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4 years ago

20x+x-2=4 rational equation

Mathematics

2 answers:

laila [671]4 years ago

8 0

Answer:

x = 2/7

Step-by-step explanation:

Step 1: Write equation

20x + x - 2 = 4

Step 2: Solve for x

Combine like terms: 21x - 2 = 4
Add 2 to both sides: 21x = 6
Divide both sides by 21: x = 6/21
Simplify: x = 2/7

Step 3: Check

Plug in x to verify it's a solution.

20(2/7) + 2/7 - 2 = 4

40/7 + 2/7 - 2 = 4

42/7 - 2 = 4

6 - 2 = 4

4 = 4

vitfil [10]4 years ago

7 0

Answer:

x = 2/7

Step-by-step explanation:

Collect like terms:

20x + x = 21x ----> 21x - 2= 4

Move the constant to the right hand side and change the sign of the constant:

21x = 4 + 2

Calculate:

21x = 4 + 2 ---> 21x = 6

Divide both sides by 21:

21/21 and 6/21 = 2/7

Solution:

x = 2/7 or x= 0.285714

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According to Nielsen Media Research. of all the U.S. households that owned at least one television set, 83% had two or more sets

Rudik [331]

Answer:

The proportion of U.S. households that owned two or more televisions is 83%.

Step-by-step explanation:

To determine whether the proportions of U.S. households that owned two or more televisions is less than 83% or not let us perform a hypothesis test for single proportion.

Assumptions:

The sample size (n) selected by the local cable company is 300 which is quite large. Then according to the Central limit theorem the sampling distribution of sample proportion follows a normal distribution with mean p and standard deviation $\sqrt{\frac{p(1-p)}{n} }$ .

Since the sampling distribution of sample proportions follows a normal distribution use the z-test for one proportion to perform the test.

The hypothesis is:

$H_{0}$ : The proportion of U.S. households that owned two or more televisions is 83%, i.e. $p=0.83$

$H_{1}$ :The proportion of U.S. households that owned two or more televisions is less than 83%, i.e. $p< 0.83$

Decision Rule:

At the level of significance α = 0.05 the critical region for a one-tailed z-test is:

$\\ Z\leq -1.645\\$

**Use the z table for the critical values.

So, if $\\ Z\leq -1.645\\$ the null hypothesis will be rejected.

Test statistic value:

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

Here $\hat{p}$ is the sample proportion.

Compute the value of $\hat{p}$ as follows:

$\hat{p}=\frac{X}{n} \\=\frac{240}{300}\\ =0.80$

Now compute the value of the test statistic as follows:

$z=\frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}\\=\frac{0.80-0.83}{\sqrt{\frac{0.83*(1-0.83)}{300} } } \\=-1.383$

The test statistic is -1.383 which is more than -1.645.

Thus, the test statistic lies in the acceptance region.

Hence we fail to reject the null hypothesis.

Conclusion:

At 0.05 level of significance we fail to reject the null hypothesis stating that the proportion of U.S. households that owned two or more televisions is 83%.

6 0

3 years ago

3 over 5 + 21 over 5 =?

kicyunya [14]

4.8

Step-by-step explanation:

3 over 5+21 over 5=4.8

7 0

3 years ago

Read 2 more answers

I really need help with this

slega [8]

Check the picture below.

the radius, so-called because if we circumscribe the triangle in a circle, that'd be the radius of the circumcircle, is 3 inches, as you see there in the picture in red.

now, bear in mind that the triangle is an equilateral one, and therefore, 180/3 = 60, meaning all its interior angles are congruently 60°.

if we run the radius of the triangle, like there, it will cut one of those interior angles in half, namely the radius is an angle bisector, and if we run a perpendicular line to the bottom side, like the dashed one there, we end up with a 30-60-90 triangle, to which we can apply the 30-60-90 rule, as you see it there.

since we know what half of a side of the triangle is, as you see it there in blue, then we can use that and plug it in at

$\bf \textit{area of an equilateral triangle}\\\\
A=\cfrac{s^2\sqrt{3}}{4}~~
\begin{cases}
s=length~of\\
\qquad a~side\\
-------\\
s=\stackrel{\frac{3\sqrt{3}}{2}+\frac{3\sqrt{3}}{2}}{3\sqrt{3}}
\end{cases}\implies A=\cfrac{(3\sqrt{3})^2\sqrt{3}}{4}
\\\\\\
A=\cfrac{(3^2\sqrt{3^2})\sqrt{3}}{4}\implies A=\cfrac{(9\cdot 3)\sqrt{3}}{4}\implies A=\cfrac{27\sqrt{3}}{4}$

8 0

4 years ago

6x + 12 = 10x − 4 1. Solve for x using two different methods

solong [7]

Answer:

x=53/4 or 4x=53

Step-by-step explanation:

First move the variable to the left-hand side and change its sign.

6x+12-10x=-41 to 6x-10x=-41-12

Then collect the like terms

6x-10x=-41-12 to -4x=-41-12 which equals to -4x=-53

Now you divide both sides of the equation by -4

-4x=-53 to x=53 over 4 then if you want you divide which gives you x=13.25

Second way:

Kind of the same thing as the first one

Move the variable to the left-hand side and change its sign

6x+12=10x-41 to 6x=12-10x=-41

Then you collect the like terms

6x-10x=-41-12 to -4x=-41-12

Now you multiply both sides of the equation by -1

-4x=-53 to 4x=53

5 0

3 years ago

What is the point slope form of the line with slope 25 that passes through the point (−4,−7) ?

Vlad [161]

Answer:

y-7=25x-4

Step-by-step explanation:

8 0

3 years ago

20x+x-2=4 rational equation​

20x+x-2=4 rational equation