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3 years ago

Solve the inequality

Mathematics

1 answer:

fredd [130]3 years ago

7 0

Answer:

x^2-6x+x-6

X(x-6)+(x-6)

(x-6)(X+1)

X=6 or X= -1

6<0

-1<0✓

so the answer is X=(-1)

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Describe the sequence of transformations from quadrilateral ABCD to A'B'C'D A: -8,8 B: 8,-2 C: 4,-8 D: 4,-2 A': 2,-10 B': 8,-10

butalik [34]

Answers:

See below

Step-by-step explanation:

First transformation

Reflection about the line y = 6.

This inter-converted Points A and C and Points B and D.

The coordinate transformations were (Fig. 1):

A: (-8, 8) ⟶ (-8, 4)

B: (-2, 8) ⟶ (-2, 4)

C: (-8, 4) ⟶ (-8, 8)

D: (-2, 4) ⟶ (-2, 8)

Second transformation

Translation 10 units to the right and 14 units down.

The coordinate transformations were (Fig. 2):

A: (-8, 4) ⟶ (2, -10)

B: (-2, 4) ⟶ (8, -10)

C: (-8, 8) ⟶ (2, -6)

D: (-2, 8) ⟶ (8, -6)

The transformations were:

Reflection about the line y = 6
Translation 10 units to the right and 14 units down

3 0

3 years ago

Find the equation of the line that is parallel to the line y=-7x+2 and passes through (-6,-3)

vodka [1.7K]

Answer: y=-7x-45

Explanation: Two parallel lines have the same slope, so that means the slope of the line would be -7. When you add that value to your equation, that would give you: y=-7x+b. Now that you have the slope, the only other value you’re missing is b. To find the value of b, you can substitute any point into the equation that’s on the line and solve for b:

-3=-7(-6)+b
-3=42+b
b=-45

Now that you have the value of b, substitute it into the final equation:

y=-7x-45

Hope this helps シ

4 0

3 years ago

Ask Your Teacher The level of nitrogen oxides (NOX) in the exhaust after 50,000 miles or fewer of driving of cars of a particula

Georgia [21]

Answer:

The level is L = 0.084

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 normally distributed samples 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 sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 0.08, \sigma = 0.01, n = 36, s = \frac{0.01}{\sqrt{36}} = 0.0017$

What is the level L such that the probability that the average NOX level x for the fleet is greater than L is only 0.01?

This is X when Z has a pvalue of 1-0.01 = 0.99. So it is X when Z = 2.325.

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

By the Central limit theorem

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

$2.325 = \frac{X - 0.08}{0.0017}$

$X - 0.08 = 2.325*0.0017$

$X = 0.084$

The level is L = 0.084

4 0

4 years ago

A triangle has one side that measures 1 foot and another side that measures 20 inches. What are possible lengths of the third si

klio [65]

Answer:

The correct options for the possible lengths of the third side are;

13 inches

28 inches

Step-by-step explanation:

The given lengths of two sides of the triangle are;

The length of one side of the triangle = 1 foot = 12 inches

The length of the other side of the triangle = 20 inches

The question can be solved by the triangle inequality theorem as follows;

A + B > C

B + C > A

A + C > B

Let the given sides be A = 12 inches and B = 20 inches

We have;

12 + 20 = 32 > C

Therefore, by the triangle inequality theorem, the third side, 'C', is less than 32 inches

Similarly, when C = 6 inches, we have;

A + C = 12 + 6 = 18 < B = 20

Therefore, the third side cannot be 6 inches

when C = 13 inches, we have;

A + C = 12 + 13 = 25 > B = 20

Therefore, the third side can be 13 inches

when C = 28 inches, we have;

A + C = 12 + 28 = 30 > B = 20

Therefore, the third side can be 28 inches

4 0

3 years ago

A recipe calls for one cup of juice concentrate for 4 cups of water. How many cups of concentrate are needed if 1 cup of water i

Mekhanik [1.2K]

Answer:

1/4 cups of juice

Step-by-step explanation:

1 cup of juice --- 4 cups of water

x cups of juice --- 1 cup of water

1/x = 4/1

1/x = 4

x = 1/4

3 0

3 years ago