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2 years ago

What are the angle measures of triangle ABC?

Mathematics

1 answer:

Schach [20]2 years ago

4 0

The angle measures of triangle ABC is ∠A=90°, ∠B= 60°, ∠C = 30°. Thus, the correct option is B.

<h3>What is a triangle?</h3>

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.

As it is known that the angles of the triangle are 30°, 60°, and 90°. Therefore, the largest angle is 90° which will be the opposite of the largest side of the triangle, therefore, the measure of ∠A=90°.

Also, the shortest angle of the triangle is 30°, which will lie at the opposite of the smallest side of the triangle, therefore, the measurement of the ∠C=30°.

Now, the angle left is ∠B therefore, the measure of ∠B=60°.

Hence, the angle measures of triangle ABC is ∠A=90°, ∠B= 60°, ∠C = 30°. Thus, the correct option is B.

Learn more about Triangle:

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Let SSS represent the number of sunflower plants and LLL represent the number of lily plants Ezra's water supply can water.

Fantom [35]

Answer:

Ezra can water at most approximately 8 sunflower plants with the remaining amount of water.

Step-by-step explanation:

Given the inequality function

0.7S+0.5L≤11 where S represent the number of sunflower plants and L represent the number of lily plants Ezra's water supply can water, if Ezra waters 10 lily plants, then we can calculate the maximum amount of sunflower plant that he can water with the remaining amount of water by simply substituting L = 10 into the inequality function as shown;

0.7S+0.5L≤11

0.7S+0.5(10)≤11

0.7S+5≤11

Taking 5 to the other side:

0.7S≤11-5

0.7S≤6

S≤6/0.7

S≤8.57

This shows that Ezra can water at most approximately 8 sunflower plants with the remaining amount of water.

3 0

4 years ago

Subtracted 3 form 5 , then multiply by one forth

Novay_Z [31]

I think -0.5
3-5= -2
-2x.25= -0.5

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3 years ago

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The ratio of yellow flowers to the total number of flowers in a bucket is 5 to 9. How many flowers are yellow if there are 45 lo

bogdanovich [222]

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3 years ago

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Use any of the methods to determine whether the series converges or diverges. Give reasons for your answer.

Aleks [24]

Answer:

It means $\sum_{n=1}^\inf} = \frac{7n^2-4n+3}{12+2n^6}$ also converges.

Step-by-step explanation:

The actual Series is::

$\sum_{n=1}^\inf} = \frac{7n^2-4n+3}{12+2n^6}$

The method we are going to use is comparison method:

According to comparison method, we have:

$\sum_{n=1}^{inf}a_n\ \ \ \ \ \ \ \ \sum_{n=1}^{inf}b_n$

If series one converges, the second converges and if second diverges series, one diverges

Now Simplify the given series:

Taking"n^2"common from numerator and "n^6"from denominator.

$=\frac{n^2[7-\frac{4}{n}+\frac{3}{n^2}]}{n^6[\frac{12}{n^6}+2]} \\\\=\frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{n^4[\frac{12}{n^6}+2]}$

$\sum_{n=1}^{inf}a_n=\sum_{n=1}^{inf}\frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{[\frac{12}{n^6}+2]}\ \ \ \ \ \ \ \ \sum_{n=1}^{inf}b_n=\sum_{n=1}^{inf} \frac{1}{n^4}$

Now:

$\sum_{n=1}^{inf}a_n=\sum_{n=1}^{inf}\frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{[\frac{12}{n^6}+2]}\\ \\\lim_{n \to \infty} a_n = \lim_{n \to \infty} \frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{[\frac{12}{n^6}+2]}\\=\frac{7-\frac{4}{inf}+\frac{3}{inf}}{\frac{12}{inf}+2}\\\\=\frac{7}{2}$

So a_n is finite, so it converges.

Similarly b_n converges according to p-test.

P-test:

General form:

$\sum_{n=1}^{inf}\frac{1}{n^p}$

if p>1 then series converges. In oue case we have:

$\sum_{n=1}^{inf}b_n=\frac{1}{n^4}$

p=4 >1, so b_n also converges.

According to comparison test if both series converges, the final series also converges.

It means $\sum_{n=1}^\inf} = \frac{7n^2-4n+3}{12+2n^6}$ also converges.

5 0

4 years ago

What is the quotient in simplified form?

Bumek [7]

(a+2)/(a-5) ÷ (a+1)/(a²-8a+15) =
Note : (a²-8a+15) = (a-3) (a-5)
∴ (a+2)/(a-5) ÷ (a+1)/(a²-8a+15) = [(a+2)/(a-5)] ÷ [(a+1)/(a-3) (a-5)] =
= [(a+2)/(a-5)] * [(a-3) (a-5)/(a+1)] = (a+2)(a-3)/(a+1)

not: the divide sign (÷) becomes (*)
and (a+1)/(a²-8a+15) becomes (a²-8a+15)/(a+1)

The original divisor of
{(a+2)/(a-5) ÷ (a+1)/(a²-8a+15)} = [(a+2)/(a-5)] * [(a-3) (a-5)/(a+1)]
If a = 1 or a = 5 that expression would be undefined, so we will restrict those values

6 0

3 years ago