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4 years ago

9

Solve for x. −1/5x≥−2

1 answer:

Rzqust [24]4 years ago

7 0

Answer:

x ≤ -10

Step-by-step explanation:

distribute -2 into your denominator (5)

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The Universal Sports Company purchases weight racks directly from the manufacturer for $46 each. The weight racks are marked up

Andrei [34K]

Answer:

Uh............

Step-by-step explanation:

7 0

4 years ago

Use the Factor Theorem and synthetic division to show x + 5 is a factor of f(x) = 2x3 + 7x2 − 14x + 5

olga2289 [7]

Answer:

Factor theorem: $f(-5) = 0$ .

Synthetic division: $f(x) = (x + 5)\, (2\, x^2 -3\, x + 1)$ .

Step-by-step explanation:

<h3>Factor Theorem</h3>

By the factor theorem, a monomial of the form $(x - a)$ (where $a$ is a constant) is a factor of polynomial $f(x)$ if and only if $f(a) = 0$ .

In this question, the monomial is $(x + 5)$ , which is equivalently $(x - (-5))$ . $a = -5$ .

$\begin{aligned}& f(-5) \\ &= 2 \times (-5)^{3} + 7 \times (-5)^{2}- 14\times (-5) + 5\\ &= -250 + 175 + 70 + 5 \\ &= 0\end{aligned}$ .

Hence, by the factor theorem, $(x + 5)$ , which is equivalent to $(x - (-5))$ , is a factor of $f(x)$ .

<h3>Synthetic Division</h3>

$\begin{aligned}& f(x) \\ &= 2\, x^{3} + 7\, x^{2} - 14\, x + 5 \\ &= \underbrace{(x + 5) \, (2\, x^2)}_{2\, x^{3} + 10\, x^{2}} - 3\, x^{2} - 14\, x + 5 \\ &= \underbrace{(x + 5) \, (2\, x^2)}_{2\, x^{3} + 10\, x^{2}} + \underbrace{(x + 5)\, (-3\, x)}_{-3\, x^{2} - 15\, x} + (x + 5) \\ &= (x + 5)\, (2\, x^{2} - 3\, x + 1)\end{aligned}$ .

The remainder is $0$ when dividing $f(x)$ by $(x + 5)$ . Hence, $(x + 5)\!$ is a factor of $f(x)\!$ .

6 0

4 years ago

Elise is a project manager

gregori [183]

Answer:

£11.85

Step-by-step explanation:

In the question, we are told that:

In 2016 she earned a monthly salary of £2,100

In 2017 she had a 3% raise

This means 3% of £2,100

3/100×£2,100 = £63

This means her salary for 2017 =

£63 + £2,100 =£2,163

Step 2

We are told in the question that she worked 42 hours per week for 45 weeks in 2017

Since her monthly pay for 2017 = £2,163

She worked 42 hours per week

There are 7 days in one week

The number of hours she worked per day = 42 hours ÷ 7 = 6 hours per day

4.345 weeks= 1 month

The number of hours she worked per month = 42 hours × 4.345 weeks

= 182.49 hours.

We can say that for 182.49 hours she was paid = £2,163

Her average pay per hour is calculated as:

If 182.49 hours = £2,163

1 hour = represented by Y

Cross multiply

182.49Y = £2,163

Y = £2,163 ÷ 182.49

Y = £11.852704258

Approximately = £11.85

Therefore, Elise Average pay per hour for the year = £11.85

8 0

3 years ago

Read 2 more answers

ella [17]

Answer:

120

Step-by-step explanation:

We are given that the function for the number of students enrolled in a new course is $f(x) = 4^{x}-1$ .

It is asked to find the average increase in the number of students enrolled per hour between 2 to 4 hours.

We know that the average rate of change is given by,

$A = \frac{f(x)-f(a)}{x-a}$ ,

where f(x)-f(a) is the change in the function as the input value (x-a) changes.

Now, the number of students enrolled at 4 = f(4) = $f(x) = 4^{4}-1$ = 255 and the number of students enrolled at 2 = f(2) = $f(x) = 4^{2}-1$ = 15

So, the average increase $A=\frac{f(4)-f(2)}{4-2}$ = $A=\frac{255-15}{4-2}$ = $A=\frac{240}{2}$ = 120.

Hence, the average increase in the number of students enrolled is 120.

3 0

4 years ago

PLEASE HELP ME IM BEGGING YOU!!!<br> FIND THE VALUE OF X

Korvikt [17]

84 I'm sure it's that I did it before

8 0

4 years ago

Read 2 more answers