MATHEMATICS HIGH SCHOOL

Let f(x) = x2 + x + 2 and g(x) = 2x2 + 5. Find f(g(x)). Show each step of your work.

Answers

Answer 1

Answer:

For given functions f(x) and g(x) the composite function f(g(x)) is $f(g(x))=4x^4+22x^2+32$

What is function?

"It defines a relation between input values and output values."
"In function, for each input there is exactly one output."

What is composition of function?

"It is applying one function to the results of another."
"It is written is $\( f\circ g(x)=f(g(x))$ "
"First apply function f, then apply function g on the result of function f "

For given question,

We have been given two functions,

$f(x) = x^2 + x + 2,~g(x) = 2x^2 + 5.$

We need to find f(g(x))

This means we need to find composite function $\( f\circ g(x)=f(g(x))$

We have, $g(x) = 2x^2 + 5$

We find the value of f(x) for x = g(x)

$f(g(x))\n\n=f(2x^2 + 5)\n\n=(2x^2 + 5)^2 + (2x^2 + 5) + 2\n\n=[(2x^2)^2+2(2x^2)(5)+5^2]+2x^2+5+2\n\n=[4x^4+20x^2+25]+2x^2+7\n\n=4x^4+20x^2+2x^2+25+7\n\n=4x^4+22x^2+32$

Therefore, for given functions f(x) and g(x) the composite function f(g(x)) is $f(g(x))=4x^4+22x^2+32$

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Answer 2

Answer: $f(g(x))=(2x^2+5)^2+2x^2+5+2\nf(g(x))=4x^4+20x^2+25+2x^2+7\nf(g(x))=4x^4+22x^2+32$

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Rhian sat a Maths test and an English test. In the Maths test she scored 14/17. In the English test she scored 31/39

Answers

MATH- 14x100/17= 82.3%
LA- 31x100/39 = 79%

82.3%>79%
She did better in the math class.

what is the question?

What is the length of QR rounded to the nearest whole number?

Answers

The answer to this question is D. 14

11 cm, probably........

Which expression is equal to 2√54 −4√24? ? A. √6 B. −√ 6 C. −√116 D. -26√

Answers

Answer:

D : - 2 $√(6)$

Step-by-step explanation:

using the rule of radicals

• $√(ab)$ = $√(a)$ × $√(b)$

given

2 $√(54)$ - 4 $√(24)$

simplifying the radicals

$√(54)$

= $√(9(6))$

= $√(9)$ × $√(6)$

= 3 $√(6)$

$√(24)$

= $√(4(6))$

= $√(4)$ × $√(6)$

= 2 $√(6)$

Then

2 $√(54)$ - 4 $√(24)$

= 2(3 $√(6)$ ) - 4(2 $√(6)$ )

= 6 $√(6)$ - 8 $√(6)$

= - 2 $√(6)$

Simplify.
10 – 5.3 • (–4 + –6)
a. 63
b. 47
c. –43
d. –47

Answers

$10-5.3*(-4+-6)$
$10-5.3*(-10)$
$10-(-53)=63$

How do you write 4.110 and 4.10 in words

Answers

Answer:

4.110: Four and eleven hundredths,

4.10: Four and one tenths.

Step-by-step explanation:

We have been given two numbers. We are asked to write these number in words.

4.110:

Ones: 4

Tenths: 1

Hundredths: 1

Thousandths: 0

Therefore, our given number would be four and eleven hundredths.

4.10:

Ones: 4

Tenths: 1

Hundredths: 0

Therefore, our given number would be four and one tenths.

4.110: "four and one hundred ten thousandths"

4.10: "four and ten hundredths"

To write the numbers 4.110 and 4.10 in words, we can break them down into their individual parts and express them accordingly:

4.110:

The wholenumber part is 4, which can be written as "four."

The decimal part is 110.

To express this in words, we can say "one hundred ten."

Putting it all together, 4.110 can be written as "four and one hundred ten thousandths."

4.10:

The whole number part is 4, which can be written as "four."

The decimalpart is 10.

To express this in words, we can say "ten."

Therefore, 4.10 can be written as "four and ten hundredths."

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What is the next two numbers for the pattern 0.006, 0.06, 0.6, and 6?

Answers

Answer: 60 and 600

Step-by-step explanation:

The pattern is times 10

6x10=60 60x10=600

Final answer:

The number pattern multiplies each subsequent number by 10. Thus, the next two numbers in the sequence 0.006, 0.06, 0.6, and 6 are 60 and 600.

Explanation:

The question asked is related to a number pattern - specifically, it's about identifying the next two numbers in the series 0.006, 0.06, 0.6, and 6. Looking at this series, we can see a pattern: each subsequent number appears to be 10 times larger than its predecessor.

To get the next number in the series, we multiply the previous one by 10. So, if we multiply 6 by 10, we get 60. Therefore, 60 is the next number in the pattern.

Following this pattern, the number after 60 would be 10 times greater, which is 600. Therefore, the next two numbers in the series after 0.006, 0.06, 0.6, and 6 are 60 and 600.

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Given the function g(x) = 8x − 2, compare and contrast g(−2) and g(4). Choose the statement that is true concerning these two values. A) The value of g(−2) is larger than the value of g(4). B) The value of g(−2) is the same as the value of g(4). C) The value of g(−2) is smaller than the value of g(4). D) The values of g(−2) and g(4) cannot be compared.