Answer:
y = -1/10x^2 -1/2
Step-by-step explanation:
The equation for a parabola with focus (a, b) and directrix y = d is ...
y = 1/(2(b -d))(x -a)² +(b +d)/2
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For the given focus and directrix, we have ...
- a = 0
- b = -3
- d = 2
- y = 1/(2(-3-2))(x -0)² +(-3+2)/2
Simplified, the equation is ...
y = -1/10x² -1/2
Answer:
8 hours
Step-by-step explanation:
If two people shovel at the same rate, they can do the job in half the time.
We have ...
(Dad) + (Mom + Isabel) ⇒ 2 hours . . . . half as long as Dad alone
Dad ⇒ 4 hours
This tells us that ...
(Mom +Isabel) = 4 hours
We know that ...
Isabel ⇒ 2×4 hours = 8 hours . . . . twice as long as Mom + Isabel
So, we conclude ...
Mom ⇒ 8 hours
It would take Mom 8 hours to shovel the driveway herself.
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<em>Additional comment</em>
The rates add when expressed as driveways per hour.
total = Dad + Mom + Isabel
1/2 = 1/4 + 1/m + 1/(2·4)
1/m = 4/8 -3/8 = 1/8
m = 8 . . . . . it takes Mom 8 hours by herself.
3/4x - 11
first calculate the sum
3/4x - 8 - 3
then calculate the difference
3/4x - 11
Answer:
“The average is 24 ounces”
Step-by-step explanation:
The null hypothesis is always a statement that is already established and we consider true, until it emerges a situation that makes us doubt about the truthfulness of that established fact.
<em>The null is very often an average or mean, but not necessarily.
</em>
In this case, as the established fact is that the boxes are filled with an average weight of 24 ounces, the null hypothesis is “The average is 24 ounces”
A rectangle with area of 12 square units would have sides of length 4 units and 3 units. Area would therefore be 4 x 5.
<h3>What are the side lengths of this rectangle?</h3><h3 />
A rectangle must be such that one side is longer than the other side.
The area of a rectangle is found as:
= Length x Width
As the area is 12, the length and width have to be numbers that when multiplied, will give you 12.
The factors of 12 which allow this to happen are:
= 1, 2, 3, 4, 6, 12
From here you can use 3 and 4.
Find out more on the area of a rectangle at brainly.com/question/2607596.