10. Mrs. Taylor wants to lay new carpet in the entrance and hallway of her home as shown below. The carpet she selected sells for $2.50 a square foot. How much will it cost to lay the carpet in the entrance and hallway?

The factorization of the expression by grouping is [tex]P(x) = (x - 3)(x + 3)(x +4)[/tex]

The polynomial function is given as:

[tex]P(x) = x^3 + 4x^2 - 9x - 36[/tex]

Factorize the given expression.

[tex]P(x) = x^2(x + 4) - 9(x +4)[/tex]

Factor out x + 4

[tex]P(x) = (x^2 - 9)(x +4)[/tex]

Express 9 as the square of 3

[tex]P(x) = (x^2 - 3^2)(x +4)[/tex]

Apply the difference of two squares

[tex]P(x) = (x - 3)(x + 3)(x +4)[/tex]

Hence, the factorization of the expression by grouping is [tex]P(x) = (x - 3)(x + 3)(x +4)[/tex]

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Answer:

21

Step-by-step explanation:

70/10=7

So 7 people are 10% of the train.

10*3=30

7*3=21

21 empty seats

Answer

21

Step-by-step explanation:

Answer:

Answer: 855

Step-by-step explanation:

I take it you want the total number of fruit? You should state the question. I will assume I am correct.

So 25% of 60 baskets = 25/100 * 60 = 15 baskets.

Each basic contains 12 pieces of fruits                     12 * 15 = 180

And 75% of 60 baskets = 0.75 * 60 = 45 baskets.

Each contains 15 pieces                                            45 * 15 = 675

The total number of fruit in all is                                              855

Answer: The answer is 3 basic toppings and 2 premium toppings.

Answer: You ate 1920 calories

Step-by-step explanation:

It’s pretty simple,

all you have to do is multiply 6 by 320.

this then gets you 1920

Answer:

1920 calories

Step-by-step explanation:

6servings*320cal/servings = 1920cal (servings cancel)

Answer:

A.32

Step-by-step explanation:

Answer:

7x

Step-by-step explanation:

4x ( linear function) + 3x ( linear function) = 7x

[tex]\huge\boxed{Hello!:)}[/tex]

Combine like terms:

4x+3x=7x

Remember, we can add terms with the same variable together, but we can't add terms with different variables.

[tex]\huge\boxed{Hence,\:the\:answer\:is\:7x.}[/tex]

[tex]\huge\underline{Hope\:it\:helps!}[/tex]

[tex]\boxed{DreamyGal\:here\:to\:help!:)}[/tex]

Answer:

Check the picture below

Step-by-step explanation:

Answer:

(-3, 5.5)

Step-by-step explanation:

To find the midpoint, you add up the corresponding coordinates (x with x and y with y) and divide each by 2.

(-7+1)/2 = -3

(8+3)/2 = 5.5

Answer:

(-3,5.5)

Step-by-step explanation:

(-7,8)

(1,3)

(-7+1)/2,(8+3)/2

-3,5.5

Answer:

it is c

Step-by-step explanation:

me big brain

Answer:

The equation of the line is x=-1.

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-9-3)/(-1-(-1))

m=-12/(-1+1)

m=-12/0

undefined.

Since the slope is undefined,

it follows that this is a vertical line with the equation x=-1.

Work Shown:

2 cm : 50 miles

3*(2 cm) : 3*(50 miles)

6 cm : 150 miles

Answer:

Scale is 1/2

Step-by-step explanation:

5*1/2=5/2

12*1/2=6

Answer:

4 ounces

Step-by-step explanation:

6c = 24

c = 4

Answer: Noah can use 4 ounces per sandwich

an equation is c=24/6

Step-by-step explanation:

Answer:

c)

Step-by-step explanation:

the closer towards 1 or -1 the more it will be in a line. the closer its to 0 the less in a line it will be.

Answer:

suma is 229,997

Step-by-step explanation:

229,997

Answer:

Step-by-step explanation:

68 1/4

The distance travelled before their first gas stop is 68 1/4 miles given in mixed fractions.

A fraction consisting of a quotient and remainder is a mixed fraction. we can convert the mixed fraction to improper fraction by first dividing the numerator by denominator and then taking the quotient as whole number and remainder as the numerator of proper fraction keeping the denominator same.

Assume the distance covered before their first stop for gas be 'x'

Total distance travelled is 381  miles

We are given that after stopping for gas they travelled 58 3/4 miles and then tripled their distance. The equation formed is

x + 3x + 58 3/4  = 381

4x + 58 3/4  = 381

x=68 1/4 in mixed fraction

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Answer:

40

Step-by-step explanation:

64 female

ratio of men to women is 5:8

5x:8x

where 8x = 64

so x = 8

5(8):8(8)

40:64

So there are 40 men.

Answer:

Let y=ax^2+bx+c be the equation of the parabola. Set up equations.

Using (0,5). 5=a(0)2+b(0)+c

5

=

a

(

0

)

2

+

b

(

0

)

+

c

Using (2,15), 15=a(2)2+b(2)+5

15

=

a

(

2

)

2

+

b

(

2

)

+

5

4a+2b=10

2a+b=5

Using (4,9)

9=a(4)2+b(4)+5

9

=

a

(

4

)

2

+

b

(

4

)

+

5

16a+4b=4

4a+b=1

Subtract each side of (1) and (2) to eliminate b and solve for a: -2a=4

a=-2

Solve for b using (1): 2(-2)+b=5

-4+b=5

b=9

So, the equation is y=−2x2+9x+5

Step-by-step explanation:

Answer:

the jar of peanut butter is $2.36

Step-by-step explanation:

Answer: $2.36

Step-by-step explanation:

Answer:

Hi the answer is x=63

x/9=7

multiply both sides by 9

(x/9)*(9)=(7)*(9)

therefore 63 is the missing number

Answer:

Below.

Step-by-step explanation:

We apply the quotient rule:

dy/dx = ( tanx * 3x^2 - x^3 * sec^2x)  /  (tan^2 x)

= x^2( 3tanx - xsec^2x) / tan^2x

From Sweatcoin, London to the residence of Santa Claus is about 4,280 km away.

The residence of Santa Clause is popularly known as the North Pole.

According to the above, we have to roughly calculate the distance from Sweatcoin in London to the North Pole. This distance is equivalent to about 4,280 km

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