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3 years ago

2x-1/2=3-x solve for x.

Mathematics

1 answer:

DanielleElmas [232]3 years ago

8 0

Given,

2x - 1/2 = 3 - x

2x + x = 3 + 1/2

3x = 7/2

3x = 3.5

x = 3.5/3

x = 1.167

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What is the solution to the system of equations? 6x – 9y = 16 2x – 3y = 7

kifflom [539]

The first step for solving this problem is to multiply both sides of the bottom equation by -3.
$\left \{ {{6x-9y=16} \atop {-6x + 9y = -21}} \right.$
Add the two equations together.
6x - 9y - 6x + 9y = 16 - 21
Eliminate the opposites.
-9y + 9y = 16 - 21
Remember that the sum of two opposites equals 0,, so the equation becomes the following:
0 = 16 - 21
Calculate the difference on the right side of the equation.
0 = -5
This means that the statement $\left \{ {{6x-9y=16} \atop {2x-3y=7}} \right.$ is false for any value of x and y. That means that the answer to your question is (x,y) ∈ ∅,, or no solution.
Let me know if you have any further questions.
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3 years ago

The temperature is less than 3.5°F. Write and graph the inequality

wel

I can’t graph it but here’s the inequality:

t = temp.

t < 3.5.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Hope this helps!

5 0

3 years ago

A line is perpendicular to y = 1/4x- 8

postnew [5]

Answer:

perp-9xc

Step-by-step explanation:

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3 years ago

Comparing observations from different populations: The heights of adult men in America are normally distributed, with a mean of

Schach [20]

Answer:

a. Z = 1.99

b. 97.67%

c. Z = 2.56

d. 0.52%

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

a. If a man is 6 feet 3 inches tall, what is his z-score (to two decimal places)?

The heights of adult men in America are normally distributed, with a mean of 69.7 inches and a standard deviation of 2.66 inches, and thus, we have $\mu = 69.7, \sigma = 2.66$

6 feet 3 inches = 6*12 + 3 = 75 inches, which means that we have to find z when X = 75. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{75 - 69.7}{2.66}$

$Z = 1.99$

b. What percentage of men are SHORTER than 6 feet 3 inches?

The proportion is the p-value of Z = 1.99.

Looking at the z-table, Z = 1.99 has a p-value of 0.9767.

0.9767*100% = 97.67%, which is the answer.

c. If a woman is 5 feet 11 inches tall, what is her z-score (to two decimal places)?

The heights of adult women in America are also normally distributed, but with a mean of 64.5 inches and a standard deviation of 2.54 inches, and thus, we have $\mu = 64.5, \sigma = 2.54$ . We have to find Z when X = 5*12 + 11 = 71. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{71 - 64.5}{2.54}$

$Z = 2.56$

d. What percentage of women are TALLER than 5 feet 11 inches?

The proportion is 1 subtracted by the p-value of Z = 2.56.

Looking at the z-table, Z = 2.56 has a p-value of 0.9948.

1 - 0.9948 = 0.0052

0.0052*100% = 0.52%, which is the answer.

3 0

3 years ago

How should we prove this ? Boc=90-1/2angle bac

Hatshy [7]

We have m(<CBO) = (1/2) · m(<CBE) = (1/2) · ( x + z );

In the same way, m(<BCO) = (1/2) ·( x + y);

m(<BOC) = 180 - [(1/2) · ( x + z ) + (1/2) ·( x + y)] = 180 - (1/2)· ( x + x + y + z );

But, x + y + z = 180;

Then, m(<BOC) = 180 - (1/2)·( x + 180 );

Finally, m(<BOC) = 90 - (1/2)·x;

So, m(<BOC) = 90 - (1/2)·m(<BAC).

8 0

3 years ago