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Veseljchak [2.6K]
3 years ago
14

What are the steps I need to solve this problem? 2x + 5 = 21

Mathematics
1 answer:
Vladimir [108]3 years ago
8 0

Step-by-step explanation:

subtract 5 under itself and 21 , then cross out the 5 and only subtract 21 and 5 which is 16 and then bring down 2x so now your equation will be 2x=5 so now your gonna divide 2 and 5

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If 8 feet of fencing costs $12.40 , how much does 36 feet of fencing cost?
Vesnalui [34]

Answer:

$55.80

Step-by-step explanation:

8, 16, 24, 32, 36

8=12.40, 16=24.80, 24=37.2, 32=49.6,

+4 makes it 36 so it's have of 8, so add 6.20 to the end and it's 55.80

6 0
3 years ago
In the xy-plane, a line crosses the y-axis at the point (0, 3) and passes through the point (4, 5). Which is the equation of the
Gelneren [198K]

Answer:D

Step-by-step explanation:

4 0
2 years ago
1) find the equation of the line parallel to
In-s [12.5K]

<u>Answer:</u>

1) The equation of the line parallel to  x-5y=6 and through (4,-2) is 5y = x -14

2) The equation of the line perpendicular to y= -2/5x + 3 and through (2,-1) is  2y = 5x -12

<u>Solution:</u>

<u><em>1) find the equation of the line parallel to  x-5y=6 and through (4,-2).</em></u>

Given, line equation is x – 5y = 6  

We have to find the line equation that is parallel to given line and passing through the point (4, -2)

Now, let us find slope of the given line.

\text { Slope }=\frac{-x \text { coefficient }}{y \text { coefficient }}=\frac{-1}{-5}=\frac{1}{5}

Now, we know that, slope of parallel lines are equal.

So, slope of required line is 1/5 and it passes through (4, -2)

Now, using point slope form

y-y_{1}=m\left(x-x_{1}\right) \text { where } m \text { is slope and }\left(x_{1}, y_{1}\right) \text { is point on line. }

y-(-2)=\frac{1}{5}(x-4) \rightarrow 5(y+2)=x-4 \rightarrow 5 y+10=x-4 \rightarrow x-5 y=14

Hence, the line equation is 5y = x -14

<u><em> 2) find the equation of the line perpendicular to y= -2/5x + 3 and through (2,-1)</em></u>

\text { Given, line equation is } y=-\frac{2}{5} x+3 \rightarrow 5 y=-2 x+15 \rightarrow 2 x+5 y=15

We have to find the line equation that is perpendicular to given line and passing through the point (2, -1)

Now, let us find slope of the given line.

\text { Slope }=\frac{-x \text { coefficient }}{y \text { coefficient }}=\frac{-2}{5}=-\frac{2}{5}

Now, we know that, product of slopes of perpendicular lines equals to -1.

So, slope of required line \times slope of given line = -1

slope of required line = -1 \times \frac{5}{-2}=\frac{5}{2}

And it passes through (2, -1)

Now, using point slope form

\begin{array}{l}{\text { Line equation is } y-(-1)=\frac{5}{2}(x-2) \rightarrow 2(y+1)=5(x-2)} \\\\ {\rightarrow 2 y+2=5 x-10 \rightarrow 5 x-2 y=12}\end{array}

Hence, the line equation is 2y = 5x -12

4 0
3 years ago
The sum of two numbers is 21. The larger number is 6 less than twice the smaller number. Find the two numbers.
never [62]
The sum of two numbers
 x + y = 21
x = smaller number
y = larger number

Larger Number = y = (2x -6)
Substitute  (2x - 6) for y
x + y = 21
x + (2x - 6) = 21
3x - 6 = 21
3x = 21 + 6
3x = 27
3x / 3 = 27 / 3
x =  9
Smaller number = x = 9
Find the larger number by inserting 9 into (2x - 6)
(2x - 6)
(2(9) - 6)
18 - 6
12

So 
x = 9
y =12

Check our answer by inserting x = 9 and y = 12 into  x + y = 21
x + y =21
9 + 12 = 21
21 = 21 
So since we have 21 = 21 we know our answer is correct. 
5 0
3 years ago
A marketing research firm wishes to compare the prices charged by two supermarket chains—Miller’s and Albert’s. The research fir
AVprozaik [17]

Answer:

a) F=\frac{s^2_2}{s^2_1}=\frac{1.84^2}{1.4^2}=1.727 \approx 1.73

b) For this case since we have a two tailed test we have two critical values, and we can find the two values since we need that on each tail the area would be \alpha/2 =0.025, the distribution is the F with 9 df for the numerator and denominator, and we can use the following excel codes to find the critical values:

"=F.INV(0.025,9,9)"

"=F.INV(1-0.025,9,9)"

The two critical values are 0.248 and 4.026, so the rejection zone would be: F>4.026 \cup F since our calculated value is not on the rejection zone we fail to rejec the null hypothesis

Step-by-step explanation:

Data given and notation  

n_1 = 10 represent the sampe size for the Miller's Stores

n_2 =10 represent the sample size for the Albert's stores

\bar X_1 =121.92 represent the sample mean for Miller's store

\bar X_2 =114.81 represent the sample mean for Albert's store

s_1 = 1.4 represent the sample deviation for the Miller's store

s_2 = 1.84 represent the sample deviation for the Albert's stores

s^2_2 = 12.25 represent the sample variance for the utility stocks

\alpha=0.05 represent the significance level provided

Confidence =0.95 or 95%

F test is a statistical test that uses a F Statistic to compare two population variances, with the sample deviations s1 and s2. The F statistic is always positive number since the variance it's always higher than 0. The statistic is given by:

F=\frac{s^2_2}{s^2_1}

Solution to the problem  

System of hypothesis

We want to test if the variation for th two groups is the same, so the system of hypothesis are:

H0: \sigma^2_1 = \sigma^2_2

H1: \sigma^2_1 \new \sigma^2_2

a) Calculate the statistic

Now we can calculate the statistic like this:

F=\frac{s^2_2}{s^2_1}=\frac{1.84^2}{1.4^2}=1.727 \approx 1.73

Now we can calculate the p value but first we need to calculate the degrees of freedom for the statistic. For the numerator we have n_1 -1 =10-1=9 and for the denominator we have n_2 -1 =10-1=9 and the F statistic have 9 degrees of freedom for the numerator and 9 for the denominator. And the P value is given by:

P value

p_v =2*P(F_{9,9}>1.727)=0.428

And we can use the following excel code to find the p value:"=2*(1-F.DIST(1.727,9,9,TRUE))"

b) Critical value

For this case since we have a two tailed test we have two critical values, and we can find the two values since we need that on each tail the area would be \alpha/2 =0.025, the distribution is the F with 9 df for the numerator and denominator, and we can use the following excel codes to find the critical values:

"=F.INV(0.025,9,9)"

"=F.INV(1-0.025,9,9)"

The two critical values are 0.248 and 4.026, so the rejection zone would be: F>4.026 \cup F since our calculated value is not on the rejection zone we fail to rejec the null hypothesis

Since our calcu

Conclusion

Since the p_v > \alpha we have enough evidence to FAIL to reject the null hypothesis. And we can say that we don't have enough evidence to conclude that the two deviations are different at 5% of significance.  

8 0
3 years ago
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