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kkurt [141]
3 years ago
14

The line PQ has equation 3x – 2y = 12. P is a point with coordinates (6, 3) and Q is the point

Mathematics
1 answer:
blondinia [14]3 years ago
8 0

Answer:

  1. -9
  2. 2x + 3y = 21
  3. 4√5

Step-by-step explanation:

1. Put the point values in the equation where x and y are, then solve.

... 3(-2) -2k = 12

... -6 -2k = 12 . . . . eliminate parentheses

... -2k = 18 . . . . . . .add 6

... k = -9 . . . . . . . . . divide by -2

2. The perpendicular line will have a slope that is the negative reciprocal of the slope of the given line. The equation for it can be found by swapping the x- and y-coefficients and negating one of them. Then, to make the line go through point (h, k), replace the constant with zero and replace x with (x-h) and y with (y-k).

... 2(x -6) +3(y -3) = 0 . . . . . a line through P perpendicular to PQ

... 2x + 3y = 21

3. The Pythagorean theorem is used for finding the lengths of line segments. The difference in coordinates between P and R is ...

... P - R = (6, 3) - (2, -5) = (6-2, 3-(-5)) = (4, 8)

The length of segment PR can be considered to be the length of the hypotenuse of a right triangle with these leg lengths.

... ║PR║ = √(4² +8²) = √80

... ║PR║ = 4√5

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If f(a)=(a•a•a)-(a•a) + a-1 what is the value of f(-3)?
Elena L [17]

Answer:

-40

Step-by-step explanation:

f(a) = a³ - a² + a - 1

f(-3) = (-3)³ - (-3)² + (-3) - 1

f(-3) = (-27) - (9) + (-3) -1

f(-3) = -27 - 9 -3 - 1

f(-3) = -40

3 0
3 years ago
The weights of certain machine components are normally distributed with a mean of 8.04 g and a standard deviation of 0.08 g. Fin
NISA [10]

Answer:

The bottom 3 is separated by weight 7.8896 g and the top 3 is separated by weight 8.1904 g.

Step-by-step explanation:

We are given that

Mean, \mu=8.04 g

Standard deviation, \sigma=0.08g

We have to find the two weights that separate the top 3% and the bottom 3%.

Let x be the weight of  machine components

P(Xx_2)=0.03

P(X

=0.03

From z- table we get

P(Z1.88)=0.03

Therefore, we get

\frac{x_1-8.04}{0.08}=-1.88

x_1-8.04=-1.88\times 0.08

x_1=-1.88\times 0.08+8.04

x_1=7.8896

\frac{x_2-8.04}{0.08}=1.88

x_2=1.88\times 0.08+8.04

x_2=8.1904

Hence, the bottom 3 is separated by weight 7.8896 g and the top 3 is separated by weight 8.1904 g.

5 0
2 years ago
Solve for x.<br> <br> 13x + 7 = 5x - 20
myrzilka [38]
The answer is -27/8= -3.375
7 0
3 years ago
Read 2 more answers
What’s the equation for this?
Bess [88]

Answer:

y = 2x-3

Step-by-step explanation:

The y intercept is -3. The slope is change in y/change in x. 2/1 = 2

3 0
2 years ago
Please help I will give brainliest
Katyanochek1 [597]

Answer:

30 in^2

Step-by-step explanation:

The formula for finding the area of a trapezoid is A=a+b/2 x h

In this case, a=5, b=10, and h=4

When you input those values into the formula and solve for A, you get A=30

Please mark as brainliest ;)

3 0
2 years ago
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