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3 years ago

Factor completely x^2-12x+36

Mathematics

1 answer:

Elenna [48]3 years ago

4 0

Answer:

${(x - 6)}^{2}$

Step-by-step explanation:

$= {x}^{2} - 12x + 36 \\ = {x}^{2} - (6 + 6)x + 36 \\ = {x }^{2} - 6x - 6x + 36 \\ = x(x - 6) - 6(x - 6) \\ =(x - 6)(x - 6) \\ = {(x - 6)}^{2}$

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2/3 x - 4 equal negative 2

Fiesta28 [93]

Answer:

x = 3

Step-by-step explanation:

Given

$\frac{2}{3}$ x - 4 = - 2

Multiply through by 3 to clear the fraction

2x - 12 = - 6 ( add 12 to both sides )

2x = 6 ( divide both sides by 2 )

x = 3

5 0

3 years ago

There were 560 people at a play. The admission price was $2 for

Flauer [41]

Answer:

• For this one we need to split this problem into two equations:

• a (adults) + c (children) = 560

• 2a + c = $860

• Then we substitute 560 - a for c in the second equation.

2a + 560 - a = 860
2a + 560 = 860
2a = 530
2a = 265

• Then we plug this into the first equation:

265 + c = 560

c = 295

Step-by-step explanation:

<h2>I hope this helps you !! </h2>

5 0

2 years ago

A devastating freeze in California's Central Valley in January 2007 wiped out approximately 75% of the state's citrus crop. It t

solniwko [45]

The relationship between the percentage of frozen citrus crop, and the cost of box of oranges is an illustration of a linear function.

The linear equation of the function is: $g(P) = 22.9P+7$ .
The inverse function is: $g^{-1}(c) = \frac{1}{22.9}(c - 7)$ .
A practical domain is from 0% to 100%
A practical range is from 7 to 29.9

A. Input quantity

The input quantity is the percentage of frozen citrus crop

B. Output quantity

The output quantity is the cost of box of oranges

C. The linear function

We have:

$(P_1,c_1) = (20\%,11.58)\\(P_2,c_2) = (80\%,25.32)$

Calculate the slope of the function

$m = \frac{c_2 - c_1}{P_2 - P_1}$

$m = \frac{25.32 - 11.58}{80\%-20\%}$

$m = \frac{13.74}{60\%}$

$m = 22.9$

The linear equation is calculated as follows:

$c -c_1 = m(P-P_1)$

$c -11.58= 22.9(P-20\%)$

$c-11.58 = 22.9P-4.58$

D. Rewrite as y = mx + b

We have:

$c-11.58 = 22.9P-4.58$

Collect like terms

$c = 22.9P - 4.58 + 11.58$

$c = 22.9P+7$

The function is:

$g(P) = 22.9P+7$

E. A practical domain

The domain is the possible values of P. Because P is a percentage, its possible values are 0% to 100%.

The domain of the function is: $[0\%,100\%]$

F. A practical range

When P = 0%

$c = 22.9 \times 0\% + 7 = 7$

When P = 100%

$c = 22.9 \times 100\% + 7 = 29.9$

Hence, the range of the function is: $[7,29.9]$

G. The meaning of $g^{-1}(12)$

The inverse function of g(P) is $g^{-1}(P)$

So:

$g^{-1}(12)$ is the percentage of frozen citrus crop, when the cost is $12.

H. The inverse formula

We have:

$c = 22.9P+7$

Subtract 7 from both sides

$c - 7 = 22.9P$

Make P the subject

$P = \frac{1}{22.9}(c - 7)$

So, the inverse formula is:

$g^{-1}(c) = \frac{1}{22.9}(c - 7)$

Substitute 12 for c

$g^{-1}(12) = \frac{1}{22.9}(12 - 7)$

$g^{-1}(12) = \frac{1}{22.9} \times 5$

$g^{-1}(12) = 22\%$

Read more about linear equations at:

brainly.com/question/19770987

6 0

3 years ago

The distance between each base on a field is 90 ft. How far does a catcher have to throw the ball from home plate to second base

Gnoma [55]

Step-by-step explanation:

A baseball field is in the shape of a square (or diamond). Home plate and second base are opposite corners of each other. So the distance is equal to the diagonal of the square.

Use Pythagorean theorem to find the diagonal, or use properties of a 45-45-90 triangle.

Using Pythagorean theorem:

c² = a² + b²

c² = (90 ft)² + (90 ft)²

c = 90√2 ft

c ≈ 127 ft

7 0

3 years ago

Can help my little bro

lisabon 2012 [21]

Answer:

$0.03

Step-by-step explanation:

chips: 7.84/16=0.49

pretzels: 12.48/24=0.52

0.52=0.49=0.03

7 0

2 years ago