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3 years ago

Find the equation of the line which passes through the point (7,2) and is perpendicular to y=5x-2

Mathematics

1 answer:

MariettaO [177]3 years ago

7 0

Answer:

$\displaystyle y=-\frac{1}{5}x+\frac{17}{5}$

Step-by-step explanation:

Equation of a line

A line can be represented by an equation of the form

$y=mx+b$

Where x is the independent variable, m is the slope of the line, b is the y-intercept and y is the dependent variable.

We need to find the equation of the line passing through the point (7,2) and is perpendicular to the line y=5x-2.

Two lines with slopes m1 and m2 are perpendicular if:

$m_1.m_2=-1$

The given line has a slope m1=5, thus the slope of our required line is:

$\displaystyle m_2=-\frac{1}{m_1}=-\frac{1}{5}$

The equation of the line now can be expressed as:

$\displaystyle y=-\frac{1}{5}x+b$

We need to find the value of b, which can be done by using the point (7,2):

$\displaystyle 2=-\frac{1}{5}*7+b$

Operating:

$\displaystyle 2=-\frac{7}{5}+b$

Multiplying by 5:

$10=-7+5b$

Operating:

$10+7=5b$

Solving for b:

$\displaystyle b=\frac{17}{5}$

The equation of the line is:

$\boxed{\displaystyle y=-\frac{1}{5}x+\frac{17}{5}}$

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Write an equation of the line below.

leva [86]

Answer:

-5,3 - 0,0

Step-by-step explanation:

i hope this helpful to u

3 0

3 years ago

A spinner has equal regions numbered 1 through 20. What is the probability that the spinner will stop on an odd number or a mult

klio [65]

Answer:

Probability that the spinner will stop on an odd number or a multiple of 5 is 0.6

Step-by-step explanation:

Probability = $\frac{Required outcomes}{Total possible outcomes}$

We are given the equal regions numbered from 1 through 20 which means that our total possible outcomes are 20

Total possible outcomes: 20

Outcomes that spinner will stop on an odd number, n(Odd): 10

1, 3, 5, 7, 9, 11, 13, 15, 17, 19

Probability of spinner stoping on Odd number:

P(Odd) = $\frac{n(Odd)}{Total}$ = $\frac{10}{20}$ = $\frac{1}{2}$ = 0.5

Outcomes that spinner will stop on a multiple of 5, n(5): 4

5, 10, 15, 20

Probability of spinner stoping on multiple of 5:

P(5) = $\frac{n(5)}{Total}$ = $\frac{4}{20}$ = $\frac{1}{5}$ = 0.2

Odd numbers which are a multiple of 5 are: 5 and 15

So,

P(Odd and 5) = $\frac{2}{20}=\frac{1}{10}=0.1$

Thus Probability of spinner stopping at odd number or a multiple of 5 becomes:

P(Odd or 5) = P(Odd) + P(5) - P(Odd and 5) = 0.5 + 0.2 - 0.1 = 0.6

7 0

3 years ago

30 points I'm struggling Find the equations of each line and show all of your work. (1, 5) (2, 6) (1, 1) (3, -8) (2, -3) (5, -2)

Free_Kalibri [48]

Answer:

1.(1,5) and (2,6) , 6-5/2-1=1/1 m=1 ,y=1x+b

5=1(1)+b 4=b

y=x+4

2.(1,1) and (3,-8) -8-1/3-1=-9/2 m=-9/2 ,y=-9/2x+b

1=-9/2(1)+b b=11/2

y=-9/x+11/2

3.(2.-3) and (5,-2) m=1/3 ,y=1/3x+b

-3=1/3(2)+b -3=2/3+b

-3-2/3=b

b=-11/3

y=1/3x-11/3

4.(2,5)and (4,3) m=-1 y=-1x+b

5=-1(2)+b 5=-2+b

5+2=b

b=7

y=-1x+7

6.(-3,-5) and (-1,-3) m=2/2=1 y=1x+b

-5=1(-3)+b -5=-3+b

-5+3=b

-2=b

y=1x-2

Step-by-step explanation:

7 0

2 years ago

Target sells 24 bottles of water for $3, and 36 bottles of water for $4. Which is the better buy and by how much

Oksana_A [137]

The better buy would be the 36 bottles of water for 4$ because it would be 9 bottles per dollar other than the 24 which is 8 bottles per every dollar. Hope it helps!

3 0

3 years ago

Can someone explain how to do this, please?

BartSMP [9]

Answer:

$\sqrt{ {28x}^{2} - 6x }$

Step-by-step explanation:

You would substitute "2x" for every "x" in the function in the same way you would substitute any other number.

So if f(x)=Sqrt[7x²-3x], then: f(2x)=Sqrt[7(2x)²-3(2x)]

=Sqrt[7(4x²)-3(2x)]

=Sqrt[28x²-6x]

6 0

3 years ago