All categories

3 years ago

A parabola can be drawn given a focus of (−4,−10) and a directrix of y=−4. What can be said about the parabola?

Mathematics

1 answer:

ANEK [815]3 years ago

6 0

Answer:

The answer to your question is: Yes a parabola can be drawn if we know the focus and the directrix.

Step-by-step explanation:

We can say that it is a vertical parabola that opens downwards.

We conclude that if we graph both the focus and the directrix. Also if we continue the process we can find the vertex (-4, -7) and p = 3.

You might be interested in

What is the value of y?

mrs_skeptik [129]

Ok so you would start by getting rid of the fraction. You should know the steps for that by now but here this is what it would look like
3y/4+10=2y/4 Simplify
3y/4+10=1y/2
10=-1y
I really simplified the last part but this is what it looks like: $\frac{2y}{4}$ - $\frac{3y}{4}$ = -1y
10=-1y
y=-10

8 0

3 years ago

Read 2 more answers

Use the function shown in the table to answer the questions below .

Lubov Fominskaja [6]

Answer:

a) -6

b) 3

c) Y = -6x + 3

Step-by-step explanation:

Pick two points and find rise/run = slope

rise y1 - y2 = 9 - 3 = 6

run x1 - x2 = -1 - 0 = -1

slope = 6 / -1 = -6

The y intercept is where x = 0 which is given in the table (0,3) so

y intercept = 3

Point slope form is y = mx + b , so

y = -6x + 3

7 0

3 years ago

Brainliest to the correct answer :)

frozen [14]

Answer:

Assume that the formula is true for the (k+1)term

Step-by-step explanation:

I learned this in class a couple weeks ago in intermediate algebra

7 0

2 years ago

Find the circumference of the circle. Then, find the length of each bolded arc. Use appropriate notation

Vaselesa [24]

Answer:

$\text{1) }\\\text{Circumference: }24\pi \text{ m}},\\\text{Length of bolded arc: }18\pi \text{ m}\\\\\text{3)}\\\text{Circumference. }4\pi \text{ mi},\\\text{Length of bolded arc: } \frac{3\pi}{2}\text{ mi}$

Step-by-step explanation:

The circumference of a circle with radius $r$ is given by $C=2\pi r$ . The length of an arc is makes up part of this circumference, and is directly proportion to the central angle of the arc. Since there are 360 degrees in a circle, the length of an arc with central angle $\theta^{\circ}$ is equal to $2\pi r\cdot \frac{\theta}{360}$ .

Formulas at a glance:

Circumference of a circle with radius $r$ : $C=2\pi r$
Length of an arc with central angle $\theta^{\circ}$ : $\ell_{arc}=2\pi r\cdot \frac{\theta}{360}$

<u>Question 1:</u>

The radius of the circle is 12 m. Therefore, the circumference is:

$C=2\pi r,\\C=2(\pi)(12)=\boxed{24\pi\text{ m}}$

The measure of the central angle of the bolded arc is 270 degrees. Therefore, the measure of the bolded arc is equal to:

$\ell_{arc}=24\pi \cdot \frac{270}{360},\\\\\ell_{arc}=24\pi \cdot \frac{3}{4},\\\\\ell_{arc}=\boxed{18\pi\text{ m}}$

<u>Question 2:</u>

In the circle shown, the radius is marked as 2 miles. Substituting $r=2$ into our circumference formula, we get:

$C=2(\pi)(2),\\C=\boxed{4\pi\text{ mi}}$

The measure of the central angle of the bolded arc is 135 degrees. Its length must then be:

$\ell_{arc}=4\pi \cdot \frac{135}{360},\\\ell_{arc}=1.5\pi=\boxed{\frac{3\pi}{2}\text{ mi}}$

8 0

3 years ago

Simplify the expression. Write the answer in scientific notation (7x10-6) (3x10-2

shtirl [24]

Answer:

21 X 10^-8 is the correct answer

Step-by-step explanation:

(7X3) X 10^(-6-2)

21 X 10^ -8

4 0

3 years ago