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3 years ago

Solve the system by substitution. SHOW WORK -X - Y - Z=-8 - 4X +4Y +5Z=7 2X + 2Z=4

1 answer:

3 0

Solve:

<span>-X - Y - Z =-8
- 4X +4Y +5Z=7
2X + 2Z =4 is the same as x + z = 2. Thus, z = 2 - x.

Subst. 2 - x for z in the 1st and second equations.

</span>-X - Y - Z =-8 becomes -x - y - (2 -x) = -8
- 4X +4Y +5Z=7 becomes -4x + 4y + 5(2-x) = 7

Now we have 2 equations in only 2 unknowns. Let's simplify them!

-x - y - 2 + x = -8 which becomes -y = -6, or y = 6
-4x + 4y + 10 - 5x = 7 which becomes -9x + 4y = 7 - 10 = -3

Now substitute 6 for y in this last equation: -9x + 4(6) = -3, or
-9x + 24 = -3, or
-9x = - 27 => x = 3

Then x = 3, y = 6 and z = 2 - x, or z = 2-3, or z = -1.

The solution is (3, 6, -1). Check it!!

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What is the length of segment AE?

nexus9112 [7]

Answer:

$AE=\frac{50}{3}\ units$

Step-by-step explanation:

step 1

In the right triangle ABC

Applying the Pythagoras Theorem fin the hypotenuse AC

$AC^{2} =AB^{2}+BC^{2}$

substitute

$AC^{2} =6^{2}+8^{2}$

$AC^{2} =100$

$AC =10\ units$

step 2

we know that

If two figures are similar, then the ratio of its corresponding sides is equal

$\frac{AB}{CD}=\frac{AC}{CE}$

substitute and solve for CE

$\frac{6}{4}=\frac{10}{CE}\\ \\CE=4*10/6\\ \\CE=\frac{20}{3}\ units$

step 3

Find the length of segment AE

AE=AC+CE

substitute the values

$AE=10\ units+\frac{20}{3}\ units=\frac{50}{3}\ units$

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3 years ago

Solve w2 =64 where w is a real number

Deffense [45]

Answer:

w=32

Step-by-step explanation:

32*2=64

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3 years ago

Describe 2 ways that an exterior angle of a triangle is related to one or more or the interior angles

shtirl [24]

The 2 angles at a vertex are supplementary (one interior and one exterior) the exterior angle is = the the sum of the 2 remote interior angles..

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3 years ago

Suppose the weights of Farmer Carl's potatoes are normally distributed with a mean of 8.0 ounces and a standard deviation of 1.1

svet-max [94.6K]

Answer:

a) 0.9959 = 99.59% probability that the mean weight is less than 9.3 ounces

b) 0.0129 = 1.29% probability that the mean weight is more than 9.0 ounces

Step-by-step explanation:

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

Normal Probability Distribution:

Problems of normal distributions can be 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.

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 $s = \frac{\sigma}{\sqrt{n}}$ .