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3 years ago

2. Solve 9 = 1 + 8x – 8. A. x = 2 B. x = 10

Mathematics

2 answers:

My name is Ann [436]3 years ago

8 0

A. X=2
Combine like terms 9=-7+8x
Add 7 to both sides 16=8x
Divide 8 from both sides x=2

Gnesinka [82]3 years ago

6 0

9 = -7 + 8x
add 7
16 = 8x
x = 2

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I need help with pre calculus.

otez555 [7]

Question 1

<h3>Answer: Choice A) -7</h3>

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Explanation:

To compute f(g(2)), we'll first need to find g(2).

Locate 2 in the x row. Then read straight down until you get to the g(x) row. You should find that g(2) = 4

This means f(g(2)) becomes f(4). We then repeat the same process as before. Locate 4 in the x row, read straight down til you get to the f(x) row to find that f(4) = -9

Overall, we can say f(g(2)) = -9

We do the same set of steps to compute g(f(-1)). You should find that f(-1) = -1 and g(f(-1)) = g(-1) = -2

Lastly, we subtract the results we got:

f(g(2)) - g(f(-1)) = -9 - (-2) = -9+2 = -7

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Question 2

<h3>Answer: Choice B) 0</h3>

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Explanation:

If you were to graph each equation, you should get what you see below.

The red and blue curves do not intersect in any way. We need an intersection point to have a solution. Because there are no intersections, we don't have any solutions. The system is considered inconsistent.

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Question 3

<h3>Answer: Choice B</h3><h3> $-2x^2+250x-2000$ </h3>

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Explanation:

x = number of scooters made and sold

Each scooter costs $150 to make. If you made x of them, then it costs 150x dollars. Then tack on the fixed cost of $2000 to get the expression $150x+2000$

The cost function is $C(x) = 150x+2000$ . We'll subtract this from the revenue function R(x) to get the profit P(x)

$\text{Profit} = \text{Revenue} - \text{Cost}\\\\P(x) = R(x) - C(x)\\\\P(x) = (400x-2x^2) - (150x+2000)\\\\P(x) = 400x-2x^2-150x-2000\\\\P(x) = -2x^2+250x-2000\\\\$

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Question 4

<h3>Answer: Choice B</h3>

$\left\{x\in \mathbb{R} \big| \ x \ne -2, x \ne 1\right\}$

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Explanation:

$g(x) = \frac{1}{x+1}\\\\g(f(x)) = \frac{1}{f(x)+1}\\\\g(f(x)) = \frac{1}{x^2+x-3+1}\\\\g(f(x)) = \frac{1}{x^2+x-2}\\\\g(f(x)) = \frac{1}{(x+2)(x-1)}\\\\(g\circ f)(x) = \frac{1}{(x+2)(x-1)}\\\\$

I started with the outer function g(x) and replaced each x with f(x) in the second step. Then I plugged in f(x) = x^2+x-3 and simplified. Factoring the denominator is helpful to determine where the denominator becomes zero. Specifically, it happens when x = -2 and x = 1. These x values must be kicked out of the domain to avoid a division by zero error.

So we start off with the real number line, and poke holes at x = -2 and x = 1.

The notation $x \in \mathbb{R}$ means x is a real number. Then we tack on $x \ne -2, x \ne 1$

Overall, the domain is $\left\{x\in \mathbb{R} \big| \ x \ne -2, x \ne 1\right\}$

Let's see what happens if we tried plugging x = -1 into this composite function:

$(g \circ f)(x) = \frac{1}{(x+2)(x-1)}\\\\(g \circ f)(-1) = \frac{1}{(-1+2)(-1-1)}\\\\(g \circ f)(-1) = \frac{1}{(1)(-2)}\\\\(g \circ f)(-1) = \frac{1}{-2}\\\\(g \circ f)(-1) = -0.5\\\\$

We don't get a division by zero error, so x = -1 is allowed. The same can be said about any other x value as long as it's not -2 and not 1 either.

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2 years ago

Let f(x) = x2 +6x +8 . What is the domain of Kx)?

Vedmedyk [2.9K]

Answer:

The domain is all real numbers

Step-by-step explanation:

f(x) = x^2 +6x +8

The domain is what numbers can we put in for x

This is a parabola, we can put in any number for x and the function is defined

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3 years ago

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3 years ago

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2.50/5 0.50 an ounce

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3 years ago

Which numbers round to 7.91 when rounded to the nearest hundredth? Select all that apply.

DENIUS [597]

Answer:
A, D and E.
Step-by-step explanation:
We're going to examine the thousandth digit to answer this question.
In the case of A, the thousandth digit is 4, therefore we can round it down to zero, this results in 7.910 which is 7.91.
In the case of 7.905, we do the same with the digit 5, this will gives us 7.90.
For C, we can round down the digit 1 to zero, this will give us 7.90.
For D, we take the 5 and round it down to zero and this gives us 7.91.
For E, we take the 9 from the thousandths and we will round it up, therefore the .709 transforms into .710, this gives us 7.91.

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3 years ago