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stira [4]
2 years ago
15

If f(x)=x^4+6, g(x)=x-2 and h(x)= sqrt (x), then f(g(h(x)))=

Mathematics
1 answer:
patriot [66]2 years ago
3 0

Answer:

x^2 + 4x * (3 - sqrt(x)) - 2(5 + sqrt(x))

Step-by-step explanation:

Firstly let us split this up, we need to first work out what g(h(x)) is:

h(x) = Sqrt(x) so g(h(x)) = g(sqrt(x)) = sqrt(x) - 2

Now to work out f(g(h(x))) = f(sqrt(x) - 2) = (sqrt(x) - 2)^4 + 6

= (sqrt(x) - 2) * (sqrt(x) - 2) * (sqrt(x) - 2) * (sqrt(x) - 2) - 6

= (x - 2 * sqrt(x) + 4) * (x - 2 * sqrt(x) + 4) - 6

= x^2 - 2x * sqrt(x) + 4x - 2x * sqrt(x) + 4x - 8 * sqrt(x) + 4x - 8 * sqrt(x) + 16 - 6

= x^2 - 4x * sqrt(x)  + 12x - 16 * sqrt(x) + 10

= x^2 + 4x * (3 - sqrt(x)) - 2(5 + sqrt(x))

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Melanie's car used 9 ballons to travel 306 miles. How far can she travel on 11 gallons?
MAVERICK [17]
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7 0
3 years ago
John received $9,000 in student loans. Part of the money he was able to borrow at 7% simple interest, but on the rest of the mon
lidiya [134]
He borrowed "a" at 7% and "b" at 8.25%

now, whatever "a" and "b" are, we know, his student loan was 9000, thus
a+b = 9000

now, he owes 7% or 7/100 for "a", what's 7% of a? well, 7/100 * a or 0.07a

he owes 8.25% of "b", how much is 8.25% of b? well, 8.25/100 * b or 0.0825b

now, we know, at the end of the year, he owed for both loans, 706.25 in interest
thus we know that 0.07a + 0.0825b = 706.25

thus   \bf \begin{cases}
a+b=9000\implies \boxed{b}=9000-a\\
0.07a+0.0825b=706.25\\
----------\\
0.07a+0.0825\left(\boxed{9000-a}  \right)=706.25
\end{cases}

solve for "a", to see how much he borrowed at 7%

what about "b"? well, b = 9000-a
6 0
3 years ago
A motorist is driving across the country at a steady speed at 54.5 miles per hour. In the 17th hour, the odometer on her car rea
timama [110]

54.5*17=926.5

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8 0
3 years ago
Can you please help me on add and subtract fractions level 1 9/8-11/8
zhannawk [14.2K]

Answer:

7/8

Step-by-step explanation:

1. Make 1 9/8 into an improper fraction

1 = 8/8

8/8 + 9/8 = 17/8

2. Subtract

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3 0
3 years ago
Read 2 more answers
In triangle NLM, point S is the centroid, QS = (3x – 5) cm, and NS = (4x) cm. What is NS? 5 cm 10 cm 20 cm 30 cm
son4ous [18]

Answer:

20 cm

Step-by-step explanation:

∵ S is the centroid of ΔNLM

∴ S divides NG at ratio 1 : 2 from the base

∴SQ = 1/2 NS

∴3x - 5 = 1/2 (4x)

∴3x - 5 = 2x

∴3x - 2x = 5

∴x = 5

∴ NS = 4 × 5 = 20 cm

5 0
3 years ago
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