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3 years ago

8

Rod is paid an overtime rate of $25 per hour after he earns his basic wage of $600 per week. Write an equation in slope- interce

pt form for the total pay p if he works h hours of over-time.

1 answer:

SpyIntel [72]3 years ago

5 0

P = 25h + 600.

This is because even if he works no overtime, he still gets his 600.

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If the sum of the zereos of the quadratic polynomial is 3x^2-(3k-2)x-(k-6) is equal to the product of the zereos, then find k?

lys-0071 [83]

Answer:

2

Step-by-step explanation:

So I'm going to use vieta's formula.

Let u and v the zeros of the given quadratic in ax^2+bx+c form.

By vieta's formula:

1) u+v=-b/a

2) uv=c/a

We are also given not by the formula but by this problem:

3) u+v=uv

If we plug 1) and 2) into 3) we get:

-b/a=c/a

Multiply both sides by a:

-b=c

Here we have:

a=3

b=-(3k-2)

c=-(k-6)

So we are solving

-b=c for k:

3k-2=-(k-6)

Distribute:

3k-2=-k+6

Add k on both sides:

4k-2=6

Add 2 on both side:

4k=8

Divide both sides by 4:

k=2

Let's check:

$3x^2-(3k-2)x-(k-6) \text{ with }k=2$ :

$3x^2-(3\cdot 2-2)x-(2-6)$

$3x^2-4x+4$

I'm going to solve $3x^2-4x+4=0$ for x using the quadratic formula:

$\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\frac{4\pm \sqrt{(-4)^2-4(3)(4)}}{2(3)}$

$\frac{4\pm \sqrt{16-16(3)}}{6}$

$\frac{4\pm \sqrt{16}\sqrt{1-(3)}}{6}$

$\frac{4\pm 4\sqrt{-2}}{6}$

$\frac{2\pm 2\sqrt{-2}}{3}$

$\frac{2\pm 2i\sqrt{2}}{3}$

Let's see if uv=u+v holds.

$uv=\frac{2+2i\sqrt{2}}{3} \cdot \frac{2-2i\sqrt{2}}{3}$

Keep in mind you are multiplying conjugates:

$uv=\frac{1}{9}(4-4i^2(2))$

$uv=\frac{1}{9}(4+4(2))$

$uv=\frac{12}{9}=\frac{4}{3}$

Let's see what u+v is now:

$u+v=\frac{2+2i\sqrt{2}}{3}+\frac{2-2i\sqrt{2}}{3}$

$u+v=\frac{2}{3}+\frac{2}{3}=\frac{4}{3}$

We have confirmed uv=u+v for k=2.

4 0

3 years ago

Solve y = −23(x + 9) + 4 for x when y = 0.

Vlad [161]

Answer:

x = -203/23

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality<u> </u>

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

y = -23(x + 9) + 4

y = 0

<u>Step 2: Solve for </u><em><u>x</u></em>

Substitute in <em>y</em>: 0 = -23(x + 9) + 4
[Subtraction Property of Equality] Subtract 4 on both sides: -4 = -23(x + 9)
[Division Property of Equality] Divide -23 on both sides: 4/23 = x + 9
[Subtraction Property of Equality] Subtract 9 on both sides: -203/23 = x
Rewrite: x = -203/23

3 0

3 years ago

Read 2 more answers

What is -2.9 = 3f + 4.3

PolarNik [594]

$-2.9 = 3f + 4.3\\3f+4.3+2.9=0\\3f+7.2=0\\3f=-7.2\\f=-7.2/3\\f=-2.4$

8 0

3 years ago

2) f(x) = x2 - 6x +11<br> Degree:<br> Lead Coefficient:<br> End behavior:

Bad White [126]

Answer:

13 - 6 x

Step-by-step explanation:

4 0

3 years ago

A rectangular garden has a length of 8 feet and a width of 5 feet. The entire garden

Katena32 [7]

Answer:

b

Step-by-step explanation:

7 0

3 years ago