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3 years ago

Let f(x) = 4x – 5 and g(x) = 3x + 7. find f(x) + g(x) and state its domain.

Mathematics

1 answer:

Tema [17]3 years ago

5 0

We are given the functions:

f(x) = 4 x – 5 ---> 1

g(x) = 3 x + 7 ---> 2

To find for the value of f(x) + g(x), all we have to do is to add equations 1 and 2:

f(x) + g(x) = 4 x – 5 + 3 x + 7

f(x) + g(x) = 7 x + 2 = y

In this case, for any real number value assign to x, we get a real number value of y. This is because the function is linear.

Therefore the domain of the function is all real numbers.

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5x-29>-34 OR 2x+31<29

Margarita [4]

5x-29>-34
5x>-5
x>-1
x<1
2x+31<29
2x<-2
x<-1
x>1

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3 years ago

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True or False: The following pair of ratios are equivalent ratios.8/9 and 72/81

dybincka [34]

True. 8*9=72 and 9*9=81. Original ratio is being multiplied by 9/9

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3 years ago

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What is the vertex of the parabola? y+1=−14(x−2)2 Enter your answer in the boxes.

iren [92.7K]

Answer:

y + 1 = -14(x - 2)^2y = -14(x - 2)^2 - 1

Step-by-step explanation:

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2 years ago

What numbers go in the sqaures?

givi [52]

On the first two pairs you need to write 3 and 4, and 6 and 2.

On the second page we have:

1) 4

2) 2 and 7

3) 1

4) 1 and 3

5) 3.

<h3>What numbers go in the squares?</h3>

a) Here we just need to use scientific notation.

For the first case, the numbers that go in the exponent boxes are the same ones that go in the example, which are 4 in the first one and 2 on the second one.

Then, if we want the difference to be 29,400, then we can use 3 on the first box and 6 on the second. OR, because this is an absolute value, we can just invert those.

This is:

6 and 2 on the first two squares, and 3 and 4 on the second two squares.

b) Here we want to make perfect squares.

For example, on the first case we have:

x*2*2

We need to find the value of x such that this is a perfect square. Notice that we can rewrite this as:

x*2*2 = x*4

Then it only is a perfect square if x = 4.

For the second case:

14*x*y

This is only a perfect square if x*y = 14

Then we can use x = 2 and y = 7.

With similar reasoning, on the next box we have:

2*8*x

2*8 = 16, is already a perfect square, so x = 1.

The next one is:

x*3*y

Here we can define x = 3 and y = 1, so we get a perfect square.

Finally:

3*x

Here the only possible value of x is 3.

If you want to learn more about perfect squares:

brainly.com/question/1538726

#SPJ1

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2 years ago

Conduct the appropriate hypothesis test and compute the test statistic. A company that produces fishing line undergoes random te

andre [41]

Answer:

Option D) Yes, because the test statistic is -2.01

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 30 pound

Sample mean, $\bar{x}$ = 29.1 pounds

Sample size, n = 20

Alpha, α = 0.05

Sample standard deviation, s = 2 pounds

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 30\text{ pounds}\\H_A: \mu < 30\text{ pounds}$

We use one-tailed(left) t test to perform this hypothesis.

Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }$

Putting all the values, we have

$t_{stat} = \displaystyle\frac{29.1 - 30}{\frac{2}{\sqrt{20}} } = -2.012$

Now,

$t_{critical} \text{ at 0.05 level of significance, 19 degree of freedom } = -1.729$

Since,

$t_{stat} < t_{critical}$

We fail to accept the null hypothesis and reject it. We accept the alternate hypothesis. Thus, there were enough evidence to conclude that the fishing line breaks with an average force of less than 30 pounds.

Option D) Yes, because the test statistic is -2.01

5 0

3 years ago