Suppose △PKN≅△BGH. Which other congruency statements are correct?

The rule for Function A is y= -2/3x

Rom4ik [11]

Answer:

Both functions have negative rates of change

Function B has a greater rate of change than Function A

Step-by-step explanation:

we know that

Function A

The rule for Function A is

$y=-\frac{2}{3}x$

This is the equation of a proportional relationship (the line passes through the origin)

The slope is equal to $m=-\frac{2}{3}$

Function B

Find the equation of the function B

we have the points (-2,0) and (0,-2)

Find the slope

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the values

$m=\frac{-2-0}{0+2}$

$m=\frac{-2}{2}$

$m=-1$

The equation of the function B in slope intercept form is equal to

$y=mx+b$

we have

$m=-1\\b=-2$

substitute

$y=-x-2$

Verify each statement

Option 1) Both functions have negative rates of change

The statement is true

Because, the rate of change is the slope of the linear equation

Function A ----> $m=-\frac{2}{3}$

Function B ----> $m=-1$

Option 2) Both functions have the same rate of change.

The statement is false (see the explanation)

The rate of change are different ( m=-2/3 and m=-1)

Option 3) When graphed, Function A and Function B are parallel

The statement is false

When graphed, Function A and Function B are intersecting lines, because their slopes are different

Option 4) Function B has a greater rate of change than Function A

The statement is true

Remember that the rate of change can be either positive (increasing function) or negative (decreasing function). To find out which function has a greater rate of change, compare the absolute value of their slopes

therefore

1 > 2/3

6 0

3 years ago

You drive 150 miles in 3 hours before stopping for 30 minutes to have lunch and gas. After lunch you travel 100 miles in an hou

KiRa [710]

Average speed = total miles driven / total driving time
average speed = (150 + 100) / (3 + 1 1/2) =
250 / (4 1/2) =
250 / (9/2) =
250 * 2/9 =
500 / 9 = 55.55 mph

7 0

3 years ago

Help me with this please

bekas [8.4K]

Answer:

f(-5) = 4(-5) + 1 = -20 + 1 = -19

f(-1) = 4(-1) + 1 = -4 + 1 = -3

f(2) = 4(2) + 1 = 8 + 1 = 9

f(3) = 4(3) + 1 = 12 + 1 = 13

f(5) = 4(5) + 1 = 20 + 1 = 21

7 0

2 years ago

There are two machines available for cutting corks intended for use in wine bottles. The first produces corks with diameters tha

uranmaximum [27]

Answer:

0.6826 = 68.26% probability that the first machine produces an acceptable cork.

0.933 = 93.3% probability that the second machine produces an acceptable cork.

The second machine is more likely to produce an acceptable cork.

Step-by-step explanation:

When the distribution is normal, we use 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.

What is the probability that the first machine produces an acceptable cork?

The first produces corks with diameters that are normally distributed with mean 3 cm and standard deviation 0.10 cm, which means that $\mu = 3, \sigma = 0.1$