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What is the length of side BC of the triangle? Enter your answer in the box. units Triangle A B C with horizontal side B C. Vert

harina [27]

Answer:

The length of BC = 28 units

Step-by-step explanation:

* In triangle ABC

∵ Angles B and C are congruent

∴ m∠B = m∠C

* In any triangle if two angles are equal in measure, then the triangle is isosceles means the two sides which opposite to the congruent angles are equal in length

∴ AB = AC

∵ AB = 4x - 7

∵ AC = 2x + 7

∴ 4x - 7 = 2x + 7 ⇒ collect like terms

∴ 4x - 2x = 7 + 7

∴ 2x = 14 ⇒ divide both sides by 2

∴ x = 14 ÷ 2 = 7

* Now we can find the length of BC

∵ The length of BC = 4x ⇒ substitute the value of x

∴ The length of BC = 4 × 7 = 28 units

6 0

3 years ago

before a renovation, a movie theater had 149 seats. After the renovation, the theater had 180 seats. what is the approximate per

liberstina [14]

180 - 149 = 31

x/100 *149 = 31

1.49x = 31

x= 31/1.46 = 20.81 %

5 0

3 years ago

A section of concrete pipe 30m long has an inside diameter of 1.2m and an outside diameter of 1.8m. what is the volume of concre

Fudgin [204]

length of pipe= 30m

Inside dia. = 1.2m

Outside dia. = 1.8m

Volume of concrete= (outside dia. - inside dia.)h

V= (pi)
v= [(3.14*0.9*0.9)-(3.14*0.6*0.6)]30

v= (3.3534-1.1304)30
v=(2.233)30 = 66.690m cube

since it's volume the answer 66.690 is in cubic meters.

5 0

4 years ago

According to the Census Bureau, in 2014 California had an estimated population of 3.88 x 10^7 and Wyoming had an population of 5

Verdich [7]

The population of California is 3.88 x 10^7 - 5.84 x 10^5 = 3.82 x 10^7 more than the population of Wyoming. Alternatively the population of California is 3.88 x 10^7 / 5.84 x 10^5 = 66 times the population of Wyoming.

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8 0

3 years ago

Each contestant in the Hunger Games must be trained to compete. Suppose that the time it takes to train a contestant has mean 5

LiRa [457]

Answer:

11.51% probability that it will take less than 450 days to train all the contestants.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use 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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .