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morpeh [17]
3 years ago
14

In two or more complete sentences, compare the number of x-intercepts in the graph of f(x) =x2 to the number of x-intercepts in

the graph of g(x) = x2 +2. Be sure to include the transformations that occurred between the parent function f(x) and its image g(x).
Mathematics
1 answer:
Natalija [7]3 years ago
7 0
Important:  Please use " ^ " to indicate exponentiation:

<span>"f(x) =x^2 to the number of x-intercepts in the graph of g(x) = x^2 +2."

Notes:  the graph of f(x) = x^2 is a vertical parabola that opens up.  It has its vertex at (0,0).  This is the only point at which f(x)=x^2 has a horiz. intercept.

g(x) = x^2 + 2 has a graph that looks the same as that of f(x) = x^2, EXCEPT that the whole graph is moved 2 units UP.  This new graph never touches or intersects the x-axis.  Therefore, g(x) has NO horiz. intercepts (no x-int.).

</span>
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How do you factor 125-x^3?
xz_007 [3.2K]

Step-by-step explanation:

We have

125 - x {}^{3}

First, 125 is a perfect cube because

5 \times 5 \times 5 = 125

and

x^3 is a perfect cube because

x \times  x \times x = x {}^{3}

so we can use the difference of cubes identity

( {x}^{3}  -  {y}^{3} ) = (x - y)( {x}^{2}  + xy +  {y}^{2} )

Let say we have two perfect cubes:

64 because 8×8×8=64

and 27 because 3×3×3=27 and let subtract

64 - 27

we know that

64 - 27 = 37

but using the difference of cubes identity we should get the same thing.

Remeber cube root of 64 is 4 and cube root of 27 is 3 so we have

(4 - 3)( {4}^{2}  + 4(3) + 3 {}^{2} )

1(16 + 12 + 9) = 1(37) = 37

So the difference of cubes works for real numbers. This is a good way to help remeber the identity using real numbers.

Back on to the topic,

we know that 5 is cube root of 125 and x is the cube root of x^3 so we have

(5 - x)( {5}^{2}  + 5x +  {x}^{2} ) =

(5 - x)(25 + 5x +  {x}^{2} )

3 0
2 years ago
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Given two points (3, 7) and (6, 8) with a line drawn through the points, calculate the slope of the line
vredina [299]

Answer:

1/3

Step-by-step explanation:

Given two points on the line, we can find the slope using

m = (y2-y1)/(x2-x1)

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3 0
2 years ago
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Write L if it is likely to happen and U if unlikely to happen.
maria [59]

Answer:

Probabilities

        Likely to happen (L)      Unlikely to happen (U)

a.      4/5                                 5/8

b.     3/5                                  3/8

c.     4/5                                  4/7

d.    0.3                                  0.09

e.    5/6 and 4/5                   2/3

Step-by-step explanation:

Probabilities in Percentages:

a. The probability of 4/5 = 80% and 5/8 = 62.5%

b. The probability of 3/8 = 37.5% and 3/5 = 60%

c. The probability of 4/5 = 80% and 4/7 = 57%

d. The probability of 0.3 = 30% and 0.09 = 9%

e. The probability of 2/3 = 67% and 4/5 = 80% and 5/6 = 83%

b) To determine the relative values of the fractional probabilities, it is best to reduce them to their fractional or percentage terms.  When this is done, the relative sizes become obvious, and then, comparisons can be made.

3 0
2 years ago
Annie borrowed $354 from her parents to buy a tablet. She plans to pay the money back in 12 equal payments.
Ber [7]
$354 divided by 12 equal payments equals $29.50 a payment
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3 years ago
Use elimination to solve the system of equations. <br> x+y=−3 <br> 2x−3y=29
attashe74 [19]

Answer:

(4,-7)

Step-by-step explanation:

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2 years ago
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