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Katena32 [7]
3 years ago
11

Point R divides in the ratio 1 : 3. If the x-coordinate of R is -1 and the x-coordinate of P is -3, what is the x-coordinate of

Q?
A.

B.
3
C.
5
D.
6
E.
-9
Mathematics
1 answer:
dimaraw [331]3 years ago
7 0

Answer:

C. 5

Step-by-step explanation:

Point R divides the line segment PQ internally. The x-coordinate of the point which divides the line segment in ration m:n internally can be calculated as:

x=(\frac{mx_{2}+nx_{1}}{m+n} )

Here, x1 is the x-coordinate of 1st point, x2 is the x-coordinate of 2nd point, x is the x-coordinate of point dividing the segment. We have all the values except x2. Using the given values in above formula, we get:

-1=\frac{x_{2}+3(-3) }{1+3} \\ \\-4=x_{2}-9\\\\ 5=x_{2}

Thus the x-coordinate of point Q will be 5

The x-coordinate of Q is 5.

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Please help I dont understand
Arisa [49]

Answer:

38 degrees

Step-by-step explanation:

By the Law of Cosines,

5² = 3² + 7² - 2(3)(7) cos A

5² - 3² - 7² = -2(3)(7) cos A

-33 = -42 cos A

cos A = 33/42

A = arccos(33/42), which is about 38 degrees.

5 0
2 years ago
2) A cab driver got a $6 tip on a bill that was $20.
soldi70 [24.7K]
The total is $26 with the tip this is a 30% tip
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2 years ago
Given f(x)= -2x -13, what is f(-3) -7?<br><br>A: -26<br>B: -14<br>C: -7<br>D: 0<br>E: 26
DochEvi [55]

Answer:

B: -14

Step-by-step explanation:

given that f(x) = -2x - 13,

we can find the value of f(-3) by simply plugging in -3 for x

f(-3) = -2(-3) - 13

f(-3) = -7

Because we are dealing with the expression f(-3) - 7, we still have one more step. Let's plug in -7 for f(-3)

- 7 - 7 = -14

Therefore, f(-3) - 7 will give us B: -14

4 0
3 years ago
The amount of time a certain brand of light bulb lasts is normally distribued with a mean of 1300 hours and a standard deviation
Bezzdna [24]

Answer:

The interval of hours that represents the lifespan of the middle 68% of light bulbs is 1210 hours - 1390 hours.

Step-by-step explanation:

In statistics, the 68–95–99.7 rule, also recognized as the Empirical rule, is a shortcut used to recall that 68%, 95% and 99.7% of the values lie within one, two and three standard deviations of the mean, respectively.

Then,

  • P (µ - σ < X < µ + σ) = 0.68
  • P (µ - 2σ < X < µ + 2σ) = 0.95
  • P (µ - 3σ < X < µ + 3σ) = 0.997

he random variable <em>X</em> can be defined as the  amount of time a certain brand of light bulb lasts.

The random variable <em>X</em> is normally distributed with parameters <em>µ</em> = 1300 hours and <em>σ</em> = 90 hours.

Compute the interval of hours that represents the lifespan of the middle 68% of light bulbs as follows:

P (\mu - \sigma < X < \mu + \sigma) = 0.68\\\\P(1300-90

Thus, the interval of hours that represents the lifespan of the middle 68% of light bulbs is 1210 hours - 1390 hours.

4 0
3 years ago
A manufacturer wishes to make a cereal box in the shape of a golden rectangle, based on the theory that this shape is the most p
Finger [1]
Choices:
<span>a. 7 in. x 11 in.            c. 8 in. x 13 in.
b. 16 in. x 20 in.          d. 6 in. x 9 in.
</span>
Area of a rectangle = length * width

We need to get the factors of 104 in² and identify which is its length and width.

1 x 104 = 104
2 x   52 = 104
4 x   26 = 104
8 x   13 = 104  This is the correct dimension of the front of the box.

Choice C. 8 inches x 13 inches


4 0
3 years ago
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