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2 years ago

Need number 8 please!!

Mathematics

1 answer:

luda_lava [24]2 years ago

3 0

Using translation concepts, the graph of function g(x) = f(x) - 2 = x² - 2 is given at the end of the question.

<h3>What is a translation?</h3>

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, the functions are given as follows:

f(x) = x².

g(x) = f(x) - 2 = x² - 2.

Which means that g(x) is a shift down of 2 units of f(x), as given by the graph in the end of the question.

More can be learned about translation concepts at brainly.com/question/4521517

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A scale model drawing of a garage is 6 centimeters wide and 9 centimeters long. The scale model uses a scale in which 3 centimet

algol13

The scale factor is 0.6. Then the area of the actual garage is 19.44 m². And dimensions are 3.6 m and 5.4 m.

<h3>What is the scale factor?</h3>

Scale factor means the changing of the size of the object without changing the shape. The size of the object may be increased or decreased based on the scale factor.

Given

A scale model drawing of a garage is 6 centimeters wide and 9 centimeters long.

The scale model uses a scale in which 3 centimeters represent 1.8 meters.

The scale factor will be

$\rm 1 \ cm = 0.6$ m

Then the dimension of the actual garage will be

Length = 0.6 x 6 = 3.6 m

Width = 0.6 x 9 = 5.4 m

Then the area of the actual garage will be

Area of garage = Length x Width

Area of garage = 3.6 x 5.4

Area of garage = 19.44 m²

Thus, the area of the actual garage is 19.44 m². And dimensions are 3.6 m and 5.4 m.

More about the scale factor link is given below.

brainly.com/question/22644306

4 0

3 years ago

The Parker family drove a total 180 miles on there road trip this distance is 1.5times the distance they drove on the first day

Alisiya [41]

Answer:

120 miles

Step-by-step explanation:

Let d represent the number of miles driven on the first day. Then 1.5 times d came to 180 miles. Dividing both sides of this equation by 1.5 to isolate d, we get:

180 miles

--------------- = 120 miles

1.5

Thefamily drove 120 miles during the first day of their trip.

7 0

4 years ago

One pipe can empty a tank 5 times faster than another pipe can fill the tank. Starting with a full tank, if both pipes are turne

xxTIMURxx [149]

Answer:

40 hours

Step-by-step explanation:

Let's say that the slower pipe can fill x amount of the tank in one hour. It adds x amount to the tank every hour. Therefore, we can say, for the slower pipe,

1 hour = x amount

Then, the faster pipe empties the tank 5 times faster than the slower pipe fills it, so it removes 5 times the amount that the smaller pipe puts in, so for the faster pipe,

1 hour = -5x amount (negative to symbolize removing).

For the problem at hand, the tank starts at full, or 100%=1. It ends empty, or at 0% = 0. After 10 hours, if we only account for the slower pipe, we add x amount to the tank every hour, so we add 10 times that total, resulting in

1 + 10 * x as the ending result if we don't include the faster pipe. Then, the faster pipe removes 5x every hour, so in 10 hours, it removes 50x, so we have

1+10 * x - 50 * x as the final amount of stuff in the tank, which is equal to 0. Therefore, we have

1 + 10 * x - 50 * x = 0

1 - 40 * x = 0

add 40*x to both sides to isolate the x and its coefficient

1 = 40 * x

divide both sides by 40 to isolate x

x= 0.025

Therefore, the slower pipe adds 0.025, or 1/40 = 2.5% to the tank every hour. We want to figure out how long it would take for the slower pipe to fill up an empty tank, or turn it from 0% to 100% full.

Because the slower pipe adds 2.5% of the tank every hour, we can say that over y hours, it fills up

2.5% * y amount of the tank. We want to figure out how many hours it would take to make it 100% (we need to add 100% of the tank in the problem), so we can say

2.5% * y = 100%

divide both sides by 2.5% to isolate y

100%/2.5% = y = 40

5 0

3 years ago

What is the solution of 3+ X-2/x-3 less than or equal to 4

Archy [21]

Answer:

Step-by-step explanation:

3+ $3+\frac{x-2}{x-3} \leq 4\\\\\frac{x-2}{x-3} \leq 4-3\\\frac{x-3+1}{x-3} \leq 1\\1+\frac{1}{x-3} \leq 1\\\frac{1}{x-3} \leq 0\\x-3 \leq 0\\x\leq 3$

5 0

3 years ago

A 12-gallon tub has a faucet that lets water in at a rate of 3 gallons per minute, and a drain

MatroZZZ [7]

3-in plus 1.5-out every minute means a net gain of 1.5 per minute. You need to fill (12 - 3) = 9 gallons. At 1.5 per minute, it takes 9/1.5 = 6 minutes if the drain and the faucet arr both open, but only (9/3)=3 minutes if you close the drain while you fill the tub.

5 0

3 years ago

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