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yan [13]
3 years ago
7

Write the equation of a line that is perpendicular to the given line and that passes through the given point.

Mathematics
1 answer:
poizon [28]3 years ago
8 0

Answer: y=-3x+29

Step-by-step explanation:

First put in y-intercept form to find the slope

4x-12y=2\\-12y=-4x+2\\y=\frac{1}{3} x-\frac{1}{6}

Slope of the 1st equation is 1/3-  the slope of the line perpendicular is the opposite reciprocal, so in the case it is -3

Use the point and the new slope to write the new equation in point slope format

y-y_{1} =m(x-x_{1} )\\y-(-1)=-3(x-10)\\y+1=-3x+30\\y=-3x+29

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Elavter of using distuburting propties a. 17×102<br> b. 477×1035 -477×35​
V125BC [204]

Answer: a. 1734    b. 477000

Step-by-step explanation:

We know that,

Distributive property : a(b+c)  = ab+ac

a. 17 x 102

=  17 (100+2)

= 17 x 100 + 17 x 2  [Distributive property ]

= 1700+34

= 1734

b. 477×1035 -477×35​

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3 0
3 years ago
What is the equation of the line that is perpendicular to the line through (1,-4) and (-2,2) and passes through the x-intercept
ss7ja [257]

Answer:

y=-\frac{1}{2}x+\frac{3}{2}

Step-by-step explanation:

First, calculate the slope of the line that is perpendicular to the equation of line we are asked to find

m=(y2-y1)/(x2-x1)

  =(2-(-4))/(-2-1)

  =6/-3

  =-2

in this equation the slope is 2, and to find the first equation, use y=mx+b

use the point (1, -4) to find b

-4=(2)(1)+b

-4=2+b

b=-6

the first equation of the line is y=2x-6

to find the x intercept of that line substitute 0 for y

0=2x-6

2x=6

x=3

the slope of a line perpendicular to this would be the opposite reciprocal of the slope which would be equal to -1/2

for the second equation of the line to pass thorugh the x-intercept of the first line, it must pass through (3, 0), so substitute and solve for b

y=mx+b

0=(-1/2)(3)+b

b=3/2

thus the equation of the line that is perpendicular to the line through (1,-4) and (-2, 2) and passes through the x intercept of that line is y=-\frac{1}{2}x+3/2

8 0
3 years ago
Which represents a measure of volume?<br> O 5 cm<br> O 5 square cm<br> 05 cm<br> 05 cm
Elena-2011 [213]

Answer:

a) 5cm^{3}

Step-by-step explanation:

Bodies have three dimensions (width, height and depth). Measuring volume is calculating the number of cubic units that can fit inside.

When raising to 3, these dimensions are included and therefore  5cm^{3} is a measure of volume.

7 0
3 years ago
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The u.s. dairy industry wants to estimate the mean yearly milk consumption. a sample of 16 people reveals the mean yearly consum
lidiya [134]
1-2. The best estimate for the population mean would be sample mean of 60 gallons. Since we know that the sample mean is the best point of estimate. Since sample size n=16 is less than 25, we use the t distribution. Assume population from normal distribution.

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3 0
3 years ago
A family is purchasing a house and needs to finance a $195,000 mortgage from the bank with an annual percentage rate (APR) of 5.
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The monthly payment amount is $860.25.

Step-by-step explanation:

Step 1; The bank offers an amount of $195,000 with an APR of 5.3%. This means that the family must pay 5.3% of the $195,000 every year for 30 years. To calculate we must determine how much 5.3% of $195,000 is. To do that we make 5.3% a fraction by dividing it by 100 and multiplying it with the amount.

5.3% of $195,000 = \frac{5.3}{100} × $195,000 = 0.053 × $195,000 = $10,335 per year.

Payment owed for 30 years = Payment owed a year × 30

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Step 2; To find the monthly payments we need to know how many months are in a 30 year period. Months in 30 years = 30 × 12 months = 360 months. The monthly payment is, therefore, payment owed in 30 years divided by the months in that 30 year period.

Monthly payment = $10,335 / 360 = $ 861.25.

So the family must pay a monthly payment of $861.25 for 30 years.

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