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3 years ago

Solve the equation 5+7 | 2x-1 | = -44

Mathematics

1 answer:

dlinn [17]3 years ago

3 0

The easy part is isolating the absolute-value term:

5 + 7 |2x - 1| = -44

7 |2x - 1| = -49

|2x - 1| = -7

Remember that the absolute value function returns a positive number that you can think of as the "size" of that number, or the positive distance between that number and zero. If x is a positive number, its absolute value is the same number, |x| = x. But if x is negative, then the absolute value returns its negative, |x| = -x, which makes it positive. (If x = 0, you can use either result, since -0 is still 0.)

The important thing to take from this is that there are 2 cases to consider: is the expression in the absolute value positive, or is it negative?

• If 2x - 1 > 0, then |2x - 1| = 2x - 1. Then the equation becomes

2x - 1 = -7

2x = -6

x = -3

• If 2x - 1 < 0, then |2x - 1| = - (2x - 1) = 1 - 2x. Then

1 - 2x = -7

-2x = -8

x = 4

You might be interested in

Which of the following represents a geometric sequence?

grin007 [14]

Answer:

Option 1 is a geometric sequence.

I 1/4, 1/4, 1/4, 1/4

II 1/4, 1/5, 1/6

III 1/4, 1, -4, 1/6

IV 1/4, -4, 1/4, -4

For any geometric sequence there should be a common ratio

To find common ratio we divide consecutive terms

lets check option I

I 1/4, 1/4, 1/4, 1/4

When we divide 1/4 by 1/4 we will get 1

Same 1 for other two terms, so common ratio is 1

Hence the first option is a geometric sequence

Please Mark Brainliest If This Helped!

6 0

2 years ago

Of the number of students in the cafeteria, 40% are girls. There are 20 girls in the cafeteria how many students are in the cafe

Yuki888 [10]

Answer:

34214

Step-by-step explanation:

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3 0

3 years ago

In a survey, 32% of the respondents stated that they talk to their pets on the telephone. A veterinarian believed this result

adoni [48]

Answer:

$z=\frac{0.29 -0.32}{\sqrt{\frac{0.32(1-0.32)}{210}}}=-0.932$

$p_v =P(z$

So the p value obtained was a very high value and using the significance level given $\alpha=0.05$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of pet owners contacted by telephone is NOT significantly lower than 0.32

Step-by-step explanation:

Data given and notation

n=210 represent the random sample taken

X=61 represent the number of pet owners contacted by telephone

$\hat p=\frac{61}{210}=0.29$ estimated proportion of pet owners contacted by telephone

$p_o=0.32$ is the value that we want to test

$\alpha=0.05$ represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the true proportions is lower than 0.32.:

Null hypothesis: $p \geq 0.32$

Alternative hypothesis: $p < 0.32$

When we conduct a proportion test we need to use the z statistic, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.29 -0.32}{\sqrt{\frac{0.32(1-0.32)}{210}}}=-0.932$

Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided $\alpha=0.05$ . The next step would be calculate the p value for this test.

Since is a left tailed test the p value would be:

$p_v =P(z$

3 0

3 years ago

Carson just lit a new candle and then let it burn all the way down to nothing. The

andreyandreev [35.5K]

Answer:

Step-by-step explanation:

L = 10 - 1.25t

t = 1 ⇒ L = 10 - 1.25 = 8.75 inches

t = 2 ⇒ L = 10 - 1.25(2) = 7.5 inches

t = 3 ⇒ L = 10 - 1.25(3) = 6.25 inches

3 0

3 years ago

If f(x) = 4x + 3, find f(3).

Mumz [18]

F(3)=4(3)+3(exchange all “x” for 3
f(3)=12+3(multiply 4 times 3)
f(3)=15(add 3 to 12)

4 0

3 years ago