Betty needs3/4 of a yard of fabric to make a skirt. she buys 9 yards. how many skirts can she make?

jeka94

The Law of Cosines features the 3 side lengths of a triangle, plus the measure of the angle opposite one of those sides.

We want angle x, which is opposite the side of length 39.

Then: a^2 = b^2 - 2ab cos C becomes 39^2 = 36^2 + 59^2 - 2(36)(59)cos x

or 1521 = 3481 + 1296 - 2(36)(59) cos x

Subtract (3481+1296) from both sides: 1521 - 4777 = -4248cos x

-3256 = -4248cos x

-3256

Then: cosx = --------------- = 0.766

-4248

Solving for x: x = arccos -0.766 = 0.698 radian, or 40 degrees (answer)

5 0

3 years ago

What is the completely factored form of 4x+20

allsm [11]

Hi there!

Since both 4x and 20 can be divisible by 4 and is greatest able to be divisible by 4, we can divide the 4 and put it outside of the parenthesis in order to factor:

4x / 4 = x
20 / 4 = 5

4 (x + 5)
would be your answer.

Hope this helps!

3 0

3 years ago

If the term of arthematic progression decrease in magnitude then common difference must be

Tpy6a [65]

We can say that if the term of arithmetic progression decrease in magnitude then the common difference must be <u>negative</u>.

An arithmetic progression is a sequence where every term is a sum of the previous term and a common difference.

If we suppose the first term of an arithmetic progression to be a, and the common difference to be d, then the arithmetic progression goes like this:

The first term, a₁ = a,

Second term, a₂ = a₁ + d = a + d,

Third term, a₃ = a₂ + d = a + 2d,

Fourth term, a₄ = a₃ + d = a + 3d, and it goes so on up to,

The n-th term, aₙ = aₙ₋₁ + d = a + (n - 1)d.

In the question, we are asked if the term of arithmetic progression decrease in magnitude then what can we say about the common difference.

As the magnitude of the term decreases, we can show that as:

The n-th term < The first term,

or, aₙ < a₁,

or, a + (n - 1)d < a,

or, a + (n - 1)d - a < a - a {Subtracting a from both sides},

or, (n - 1)d < 0.

Since, n > 1, (n - 1) > 0, thus we get the common difference, d < 0, that is, the common difference is negative.

Thus, we can say that if the term of arithmetic progression decrease in magnitude then the common difference must be <u>negative</u>.

Learn more about arithmetic progressions at

brainly.com/question/6561461

#SPJ4

8 0

2 years ago

A country's education department reported that in 2015, 70.8% of students enrolled in college or a trade school within 12 months

Gennadij [26K]

Answer:

The confidence interval has a lower limit of 0.546 and an upper limit of 0.675.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the z-score that has a p-value of $1 - \frac{\alpha}{2}$ .

In 2017, a random sample of 154 individuals who graduated from high school 12 months prior was selected. From this sample, 94 students were found to be enrolled in college or a trade school.

This means that $n = 154, \pi = \frac{94}{154} = 0.6104$