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3 years ago

Determine the value of x in the diagram below

Mathematics

2 answers:

podryga [215]3 years ago

7 0

Answer:

x = 15

Step-by-step explanation:

The 2 angles are corresponding angles and they are always equal to each other.

5x + 55 = 2x + 100

Subtract 2x from each other;

3x + 55 = 100

Subtract 55 from both sides;

3x = 45

Divide both sides by 3;

x = 15

Check:

5x + 55

Substitute x;

5(15) + 55 = 75 + 55 = 130

2x + 100

Substitute x;

2(15) + 100 = 30 + 100 = 130

aivan3 [116]3 years ago

5 0

Answer:

x = 15

5x + 55 = 2x +100, plug in 15 and they are equal

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A painter has a 24 foot ladder that he is using to paint a house. For safety reasons, the ladder must be placed at least 8 feet

Lana71 [14]

Answer:

The ladder can reach a height of 22.6 feet.

Step-by-step explanation:

In order to find the height that the ladder can reach, you need to use the Pythagorean Theorem. The Pythagorean Theorem assumes that the house to the ground will form a right triangle and the leaning ladder is the hypotenuse. Using the formula: a² + b² = c², we can plug in the values that we know and solve for the missing variable. In this case we know the base of the triangle 'b' and the hypotenuse 'c': a² + 8² = 24² or a² + 64 = 576. To solve for a, we must first subtract 64 from both sides: a² + 64 - 64 = 576 - 64 or a² = 512. In order to find just the value of 'a', which represents the height, we need to take the square root of both sides: √a² = √512 or a ≈ 22.6 feet.

4 0

3 years ago

No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100

Mariana [72]

This is the question:

A bicycle manufacturing company makes a particular type of bike.

Each child bike requires 4 hours to build and 4 hours to test.

Each adult bike requires 6 hours to build and 4 hours to test.

With the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week.

If c represents child bikes and a represents adult bikes,

determine which system of inequality best explains whether the company can build 10 child bikes and 12 adult bikes in the week

Now you can state the system of inequalities from the statements

1) First inequality based on the hours availble to buiding

Each child bike requires 4 hours, each adult bike requires 6 hours to build and the company is able to have up to 120 hours of building =>

4c + 6a ≤ 120

2) Second inequality based of the hours available to testing.

Each child bike requires 4 hours to test, each adult bike 4 hours to test and the company is able to have up 100 hours of testing time for a week =>

4c + 4a ≤ 100

Then the two inequalities are:

4c + 6a ≤ 120
4c + 4a ≤ 100

The answer is Yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100

Which you can verify by replacing in both equations 10 for c and 12 for a. Look:

1) 4(10) + 6(12) = 40 + 72 = 112 ≤ 120

2) 4(10) + 4(12) = 40 + 48 = 88 ≤ 100

6 0

2 years ago

Read 2 more answers

Mary and Jane both took PSY230 last semester but they were in two different sections taught by different professors. Mary's clas

Greeley [361]

Answer:

Due to the higher z-score, Jane did better in class.

Step-by-step explanation:

Z-score:

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 question:

Whoever's grade had the better z-score did better in class.

Mary's:

Mean of 85, standard deviation of 5, grade of 88. This means that $\mu = 85, \sigma = 5, X = 88$ . So