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Orlov [11]
3 years ago
7

Which equations represent the line that is parallel to 3x − 4y = 7 and passes through the point (−4, −2)? Check all that apply.

Mathematics
1 answer:
jonny [76]3 years ago
8 0
First, we find the slope of the given line.

<span>3x − 4y = 7

-4y = -3x + 7

y = (3/4)x - 7/4

The slope of the given line is 3/4.
The slope of the parallel line is also 3/4.

Now we need the equation of the line that has slope 3/4 and passes through point (-4, -2),

We use the point-slope form of the equation of a line.

y - y1 = m(x - x1)

y - (-2) = (3/4)(x - (-4))

y + 2 = (3/4)(x + 4)     <---- check option E. Is the fraction 3/4 not there?

y + 2 = (3/4)x + 3

y = (3/4)x + 1

4y = 3x + 4

3x - 4y = -4    <------ this is choice B.
</span>
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moana openes a savings account that has an annual simple interest rate of 4.5% if she open the account with $2300 how much will
Jlenok [28]
She will have $621 in interest and $2921 total.

2300 x 4.5% x 6 (or i=prt formula) then add 2300 to 621 to get your answer.
3 0
3 years ago
The fracture strength of tempered glass averages 14 (measured in thousands of pounds per square inch) and has standard deviation
Wewaii [24]

Answer:

0.1587 = 15.87% probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.2.

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 z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes 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.

The fracture strength of tempered glass averages 14 (measured in thousands of pounds per square inch) and has standard deviation 2.

This means that \mu = 14, \sigma = 2

Sample of 100:

This means that n = 100, s = \frac{2}{\sqrt{100}} = 0.2

What is the probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.2?

This is 1 subtracted by the p-value of Z when X = 14.2. So

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

By the Central Limit Theorem

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

Z = \frac{14.2 - 14}{0.2}

Z = 1

Z = 1 has a p-value of 0.8413.

1 - 0.8413 = 0.1587

0.1587 = 15.87% probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.2.

6 0
3 years ago
GIVING BRAINLIEST TO PERSON AHO ANSWERS FIRST!!
zavuch27 [327]
Please refer to the photograph attached for the answer
Hope you find the answers correct
Sorry you will find it really small please zoom in to see the answer to this question
Sorry for the inconvenience about the small answers

4 0
2 years ago
Consider the following equation. 9x2 − y2 = 6 (a) Find y' by implicit differentiation. y' = (b) Solve the equation explicitly fo
qaws [65]

Answer:

Step-by-step explanation:

Given is an equation in x and y as

9x^2 - y^2 = 6

We use implicit method to differentiate the above equation

18x-2yy'=0

y' = 9x/y

b) to solve the equation explicitly for y and differentiate to get y' in terms of x. y' = ±

We separate the variables as

yy' =9x\\\frac{y^2}{2} =\frac{9x^2}{2} +C\\y^2 =9x^2+2C

Take square root

y=\sqrt{9x^2+2C} \\y=-\sqrt{9x^2+2C}

6 0
3 years ago
What is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (2,
vekshin1

Answer:

all work is shown and pictured

7 0
3 years ago
Read 2 more answers
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