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3 years ago

Given the points below, are the two lines parallel, perpendicular, or neither.

Mathematics

1 answer:

Nookie1986 [14]3 years ago

6 0

Answer:

perpendicular

Step-by-step explanation:

First we need to dtemine the slopes of the line

For line 1

L1: (-4, 6) (-3,-1)

m1 = y2-y1/x2-x1

m1= -1-6/-3+4

m1 = -7/1

m1 = -7

For line 2:

L2: (8,9) (15, 10)

m2 = 10-9/15-8

m2 = 1/8

Take their product

m1 * m2 = -7 * 1/7

m1m2 = -1

Since the product of their slopes is -1, hence they are perpendicular

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stepan [7]

${x}^{2} + x - 10506 = 0$

Step-by-step explanation:

-x, -(x+1)

-x-(x+1)=10506

x^2+x-10506=0

4 0

3 years ago

Problem page isabel runs 7 miles in 50 minutes. at the same rate, how many miles would she run in 75 minutes?

sammy [17]

if isabel runs 7 miles in 50 minutes, then you know she runs 7/50 miles in one minute, right? So multiply that by the number of minutes she did run, and you can find the distance:

 7
------ x 75 =
50

525
------
50

 If you plug that fraction into your calculator, you get 10.5, so 10 and a half miles.

8 0

3 years ago

1. An AP has a common difference of 3. Given that the nth term is 32, and the sum of the first n terms is 185, calculate the

netineya [11]

Answer:

The value of n is 10

Step-by-step explanation:

The formula of the nth term of the arithmetic progression is a $_{n}$ = a + (n - 1)d

a is the first term

d is the common difference between each 2 consecutive terms

n is the position of the term

The formula of the sum of nth terms is S $_{n}$ = $\frac{n}{2}$ [2a + (n - 1)d]

∵ An AP has a common difference of 3

∴ d = 3

∵ The nth term is 32

∴ a $_{n}$ = 32

→ Substitute them in the 1st rule above

∵ 32 = a + (n - 1)3

∴ 32 = a + 3(n) - 3(1)

∴ 32 = a + 3n - 3

→ Add 3 to both sides

∴ 35 = a + 3n

→ Switch the two sides

∴ a + 3n = 35

→ Subtract 3n from both sides

∴ a = 35 - 3n ⇒ (1)

∵ The sum of the first n terms is 185

∴ S $_{n}$ = 185

→ Substitute the value of S $_{n}$ and d in the 2nd rule above

∵ 185 = $\frac{n}{2}$ [ 2a + (n - 1)3]

∴ 185 = $\frac{n}{2}$ [2a + 3(n) - 3(1)]

∴ 185 = $\frac{n}{2}$ [2a + 3n - 3]

→ Multiply both sides by 2

∴ 370 = n(2a + 3n - 3)

∴ 370 = 2an + 3n² - 3n

→ Substitute a by equation (1)

∴ 370 = 2n(35 - 3n) + 3n² - 3n

∴ 370 = 70n - 6n²+ 3n² - 3n

→ Add the like terms in the right side

∵ 370 = -3n² + 67n

→ Add 3n² to both sides

∴ 3n² + 370 = 67n

→ Subtract 67 from both sides

∴ 3n² - 67n + 370 = 0

→ Use your calculator to find n

∴ n = 10 and n = 37/3

∵ n must be a positive integer ⇒ 37/3 neglecting

∴ n = 10

∴ The value of n is 10

4 0

3 years ago

The distribution of resistance for resistors of a certain type is known to be normal, with 10% of all resistors having a resista

baherus [9]

Answer:

The mean is 9.65 ohms and the standard deviation is 0.2742 ohms.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

10% of all resistors having a resistance exceeding 10.634 ohms

This means that when X = 10.634, Z has a pvalue of 1-0.1 = 0.9. So when X = 10.634, Z = 1.28.

$Z = \frac{X - \mu}{\sigma}$

$1.28 = \frac{10.634 - \mu}{\sigma}$