Expand and simplify (x − 3)(2x + 1)(3x - 2)

Answer:

whats up? whatja need help with

Step-by-step explanation:

Given:

The function is

[tex]f(x)=-x^2-5x+12[/tex]

To find:

The average rate of change of the function over the interval −5 ≤ x ≤ 4.

Solution:

The average rate of change of a function f(x) over the interval [a,b] is

[tex]m=\dfrac{f(b)-f(a)}{b-a}[/tex]

Putting x=-5 in the given function, we get

[tex]f(-5)=-(-5)^2-5(-5)+12[/tex]

[tex]f(-5)=-25+25+12[/tex]

[tex]f(-5)=12[/tex]

Putting x=4 in the given function, we get

[tex]f(4)=-(4)^2-5(4)+12[/tex]

[tex]f(4)=-16-20+12[/tex]

[tex]f(4)=-24[/tex]

Now, the average rate of change of the function over the interval −5 ≤ x ≤ 4 is

[tex]m=\dfrac{f(4)-f(-5)}{4-(-5)}[/tex]

[tex]m=\dfrac{-24-12}{4+5}[/tex]

[tex]m=\dfrac{-36}{9}[/tex]

[tex]m=-4[/tex]

Therefore, the average rate of change of the function over the interval −5 ≤ x ≤ 4 is -4.

Answer:

70 pushups in 5 mins.

Step-by-step explanation:

42 ÷ 3 = 14

So you can do 14 pushups in one minute.

14 × 5 = 70

good luck, i hope this helps :)

Answer:

729

Step-by-step explanation:

Answer:

78°

Step-by-step explanation:

angle CAW=180-168

angle CAW=12

angle DWB=12 vertically opposite to angle CAW

Sum of angles at a point=360

168+12+12+90+w=360

282+w=360

Collect like terms

w=360-282

w=78

Answer:

Simplify the following algebraic expressions.

- 6x + 5 + 12x -6

2(x - 9) + 6(-x + 2) + 4x

3x2 + 12 + 9x - 20 + 6x2 - x

(x + 2)(x + 4) + (x + 5)(-x - 1)

1.2(x - 9) - 2.3(x + 4)

(x2y)(xy2)

(-x2y2)(xy2)

Solution

Group like terms and simplify.

- 6x + 5 + 12x -6 = (- 6x + 12x) + (5 - by

Solution

Use rules of exponential to simplify the numerator first.

(a b2)(a3 b) / (a2 b3) = (a4 b3) / (a2 b3)

Rewrite as follows.

(a4 / a2) (b3 / b3)

Use rule of quotient of exponentials to simplify.

= a2

Rewrite as follows.

(21 x5) / (3 x4) = (21 / 3)(x5 / x4)

Simplify.

= 7 x

(6 x4)(4 y2) / [ (3 x2)(16 y) ]

Multiply terms in numerator and denominator and simplify.

(6 x4)(4 y2) / [ (3 x2)(16 y) ] = (24 x4 y2) / (48 x2 y)

Rewrite as follows.

= (24 / 48)(x4 / x2)(y2 / y)

Simplify.

= (1 / 2) x2 y

Factor 4 out in the numerator.

(4x - 12) / 4 = 4(x - 3) / 4

Simplify.

= x - 3

Factor -5 out in the numerator.

(-5x - 10) / (x + 2) = - 5 (x + 2) / (x + 2)

Simplify.

= - 5

Factor numerator and denominator as follows.

(x2 - 4x - 12) / (x2 - 2x - 24) = [(x - 6)(x + 2)] / [(x - 6)(x + 4)]

Simplify.

= (x + 2) / (x + 4) , for all x not equal to 6

Solve for x the following linear equations.

2x = 6

6x - 8 = 4x + 4

4(x - 2) = 2(x + 3) + 7

0.1 x - 1.6 = 0.2 x + 2.3

- x / 5 = 2

(x - 4) / (- 6) = 3

(-3x + 1) / (x - 2) = -3

x / 5 + (x - 1) / 3 = 1/5

Solution

Divide both sides of the equation by 2 and simplify.

2x / 2 = 6 / 2

x = 3

Add 8 to both sides and group like terms.

6x - 8 + 8 = 4x + 4 + 8

6x = 4x + 12

Add - 4x to both sides and group like terms.

6x - 4x = 4x + 12 - 4x

2x = 12

Divide both sides by 2 and simplify.

x = 6

Expand brackets.

4x - 8 = 2x + 6 + 7

Add 8 to both sides and group like terms.

4x - 8 + 8 = 2x + 6 + 7 + 8

4x = 2x + 21

Add - 2x to both sides and group like terms.

4x - 2x = 2x + 21 - 2x

2x = 21

Divide both sides by 2.

x = 21 / 2

Add 1.6 to both sides and simplify.

0.1 x - 1.6 = 0.2 x + 2.3

0.1 x - 1.6 + 1.6 = 0.2 x + 2.3 + 1.6

0.1 x = 0.2 x + 3.9

Add - 0.2 x to both sides and simplify.

0.1 x - 0.2 x = 0.2 x + 3.9 - 0.2 x

- 0.1 x = 3.9

Divide both sides by - 0.1 and simplify.

x = - 39

Multiply both sides by - 5 and simplify.

- 5(- x / 5) = - 5(2

What is the y intercept of the line - 4 x + 6 y = - 12?

Solution

Set x = 0 in the equation and solve for y.

- 4 (0) + 6 y = - 12

6 y = - 12

y = - 2

y intercept: (0 , - 2)

What is the x intercept of the line - 3 x + y = 3?

Solution

Set y = 0 in the equation and solve for x.

- 3 x + 0 = 3

x = -1

x intercept: (-1 , 0)

What is point of intersection of the lines x - y = 3 and - 5 x - 2 y = - 22?

Solution

A point of intersection of two lines is solution to the equations of both lines. To find the point of intersection of the two lines, we need to solve the system of equations x - y = 3 and -5 x - 2 y = -22 simultaneously. Equation x - y = 3 can be solved for x to give

x = 3 + y

Substitute x by 3 + y in the equation - 5 x - 2 y = -22 and solve for y

-5 (3 + y) - 2 y = - 22

-15 - 5 y - 2 y = - 22

-7 y = - 22 + 15

-7 y = - 7

y = 1

Substitute x by 3 + y in the equation -5 x - 2 y = - 22 and solve for y

x = 3 + y = 3 + 1 = 4

Point of intersection: (4 , 1)

For what value of the constant k does the line - 4 x + k y = 2 pass through the point (2,-3)?

Solution

For the line to pass through the point (2,-3), the ordered pair (2,-3) must be a solution to the equation of the line. We substitute x by 2 abd y by - 3 in the equation.

- 4(2) + k(-3) = 2

Solve the for k to obtain

k = - 10 / 3

What is the slope of the line with equation y - 4 = 10?

Solution

Write the given equation in slope intercept form y = m x + b and identify the slope m.

y = 14

It is a horizontal line and therefore the slope is equal to 0.

What is the slope of the line with equation 2 x = -8?

Solution

The above equation may be written as

x = - 4

It is a vertical line and therefore the slope is undefined.

Find the x and y intercepts of the line with equation x = - 3?

Solution

The above is a vertical line with x intercept only given by

(-3 , 0)

Find the x and y intercepts of the line with equation 3 y - 6 = 3?

Solution

The given equation may be written as

y = 3

The above is a horizontal line with y intercept only given by

(0 , 3)

What is the slope of a line parallel to the x axis?

Solution

A line parallel to the x axis is a horizontal line and its slope is equal to 0.

What is the slope of a line perpendicular to the x axis?

Solution

A line perpendicular to the x axis is a vertical line and its slope is undefined

Step-by-step explanation:

y = -22 and solve for y

-5 (3 + y) - 2 y = - 22

-15 - 5 y - 2 y = - 22

-7 y = - 22 + 15

-7 y = - 7

y = 1

Answer:

Spanish.

Step-by-step explanation:

It is the language Spanish but the word is in spanish hahahahahah.

Answer:

b = 6

Step-by-step explanation:

Let's solve for b.

(3x−1)2=9x2−bx+1

Step 1: Flip the equation.

−bx+9x2+1=9x2−6x+1

Step 2: Add -9x^2 to both sides.

−bx+9x2+1+−9x2=9x2−6x+1+−9x2

−bx+1=−6x+1

Step 3: Add -1 to both sides.

−bx+1+−1=−6x+1+−1

−bx=−6x

Step 4: Divide both sides by -x.

b = 6

Hope this helpss!!!

Answer:

a

Step-by-step explanation:

mx+c

c is y intersect in this case -2

m is gradient, in this case its positive, therefore a

Answer: 50 miles per hour

Step-by-step explanation:

The average speed of the car will be gotten by using the formula:

= Distance/Time

where,

Distance = 65 miles

Time = 14:48 - 13:30 = 1:18 hours = 1 hour 18 minutes = 1 18/60 = 1.3 hours

Speed = Distance / Time

= 65 miles / 1.3 hours

= 50 miles per hour

Answer:

7

Step-by-step explanation:

3x+9=12

3x=21

x=7

Answer:

[tex] - 5[/tex]

Step-by-step explanation:

[tex]3(x + 9) = 12[/tex]

Answer:

80%

Step-by-step explanation:

How much is 32 out of 40 written as a percent value? Convert fraction (ratio) 32 / 40 Answer: 80%

Answer:

X dot on graph (-0.333,0) Y dot on graph (0,1)

Step-by-step explanation:

It intercepts on the X line on (-0.33,0)

It intercepts on the Y line on (0,1)

Answer:

Hi so the graph will look like this

Hope This Helps!

Answer:

Three

Step-by-step explanation:

A triangle has three sides and three corners hence the name TRI-angle

Step-by-step explanation:

a triangle has 3 sides. just count the sides and it's 3

Step-by-step explanation:

14x+y=60

4x-6= 10

4x= 16

x= 4

56+y=60

y= 4

Answer:

2/3 begins w a 2 and 1/3 begins w a 1. thats the difference.. hope this helped :)

Step-by-step explanation:

Answer:

.3333333

Step-by-step explanation:

because u have to math ight

Answer:

72 is the correct answer

Answer:

If you got 35% off, you only paid 65% of the original price. Call that x. Then we write

x = $468 / .65 = $720 is the original price.

\

Answer:

60.75

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

yes because 135 is the same as 135

Step-by-step explanation:

2 9/12×6=(2×12+9)/12×6=33×6/12=33/2=16.5is answer

Answer:

0.96

Step-by-step explanation:

Total samples of window = 10smaples

Total seal break = 4% of 10

Total seal break = 0.04 * 10

Total seal break = 0.4

THis means that no seal will be break on 96% of the window i.e 9.6 windows

The probability that, in a sample of 10 windows, no seals will break is expressed

as;

Pr(no seal will break) = 9.6/10

Pr(no seal will break)  = 0.96

Hence the probability that no seals will break is 0.96

Answer:

2 Boxs

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Calculator

Answer: x = 16/17; y = 1/17

condition: x,y > 0

we have:

[tex]\left \{ {{\sqrt{\frac{x}{y} } =4} \atop {\frac{1}{x}+\frac{1}{y}=\frac{1}{xy} }} \right. \\\\<=>\left \{ {{\frac{x}{y} =16} \atop {\frac{1}{x}+\frac{1}{y} =\frac{1}{xy} }} \right.[/tex]

because x > 0, multiply x by the second equation, we have:

[tex]\left \{ {{\frac{x}{y} =16} \atop {x(\frac{1}{y}+\frac{1}{x}) =\frac{x}{xy} }} \right. \\\\<=>\left \{ {{\frac{x}{y} =16} \atop {\frac{x}{y} +1=\frac{1}{y} }} \right.\\\\<=>\left \{ {{\frac{x}{y} +1=17} \atop {\frac{x}{y} +1=\frac{1}{y} }} \right.\\\\=>\left \{ {{17-\frac{1}{y} =0} \atop {\frac{x}{y} =16}} \right.\\\\<=>\left \{ {{\frac{1}{y} =17} \atop {x=16y}} \right.\\\\<=>\left \{ {{y=\frac{1}{17} } \atop {x=\frac{16}{17} }} \right.[/tex]

Step-by-step explanation:

Answer:

none/0

Step-by-step explanation:

they ate all the cake.

now harry is gonna get sick

Answer:

79/79 or 1

Step-by-step explanation:

47+14+10+8=79

If Harry, Jack, Dave, and Mary all ate 79 slices in total, then there would be no more cake left since there are only 79 slices. The fraction answer would be 79/79 or 1, because they 79/79 is equivalent to 1.

Answer:

x = - 18

Step-by-step explanation:

Given

- 7 + [tex]\frac{x}{3}[/tex] = - 13 ( add 7 to both sides )

[tex]\frac{x}{3}[/tex] = - 6 ( multiply both sides by 3 to clear the fraction )

x = - 18

Answer:

x = -32  or x = -18    Depends on how the equation is written

Step-by-step explanation:

-7 + x/3 = -13

Find the answer by solving for x.

If the equation is written like this:

[tex]\frac{-7+x}{3} = -13[/tex]           Multiply both sides by 3 and add 7 to both sides

x = -32

Or if the equation is written like this:

[tex]-7+\frac{x}{3} =-13[/tex]        Add 7 to both sides and then multiply by 3

x = -18