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viva [34]
3 years ago
11

Find the point on the line 6x+y=9 that is closest to the point (-3,1).

Mathematics
1 answer:
Snowcat [4.5K]3 years ago
7 0
 Basically, you have to find the line through (-3, 1) that is perpendicular to the line 6x + y = 9 and then find where the two lines intersect. Dropping a perpendicular from the point to the line is the shortest distance from the point to the line. 

6x + y = 9
y = -6x + 9 
slope is -6 

perpendicular would have slope 1/6
(y - 1) = (1/6) (x + 3) 
y - 1 = (1/6) x + (1/2) 
multiplying both sides by 6
6y - 6 = x + 3 
x - 6y = -9 


Where do these two lines intersect? 

From above we know given equation is y = -6x + 9
Plugging into other equation
x - 6(-6x + 9) = -9
x + 36x - 54 = -9 
37 x = 45
x = 45/37 
y = -6(45/37) + 9 
y = -270/37 + (333/37) 
y = 63/37 

point is (45/37, 63/37)
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Consumer Math TestYou borrow $13,000 to buy a car. You borrow the money for 4 years and the interest rate is 2.5%. How much inte
enot [183]

Answer:

You will pay $1,300 in interest.

The final price of the car is of $14,300

Step-by-step explanation:

Simple interest formula:

I=P\ast r\ast t

In which:

I is the interest

P is the principal(initial value of the investment, amount borrowed,...)

r is the interest rate, as a decimal

t is the time, in years.

In this question:

Borrow $13,000, so P = 13000

4 years, so t = 4

Interest rate of 2.5%, so r = 0.025

I=13000\ast0.025\ast4=1300

You will pay $1,300 in interest.

Final price of the car:

Principal plus interest.

T=P+I=13000+1300=14300

The final price of the car is of $14,300

4 0
9 months ago
What’s the answer and could you explain it
Nadusha1986 [10]
The answer is B.   Because there are 8 ribbons in all. 1 ribbon is black. so the equation would be 1/8. Assuming you don't draw the black ribbon on the first try, then you would try again. The second time you draw a ribbon you don't put the ribbon you drew back in. That means there are only 7 ribbons the second time. The 1 black ribbon is still in the bag than the equation would be 1/7. Then you add the two together. So it would be 1/8 + 1/7 = 1/15. Remember to only add the bottom numbers. not the top ones unless they are different colors or objects.
3 0
2 years ago
Please help, I will mark!!
Alik [6]

Answer:

d=28.28

Step-by-step explanation:

To calculate the lenght of the diagonal d across the square, we can assume that the square it is compound of two right triangles. So, we can resolve this exercise using The Pythagorean Theorem.

<em>The Pythagorean theorem</em> states that in every right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the respective lengths of the legs. It is the best-known proposition among those that have their own name in mathematics.

If in a right triangle there are legs of length a and b, and the measure of the hypotenuse is c, then the following relation is fulfilled:

a^{2} +b^{2} =c^{2} a is the height, b is the base, and c is  

the hypotenuse.

To obtain the value of the hypotenuse

c= \sqrt{a^{2} +b^{2} }

To find the value of the lenght of the diagonal d across the square, we have:

d=\sqrt{a^{2} +b^{2} } Where a = b = 20

Substituting the values

d=\sqrt{(20)^{2} +(20)^{2} }\\d=\sqrt{400+400} =\sqrt{800} \\d=28.284

Round the answer to 2 decimal places

d=28.28

6 0
2 years ago
What is the answer to 1/4 - (-1/6)​
Aloiza [94]

Answer:

5/12

Step-by-step explanation:

1/4 + 1/6 = (6+4)/24 = 10/24 = 5/12

why +1/6?

because: - (-) = +

4 0
3 years ago
The length of a rectangle is 6m longer than its width. If the perimeter of the rectangle is 52m, find its area
sveticcg [70]
If length is x, then width is 6+x 
<span>Perimeter = 2*(x + 6+x) = 52 </span>
<span>2*6 + 2*2x = 52 </span>
<span>4x = 52 - 12 = 40 </span>
<span>x = 40/4 = 10 </span>

<span>Area = length*width = 10*(6+10) </span>
<span>Area = 10*16 = 160 meter square</span>
4 0
3 years ago
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