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3 years ago

E

Mathematics

1 answer:

AlexFokin [52]3 years ago

5 0

For this case we have that by definition, the point-slope equation of a line is given by:

$y-y_ {0} = m (x-x_ {0})$

Where:

m: It's the slope

$(x_ {0}, y_ {0}):$ It is a point through which the line passes

According to the statement data we have:

$m = 5\\(x_ {0}, y_ {0}): (- 8,1)$

Substituting we have:

$y-1 = 5 (x - (- 8))$

By law of signs of multiplication we have to:

$- * - = +\\y-1 = 5 (x + 8)$

Answer:

The requested equation is: $y-1 = 5 (x + 8)$

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Which polynomial function could be represented by the graph below?

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x2 + x – 2=4x

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Step-by-step explanation:

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stiks02 [169]

Answer:

Therefore

15.

$25c^{2}-9$

16.

$(y+8)(y+1)$

17.

$(x-3y)(x-7y)$

Step-by-step explanation:

15.

$(5c^{2} +3)(5c^{2}-3)$

Using the Identity (a + b)(a - b) = (a² - b²) we get

Consider here a = 5c and b = 3 then we will have

$((5c)^{2} -(3)^{2})=25c^{2}-9$ .....as required

16.

$y^{2}+9y+8$

Here Factorize 8 such that sum up to be 9

∴ 8 × 1 = 8 and 8 + 1 =9

$y^{2}+9y+8\\y^{2}+8y+y+8\\y(y+8)+1(y+8)\\(y+8)(y+1)$ ... as required

17.

$x^{2}-10xy+21y^{2}$

Here Factorize 21 such that sum up to be -10

∴ -3 × -7 = + 21 and -3 - 7 = - 10

$x^{2}-10xy+21y^{2}\\x^{2}-3xy-7xy+21y^{2}\\x(x-3y)-7y(x-3y)\\(x-3y)(x-7y)$ ........as required

Therefore

15.

$25c^{2}-9$

16.

$(y+8)(y+1)$

17.

$(x-3y)(x-7y)$

4 0

2 years ago

Read 2 more answers

P(x)=Third-degree, with zeros of −3, −1, and 2, and passes through the point (1,12).

Mila [183]

Answer:

The polynomial is:

$p(x) = -x^3 - 2x^2 + 5x + 6$

Step-by-step explanation:

Zeros of a function:

Given a polynomial f(x), this polynomial has roots $x_{1}, x_{2}, x_{n}$ such that it can be written as: $a(x - x_{1})*(x - x_{2})*...*(x-x_n)$ , in which a is the leading coefficient.

Zeros of −3, −1, and 2

This means that $x_1 = -3, x_2 = -1, x_3 = 2$ . Thus

$p(x) = a(x - x_{1})*(x - x_{2})*(x-x_3)$

$p(x) = a(x - (-3))*(x - (-1))*(x-2)$

$p(x) = a(x+3)(x+1)(x-2)$

$p(x) = a(x^2+4x+3)(x-2)$

$p(x) = a(x^3+2x^2-5x-6)$

Passes through the point (1,12).

This means that when $x = 1, p(x) = 12$ . We use this to find a.

$12 = a(1 + 2 - 5 - 6)$

$-12a = 12$

$a = -\frac{12}{12}$

$a = -1$

Thus

$p(x) = -(x^3+2x^2-5x-6)$

$p(x) = -x^3 - 2x^2 + 5x + 6$

6 0

3 years ago

A cleaning company charged $125 to clean a 2500 square foot house. The same company charged $146 to clean a 3200 square foot hou

HACTEHA [7]

Answer:

The cost is y = $185

Step-by-step explanation:

Let us have points spelt out here

(2500,125) and (3200,146)

The general form of a straight line equation is;

y = mx + b

where m is slope

So to calculate the slope in this case, we have

m = (146-125)/(3200-2500)

m = 21/700 = 0.03

So we have the equation as

y = 0.03x + b

To get b, we use any of the two points

Let us use (2500,125)

So we have

125 = 0.03(2500) + b

125 = 75 + b

b = 125-75

b = 50

So the complete equation of the line is;

y = 0.03x + 50

So here, we want to find the cost of a house with 4500 square feet

simply substitute 4,500 for x

y = 0.03(4500) + 50

y = 135 + 50

y = $185

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3 years ago