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irina1246 [14]
2 years ago
8

Determine the solution to the system of equations graphed below and explain

Mathematics
1 answer:
lawyer [7]2 years ago
7 0

If x - 4 ≥ 0, then |x - 4| = x - 4, so

G(x) = F(x)   ⇒   3x + 2 = (x - 4) + 2

⇒   3x + 2 = x - 2

⇒   2x = -4

⇒   x = -2

Otherwise, if x - 4 < 0, then |x - 4| = -(x - 4), so

G(x) = F(x)   ⇒   3x + 2 = -(x - 4) + 2

⇒   3x + 2 = -x + 6

⇒   4x = 4

⇒   x = 1

However,

• when x = -2, we have

G(-2) = 3(-2) + 2 = -4

F(-2) = |-2 - 4| + 2 = 8

• when x = 1, we have

G(1) = 3(1) + 2 = 5

F(1) = |1 - 4| + 2 = 5

so only x = 1 is a solution to G(x) = F(x).

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kherson [118]

The answers are as follows.

a. 9x

In order to get this, you need to reevaluate 64 as a base of 4. Since 64 is equal to 4^3, we can rewrite the right side as

64^3x = (4^3)^3x = 4^9x

Which gives you the first answer.

b. 10

Similar to the first problem, we need to express 16 as a base of 2. 2^4 is equal to 16, so we use that in it's place and simplify.

16^5/2 = (2^4)^5/2 = 2^20/2 = 2^10

c. Sqrt(7.31)

This one is more simple. Raising something to a 1/2 power (.5) is the same as taking the square root.

4 0
3 years ago
Plz help I really need it 15 points
Ivenika [448]

Answer:

I'm pretty sure its 40

hope I helped

6 0
3 years ago
Read 2 more answers
Is 0.6 repeating a rational number
julsineya [31]
Any decimal number that is repeating can be written in the form <span>\frac{a}{b}</span> with b not equal to zero, so they are rational numbers.

The short answer is yes, 0.6 repeating is a rational number.

Hope this helped :)
6 0
3 years ago
A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 450 gram setting. It
Arturiano [62]

Answer:

Test statistic = -2.25

P-value = 0.0199

Step-by-step explanation:

We are given the following in the question:  

Population mean, μ = 450 gram

Sample mean, \bar{x} = 441 grams

Sample size, n = 16

Alpha, α = 0.05

Sample variance = 256

\sigma^2 = 256\\\sigma = \sqrt{256} = 16

First, we design the null and the alternate hypothesis

H_{0}: \mu = 450\text{ grams}\\H_A: \mu < 450\text{ grams}

We use one-tailed 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{441 - 450}{\frac{16}{\sqrt{16}} } = -2.25

Now,

Degree of freedom =

=n-1 = 16-1=15

We can calculate the p-value from the table as:

P-value = 0.0199

Conclusion:

Since the p-value is smaller than the significance level we fail to accept the null hypothesis and reject it.

Thus, there is enough evidence to support the claim that the machine is under filling the bags .            

5 0
3 years ago
If 75% of x is 150, what is the value of x?
vagabundo [1.1K]
I'm not sure if this is correct but you would put it into an equation while you solve for X. so 0.75x=150  or equivalently would be like  (3/4)x=150 Then after that you would divide both sides by 0.75 or 3/4 
7 0
3 years ago
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