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Elodia [21]
3 years ago
5

8. A dolphin in an aquarium is 12 feet long. A scale model

Mathematics
1 answer:
Nadusha1986 [10]3 years ago
8 0

41.14  or 3.5inches over 144inches

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Which statements are true about the graph of the function f(x) = x2 – 8x + 5? Check all that apply.
statuscvo [17]

Answer:

A, D, E are true

Step-by-step explanation:

You have to complete the square to prove A.  Do this by first setting the function equal to 0, then moving the 5 to the other side.

x^2-8x=-5

Now we can complete the square.  Take half the linear term, square it, and add it to both sides.  Our linear term is 8 (from the -8x).  Half of 8 is 4, and 4 squared is 16.  So we add 16 to both sides.

(x^2-8x+16)=-5+16

We will do the addition on the right, no big deal.  On the left, however, what we have done in the process of completing the square is to create a perfect square binomial, which gives us the h coordinate of the vertex.  We will rewrite with that perfect square on the left and the addition done on the right,

(x-4)^2=11

Now we will move the 11 back over, which gives us the k coordinate of the vertex.

(x-4)^2-11=y

From this you can see that A is correct.

Also we can see that the vertex of this parabola is (4, -11), which is why B is NOT correct.

The axis of symmetry is also found in the h value.  This is, by definition, a positive x-squared parabola (opens upwards), so its axis of symmetry will be an "x = " equation.  In the case of this type of parabola, that "x = " will always be equal to the h value.  So the axis of symmetry is

x = 4, which is why C is NOT correct, either.

We can find the y-intercept of the function by going back to the standard form of the parabola (NOT the vertex form we found by completing the square) and sub in a 0 for x.  When we do that, and then solve for y, we find that when x = 0, y = 5.  So the y-intercept is (0, 5).

From this you can see that D is also correct.

To determine if the parabola has real solutions (meaning it will go through the x-axis twice), you can plug it into the quadratic formula to find these values of x.  I just plugged the formula into my graphing calculator and graphed it to see that it did, indeed, go through the x-axis twice.  Just so you know, the values of x where the function go through are (.6833752, 0) and (7.3166248, 0).  That's why you need the quadratic formula to find these values.

7 0
3 years ago
The sum of, half of a number and double the number is 20. Find the number.​
LiRa [457]

Answer:

The number is 8.

Step-by-step explanation:

Rewrite the word problem as an equation.

The sum of (we will be adding.), half of a number (we can use x, this will be written as x/2.) and double the number (this will be written as 2x) is 20.

To find the number, solve the equation.

x/2 + 2x = 20

Multiply both sides by 2.

x + 4x = 40

Combine terms.

5x = 40

Divide both sides.

x = 8.

8 0
2 years ago
Read 2 more answers
Show that the function of f(x) = a - x is its own inverse for all real numbers a
tatuchka [14]

f(x) = a - x

y = a - x

y + x = a - x + x

y + x = a

y + x - y = a - y

x = a - y

f-¹(x) = a - x

5 0
3 years ago
Simplify: 2(4x + 8)<br> (X)<br> /h<br> X<br> X
jasenka [17]

Answer:

x = -2

Step-by-step explanation:

2(4x+8)

= 8x+16

8x+16 = 0

-16 -16

8x = -16 (do -16÷8 & get)

x = -2

8 0
3 years ago
a cylinder has a height of 9 cm and a radius of 15 cm what is the exact volume A( 225 pi B( 405 pi C(675 pi D( 90 pi
egoroff_w [7]
The answer is for this question would obviously be D.
7 0
3 years ago
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