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2 years ago

-6x-14y=16 and -2x+7y=17 solve by elimination show the work

Mathematics

1 answer:

professor190 [17]2 years ago

6 0

Answer:

(- 5, 1 )

Step-by-step explanation:

- 6x - 14y = 16 → (1)

- 2x + 7y = 17 → (2)

Multiplying (2) by - 3 and adding to (1) will eliminate the x- term

6x - 21y = - 51 → (3)

Add (1) and (3) term by term to eliminate x

0 - 35y = - 35

- 35y = - 35 ( divide both sides by - 35 )

y = 1

Substitute y = 1 into either of the 2 equations and solve for x

Substituting into (1)

- 6x - 14(1) = 16

- 6x - 14 = 16 ( add 14 to both sides )

- 6x = 30 ( divide both sides by - 6 )

x = - 5

solution is (- 5, 1 )

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Which is equivalent to the expression -8 i squared +3?

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Answer:

Step-by-step explanation:

i² = -1

-8(-1) + 3 = 8 + 3 = 11

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3 years ago

In a survey of 22,000 people, 14,300 responded that salary was the most important consideration in their ideal career. What perc

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3 years ago

What are the values a, b, and c in the following quadratic equation?<br><br> −6x = −8x2 − 13

lesya692 [45]

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

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 8.0 ounces and a standard deviation of 1.1 ounces.

This means that $\mu = 8, \sigma = 1.1$

(a) If 5 potatoes are randomly selected, find the probability that the mean weight is less than 9.3 ounces?

$n = 5$ means that $s = \frac{1.1}{\sqrt{5}} = 0.4919$

This probability is the pvalue of Z when X = 9.3. So

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

By the Central Limit Theorem

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

$Z = \frac{9.3 - 8}{0.4919}$

$Z = 2.64$

$Z = 2.64$ has a pvalue of 0.9959

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

(b) If 6 potatoes are randomly selected, find the probability that the mean weight is more than 9.0 ounces?

$n = 6$ means that $s = \frac{1.1}{\sqrt{6}} = 0.4491$

This probability is 1 subtracted by the pvalue of Z when X = 9. So

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

$Z = \frac{9 - 8}{0.4491}$

$Z = 2.23$

$Z = 2.23$ has a pvalue of 0.9871

1 - 0.9871 = 0.0129

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

8 0

3 years ago

BRAINLIESTT ASAP! PLEASE HELP ME :)

Lubov Fominskaja [6]

Answer: $\sqrt{37}$

=====================================

Work Shown:

6x-y = -3 is the same as 6x-y+3 = 0

6x-y+3 = 0 is the form Ax+By+C = 0 with A = 6, B = -1, C = 3.

The distance d that line is from the point (p,q) = (6, 2) is found by the following

$d = \frac{A*p+B*q+C}{\sqrt{A^2+B^2}}\\\\d = \frac{6*6-1*2+3}{\sqrt{6^2+(-1)^2}}\\\\d = \frac{36-2+3}{\sqrt{36+1}}\\\\d = \frac{37}{\sqrt{37}}\\\\d = \frac{37\sqrt{37}}{37}\\\\d = \sqrt{37}\\\\d \approx 6.08276\\\\$

7 0

3 years ago