Plug y=-5 into the equation
6x+8(-5)=-22
6x-40=-22
6x=-22+40
6x=18
x=3
Let's call the two numbers
and
.
Given these variables, we can say:
, based on the first sentence in the problem.
Also, remember that the reciprocal of a number is simply 1 divided by the number. Thus, we can say that:

To solve, we can simply substitute
in for
in the second equation and solve.


- Get terms on the left side to a common denominator for easier addition


- Cross multiplication (
)


- Subtract
from both sides of the equation

- Factor left side of the equation

Now, notice that we have found two solutions, but the problem is only asking for one. This <em>likely </em>means that one of our solutions is extraneous. Let's take a look. Remember that the smaller positive number is equal to 14 less than the larger number. However,
,
Since
is not positive in this case,
is not a solution.
Thus,
is our only solution. In this case,
,
which means that the smaller number is 14 and the larger number is 28.
Answer:
59 to 66
Step-by-step explanation:
Mean test scores = u = 74.2
Standard Deviation =
= 9.6
According to the given data, following is the range of grades:
Grade A: 85% to 100%
Grade B: 55% to 85%
Grade C: 19% to 55%
Grade D: 6% to 19%
Grade F: 0% to 6%
So, the grade D will be given to the students from 6% to 19% scores. We can convert these percentages to numerical limits using the z scores. First we need to to identify the corresponding z scores of these limits.
6% to 19% in decimal form would be 0.06 to 0.19. Corresponding z score for 0.06 is -1.56 and that for 0.19 is -0.88 (From the z table)
The formula for z score is:

For z = -1.56, we get:

For z = -0.88, we get:

Therefore, a numerical limits for a D grade would be from 59 to 66 (rounded to nearest whole numbers)
Answer:
The volume of P is <u>1728 cubic yards.</u>
<u></u>
Step-by-step explanation:
For similar shapes, the ratio of volumes are defined as:
= 
where h1 and h2 are the heights of each pyramid respectively.
We know that the scale factor of P to Q is 6:1 i.e. the ratio of heights is also 6:1. And the volume of Q is given as 8 cubic yards. so, using the relation defined above we can write:
= 
= 
Vp = 6³ * 8
= 216 * 8
Vp = 1728 cubic yards
The volume of P is <u>1728 cubic yards.</u>
Answer:
Hello! I am a Percy Jackson fan.
60,000
Step-by-step explanation:
This is because 435000 + 55000 = 490000.
Then, subtract that from 550000.