The formula for determining the distance of the focus from the vertex is as follows,
f = x² / 4a
where f is focus, x is the radius (half the value of diameter), and a is the depth. Substituting the known values to the given equation,
f = (30/2 mm)² / (4)(5 mm)
f = 11.25 mm
<em>ANSWER: 11.25 mm</em>
Answer: THE GRAPH IS ATTACHED.
Step-by-step explanation:
We know that the lines are:

Solving for "y" from the first line, we get:

In order to graph them, we can find the x-intercepts and the y-intercepts.
For the line
the x-intercepts is:

And the y-intercept is:

For the line
the x-intercepts is:

And the y-intercept is:

Now we can graph both lines, as you can observe in the image attached (The symbols
and
indicates that the lines must be dashed).
By definition, the solution is the intersection region of all the solutions in the system of inequalities.
Answer:
<h2>25.5 cm</h2>
Step-by-step explanation:
<h3>

</h3>

Answer:
<em>The plant grew </em>
<em> inches</em>
Step-by-step explanation:
<u>Operations with Fractions</u>
Felipe planted seeds for a science project. One of the plants grew 6 2/7 inches in the first week and 5 11/14 inches in the second week.
We are required to find the total growth during the two weeks. We have to find the sum of:

Let's convert both fractions to improper form:

Adding the integers:

Now we find the LCM of 7 and 14 is 14, thus:




Rewriting as a mixed number:
The plant grew
inches
Answer:
Subtraction property ; x = 3.25
Division property ; - 6
multiplication property ; - 125
Addition property ; 13
Step-by-step explanation:
A.)
x + 3.75 = 7
Using the subtraction property : subtract 3.75 from both sides
x + 3.75 - 3.75 = 7 - 3.75
x = 3.25
B. )
–3b = 18
According to the division property :
Divide both sides by - 3
-3b / - 3 = 18 / - 3
b = - 6
C.)
m/5 = - 25
Using the multiplication property :
m/5 * 5 = - 25 * 5
m = - 125
D.)
m – 4 = 9
Using the addition property :
Add 4 to both sides :
m - 4 + 4 = 9 + 4
m = 13