Mathematics: If f(x) = 2x^2 - x - 6 and g(x) = x2 -4 , find f(x ÷g(x)

05.08.2022

If f(x) = 2x^2 - x - 6 and g(x) = x2 -4 , find f(x ÷g(x)

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Mathematics

If: f(x) = 2.50x + 15; then: f(6) = if f(x) = 42 - 3.75x; then f(4) = g(x) = 6 - x; then g(-4) = if g(x) = 5x + 16; then g(-2) = which of the following functions match these outcomes: f(1) = 6 f(2) = 8 f(3) = 10 f(4) = 12 f(x) = 5x + 1 f(x) = 4x + 2 f(x) = x2 + 4 f(x) = 2x + 4 f(x) = 12 - 2x

Step-by-step answer

P Answered by PhD

Part 1) f(6)=30

Part 2) f(4)=27

Part 3) g(-2)=6

Part 4) Part 5) Part 6) and part 7) in the procedure

Step-by-step explanation:

Part 1) we have

f(x)=2.50x+15

we know that

f(6) is the value of the function when x=6

substitute the value of x in the function

f(6)=2.50(6)+15=30

Part 2) we have

f(x)=42-3.75x

we know that

f(4) is the value of the function when x=4

substitute the value of x in the function

f(4)=42-3.75(4)=27

Part 3) we have

g(x)=5x+16

we know that

g(-2) is the value of the function when x=-2

substitute the value of x in the function

g(-2)=5(-2)+16=6

Part 4) Which of the following functions match these outcomes:

f(1)=6

we know that

f(1) is the value of the function when x=1

substitute the value of x in each of the functions and then compare

f(1)=5(1)+1=6 -----> this function matches the outcome

f(1)=4(1)+2=6 -----> this function matches the outcome

$f(1)=(1)^{2}+4 =5$ -----> this function does not match the outcome

f(1)=2(1)+4=6 -----> this function matches the outcome

f(1)=12-2(1)=10 -----> this function does not match the outcome

Part 5) Which of the following functions match these outcomes:

f(2)=8

we know that

f(2) is the value of the function when x=2

substitute the value of x in each of the functions and then compare

f(2)=5(2)+1=11 -----> this function does not match the outcome

f(2)=4(2)+2=10 -----> this function does not match the outcome

$f(2)=(2)^{2}+4 =8$ -----> this function matches the outcome

f(2)=2(2)+4=8 -----> this function matches the outcome

f(2)=12-2(2)=6 -----> this function does not match the outcome

Part 6) Which of the following functions match these outcomes:

f(3)=10

we know that

f(3) is the value of the function when x=3

substitute the value of x in each of the functions and then compare

f(3)=5(3)+1=16 -----> this function does not match the outcome

f(3)=4(3)+2=14 -----> this function does not match the outcome

$f(3)=(3)^{2}+4 =13$ -----> this function does not match the outcome

f(3)=2(3)+4=10 -----> this function matches the outcome

f(3)=12-2(3)=6 -----> this function does not match the outcome

Part 7) Which of the following functions match these outcomes:

f(4)=12

we know that

f(4) is the value of the function when x=4

substitute the value of x in each of the functions and then compare

f(4)=5(4)+1=21 -----> this function does not match the outcome

f(4)=4(4)+2=18 -----> this function does not match the outcome

$f(4)=(4)^{2}+4 =20$ -----> this function does not match the outcome

f(4)=2(4)+4=12 -----> this function matches the outcome

f(4)=12-2(4)=4 -----> this function does not match the outcome

Mathematics

Step-by-step answer

P Answered by PhD

Part 1) f(6)=30

Part 2) f(4)=27

Part 3) g(-2)=6

Part 4) Part 5) Part 6) and part 7) in the procedure

Step-by-step explanation:

Part 1) we have

f(x)=2.50x+15

we know that

f(6) is the value of the function when x=6

substitute the value of x in the function

f(6)=2.50(6)+15=30

Part 2) we have

f(x)=42-3.75x

we know that

f(4) is the value of the function when x=4

substitute the value of x in the function

f(4)=42-3.75(4)=27

Part 3) we have

g(x)=5x+16

we know that

g(-2) is the value of the function when x=-2

substitute the value of x in the function

g(-2)=5(-2)+16=6

Part 4) Which of the following functions match these outcomes:

f(1)=6

we know that

f(1) is the value of the function when x=1

substitute the value of x in each of the functions and then compare

f(1)=5(1)+1=6 -----> this function matches the outcome

f(1)=4(1)+2=6 -----> this function matches the outcome

$f(1)=(1)^{2}+4 =5$ -----> this function does not match the outcome

f(1)=2(1)+4=6 -----> this function matches the outcome

f(1)=12-2(1)=10 -----> this function does not match the outcome

Part 5) Which of the following functions match these outcomes:

f(2)=8

we know that

f(2) is the value of the function when x=2

substitute the value of x in each of the functions and then compare

f(2)=5(2)+1=11 -----> this function does not match the outcome

f(2)=4(2)+2=10 -----> this function does not match the outcome

$f(2)=(2)^{2}+4 =8$ -----> this function matches the outcome

f(2)=2(2)+4=8 -----> this function matches the outcome

f(2)=12-2(2)=6 -----> this function does not match the outcome

Part 6) Which of the following functions match these outcomes:

f(3)=10

we know that

f(3) is the value of the function when x=3

substitute the value of x in each of the functions and then compare

f(3)=5(3)+1=16 -----> this function does not match the outcome

f(3)=4(3)+2=14 -----> this function does not match the outcome

$f(3)=(3)^{2}+4 =13$ -----> this function does not match the outcome

f(3)=2(3)+4=10 -----> this function matches the outcome

f(3)=12-2(3)=6 -----> this function does not match the outcome

Part 7) Which of the following functions match these outcomes:

f(4)=12

we know that

f(4) is the value of the function when x=4

substitute the value of x in each of the functions and then compare

f(4)=5(4)+1=21 -----> this function does not match the outcome

f(4)=4(4)+2=18 -----> this function does not match the outcome

$f(4)=(4)^{2}+4 =20$ -----> this function does not match the outcome

f(4)=2(4)+4=12 -----> this function matches the outcome

f(4)=12-2(4)=4 -----> this function does not match the outcome

Mathematics

Neil places £2000 in a bank account that pays 1.5% simple interest per year. How much interest will he earn in 6 years?

Step-by-step answer

P Answered by PhD

SI=(P*R*T)/100

P=2000

R=1.5

T=6

SI=(2000*1.5*6)/100

=(2000*9)/100

=180

Neil will earn interest of 180

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A new school randomly assigns a six-character student code to every prospective student. The school uses the characters 1, 2, 3, 4, 5, X, Y, and Z. If none of the student codes contain a repeated character, what is the total number of codes that can be randomly assigned?

Step-by-step answer

P Answered by PhD

The total nom of code that can be used is equal to 5+3 = 8

Mathematics

The ratio of tables to chairs at the furniture store is 1:6. There are 30 chairs. How many tables are there?

Step-by-step answer

P Answered by PhD

The solution is in the following image

Mathematics

The value of a collectible coin can be represented by the equation y = 2 x + 15, where x represents its age in years and y represents its total value in dollars. What is the value of the coin after 19 years? $2 $23 $38 $53

Step-by-step answer

P Answered by PhD

y=2x+15

where y=Value of coin

x=Age in years

Value of coin after 19 years=2*19+15

=$53

Therefore, Value after 19 years=$53

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Use the X method to find the solutions of6x2 + 2x – 20 = 0.

Step-by-step answer

P Answered by PhD

The answer is in the image

Mathematics

A 4300-N force from a car s engines produces an acceleration of 3.3 m/s2. What is the mass of the car? A. 4300 kg B. 1300 kg C. 14,000 kg D. 390 kg

Step-by-step answer

P Answered by PhD

F=ma

where F=force

m=mass

a=acceleration

Here,

F=4300

a=3.3m/s2

m=F/a

=4300/3.3

=1303.03kg

Mathematics

A 4300-N force from a car s engines produces an acceleration of 3.3 m/s2. What is the mass of the car? A. 4300 kg B. 1300 kg C. 14,000 kg D. 390 kg

Step-by-step answer

P Answered by PhD

F=ma

where F=force

m=mass

a=acceleration

Here,

F=4300

a=3.3m/s2

m=F/a

=4300/3.3

=1303.03kg

Approximately it is aqual to 1300kg

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Step-by-step answer

P Answered by PhD

The answer is in the image

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