that do not alter the shape of the triangle (a triangle remains a triangle only with different side lengths)

6- The rotation reduces the size of the triangle:

This option is incorrect as rotation does not alter the size of the shape. It only changes its position

Hope this helps :)

Options 2, 4 and 5 are the correct answer.

Given that, a triangle is dilated by a scale factor of 1/5 and then rotated 90 degrees clockwise about the origin.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size.

Now, a scale factor of 0.2 means that the sides of the image are 0.2 of the length of the original shape. However, angles are not changes

Let's check the choices:

1- The corresponding sides of the triangles are congruent:

This option is incorrect as dilation changes the lengths of the sides.

2- The corresponding angles of the triangles are congruent:

This option is correct as neither dilation nor rotation alters the measures of the angles.

3- The corresponding sides of the image are 5 times as long as those of the pre-image:

This option is incorrect as the sides of the image are only 0.2 times as long as those of the pre-image.

4- The image is a reduction of the pre-image:

This option is correct as the sides of the image are 0.2 times those of the pre-image which means that the shape is reduced.

5- Neither the dilation nor the rotation change the shape of the triangle:

This option is correct as both dilation and rotation are rigid transformations that do not alter the shape of the triangle (a triangle remains a triangle only with different side lengths).

6- The rotation reduces the size of the triangle:

This option is incorrect as rotation does not alter the size of the shape. It only changes its position.

Therefore, options 2, 4 and 5 are the correct answer.

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Answer:

Step-by-step explanation:

-8x³y²(x²-4y) = -8x³y²x² + 8x³y²4y

= -8x³⁺⁵y² + 32x³y²⁺¹

= -8x⁸y² + 32x³y³

Answer:

(2,7)

Step-by-step explanation:

Step-by-step explanation:

Given

sin³ø cos ø + cos³ø sinø

= sin ø cos ø ( sin²ø + cos²ø)

= sinø cosø * 1

= sinø cosø

Hope it will help :)

Answer:

Sure thing. Which question do you need help with? ill do the best i can.

Answer:

see below, I hope it's helpful

Step-by-step explanation:

Simplifying expressions...

1. use as many steps as you need, don't take shortcuts or try to do too much in one step... only touch each item in the expression once at most at each step

2. Follow PEMDAS

3. consider some of the rules of exponents: (a/b)^n = (a^n)/(b^n) and (x)^(-n) = 1/(x^n) and a^(b^c) = a^(bc)

examples x^(-4) = 1/(x^4)

                3^(-x) = 1/(3^x)

                (2/x)^(-n) = (1/(2/x))^n = (x/2)^n

                 2^(-x^3) = 2^(-3x) = 1/(2^3x)

so for example

2^(-x) - (x)^(-n) + (-n)^(x^(-2)) touch each part only once, do what you can

1/(2^x) - 1/(x^n) + (-n)^(-2x) the third part needed two steps, so be it

1/(x^n) - 1/(x^n) + (1/((-n)^2x)

Answer:

0.16

Step-by-step explanation:

Answer:

Commutative property of addition: Changing the order of addends does not change the sum.

Step-by-step explanation:

For example, 4 + 2 = 2 + 4 4 + 2 = 2 + 4 4+2=2+44, plus, 2, equals, 2, plus, 4.

Answer:

The answer is in Picture.

Step-by-step explanation:

Hope it is helpful....

Answer:

Answer:

As you can see, the -4 and -1/4 coefficient values are automatically different, and will resultantly produce different answers in the solutions.

The solutions are related, as the two numbers are reciprocals, as well as both being negative values.

Hope this helped !

Answer:

hm the 8 per hour seems more accurate because if you multiply or divide 8 could almost get you to 120

Step-by-step explanation:

Answer:

Hey!

0.309<0.32<0.35<0.4

hope this helps you

The numbers in order of size start with the smallest can be done as 0.309 < 0.32 < 0.35 < 0.40.

The decimal numeral system is the most widely used system for representing both integer and non-integer values. It is the Hindu-Arabic numeral system's expansion to non-integer numbers. Decimal notation is the method of representing numbers in the decimal system.

The given number can be arranged from smallest to largest can be arranged as shown below. Therefore, we can write,

0.309 < 0.32 < 0.35 < 0.40

Hence, the numbers in order of size start with the smallest can be done as 0.309 < 0.32 < 0.35 < 0.40.

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Answer:

about 31 percent

Step-by-step explanation:

Answer:

73:42

Step-by-step explanation:

1115-73=42

G : B

73 : 42

Answer

43

Step-by-step explanation: