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IrinaVladis [17]
2 years ago
5

Which equations represent the line that is perpendicular to the line 5x − 2y = −6 and passes through the point (5, −4)? Check al

l that apply. y = –2/5x – 2 2x + 5y = −10 2x − 5y = −10 y + 4 = –2/5(x – 5) y – 4 =5/2 (x + 5)
Mathematics
2 answers:
Alla [95]2 years ago
8 0

Let's rewrite each equation in the Slope-Intercept Form of the Equation of a Line. First, let's start with the main equation:


\bullet \ 5x-2y=-6 \therefore y=\frac{5}{2}x+3


Then, our options are the following:

A) \ y = -\frac{2}{5}x-2 \\ \\ B) \ 2x+5y=-10 \therefore y=-\frac{2}{5}x-2 \\ \\ C) \ 2x-5y=-10 \therefore y=\frac{2}{5}x+2 \\ \\ D) \ y+4=-\frac{2}{5}(x-5) \therefore y=-\frac{2}{5}x-2 \\ \\ E) \ y-4=\frac{5}{2}(x + 5) \therefore y=\frac{5}{2}x+\frac{33}{2}


For two perpendicular lines it is true that the product of its slopes is:

m_{1}m_{2}=-1


m_{1}m_{2}=-1 \\ \\ m_{1} \ is \ the \ slope \ of \ y=\frac{5}{2}x+3, \ that \ is, \ m_{1}=\frac{5}{2} \\ \\ Then, \ the \ slope \ of \ a \ perpendicular \ line \ is: \\ \\ m_{2}=-\frac{2}{5}


According to this, only A) B) and D) might be the perpendicular lines we are looking for. Notice that these lines are the same. The other condition is that the line must pass through the point (5, -4). By substituting this point in the equation, we have:

y = -\frac{2}{5}x-2 \\ \\ -4=-\frac{2}{5}(5)-2 \\ \\ -4=-2-2 \\ \\ \boxed{-4=-4} \ True!


Finally, the right answer are:

A) \ y = -\frac{2}{5}x-2 \\ \\ B) \ 2x+5y=-10 \\ \\ D) \ y+4=-\frac{2}{5}(x-5)

devlian [24]2 years ago
3 0

The perpendicular equation is y = -2/5x - 2

You can find this by first realizing that perpendicular lines have opposite and reciprocal slopes. So since it starts at 5/2 we flip it and make it a negative and the new slope is -2/5. Now we can use that and the point to get the y intercept using slope intercept form.

y = mx + b

-4 = (-2/5)(5) + b

-4 = -2 + b

-2 = b

And now we can use our new slope and new intercept to model the equation.

y = -2/5x - 2

This equation is also equal to 2x + 5y = -10 and y + 4 = -2/5(x - 5)

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In order to remove water from a flooded basement, two pumps, each rated at 40 gallons per minute, are used. After half an hour,
Scrat [10]

Answer:

3600 gallons of water was removed from the basement.

Step-by-step explanation:

Given:

Rate of each pump = 40 gallons/min

We need to find find the number of gallons of water removed from the basement.

Solution:

Now Given:

After half an hour, the one pump burns out.

Now we know that;

1 hour = 60 mins

\frac12 hour = \frac{60}{2}=30\ mins

Now for 30 mins both the pumps were working and removing the water.

So we can say that;

Water remove for first 30 mins = 40\times2\times30=2400\ gallons

Also Given:

the second pump finishes removing the water half an hour later.

So we can say that;

Water removed for next 30 mins = 40\times 30\times1 =1200\ gallons

Now we can say that;

Total water removed from the basement is equal to sum of Water remove for first 30 mins and Water removed for next 30 mins .

framing in equation form we get;

Total water removed from the basement = 2400+1200=3600\ gallons.

Hence 3600 gallons of water was removed from the basement.

6 0
3 years ago
4. The sum of three consecutive odd integers is 36.
PilotLPTM [1.2K]

Answer:

11, 12, 13

Step-by-step explanation:

n, n + 1, n +2

The sum will add to 36

5 0
3 years ago
He determines that 6 is an extraneous solution because the difference of the numerators is 6, so the 6s cancel to 0. which best
seropon [69]

The question is incomplete. Completed question is given below the answer.

His solution for x is correct, but in order for 6 to be an extraneous solution, one denominator has to result in 0 when 6 is substituted for x.

Given  

Then the solution follows thus:

Step 1: 8(x – 4) = 2(x + 2)

Step 2: 4(x – 4) = (x + 2)

Step 3: 4x – 16 = x + 2

Step 4: 3x = 18

Step 5: x = 6

It can be seen that his solution is correct. But 6 is not an extraneous solution.

An extraneous solution is a solution to an equation that emerges from the process of solving the problem but is not a valid solution to the original problem.

When 6 is substituted into the original equation, the original equation holds.

Therefore, his solution for x is correct, but in order for 6 to be an extraneous solution, one denominator has to result in 0 when 6 is substituted for x.

Learn more about extraneous solution here: brainly.com/question/3751209

#SPJ4

Completed question:-

A student solves the following equation for all possible values of x:His solution is as follows:

Step 1: 8(x – 4) = 2(x + 2)

Step 2: 4(x – 4) = (x + 2)

Step 3: 4x – 16 = x + 2

Step 4: 3x = 18

Step 5: x = 6

He determines that 6 is an extraneous solution because the difference of the numerators is 6, so the 6s cancel to 0.

Which best describes the reasonableness of the student’s solution?

His solution for x is correct and his explanation of the extraneous solution is reasonable.

His solution for x is correct, but in order for 6 to be an extraneous solution, both denominators have to result in 0 when 6 is substituted for x.

His solution for x is correct, but in order for 6 to be an extraneous solution, one denominator has to result in 0 when 6 is substituted for x.

His solution for x is incorrect. When solved correctly, there are no extraneous solutions.

5 0
1 year ago
22.5 + 7(n−3.4) simplified
NARA [144]
-1.3+7n is the answer
7 0
3 years ago
A survey of 1 comma 558 randomly selected adults showed that 522 of them have heard of a new electronic reader. The accompanying
sineoko [7]

Answer with explanation:

Let  p be the proportion of adults have heard of the new electronic reader.

Given claim : The accompanying technology display results from a test of the claim that 38​% of adults have heard of the new electronic reader.

i.e. p=0.38

Then , the set of hypothesis will be :-

H_0: p=0.38\\\\H_a:p\neq0.38

Since, the alternative hypothesis is two tailed , so the test is two-tailed test.

Also, it is given that the sample size : n=1558

Number of adults showed that they have heard of a new electronic reader=522

So the sample proportion for adults have heard of the new electronic reader : \hat{p}=\dfrac{522}{1558}\approx0.34



The test statistic for proportion is given by :-

z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}\\\\\\\Rightarrow\ z=\dfrac{0.34-0.38}{\sqrt{\dfrac{0.38(1-0.38)}{1558}}}\\\\\\\Rightarrow\ z=-3.25279036541\approx-3.25

By using standard normal distribution table , the P-value for two tailed test corresponds to the obtained z-value ==0.0011541

6 0
3 years ago
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