1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
schepotkina [342]
3 years ago
9

Which translation for: y = (x+3)^2+4 If you can't see the picture zoom in.

Mathematics
1 answer:
Savatey [412]3 years ago
5 0

Answer:

The answer is B.

Step-by-step explanation:

The original graph of y = x^2 has a vertex at (0,0)

The formula for graph translations is y = (x-#)^2+#

The number inside the parentheses is a horizontal translation.

So, we are given y = (x-(-3))^2+#

The vertex of the graph moves 3 points left, since the number is negative (-3).

The number at the end of the equation is a vertical translation.

So, we are given y = (x+3)^2+4

The vertex of the graph moves 4 points up, since the number is positive (4).

The new vertex is at (-3,4)

You might be interested in
A truncated cone has horizontal bases with radii 18 and 2. A sphere is tangent to the top, bottom, and lateral surface of the tr
MariettaO [177]
<h3>Answer:  6 units</h3>

===================================================

Explanation:

A truncated cone is where we start with a regular 3D cone and chop off the top. The portion up top is a smaller cone, which we'll ignore. The bottom part is the truncated cone portion.

In the real world, a lampshade is one example of a truncated cone.

----------------

Let x be the radius of the sphere.

We'll be focusing on a vertical cross section of the truncated cone. Refer to figure 1 in the diagram below.

We have the following points

  • A = center of the sphere
  • B = center of the circular base of the truncated cone
  • C = point 18 units to the right of point B
  • E = point directly above point A, and its the center of the circular top of the truncated cone
  • D = point 2 units to the right of point E
  • F = the location where the circle touches the slanted curved side of the truncated cone
  • G = point directly below point D, and located on segment BC

We'll connect a few of those points forming the dashed lines in figure 1.

To start off, draw a segment from D to G. This forms rectangle BGDE with sides of EB = 2x and BG = 2. The side BC is 18 units, so that must mean GC = BC - BG = 18 - 2 = 16.

Since EB = 2x, this means DG is also 2x.

------------------

Now focus on triangles ABC and AFC. They are congruent right triangles. We can prove this using the HL (hypotenuse leg) theorem. Recall that the radius of a circle is perpendicular to the tangent line, which is why angle AFC is 90 degrees. Angle ABC is a similar story.

Because they are congruent right triangles, this indicates side BC is the same length as side FC. Therefore, FC = 18

Through similar logic, triangles ADE and ADF are congruent as well which leads to ED = FD = 2.

Combine sides FD and FC to get the length of DC

DC = FD+FC = 2+18 = 20

This is the hypotenuse of the right triangle GCD

------------------

After all that, we have the right triangle GCD with the legs of 2x and 16. The hypotenuse is 20. Refer to figure 2 shown below.

As you can probably guess, we'll use the pythagorean theorem to find the value of x.

a^2 + b^2 = c^2

(DG)^2 + (GC)^2 = (CD)^2

(2x)^2 + (16)^2 = (20)^2

4x^2 + 256 = 400

4x^2 = 400-256

4x^2 = 144

x^2 = 144/4

x^2 = 36

x = sqrt(36)

x = 6 is the radius of the sphere.

7 0
2 years ago
3/4 c - 7/12 + 7/24 c + 2/3 - 1/6 c
CaHeK987 [17]

Answer:

c+1/12

Step-by-step explanation:

18/24c-7/12+7/24c+8/12-4/24c=c+1/12

8 0
2 years ago
Read 2 more answers
50 POINTS!!!!
tatiyna

Answer:

90 cubic inches

Step-by-step explanation:

V = 1/3 · area of base · height

V = 1/3 · 18 · 15

V = 6 · 15

V = 90

6 0
3 years ago
-3x - 6 = 2x - 14x - 6
Harman [31]

Answer:

x=0

Step-by-step explanation:

3 0
3 years ago
Determine the value of each variable in the figure below. Keep answers in simplest<br> radical form.
Tanzania [10]

Answer:

  a = 21

  b = 63

  c = 42√3

  d = 21√3

Step-by-step explanation:

The sides of a 30°-60°-90° triangle have the ratios 1 : √3 : 2. The given side (42) is the longest side of the smallest triangle, and the shortest side of the largest triangle.

That means the other sides of the smallest triangle will be ...

  a = 42/2 = 21

  a+b = 2(42) = 84

  b = (a+b) -a = 84 -21 = 63

  d = 21√3 . . . . middle-length side of the smallest triangle

  c = 42√3 . . . . middle-length side of the largest triangle

The values of the variables are ...

  • a = 21
  • b = 63
  • c = 42√3
  • d = 21√3

7 0
2 years ago
Other questions:
  • The quotient of a number and -7 decreased by2 is 10
    7·1 answer
  • NEED THE HELP PLEAASE !!!
    14·2 answers
  • Help asap<br> show work<br> i will make u brainlest.
    9·1 answer
  • What percent of 137.4 is 96
    5·1 answer
  • Find x, y and z. <br><br> A. B. C. Or D.
    7·2 answers
  • Solve the system of linear equations by substitution
    7·1 answer
  • Lesson 6.4 areal world problem:percent
    14·1 answer
  • After scoring a touchdown, a football team may elect to attempt a two-point conversion, by running or passing the ball into the
    13·1 answer
  • Help please this is for geometry. its easy.
    10·2 answers
  • A bike trail is 5 1/10 long.Jade rides 1/4 of the trail before stopping for a water break. How many miles does jade ride before
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!