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3 years ago

10. Jack and Dion sold a total of 33 appliances for their store. Dion sold 3 less than twice as

Mathematics

1 answer:

podryga [215]3 years ago

8 0

Let x = amount of appliances Jack sold

Let y = amount of appliances Dion sold.

We need to construct a system of equations to solve this problem

33 = x + y

y = 2x - 3.

Let's solve this system of equations by substitution.

33 = x + (2x - 3). Combine like terms.

33 = 3x - 3. Add 3 to both sides.

36 = 3x. Divide both sides by 3

12 = x. Plug this value into one of our original equations.

33 = 12 + y. Subtract 12 from both sides

y = 21

Jack sold 12 appliances and Dion sold 21 appliances.

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It 55% of 78 and heyyy pls help

atroni [7]

Answer:

Yea 43 bc technically its 42.9 round up and you get 43 (:

Step-by-step explanation:

3 0

3 years ago

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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

==============================================

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.

==============================================

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)

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

==============================================

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.

4 0

2 years ago

Find the equation of the linear function represented by the table below in slope-

Harman [31]

Answer:

y = 4x+4

Step-by-step explanation:

Using the coordinate point (1, 8) and (2, 12) from the table

Slope m = 12-8/2-1

m = 4/1

m = 4

Get the intercept

Substitute m = 4 and (1, 8) into y = mx+c

8 = 4(1) + c

8 - 4 = c

c = 4

Get the required equation

y = 4x + 4

Hence the required linear equation is y = 4x+4

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3 years ago

20 liters of mixture contain milk nad water in the ratio 5:3 of 4 liters of the mixture are replaced by 4 liters of milk find th

pantera1 [17]

Answer:

7:3

Step-by-step explanation:

5 + 3 = 8

The ratio is

5 milk : 3 water : 8 total

Milk is 5/8 of the total.

Water is 3/8 of the total.

The 20-liter mixture contains:

5/8 * 20 = 12.5 liters of milk, and

3/8 * 20 = 7.5 liters of water

4 liters of the mixture contain:

5/8 * 4 = 2.5 liters of milk, and

3/8 * 4 = 1.5 liter of water

When you remove 4 liters of the mixture from 20 liters of the mixture, you end up with

12.5 L - 2.5 L = 10 L milk, and

7.5 L - 1.5 L = 6 L water

Now you add 4 liters of milk. Now you have

10 L + 4 L = 14 L milk

6 L water

The new ratio of milk to water is 14:6 = 7:3

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3 years ago

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The equation below describes a circle. What are the coordinates of the center

Rzqust [24]

The equation of a circle: $(x-h)^2 + (y-k)^2 = r^2 \ Where \ (h, k) \ the \ origin \ of \ the \ circle\\(x-6)^2 + (y+5)^2 = 152 => C(6, -5)$

3 0

3 years ago

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