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2 years ago

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Josh worked 30 hours last week and earned $8.50 per hour. If $32.50 was withheld from his paycheck, what was Josh's net pay?

1 answer:

MA_775_DIABLO [31]2 years ago

4 0

Answer:

$222.50

Step-by-step explanation:

Hours Josh worked last week = 30

Money earned per hour = $8.50

Money withheld = $32.50

Josh's net pay = (30 x 8.50) - 32.50

= 255 - 32.50

= $222.50

Pls mark as brainliest <3

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2x^3-x^2-3x=210<br> the answer is 5 but I want to know why.

mel-nik [20]

Answer:

$x=5,\frac{-9+\sqrt{255}i }{4} ,\frac{-9-\sqrt{255}i }{4}$

Step-by-step explanation:

1) Move all terms to one side.

$2x^{3} -x^{2} -3x-210=0$

2) Factor $2{x}^{3}-{x}^{2}-3x-210$ using Polynomial Division.

1 - Factor the following.

$2x^{3} -x^{2} -3x-210$

2 - First, find all factors of the constant term 210.

$1,2,3,4,5,6,7,10,14,15,21,30,35,42,70,105,210$

3) Try each factor above using the Remainder Theorem.

Substitute 1 into x. Since the result is not 0, x-1 is not a factor..

$2*1^{3} -1^{2} -3*1-210=-212$

Substitute -1 into x. Since the result is not 0, x+1 is not a factor..

$2(-1)^{3} -(-1)^{2} -3*-1-210=-210$

Substitute 2 into x. Since the result is not 0, x-2 is not a factor..

$2*2^{3} -2^{2} -3*2-210=-204$

Substitute -2 into x. Since the result is not 0, x+2 is not a factor..

$2{(-2)}^{3}-{(-2)}^{2}-3\times -2-210 = -224$

Substitute 3 into x. Since the result is not 0, x-3 is not a factor..

$2\times {3}^{3}-{3}^{2}-3\times 3-210 = -174$

Substitute -3 into x. Since the result is not 0, x+3 is not a factor..

$2{(-3)}^{3}-{(-3)}^{2}-3\times -3-210 = -264$

Substitute 5 into x. Since the result is 0, x-5 is a factor..

$2\times {5}^{3}-{5}^{2}-3\times 5-210 =0$

------------------------------------------------------------------------------------------

⇒ $x-5$

4) Polynomial Division: Divide $2{x}^{3}-{x}^{2}-3x-210$ by $x-5$ .

$2x^{2}$ $9x$ $42$

-------------------------------------------------------------------------

$x-5$ | $2x^{3}$ $-x^{2}$ $-3x$ $-210$

$2x^{3}$ $-10x^{2}$

-----------------------------------------------------------------------

$9x^{2}$ $-3x$ $-210$

--------------------------------------------------------------------------

$42x$ $-210$

$42x$ $-210$

-------------------------------------------------------------------------

5) Rewrite the expression using the above.

$2x^2+9x+42$

$(2x^2+9x+42)(x-5)=0$

3) Solve for $x.$

$x=5$

4) Use the Quadratic Formula.

1 - In general, given $a{x}^{2}+bx+c=0$ , there exists two solutions where:

$x=\frac{-b+\sqrt{b^{2} -4ac} }{2a} ,\frac{-b-\sqrt{b^2-4ac} }{2a}$

2 - In this case, $a=2,b=9$ and $c = 42.$

$x=\frac{-9+\sqrt{9^2*-4*2*42} }{2*2} ,\frac{-9-\sqrt{9^2-4*2*42} }{2*2}$

3 - Simplify.

$x=\frac{-9+\sqrt{255}i }{4} ,\frac{-9-\sqrt{255}i }{4}$

5) Collect all solutions from the previous steps.

$x=5,\frac{-9+\sqrt{255}i }{4} ,\frac{-9-\sqrt{255}i }{4}$

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2 years ago

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If the graph of the linear equations in a system are parallel what does that mean about possible solutions of the system?

professor190 [17]

Since, the system of linear equations are parallel

so, they will never cross or intersect each other

And we know that

solution can only be found if both lines intersect atleast one point

But here , lines are parallel

so, they never intersect each other throughout number line

Since, they never intersect

so, we won't get any common value between both lines

Hence,

There is no solution...........Answer

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3 years ago

A triangle has sides with lengths of 43 millimeters, 52 millimeters, and 65 millimeters. Is it a right triangle

Mrrafil [7]

Use pythagora's theorem to test if it is a right triangle

c^2 = a^2 + b^2
65^2 = 52^2 + 43^2
4225 = 2704 + 1849
4225 =/= 4553
therefore it is not a right triangle as it does not comply to pythagora's theorem

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2 years ago

What is y=\dfrac{2}{3}x+4y=

lara [203]

Answer:

$12y+x-12=0$

Step-by-step explanation:

If I'm not mistaken by the question, we have

$x+4y=\dfrac{2}{3}x+4$

Multiply through by the LCM of all the denominators to clear the fractions. Since we have only one fraction, we multiply through by its LCM (3)

$3\timesx+3\times4y=3\times\dfrac{2}{3}x+3\times4$

$3x+12y=2x+12$

Putting all terms on the LHS (left hand side) and evaluating,

$12y+x-12=0$

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3 years ago

Write and equation of the line that passes through the pair of points (4,6) and (-1,1)

bazaltina [42]

Answer:

y = x + 2

Step-by-step explanation:

Step 1: Find the slope

$m=\frac{y2-y1}{x2-x1} = \frac{6-1}{4-(-1)}=\frac{6}{6} =1$

Step 2: Substitute the slope and a point in to find y intercept

(6)=(1)(4)+b

6 = 4 + b

b = 2

Step 3: Substitute all the information in

y = x + 2

Therefore the equation for a line that passes through (4,6) and (-1,1) is y = x + 2

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3 years ago

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