All categories

3 years ago

If m ∥ n, m∠1 = (5x + 12)°, and m∠2 = (7x – 16)°, what is m∠3?

Mathematics

2 answers:

asambeis [7]3 years ago

6 0

Answer:

98°

Step-by-step explanation:

m∠1 = m∠2

5x + 12 = 7x - 16; substitute the given

2x = 28

x = 14

m∠2 + m∠3 = 180; supplementary angles

82 + m∠3 = 180

m∠3 = 180 - 82

m∠3 = 98 degrees

Ket [755]3 years ago

5 0

Answer: m<3 = 98

Explanation: If two parallel lines are cut by a transversal,

then alternate interior angles are congruent.

This means that the m<1 = m<2.

So we can setup the equation 5x + 12 = 7x - 16

and solving this equation gives us x = 14.

Now let's use <2 to help us find the m<3.

Since x = 14, we can plug a 14 into the equation for x

to find the m<2 and this gives us 7(14) - 16 which is 82.

Now, we know that <2 and <3 form a straight

angle which is equal to 180 degrees.

So we can say that 82 + m<3 = 180 and we find that m<3 = 98.

You might be interested in

Josh is hiking Glacier National Park. He has now hiked a total of 17 \text{ km}17 km17, start text, space, k, m, end text and is

EastWind [94]

Answer:

The equation to determine the total length in kilometers is $\frac{h}{2} =(17+2)$

The total length in kilometers of Josh’s hike is 38 km.

Step-by-step explanation:

Given:

Let the total length in kilometers of Josh’s hike be h.

Now Given that He has now hiked a total of 17 km and is 2 km short of being 1/2 of the way done with his hike.

It means that to reach half of the length of total length Josh needs 2 more km to add in his hiking which is done which is of 17 km.

Framing the above sentence in equation form we get;

$\frac{h}{2}=(17+2)$

Hence, The equation to determine the total length in kilometers is $\frac{h}{2} =(17+2)$

Now Solving the above equation we get;

First we will multiply 2 on both side using Multiplication property we get;

$2\times \frac{h}{2}= 2\times(17+2)\\\\h =2\times 19 =38 \ km$

Hence, The total length in kilometers of Josh’s hike is 38 km.

4 0

3 years ago

Read 2 more answers

Last year Chesa made 32 one-cup servings of soup for a school party. This year, she will make two times the amount of soup that

Nezavi [6.7K]

Answer:

Step-by-step explanation:

6 0

3 years ago

Assume the population has a normal distribution. A sample of 25 randomly selected students Has a mean test score of 81.5 With a

Natasha_Volkova [10]

Answer:

The 90% confidence interval for the mean test score is between 77.29 and 85.71.

Step-by-step explanation:

We have the standard deviation for the sample, so we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 25 - 1 = 24

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 24 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.9}{2} = 0.95$ . So we have T = 2.064

The margin of error is:

$M = T\frac{s}{\sqrt{n}} = 2.064\frac{10.2}{\sqrt{25}} = 4.21$

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 81.5 - 4.21 = 77.29

The upper end of the interval is the sample mean added to M. So it is 81.5 + 4.21 = 85.71.

The 90% confidence interval for the mean test score is between 77.29 and 85.71.

6 0

3 years ago

a storage room measures 20 feet by 15 feet. the floor is covered by tiles that cost $7.50 per square foot. what will be the cost

Sidana [21]

Answer: $2250

Step-by-step explanation:

Given information

Dimension of the room = 20 feet × 15 feet

Cost of tiles = $7.50 / ft²

Derived formula from the given information

Total cost = Floor area × Cost of tiles

Substitute values into the formula

Total cost = Floor area × Cost of tiles

Total cost = (20 × 15) × (7.5)

Simplify by multiplication

Total cost = 300 × (7.5)

$\Large\boxed{Total~cost~=~2250~Dollars}$

Hope this helps!! :)

Please let me know if you have any questions

4 0

2 years ago

47.2 is what percent of 118

earnstyle [38]

Answer:

you multiply both sides of the equation by x

you divide both sides of the equation by (2.5) to get x

47.2 is 40% of 118

Step-by-step explanation:

5 0

3 years ago