The answer and how you got it

What is the equation of a line that passes through the point (5, −4) and is parallel to the line whose equation is 2x + 5y = 10?

dybincka [34]

What you should do first is simplify the equation into the y = mx + b format. Move 2x to the other side. Know that in doing this, 2x must become the opposite of what it currently is (-2) in order for the equation to remain true. We also have to take away the '10' because the line is parallel, not exactly the same, which means a different y intercept. This looks like:

$5y = -2x + b$

Next, simplify y to make things easier. This can be done by dividing both sides by 5, like so:

$\frac{5}{5}y = -\frac{2}{5}x + b$

What you should also know is that if a line is parallel to another, then this means the slope has to be the same because they both have the same changes in rise and run. With this in mind, simply plug in the x and y values.

$(-4) = -\frac{2}{5} * (5) + b$

$--> -4 = \frac{10}{5} + b$

$---> -4 = -2 + b$

Add 2 to both sides to isolate b.

$-4 + 2 = b$

Which means that -2 = b.

Now that we have the y intercept, we can write the equation of the line, which is $y = -\frac{2}{5}x - 2$ .

Hope this was helpful.

3 0

3 years ago

(p^2-7pq-q^2)+(-3p^2-2pq+7q^2)<br><br>

Alex Ar [27]

Answer:

-2p² - 9pq + 6q²

Step-by-step explanation:

Add the like terms

p² + - 3p² = -2p²

-7pq + - 2pq = -9pq

-q² + 7q² = 6q²

6 0

2 years ago

-8y-2(5y+9)<br> can yall help me!!!!!!!!!!!!<br> it is 10 points

My name is Ann [436]

Answer:

-18y - 18

Step-by-step explanation:

The -2 needs to be distributed into both values in the parenthesis. This will make the equation -8y - 10y - 18. Then, you put the like terms together. This will result in the final equation, -18y - 18

5 0

2 years ago

The mean life of a television set is 119119 months with a standard deviation of 1414 months. If a sample of 7474 televisions is

Pepsi [2]

Answer:

0.5034 = 50.34% probability that the sample mean would differ from the true mean by less than 1.1 months

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 random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sample means with size n of at least 30 can be approximated to a normal distribution with mean

In this problem, we have that:

$\mu = 119, \sigma = 14, n = 74, s = \frac{14}{\sqrt{74}} = 1.6275$