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3 years ago

Solve the inequality -×/2 <4

1 answer:

5 0

Multiply by -2.
x > -8

_____
Multiplying or dividing by a negative number causes the direction of the relationship to change.

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2. Carl needs 15 hours longer than Jennifer to paint a room. If they work together, they can complete the job in 4 hours. Explai

nasty-shy [4]

Answer:

Jennifer would complete the job on her own in 5 hours.

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$ .

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})$ , given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}$

$\Delta = b^{2} - 4ac$

Rates

The together rate is the sum of their separates rate.

We have that:

Jennifer takes x hours to complete the job on her own, so her rate is 1/x.

Carl needs 15 hours longer than Jennifer, that is, 15 + x hours, so his rate is 1/(15+x).

The together rate is 1/4. So

$\frac{1}{4} = \frac{1}{x} + \frac{1}{15+x}$

$\frac{1}{4} = \frac{15 + x + x}{x(15+x)}$

$\frac{1}{4} = \frac{15 + 2x}{x(15+x)}$

Applying cross multiplication.

$x^2 + 15x = 4(15 + 2x)$

$x^2 + 15x = 60 + 8x$

$x^2 + 7x - 60 = 0$

Quadratic equation with $a = 1, b = 7, c = -60$ . So

$\Delta = 7^{2} - 4*1*60 = 289$

$x_{1} = \frac{-7 + \sqrt{289}}{2} = 5$

$x_{2} = \frac{-7 - \sqrt{289}}{2} = -12$

Since the time to complete the job has to be a positive value.

Jennifer would complete the job on her own in 5 hours.

4 0

2 years ago

Please please answer

gizmo_the_mogwai [7]

Answer:

$-5$

Step-by-step explanation:

$(f\circ g)(-1)=f(g(-1))=f(1-3)=f(-2)=-4-1=-5$

7 0

3 years ago

What is the diameter of a circular field whose area is 616cm^2<br><br>

Oksana_A [137]

Answer:

Step-by-step explanation:

$d=2\sqrt{\frac{A}{\pi}} =2\sqrt{\frac{616}{\pi} }$ ≈ $28.00563cm$

rounding 28.00563 to 28.

So hence, your answer is 28cm

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3 0

2 years ago

Read 2 more answers

Mathswatch Question! Mr Powers checks his electricity bill. Here are his meter readings. New reading: 6538 units, Old reading: 6

Setler79 [48]

Answer:

$Cost = 284 x$

Step-by-step explanation:

Given

$Old = 6245\ units$

$New = 6538\ units$

Required

The cost of units used

First, calculate the number of units used.

$Units = New - Old$

$Units = 6538 - 6254$

$Units = 284$

Next, multiply the units used by the cost per units,

Since the cost per unit is not given, we assume that it is x.

So, the total cost is:

$Cost = Units * Cost\ per\ units$

$Cost = 284 * x$

$Cost = 284 x$

3 0

3 years ago

7. Write an equation for the line that is parallel to the given line and that passes through the given point.

Vlad1618 [11]

Answer:

C. y = 1/2x - 14

Step-by-step explanation:

Find the slope of the original line and use the point-slope formula y − y 1 = m ( x − x 1 ) to find the line parallel to y = 1 /2 x − 8 .

y = 1 /2 x − 14 PARALLEL

...................................................................................................................................................

Find the negative reciprocal of the slope of the original line and use the point-slope formula y − y 1 = m ( x − x 1 ) to find the line perpendicular to y = 1 /2 x − 8 .

y = − 2 x − 29 PERPENDICULAR

8 0

2 years ago