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3 years ago

9

It costs $109 per night to rent a motel room in Georgia. There is a one-time $30 non-refundable deposit required. How much will

it cost your family to rent a room for a week in Hampton?

2 answers:

Ne4ueva [31]3 years ago

8 0

Answer:

$793.00

Step-by-step explanation:

109x7=763

763+30=793

V125BC [204]3 years ago

4 0

109x7=763+30=793 dollars for one week

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Given the polynomial 2x3 18x2 − 18x − 162, what is the value of the constant 'k' in the factored form? 2x3 18x2 − 18x − 162 = 2(

oee [108]

The value of the constant 'k' in the factored form factorization the provided polynomial equation is 3.

<h3>What is polynomial equation?</h3>

Polynomial equations is the expression in which the highest power of the unknown variable is n (n is real number).

The factor of a polynomial is the terms in linear or equation form, which are when multiplied together, give the original polynomial equation as result.

The given polynomial equation in the problem is,

$2x^3 +18x^2 - 18x - 162$

The factor of the polynomial equation are given as,

$2(x+ k)(x - k)(x +9)$

First find out the factors to compare and find the value of k.The above equation has the unknown variable x and the highest power of this unknown variable is 3.

Take out the highest common factor 2, which can divide each term of the above equation (2, 18, -18, -162). Thus,

$2(x+ k)(x - k)(x +9)=2(x^3 +9x^2 - 9x - 81)$

Take out the highest common factor to make the groups as,

$2(x+ k)(x - k)(x +9)=2(x^2( x+9) - 9(x + 9))\\2(x+ k)(x - k)(x +9)=2( x+9) (x^2 - 9)\\2(x+ k)(x - k)(x +9)=2( x+9) (x^2 - 3^2)$

Use the property of difference of the square for the (x²-3²) term as,

$2(x+ k)(x - k)(x +9)=2( x+9) (x+3)(x-3)\\2(x+ k)(x - k)(x +9)=2 (x+3)(x-3)( x+9)$

On comparing the two equation, we get the value of k as 3. Thus, the value of the constant 'k' in the factored form factorization the provided polynomial equation is 3.

Learn more about factor of polynomial here;

brainly.com/question/24380382

7 0

2 years ago

A 2x2 square is centered on the origin. It is dilated by a factor of 3. What are the coordinated of the vertices of the square?

Alexxx [7]

<u>Answer</u>:

The vertices are:

A' = (-3, -3)

B' = (3, -3)

C' = (3, 3)

D' = (-3, 3)

The ratio of area of larger square to smaller square is 9:1

<u>Step-by-step explanation:</u>

Given:

A 2 x 2 square is centered at the origin.

So, the center of the square is (0, 0)

Since it is 2 x 2 square, the side of the square is 2 units.

So, the vertices of the 2 x 2 square are A (-1, -1), B(1, -1), C(1. 1), D(-1, 1)

The above square is dilated by a factor of 3.

Let's name the dilated square A'B'C'D'

To find the coordinates of the vertices of dilated square, we need to multiply each vertices of ABCD by 3.

A(-1, -1) = 3(-1, -1) = A'(-3, -3)

B(1, -1) = 3(1, -1) = B'(3, -3)

C(1, 1) = 3(1, 1) = C'(3, 3)

D(-1, 1) = 3(-1, 1) = D'(-3, 3)

To find the area of the small square

the side of the small square is 2 units

so the are of the small square is $2^2$ = 4 square units

To find the area of the larger square

lets find the side AB of the square using distance formula

=> $\sqrt{(x_2 -x_1)^2 +(y_2-y_1)^2}$

=> $\sqrt{(3 - (-3))^2 +(-3 - (-3))^2}$

=> $\sqrt{(3 +3)^2 +(-3 +3)^2}$

=> $\sqrt{(6)^2 +(0)^2}$

=> $\sqrt{36}$

=>6

AB =6 units

In a square all the sides will be equal

Now the area of the larger square will be

$6^2$

36 square units

The ratio of larger square to smaller square is

=>36 : 4

=>9 : 1

5 0

3 years ago

There are 87 first graders in after care.after 39 students are picked up, the teacher put the remaining students into 4 groups f

Elden [556K]

Answer:

There are 12 students in each group

Step-by-step explanation:

87-39= 48

48/4= 12

Hope this helped. ;)

5 0

3 years ago

Read 2 more answers

SHOW STEP BY STEP FOR BRAINLIEST

Nostrana [21]

Answer:

The y-coordinate of F is 8.

Step-by-step explanation:

The area of the large triangle = 1/2 * base * height.

From the given coordinates:

The base of the large triangle = x coordinate of C - x coordinate of A

= 11 - 3 = 8 units.

It's height = y coordinate of A = 12, so

Area of large triangle = 1/2 * 8 * 12 = 48 unit^2.

Using a similar calculation for the small triangle:

Base = 10 - 6 = 4 and height = k units.

So it's area = 1/2 * 4 * k = 2k unit^2.

So from given area of the shaded part:

48 - 2k = 32

-2k = -16

k = 8.

8 0

3 years ago

One cup of grated, fresh Parmesan cheese weighs 3 ounces. How many cups of grated cheese can you expect to get from a 4.5-poun

Ksenya-84 [330]

Answer:

9 cups

Step-by-step explanation:

If one pound is equal to 2 cups, then you would multiply 2 by 4, which gives you 8. If one pound equals 2 cups, then half a pound equals 1 cup. So since we already have 8 cups, you just add one more cup, which gives you 9 cups total

SUMMARY: You can expect to get 9 cups of grated parmesan cheese from a 4.5-pound block.

5 0

2 years ago