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Tamiku [17]
3 years ago
6

Complete the equation: x^2-14x + __ = (__)^2

Mathematics
1 answer:
slamgirl [31]3 years ago
5 0

Answer:

C. 49, x-7

Step-by-step explanation:

(A+B)^2 = A^2 + 2AB + B^2

-14x = 2*A*B

where A=x

Therefore B=-7

and (x-7)^2=x^2-14x+49

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If h(x)=(f o g) (x) and h(x)= ∛x+3, find g( x) if f(x)= ∛x+2 (picture attached)
Aleksandr-060686 [28]

Answer:

g(x) = x+1

Step-by-step explanation:

Informally, you can see that the function h(x) takes the root of a value that is 1 more than the value under the same radical in f(x). This suggests that adding 1 to x in f(x) will give you h(x). That is, ...

h(x) = f(x+1) = f(g(x))

so

g(x) = x+1

_____

More formally, you can apply the inverse of the function f(x) to the equation ...

h(x) = f(g(x))

f^-1(h(x)) = f^-1(f(g(x))) . . . inverse function applied

f^-1(h(x)) = g(x) . . . . . . . . . simplified

Now f^-1(x) can be found by solving for y in ...

x = f(y)

x = ∛(y+2) . . . . . . . . . definition of f(y)

x^3 = y+2 . . . . . . . . . cube both sides

x^3 -2 = y = f^-1(x) . . . subtract 2 from both sides

So, f^-1(h(x)) is ...

f^-1(h(x)) = g(x) = (∛(x+3))^3 -2 = x+3 -2

g(x) = x+1

5 0
3 years ago
A landscaper is comparing the costs of potted plants from two nurseries. Nursery P charges $15 per plant plus a $50 delivery fee
photoshop1234 [79]

Answer:

The required number of plants is 10.

Step-by-step explanation:

Nursery P charges $15 per plant plus a $50 delivery fee on any order. Nursery Q charges $20 per plant and no delivery fee.

If x number of plants that must be delivered for the total cost to be the same at both nurseries, then

15x + 50 = 20x

⇒ 5x = 50

⇒ x = 10

Therefore, the required number of plants is 10. (Answer)

4 0
3 years ago
Help! What is the average rate of change of f(x)=x^2+3x+6 over the interval -3 less-than-or-equal-to x less-than-or-equal-to 3?
Makovka662 [10]

Answer:

The average rate of change of the function over the interval is 5.

Step-by-step explanation:

Average rate of change of a function:

The average rate of change of a function f(x) over an interval [a,b] is given by:

A = \frac{f(b)-f(a)}{b-a}

Interval -3 less-than-or-equal-to x less-than-or-equal-to 3

This means that a = -3, b = 3

f(x) = x^2 + 3x + 6

So

f(b) = f(3) = (3)^2 + 3(3) + 6 = 9 + 9 + 6 = 24

f(a) = f(-3) = (-3)^2 + 3(-3) + 6 = 9 - 9 + 6 = 6

Average rate of change

A = \frac{f(b)-f(a)}{b-a} = \frac{24+6}{3-(-3)} = \frac{30}{6} = 5

The average rate of change of the function over the interval is 5.

8 0
3 years ago
What is the gcf of 3xy and 42xy​
nignag [31]

Since 3 divides 42, 3xy itself is the greatest common factor of 3xy and 42xy.

Answer: 3xy

7 0
3 years ago
Among two supplementary angles, the measure of the larger angle is 44°
zhuklara [117]

Answer:

68° and 112°

Step-by-step explanation:

Supplementary angles sum to 180°

let the smaller angle be x then the larger angle is x + 44 , then

x + x + 44 = 180 , that is

2x + 44 = 180 ( subtract 44 from both sides )

2x = 136 ( divide both sides by 2 )

x = 68

Smaller angle = 68° and

larger angle = x + 44 = 68 + 44 = 112°

6 0
3 years ago
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