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
Elenna [48]
3 years ago
8

The parabola y=x^2 is shifted up by 4 units , what is the equation of the new parabola

Mathematics
1 answer:
Gekata [30.6K]3 years ago
5 0

Answer:

y= (x^2)+4

Step-by-step explanation:

If outside of the parentheses, the function can move up or down. So, by adding 4 to the function/parabola, you shift the equation up by 4 units.

You might be interested in
Write the equation of a circle with a center at (2.5, –3.5) and a diameter of 12.
Paul [167]

Answer:

second option

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Here diameter = 12, thus radius = 12 ÷ 2 = 6 and (h, k) = (2.5, - 3.5), thus

(x - 2.5)² + (y - (- 3.5))² = 6², that is

(x - 2.5)² + (y + 3.5)² = 36 ← equation of circle

3 0
3 years ago
A cash box of $1 and $5 bills is worth $45. The number of $1 bills is three more than the number of $5 bills. How many of each b
Softa [21]

Answer:

  • 7 $5 bills
  • 10 $1 bills

Step-by-step explanation:

If we take out the extra $3, we can group the bills into one each of $5 and $1, for a value of $6. There will be 7 such groups in the remaining $42.

That means there are 7 bills of the $5 denomination, and 3 more than that (10 bills) of the $1 denomination.

There are 7 $5 bills and 10 $1 bills.

_____

If you want to write an equation, it is usually best to let a variable stand for the most-valuable contributor. Here, we can let x represent then number of $5 bills. Then the value of the cash box is ...

  5x +(x+3) = 45

  6x = 42 . . . . . . . . subtract 3, collect terms

  x = 7 . . . . . . . . . . . there are 7 $5 bills

  x+3 = 10 . . . . . . . . there are 10 $1 bills

You may notice that this working parallels the verbal description above. (After we subtract $3, x is the number of $6 groups.)

6 0
3 years ago
A high school will graduate 100 students. of these, 52 students plan to attend college.
marishachu [46]
A total of 48 students will not go to college
8 0
3 years ago
Part A: Billy rented a canoe at $14 for 2 hours. If he rents the same canoe for 5 hours, he has to pay a total rent of $29. Writ
zepelin [54]

Part A)

So we need the graph to pass through these points:

time = 2 and price=$14 -> (2,14)

time= 5 and price = $29 -> (5,29)

Standard form:

Ax+By = C

Let’s replace the points:

A*2+B*14=C

A*5+B*29=C

Let’s eliminate variables:

(A*2+B*14)-(A*5+B*29)=C-C

A*2+B*14-A*5-B*29=0

-3A-15B=0

-3A=15B

A=15B/-3

A=-5B

There are several numbers that verify this proportion. For example, if B=1, A=-5 (you can try others, there is not only 1 correct answer).

So we can make this equation:

-5x+y=C

Then we can calculate C using one point:

-5*2+14=C

-10+14=C

4=C

So one of the possible equations is: -5x+y=4

(Remember there are multiple correct answers for this item)

You can verify it with the other point:

-5*5+29=-25+29=4 ->OK

 

Part B)

Whatever you have found in Part A, you will find the same in Part B when you convert it to function notation. All you have to do is clear y:

-5x+y=4

y=4+5x

So the equation is: f(x)=4+5x


Part C)

First of all, you have to find f(0)

f(x)=4+5x

f(0) =4+5*0=4+0=0

f(0) is ALWAYS the constant not multiplied by x.

So you know it has to cross the y axes in y=4

Now let’s put 0 as y-value:

4+5x=0

5x=0-4=-4

x=-4/5

So now you know it has to cross the x axes in x=-4/5.

So you can put those intersections in the graph and you draw the line through those points. Labels: horizontal axes is x, and in this case represents time; vertical axes is y, and in this case represents price.

Remember there are other methods, too :)

5 0
3 years ago
Write the quotient as a mixed number.<br> 63 divided by 5 = 12 R3
Whitepunk [10]
12 1/4 because the original answer is 12 3/12 but you should simplify it to 12 1/4.
6 0
3 years ago
Other questions:
  • The diagram shows rectangle ABCD on a pair of aces. The lengths of its sides are 20 units and 5 units. The coordinates of point
    8·1 answer
  • The radius of a semicircle is 4 millimeters. What is the semicircle's diameter?
    12·2 answers
  • Please helpppp it has to do with P(A U B)
    5·1 answer
  • What are they asking me?
    5·1 answer
  • Divide 32 in ratio of 3:7
    13·1 answer
  • Which attribute is true of one of the shapes but not of both?
    11·1 answer
  • Special Triangles
    14·1 answer
  • Correct answers only! 20 points and brainliest to the correct answer!
    9·1 answer
  • The pair of 13 and 64 are co prime are true or flase​
    11·1 answer
  • Offering brainliest!!! Find the Volume of each cylinder pictured below. Use 3.14 for π and round to the nearest tenth:
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!