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2 years ago

In the triangle below, determine the value of a.

Mathematics

1 answer:

makkiz [27]2 years ago

4 0

Answer:

Step-by-step explanation:

This is classic right triangle trig. Side a, our unknown, is adjacent to angle C which is a given. You always have to use a given angle and side to find a missing side, so we have to figure out how the two givens are related to our unknown. Side a is adjacent to angle C, and we are also given the hypotenuse. We know side a is not the hypotenuse since the hypotenuse is ALWAYS the side across from the 90 degree angle. The tan ratio of angle C will give us a way to have only one unknown.

tan 43 = a/26 and

26 tan 43 = a

Use your calculator now to find the missing side.

a = 24.2 units long

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Unknown angle problems (with ale<br> Solve for I in the diagrarn below.<br> (24 + 45)<br> f<br> TE

astraxan [27]

Answer:

x = 45

Step-by-step explanation:

The angles with (2x + 45) and x are supplementary angles, meaning they add up to 180°. We can write this statement as an algebraic equation of $2x + 45 + x = 180$ and solve it.

Step 1: Combine like terms.

$(2x+x)+45=180$
$3x+45=180$

Step 2: Subtract 45 from both sides.

$3x + 45 - 45 = 180 - 45$
$3x = 135$

Step 3: Divide both sides by 3.

$3x/3 = 135/3$
$x = 45$

Step 4: Check if solution is correct.

$2(45) + 45 + 45 = 180$
$90 + 90 = 180$
$180=180$

Therefore, x = 45.

Have a lovely rest of your day/night, and good luck with your assignments! ♡

8 0

2 years ago

Johan always wears a shirt, pants, socks, and shoes. He owns 20 pairs of socks, 5 pairs of shoes, 10 pairs of pants, and 8 shirt

DerKrebs [107]

Answer:

Johan can make 8000 different outfits.

Step-by-step explanation:

Johan needs to pick one of each (shirt, pants, socks and shoes) to make a outfit. The number of socks he has is 20 pairs, so he has 20 possibilities for socks. In the same way, the number of possibilities for shoes is 5, for pants is 10 and for shirts is 8.

So, to find the number of outfits he can make, we need to multiply all the possibilities for each case, so:

Number of different outfits = 20 * 5 * 10 * 8 = 8000.

6 0

3 years ago

Read 2 more answers

Today only a table is being sold at a 15% discount. The sale price is $629

Musya8 [376]

Answer:

740

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers

i have 17 coins. N of them are nickels and the rest are dimes. write an expression in two different ways for the amount of money

valkas [14]

Answer:

Step-by-step explanation:

(N)0.05 + (17-N)0.1 = M; M = amount of money I have.

Or 1.7-0.05N = M.

7 0

2 years ago

According to the College Board website, the scores on the math part of the SAT (SAT-M) in a recent year had a mean of 507 and st

Leviafan [203]

Answer:

The actual SAT-M score marking the 98th percentile is 735.

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:

$\mu = 507, \sigma = 111$

Find the actual SAT-M score marking the 98th percentile

This is X when Z has a pvalue of 0.98. So it is X when Z = 2.054. So

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

$2.054 = \frac{X - 507}{111}$

$X - 507 = 2.054*111$

$X = 735$

8 0

2 years ago