Let f(x) = 27x5 − 33x4 − 21x3 and g(x) = 3x2. Find f of x over g of x

Answer:

x= 3, y=0, z= 1

Step-by-step explanation:

Let's label the 3 given equations first.

2x +3y +4z= 10 -----(1)

3x +2y -4z= 5 -----(2)

x +4y +2z= 5 -----(3)

(1) +(2):

This is to eliminate the z term.

2x +3y +4z +3x +2y -4z= 10 +5

5x +5y= 15

Divide by 5 on both sides:

x +y= 3 -----(4)

(3) ×2:

2x +8y +4z= 10 -----(5)

(2) +(5):

This is to eliminate z term.

3x +2y -4z + 2x +8y +4z= 5 +10

5x +10y= 15

Divide by 5 throughout.

x +2y= 3 -----(6)

(6) -(4):

x +2y -(x +y)= 3 -3

x +2y -x -y= 0

y= 0

subst. y=0 into (4):

x +0= 3

x= 3

subst. x=3, y=0 into (3):

3 +4(0) +2z= 5

3 +2z= 5

2z= 5 -3

2z= 2

z= 2÷2

z= 1

Answer:

x = - [tex]\frac{7}{4}[/tex]

Step-by-step explanation:

Given

20x + 12 = 4x - 16 ( subtract 4x from both sides )

16x + 12 = - 16 ( subtract 12 from both sides )

16x = - 28 ( divide both sides by 16 )

x = [tex]\frac{-28}{16}[/tex] = - [tex]\frac{7}{4}[/tex] [ = - 1.75 ]

Answer:

D. 280miles

*Step by step explanation*

miles= 160miles × 7gallons / 4 gallons

miles = 280 miles

Answer:

First distribute the negative -(10)

it becomes a -10

them add the -10 and -2

and the answer in - 12 because a negative plus a negative equals a negative

Answer:

Step-by-step explanation:

12z - 3 > 27z - 15

-15z - 3 > -15

-15z > -12

z < 12/15= 4/5

Answer:

11/4 the second one

multiply 2 and 4 then add 3

Answer:

1 Mile = 1609000  mm.

1.03 × 10^5 × 6.21371192237337 = 0.064 mile

103000 /1609344= 103000 mm.

Step-by-step explanation:

The beginning process is just to find the amount that mm = miles. After that you will move the decimal to then get 0.064 of a mile.

103,000 mm is 0.064 miles

So he can run 0.064 miles.

Given,

He can run = 103,000 mm

We need to find how many miles he can run.

1 mile = 1609344 mm

Find how many miles is 103,000 mm.

We have,

1 mile = 1609344 mm

Multiplying both sides by 103,000

103,000 x 1 mile = 103,000 mm x 1609344

Divide both sides by 1609344

( 103,000 x 1 mile ) / 1609344 = (103,000 mm x 1609344) / 1609344

0.064 miles = 103,000 mm

This means 103,000 mm is 0.064 miles.

Thus 103,000 mm is 0.064 miles

Learn more about the conversion of meters and millimeters here:

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Answer:

the lines are sinceatect

Step-by-step explanation:

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{14x - y}}}}}[/tex]

Step-by-step explanation:

[tex] \sf{3(2x - y) + 2(4x + y)}[/tex]

Distribute 3 through the parentheses

Similarly , distribute 2 through the parentheses

[tex] \dashrightarrow{ \sf{6x - 3y + 8x + 2y}}[/tex]

Combine like terms and simplify

[tex] \dashrightarrow{ \sf{6x + 8x - 3y + 2y}}[/tex]

[tex] \dashrightarrow{ \boxed{ \sf{14x - y}}}[/tex]

Hope I helped!

Best regards! :D

Answer:

f(x) = 2(x + 3)²

Step-by-step explanation:

Parent Graph: f(x) = a(bx - h)² + k

a is vertical shrink/stretch

b is horizontal shrink/stretch

h is horizontal movement left/right

k is vertical movement up/down

h, k is vertex

Step 1: Define variables

h = -3

k = 0

a = 2

Step 2: Write quadratic

f(x) = 2(x + 3)²

Answer:

6/21

Step-by-step explanation:

bc thats the answer

Answer:

Simplified: 6/15 = 2/5

Step by-step explanation:

Answer:

since they are corresponding angle

(6x)°= (5x =10)°

or (6x) - (5x) = 10°

x = 10°

Answer:

complex solutions:  x = -7 ± i√2

Step-by-step explanation:

[tex]-2x^2-28x-102=0\\{}\qquad\qquad^{\div(-2)}\qquad\ \ ^{\div(-2)}\\x^2+14+51=0\quad\implies\quad a=1\,,\ b=14\,,\ c=51\\\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-14\pm\sqrt{14^2-4\cdot1\cdot51}}{2\cdot1}=\dfrac{-14\pm\sqrt{196-204}}{2}[/tex]

[tex]x=\dfrac{-14\pm\sqrt{-8}}{2}[/tex]    means NO REAL SOLUTIONS  (as there is no real √[-8])

However in complex numbers we have:[tex]x=\dfrac{-14\pm\sqrt{-8}}{2}=\dfrac{-14\pm2\sqrt{-2}}{2}=\dfrac{2(-7\pm\sqrt{-2})}{2}=-7\pm\sqrt{-2}\\\\\\x_1=-7+i\sqrt2\ ,\qquad x_2=-7-i\sqrt2[/tex]

Answer:

[tex]C = 180 - 3a[/tex]

Step-by-step explanation:

Given

[tex]A = a[/tex]

[tex]B = 2a[/tex]

Required

[tex]Find\ C[/tex]

Since, ABC is a triangle, we have:

[tex]A + B + C = 180[/tex]

Substitute values for A and C

[tex]a + 2a + C = 180[/tex]

[tex]3a + C = 180[/tex]

Subtract 3a from both sides

[tex]C = 180 - 3a[/tex]

Answer:

180°-3α

Step-by-step explanation:

If you forgot to put the degree sign on 180, that's why you got it wrong!

Answer:

15,420 cm

Step-by-step explanation:

Given the actual distance between the library and train station to be 500 ft, to find the distance between them in centimeters, we ill convert 500 ft to cm as shown;

Given the conversion:

1 ft = 30.48cm

500ft = x cm

Cross multiply

x cm * 1ft= 30.48 cm * 500ft

x cm = 30.48 cm * 500ft/1ft

x cm = 15,240 cm

Hence the distance between them in centimeters on the map is 15,420 cm

18 + 3r

3      3

6  +  r

3(r+6)

Answer:

0

Step-by-step explanation:

[tex]2018 \times (|\frac{1}{2017} - \frac{1}{2016} | + |\frac{1}{2018} - \frac{1}{2017}| - |\frac{1}{2018} - \frac{1}{2016}|)[/tex]

1/2017 is smaller than 1/2016. 1/2018 is smaller than 1/2017. And 1/2018 is smaller than 1/2016. So we can rewrite this as:

[tex]2018 \times ((\frac{1}{2016} - \frac{1}{2017} ) + (\frac{1}{2017} - \frac{1}{2018}) - (\frac{1}{2016} - \frac{1}{2018}))[/tex]

Distribute:

[tex]2018 \times (\frac{1}{2016} - \frac{1}{2017} + \frac{1}{2017} - \frac{1}{2018} - \frac{1}{2016} + \frac{1}{2018})[/tex]

Simplify:

[tex]2018 \times (0)[/tex]

[tex]0[/tex]

Answer:

B: 200

Step-by-step explanation:

The sqr of 200 is equal to 14.14. when plugged into the perimeters 13.8<x<14.5 , 14.14 satisfies the condition

The square root has a value between 13.8 and 14.5 is 200.

Option (B) is correct.

A factor of a number that, when multiplied by itself, gives the original number. The square root of any number can be expressed using the formula: √y = y½.

Given:

The square root has a value between 13.8 and 14.5.

We have to find the square root has a value between 13.8 and 14.5.

According to given question we have

[tex]13.8 ^{2} =190.44\\\\14.5^{2} =210.25\\[/tex]

So, the square root has a value between 13.8 and 14.5 is 200.

when plugged into the perimeters 13.8<x<14.5.

Therefore, the square root has a value between 13.8 and 14.5 is 200.

Learn more details about square root here:

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Answer:

-5a + 9b

Step-by-step explanation:

- (5a - 9b)

Distribute the minus sign

-5a + 9b

Answer:

see attached

Step-by-step explanation:

Answer:

A. c=b-4

Step-by-step explanation:

Answer:

x = 4 ; x = 8

Step-by-step explanation:

[tex]x^2 + 32 = 12x[/tex]

bring all the terms to one side and set equal to 0

[tex]x^2 - 12x + 32 = 0[/tex]

factor the polynomial

[tex](x-8)(x-4) = 0[/tex]

set each factor equal to zero and solve

[tex](x-8) = 0 \\x - 8 = 0 \\x = 8[/tex]

[tex](x-4)=0\\x-4 = 0\\x = 4[/tex]

Answer:

0.8

Step-by-step explanation:

"percent" means "per 100" which is the same as "divide by 100."

To change a percent to a decimal, divide the percent by 100.

80% = 80/100 = 0.8

Answer:

m=1/7

Step-by-step explanation:

Labeled the points and used Slope of a line formula.

Start with out given statement:

Line KM bisects <JKL and the reason for that is because it's given.

For statement 2, we know that m<JKM = m<MKL

because of the definition of an angle bisector.

For statement 3, we can use the angle addition

postulate to get m<JKM + m<MKL = m<JKL.

For statement 4, we use substitution from

the info in statement 2 to get m<MKL + m<MKL = m<JKL.

For statement 5, we simplify to get 2(m < KML) = m<JKL.

For statement 5, we use the division property of equality.

All the reasons are underlined.

Answer:

c. 3.2

Step-by-step explanation:

5(x+2)=7(4-x)

5(x+2)=7(-x+4)

5x+5*2=-7x+7*4

Answer: x = 2y

Step-by-step explanation:

Let's solve for x.

2(3x+4y)=4x+12y

Step 1: Add -4x to both sides.

6x+8y+−4x=4x+12y+−4x

2x+8y=12y

Step 2: Add -8y to both sides.

2x+8y+−8y=12y+−8y

2x=4y

Step 3: Divide both sides by 2.

2x

2

=

4y

2

x=2y

Answer:

x=2y

Solve for x

2 ( 3x + 4y ) = 4x + 12y

6x + 8y = 4x + 12y

6x + 8y - 4x = 12y

2x + 8y = 12y

2x = 12y - 8y

2x = 4y

2x / 2 = 4y / 2

x = 4y / 2

x = 2y

Sorry if I'm wrong