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2 years ago

The equation of a line in slope intercept form that is perpendicular to y=-1/3 x +5 and goes through the point (-1,3)

Mathematics

1 answer:

sertanlavr [38]2 years ago

7 0

Answer:

y = 3x + 6

Step-by-step explanation:

The general equation of a line is;

y = mx + b

where m is the slope and b is the y intercept

The slope of the first line is -1/3

when two lines are perpendicular, the product of their slopes is equal to -1

Thus;

-1/3 * m2 = -1

-m2 = -3

m2 = 3

So the equation of the second line is;

y = 3x + b

To get b, we substitute the coordinates of the point (-1,3)

We substitute -1 for x and 3 for y

so, we have;

3 = 3(-1) + b

3 = -3 + b

b = 3 + 3

b = 6

So we have the second equation as;

y = 3x + 6

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I need to use the Pythagorean Theorem to find X. I don’t know how to do that!!

frutty [35]

Answer:

17) x=8

18) $x=\sqrt{189}$ or $x= 3\sqrt{21}$

Step-by-step explanation:

So the rule is $a^{2} +b^{2} =c^{2}$ , "c" being the hypothenuse, or the long line that is opposite to the right angle.

17) We know that both values of x are equal to each other, which makes everything 10x easier!

$x^{2} +x^{2} =(8\sqrt{2}) ^{2}$

(by the way we know the x values are our a and b values because they are legs! the way I like to remember the legs is that they are connected to the right angle box, and therefore support the hypothenuse)

<em>simplify</em> (╥︣﹏╥)

$2x^2=8^2(\sqrt{2} )^{2}$

$2x^2=64(2)$

$2x^2=128$

$x^{2}= 128/2$

$x^{2} =64$

x=8

18) Just pretend that the flipped triangle doesn't exist. It's parallel to the other triangle with values on it, and basically servers no purpose other than being parallel to the sister triangle :)

Anyways, since we know the hypothenuse (15) but we don't know one of our leg values (x), we're going to change our equation a bit!

$c^{2} - b^{2} = a^{2}$

It doesn't matter if you put the one leg value in a or b, just as long as you stick to that same equation you started with the entire time!

$15^{2} -6^{2} =x^{2}$

$225-36=x^{2}$

$x^{2} =189$

$x=\sqrt{189}=3\sqrt{21}$

The more you do these, the easier they'll get, so don't worry!

4 0

3 years ago

6. Find the product:<br> (x² + 8x - 3)(x + 1)

olga_2 [115]

Answer:

x^3+9x^2-3x^2-3

Step-by-step explanation:

You can use a various of methods but when you use the box method you multiply each separately.

Like you would multiply x² by x, 8x by x, -3 by x (thats the first row)

x² by 1, 8x by 1, -3 by 1 ( for the second row)

Then you get those final variables and combine like terms getting the answer above

8 0

3 years ago

A circle has a diameter with endpoints at -2 + i and -6 -11i. What is the center of the circle?

pashok25 [27]

Answer:

- 4 - 5i

Step-by-step explanation:

The centre of the circle is the average of the endpoints

centre = (- 2 + i - 6 - 11i ) ÷ 2

= (- 8 - 10i ) ÷ 2

= - 4 - 5i

7 0

2 years ago

If 50 students prefer vanilla ice cream, how many students were surveyed? 21% were vanilla, 19% were strawberry, 60% were chocol

AURORKA [14]

If 50 students prefer vanilla ice cream then 259 students were surveyed.

4 0

3 years ago

Lucy drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took hours. When Lucy drove hom

Anastasy [175]

Answer:

The question is incomplete, the complete complete question will be:

Lucy drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 9 hours. When Lucy drove home, there was no traffic and the trip only took 4 hours. If her average rate was 40 miles per hour faster on the trip home, how far away does Lucy live from the mountains?

Lucy live at a distance of 288 miles from the mountains.

Step-by-step explanation:

DATA:

To the mts DATA:

Time = 9 hrs

Rate = r mph

Distance = 9r miles

From the mts DATA:

time = 4 hrs

rate = r+40 mph

distance = 4(r+40) miles

SOLUTION

Distance to = Distance from

9r = 4r + 160

5r = 160

r = 32 mph

RESULT:

Distance = 9r = 9*32 = 288 miles

8 0

3 years ago