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4 years ago

What is the solution of the equation 4[x + 2(3x – 7)] = 22x – 65?

Mathematics

2 answers:

Anni [7]4 years ago

5 0

4 (X + 2 (3X - 7)) = 22X - 65
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation:
4 * (X + 2 * (3 * X - 7)) - (22 * X - 65) = 0
Pull out like factors:
7X - 14 = 7 * (X - 2)
28 * (X - 2) - (22X - 65) = 0
Pull out like factors:
6X + 9 = 3 * (2X + 3)
3 * (2X + 3) = 0
3 = 0... (equation never true, has no solution; a a non-zero constant never equals zero)
2X + 3 = 0
Subtract (-3) from both sides of the equation:
2X + 3 (-3) = 0 + (-3)
2X + 3 - 3 = 0 - 3
2X + 0 = -3
2X = -3

Divide both sides of the equation by 2:
2x / 2 = -3 / 2
X = -3 / 2
X = - 1.500

Lelu [443]4 years ago

3 0

X = -3/2
I hope my work .... helped you out a little.

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4x/3+3=x-2 <br>value of x ?

Gekata [30.6K]

Answer:

x = - 15

Step-by-step explanation:

Given

$\frac{4x}{3}$ + 3 = x - 2

Multiply through by 3 to clear the fraction

4x + 9 = 3x - 6 ( subtract 3x from both sides )

x + 9 = - 6 ( subtract 9 from both sides )

x = - 15

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3 years ago

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The US Census reported that it takes workers an average of 28 minutes to get home from work with standard deviation 5 minutes. A

xz_007 [3.2K]

Using the z-distribution, as we have the standard deviation for the population, to test the hypothesis, it is found that this is evidence that workers in the large city take longer than 28 minutes to get home from work.

<h3>What are the hypothesis tested?</h3>

At the null hypothesis, it is tested if the mean time is of 28 minutes, that is:

$H_0: \mu = 28$

At the alternative hypothesis, it is tested if the mean time is greater than 28 minutes, that is:

$H_1: \mu > 28$ .

<h3>What is the test statistic?</h3>

The test statistic is given by:

$z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$

The parameters are:

$\overline{x}$ is the sample mean.

$\mu$ is the value tested at the null hypothesis.

$\sigma$ is the standard deviation of the sample.

n is the sample size.

In this problem, the values of the parameters are given by:

$\overline{x} = 32, \mu = 28, \sigma = 5, n = 10$

Hence:

$z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{32 - 28}{\frac{5}{\sqrt{10}}}$

$z = 2.53$

<h3>What is the decision?</h3>

Considering that we have a <em>right-tailed test</em>, as we are testing if the mean is greater than a value, with a standard <em>significance level of 0.05</em>, the critical value is of $z^\ast = 1.645$ .

Since the test statistic is greater than the critical value, it is found that this is evidence that workers in the large city take longer than 28 minutes to get home from work.

To learn more about the z-distribution, you can check brainly.com/question/26454209

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2 years ago

The mass of a proton is about 1.7 \times 10^(-24). Write this number in standard notation.

OLga [1]

Now we have a negative exponent, which is the opposite of a positive exponent.

If a positive exponent means you're multiplying by 10s and it makes a number bigger by moving the decimal to the right, then

the opposite of this is that a negative exponent means you're dividing by 10s and making the number smaller by moving the decimal point to the left.

Examples:

$930 \div 10 = 93$

${\bf930 \div 10} \div 10 = {\bf 93} \div 10 = 9.3$

The trick is to recognize that

$930 \div 10$ is the same thing as $930 \times 10^{-1}$

${}\div 10$ and ${}\times 10^{-1}$ mean the same thing.

So, $930 {\bf {}\div 10 \div 10} = 930 {\bf {}\times 10^{-1} \times 10^{-1}} = 930 {\bf {}\times 10^{-2}} = 9.3$

For your exercise, ${}\times10^{-24}$ means you'll move the decimal point 24 places to the left, to make the number smaller.

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3 years ago

What is the equation of a line, in point-slope form, that passes through (-4, -1) and has a slope of (5, 7)

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Answer:

The corresponding point for the function 4f(x) is (5 , 24)

Step-by-step explanation:

* Lets revise some transformation

- A vertical stretching: is the stretching of the graph away from

the x-axis

- A vertical compression: is the squeezing of the graph toward

the x-axis.

• if k > 1, the graph of y = k • f(x) is the graph of f (x) vertically

stretched by multiplying each of its y-coordinates by k.

• if 0 < k < 1 (a fraction), the graph is f (x) vertically compressed

by multiplying each of its y-coordinates by k.

* In our problem:

- Point (5 , 6) is on the graph of f(x)

- The function will be 4f(x), that means vertical stretching

or vertical compression

∵ k = 4

∵ 4 > 1

∴ It is a vertical stretch

∴ We will multiply the y-coordinate by 4

∴ y' = 4 × 6 = 24

* The corresponding point for the function 4f(x) is (5 , 24)

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3 years ago