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3 years ago

If line T is a transversal of lines I and m, name the angel relationship of the given angle pairs

Mathematics

1 answer:

kolbaska11 [484]3 years ago

3 0

Answer:

a. corresponding angles (congruent)

b. alternate exterior angles (congruent)

c. same-side interior angles (supplementary)

Step-by-step explanation:

The vocabulary associated with angles created by a transversal and parallel lines is not so difficult.

If angles are on the same side of the transversal, they are same-side angles. If not, they are alternate angles.

If angles are between the parallel lines, they are interior angles. If not, they are exterior angles.

If the angles are in the same direction from the point of intersection of the transversal with the parallel line, they are corresponding. Corresponding angles are same-side; one is interior and the other is exterior.

These names generally apply to angles with different vertices.

a. Both angles are northwest of the intersection point; they are same-side, and one is interior and one is exterior. They are corresponding angles. (congruent)

b. The angles are on opposite sides of the transversal and are outside the parallel lines. They are alternate exterior angles. (congruent)

c. The angles are on the same side of the transversal, and both are between the parallel lines. The are same-side interior angles. (supplementary)

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2 years ago

A) If the 5th term of an A.P. is double the 7th term, show that the sum of the 17 terms zero.

gayaneshka [121]

Answer:

see explanation

Step-by-step explanation:

The nth term of an AP is

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₅ is double a₇ , then

a₁ + 4d = 2(a₁ + 6d) , that is

a₁ + 4d = 2a₁ + 12d ( subtract a₁ from both sides )

4d = a₁ + 12d ( subtract 12d from both sides )

- 8d = a₁

The sum of n terms of an AP is

$S_{n}$ = $\frac{n}{2}$ [ 2a₁ + (n - 1)d ] , substitute values

$S_{17}$ = $\frac{17}{2}$ ( 2(- 8d) + 16d)

= 8.5(- 16d + 16d)

= 8.5 × 0

= 0

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2 years ago

It has a time to failure distribution which is normal with a mean of 35,000 vehicle miles and a standard deviation of 7,000 vehi

Triss [41]

Answer:

The designed life should be of 21,840 vehicle miles.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Mean of 35,000 vehicle miles and a standard deviation of 7,000 vehicle miles.

This means that $\mu = 35000, \sigma = 7000$

Find its designed life if a .97 reliability is desired.

The designed life should be the 100 - 97 = 3rd percentile(we want only 3% of the vehicles to fail within this time), which is X when Z has a p-value of 0.03, so X when Z = -1.88.

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

$-1.88 = \frac{X - 35000}{7000}$