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Yakvenalex [24]
3 years ago
15

Two angles form a linear pair. The measure of one angle is x and the measure of the other angle is 1.4 times x plus 12∘ . Find t

he measure of each angle.
Mathematics
1 answer:
nekit [7.7K]3 years ago
6 0

Answer:

70° and 110°

Step-by-step explanation:

If two angles forms a linear pair, this means that the sum of the angles is 180°. If the measure of one angle is x and the measure of the other angle is 1.4 times x plus 12∘

Let A be the first angle = x°

Let B be the second angle = (1.4x+12)°

Since they form a linear pair, then

A+B = 180°

x + 1.4x+12 = 180°

2.4x = 180-12

2.4x = 168

x = 168/2.4

x = 70°

The measure of angle A = 70°

The measure if angle B = 1.4x+12

B = 1.4(70)+12

B = 98+12

B = 110°

The measure of both angles are 70° and 110°

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Answer:

2√13

Step-by-step explanation:

using the distance formula;

d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}

you plug the numbers in. once done you get 2√13.

Hope it helps!

7 0
3 years ago
Solve the following equation by using the distributive property: 5(x - 4) = 6
Pani-rosa [81]
You do 5 times x and 5 times 4 and you’d end up with equation that says 5x-4=6. The you add 4 to both sides of the equation to cancel out the 4. Your equation should now say 5x=10. You divide both sides by 5 and you have your answer x=2
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3 years ago
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Can you help me please?
ExtremeBDS [4]

Answer:

0≤x≤8

Step-by-step explanation:

the domain is basically all the x-values that are applicable to the graph.

Here we can clearly see that the graph starts at x = 0 and ends at x = 8. There are no other possible x-values which is applicable to the graph,

hence the domain is 0≤x≤8

6 0
2 years ago
Read 2 more answers
36. GEOMETRY Write an algebraic expression to
Stels [109]

Answer:

108 in²

Step-by-step explanation:

Area of a triangle is given as ½*base*height

The base of the given triangle = h + 6

height = h

Algebraic expression for its area = \frac{1}{2}*(h + 6)*h = \frac{1}{2}(h^2 + 6h) = \frac{h^2 + 6h}{2}

Evaluate the area if h is given as 12 inches.

Plug in the value of h into the algebraic expression:

\frac{h^2 + 6h}{2} = \frac{12^2 + 6(12)}{2}

= \frac{144 + 72}{2}

= \frac{216}{2} = 108 in^2

6 0
3 years ago
You are asked to do a study of shelters for abused and battered women to determine the necessary capacity in your city to provid
ohaa [14]

Answer:

Using the normal probability distribution, with a capacity of 350, it is enough for all abused on 90.82% of nights.

274 shelters will be needed.

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.

In this problem, we have that:

\mu = 250, \sigma = 75

If the city’s shelters have a capacity of 350, will that be enough places for abused women on 95% of all nights?

What is the percentile of 350?

This is the pvalue of Z when X = 350.

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

Z = \frac{250 - 150}{75}

Z = 1.33

Z = 1.33 has a pvalue of 0.9082.

Using the normal probability distribution, with a capacity of 350, it is enough for all abused on 90.82% of nights.

If not, what number of shelter openings will be needed?

The 95th percentile, which is X when Z = 1.645. So

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

1.645 = \frac{X - 150}{75}

X - 150 = 1.645*75

X = 274

274 shelters will be needed.

5 0
2 years ago
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