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bogdanovich [222]
3 years ago
10

Can someone help me with all these? .

Mathematics
1 answer:
Alika [10]3 years ago
3 0
Is that homework done
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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 trapezoidal window is 8 feet tall and has base lengths of 1 foot and 7 feet. What is the area of the window? The area of the w
Ahat [919]

Answer: 32 ft²

Step-by-step explanation:

The area of a trapezoid is calculable using the formula:

= (a + b)/ 2 * height

Where a and b are the base lengths.

= (1 + 7) / 2 * 8

= 8/2 * 8

= 4 * 8

= 32 ft²

8 0
3 years ago
4x - 9y + 6z = -3<br> x - 7y + 8z = 4<br> y - 6z = -1
SVEN [57.7K]
-3
-1
0 (if you are talking about matrices and I used the formula A^-1 B)
6 0
3 years ago
Someone plz solve and check thanks
maksim [4K]

Remember to follow the order of operation, PEMDAS. PEMDAS stands for:

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

~

5. 9(7x - 4) = 27

First, distribute 9 to all terms within the parenthesis:

9(7x - 4) = 27

(9 * 7x) - (9 * 4) = 27

63x - 36 = 27

Next, isolate the variable, x. Do the opposite of PEMDAS.

First, add 36 to both sides:

63x - 36 (+36) = 27 (+36)

63x = 27 + 36

63x = 63

Isolate the variable, x. Divide 63 from both sides:

(63x)/63 = (63)/63

x = 63/63 = 1

x = 1

~

6. 5(3x + 8) = 175

First, distribute 5 to all terms within the parenthesis:

5(3x + 8) = (5 * 3x) + (5 * 8) = 15x + 40

15x + 40 = 175

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

First, subtract 40 from both sides:

15x + 40 (-40) = 175 (-40)

15x = 175 - 40

15x = 135

Next, divide 15 from both sides of the equation:

(15x)/15 = (135)/15

x = 135/15 = 9

x = 9

~

8 0
2 years ago
Determine the intercepts of the line .
tester [92]

Answer:

x- int = (1.5,0)

y-int = (0, -2)

Step-by-step explanation:

Graphing Calculator

6 0
2 years ago
Read 2 more answers
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