Factor completely 2x2 + 2x − 12.

2(x − 3)(x + 4)
2(x − 2)(x + 3)
(2x − 4)(x + 3)
(2x − 3)(x + 4)

Answer:

W = 7.5 in

Step-by-step explanation:

We'll use the formula for the perimeter of a rectangle:  P = 2W + 2L.

Here, L = W + 5, so P = 2W + 2L becomes:

P = 2W + 2(W + 5), and this equals 40 in.

Thus we have the equation in W (the desired variable) as follows:

2W + 2(W + 5) = 40 in, or 4W + 10 = 40.

Then 4W = 30, and W = 7.5 in.

Based on the perimeter of this rectangle, the width is 7.5 inches.

The perimeter of a rectangle is calculated by:

= Length + Width + Length + Width

Assuming the width is denoted by x, the length would be:

Length = 5 + Width

Length = 5 + x

The perimeter is given so we can solve for the width:

Length + Width + Length + Width  = Perimeter

5 + x + x + 5 + x + x = 40

10 + 4x = 40

4x = 40 - 10

x = 30/4

x = 7.5 inches

In conclusion, the width is 7.5 inches.

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Answer:

f(x) = x + 4

Step-by-step explanation:

Given

y - x - 4 = 0 ( add x to both sides )

y - 4 = x ( add 4 to both sides )

y = x + 4 ( let y = f(x) )

f(x) = x + 4

Final result :

 (x + 5) • (x + 4)

 ———————

         2        

Step by step solution :

Step  1  :

           x2 - 16

Simplify   ———————

           2x + 6

Step  2  :

Pulling out like terms :

2.1     Pull out like factors :

  2x + 6  =   2 • (x + 3)

Trying to factor as a Difference of Squares :

2.2      Factoring:  x2 - 16

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 16 is the square of 4

Check :  x2  is the square of  x1

Factorization is :       (x + 4)  •  (x - 4)

Polynomial Long Division :

2.3    Polynomial Long Division

Dividing :  x + 4

                             ("Dividend")

By         :    x + 3    ("Divisor")

dividend     x  +  4

- divisor  * x0     x  +  3

remainder         1

Quotient :  1  

Remainder :  1  

Equation at the end of step  2  :

 (((x2)+8x)+15) (x+4)•(x-4)

 ——————————————•———————————

     (x-4)        2•(x+3)  

Step  3  :

           x2 + 8x + 15

Simplify   ————————————

              x - 4    

Trying to factor by splitting the middle term

3.1     Factoring  x2 + 8x + 15

The first term is,  x2  its coefficient is  1 .

The middle term is,  +8x  its coefficient is  8 .

The last term, "the constant", is  +15

Step-1 : Multiply the coefficient of the first term by the constant   1 • 15 = 15

Step-2 : Find two factors of  15  whose sum equals the coefficient of the middle term, which is   8 .

     -15    +    -1    =    -16

     -5    +    -3    =    -8

     -3    +    -5    =    -8

     -1    +    -15    =    -16

     1    +    15    =    16

     3    +    5    =    8    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  3  and  5

                    x2 + 3x + 5x + 15

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x+3)

             Add up the last 2 terms, pulling out common factors :

                   5 • (x+3)

Step-5 : Add up the four terms of step 4 :

                   (x+5)  •  (x+3)

            Which is the desired factorization

Equation at the end of step  3  :

 (x + 5) • (x + 3)   (x + 4) • (x - 4)

 ————————————————— • —————————————————

       x - 4            2 • (x + 3)  

Step  4  :

Canceling Out :

4.1    Cancel out  (x+3)  which appears on both sides of the fraction line.

Canceling Out :

4.2    Cancel out  (x-4)  which appears on both sides of the fraction line.

Final result :

 (x + 5) • (x + 4)

 ——————---

         2        

Answer:0.063

Step-by-step explanation:

All I did was multiply 6.3 by 0.01 and I got 0.063.

The answers are:

- The quantity that represents the initial number of bacteria is 64.

- The quantity that represents the rate at which the number of bacteria is increasing is (1+0.12) or 1.12 which means the growth rate percentage for the bacteria is 0.12 or (0.12*100), it will be 12%.

To solve the problem, and complete the statements, we need to remember the form of the exponential growth.

The exponential growth formula is given by the following formula:

[tex]P(t)=StartAmount(1+PercentageRate)^{t}[/tex]

Where,

Start Amount, is the starting population or amount.

(1+Percentage Rate), is the increasing rate

Percentage Rate, is the growth rate percentage.

t, is the time elapsed.

Now, we are given the following expression:

[tex]P(3)=64(1.12)^{3}[/tex]

Which can be rewrited as:

[tex]P(3)=64(1+0.12)^{3}[/tex]

So, we have that:

- The quantity that represents the initial number of bacteria is 64.

- The quantity that represents the rate at which the number of bacteria is increasing is (1+0.12) or 1.12 which means the growth rate percentage for the bacteria is 0.12 or (0.12*100), it will be 12%.

Have a nice day!

Answer:

b

Step-by-step explanation:

Answer:

The three friends took 6p + 5 peaches home

Explanation:

We are given that the three friends picked 2p, 4p+3 and 3p+2 peaches

This means that:

Total picked = 2p + 4p + 3 + 3p + 2 = 9p+5 peaches

Now, we know that the owner will take p peaches from each of the three friends

This means that:

Amount taken by owner = 3p peaches

Finally, to get the amount that the three friends will take home, we subtract the amount that the owner will take from the total amount they picked

This means that:

Number of peaches they took home = total picked - amount taken by owner

Number of peaches they took home = 9p + 5 - 3p

Number of peaches they took home = 6p + 5 peaches

Hope this helps :)

Answer:

{-2, -14, -26, -50}

Step-by-step explanation:

The range of the function is the function evaluated at each point of the given domain. So to find the range of the function we need to find the value of the function for each point in the domain:

- For x = -8

[tex]f(x)=-2x-18[/tex]

[tex]f(-8)=-2(-8)-18[/tex]

[tex]f(-8)=16-18[/tex]

[tex]f(-8)=-2[/tex]

The first value of the range of the function is -2

- For x = -2

[tex]f(x)=-2x-18[/tex]

[tex]f(-2)=-2(-2)-18[/tex]

[tex]f(-2)=4-18[/tex]

[tex]f(-2)=-14[/tex]

The second value of the range is -14

- For x = 4

[tex]f(x)=-2x-18[/tex]

[tex]f(4)=-2(4)-18[/tex]

[tex]f(4)=-8-18[/tex]

[tex]f(4)=-26[/tex]

Th third values of the range is -26

- For x = 16

[tex]f(x)=-2x-18[/tex]

[tex]f(16)=-2(16)-18[/tex]

[tex]f(16)=-32-18[/tex]

[tex]f(16)=-50[/tex]

The fourth and last value of the range is -50

Now we can put all the values of the range together

The range of the function is {-2, -14, -26, -50}

Answer:

[tex](x-1)^{2} + (y-2)^{2}[/tex][tex]=9[/tex]

Step-by-step explanation:

The equation of a circle is [tex](x-h)^{2} +(y-k)^{2} = r^{2}[/tex] in which (h,k) is the center of the circle and r is the radius of the circle. (x,y) can represent any point on the circle but when the equation is written standardly, it is left as (x,y).

Because (1,2) is (h,k) it will be inputted as:

[tex](x-1)^{2} + (y-2)^{2}[/tex]

The radius is 3 but in the equation it must be squared.

3 x 3 is 9, so the full equation is:

[tex](x-1)^{2} + (y-2)^{2}[/tex][tex]=9[/tex]

Answer:

(x-1)^2+(y+2)^2=9

Step-by-step explanation:

D, because everything in front of the x is the slope and everything after the x is the y- intercept

Answer:

The correct answer is (D) slope=-3 and y-intercept=-2

Step-by-step explanation:

Answer:

w/5 ≥ 25

Step-by-step explanation:

Quotient means division

w/5

is at least means great than or equal to

w/5 ≥ 25

Answer: 132

Step-by-step explanation:

There are three different things to choose from: size, flavors, and toppings

3 kinds of sizes x 11 kinds of flavors x 4 kinds of toppings

= 3x11x4

= 12x11

= 132

Answer:

x=5, Now you just have to insert x into the equation for DG

Step-by-step explanation:

2x+4=4x-6

-2x     -2x

 4=2x-6

+6     +6

 10=2x

÷2   ÷2

5=x

Answer:

the answer is a. y=2x+4

Answer: A y = 2x + 4

for USATestprep

Answer:

[tex]a.\ 54ft^3\\b.\ 5yd^3\\c.\ 11,943,936in^3\\d.\ 162ft^3[/tex]

Step-by-step explanation:

a. Remember that:

[tex]1yd^3=27ft^3[/tex]

Then, 2  cubic yards to cubic feet is:

[tex](2yd^3)(\frac{27ft^3}{1yd^3})=54ft^3[/tex]

b. 135 cubic feet to cubic yards is:

[tex](135ft^3)(\frac{1yd^3}{27ft^3})=5yd^3[/tex]

c. Remember that:

[tex]1ft^3=1,728in^3[/tex]

Then, 6,912 cubic feet to cubic inches:

[tex](6,912ft^3)(\frac{1,728in^3}{1ft^3})=11,943,936in^3[/tex]

d. 279,936 cubic inches to cubic feet is:

 [tex](279,936in^3)(\frac{ft^3}{1,728in^3})=162ft^3[/tex]

Answer:

A 54ft3

B 5yd3

C 11,943,936in3

D 162ft3

Step-by-step explanation:

ANSWER

C)

[tex]y = {x}^{2} [/tex]

EXPLANATION

A linear function is a function whose graph is a straight line.

The graph of y=x is a straight line.

The graph of y=3x -7 is also a straight line.

The graph of y=x² is a parabola.

This graph is not a straight line .

It is a non-linear function.

y=3 and y=13 are also straight lines.

The correct choice is C.

Answer:

i think its A if it isnt im sorry

Step-by-step explanation:

Answer:

The second option :: V = [tex](25-2x)(20-2x)x[/tex] is correct.

Step-by-step explanation:

The vertical side was 25 inches before cutting out the corners.  

The horizontal side was 20 inches before cutting out the corners.

So now, if you fold all of the corner up, you get a box that has a height of "x".  

The sides are now missing a length of x from each end.  

So the longer edges of the box are now [tex](25-2x)[/tex] inches

The shorter edges of the box are now [tex](20-2x)[/tex] inches

The volume of a box is given by V = length x width x height

So, here the volume becomes:

V = [tex](25-2x)(20-2x)x[/tex] cubic inches.

Answer:

C

Because of the markings showing equal length lines 7x + 4 is double 4x or 48 is three times the length of 4x

Either solve 7x + 4 = 8x

4 = x

Or solve 48 = 12x

4 = x

Substitute back in to 7x + 4 ......MN = 7 x 4 + 4 = 32

±1/2. The equation [tex]4x^{2} =1[/tex] has two possible solutions +1/2 and -1/2.

The problem is a quadratic equations and it can be solved using the equation [tex]x=-b±\frac{\sqrt{b^{2} -4ac} }{2a}[/tex].

Ordering the quadratic equation given in the problem, we obtain [tex]4x^{2} -1=0[/tex] where a = 4, b = 0, and c = -1

Substituting the values

[tex]x=±\frac{\sqrt{-4(4)(-1)} }{2(4)}=±\frac{\sqrt{16}}{8} =±\frac{4}{8} \\x=±\frac{1}{2}[/tex]

The answer is:

The correct option is the second option,

[tex]4x^{2}=+-\frac{1}{2}[/tex]

We are given the expression:

[tex]4x^{2}[/tex]

Now, solving we have:

Applying square root to both sides of the equation in order to isolate x:

[tex]4x^{2}=1\\\\\sqrt{4x^{2} } =+-\sqrt{1}\\\\2x=+-1\\\\x=+-\frac{1}{2}[/tex]

Hence, the correct option is the second option,

[tex]4x^{2}=+-\frac{1}{2}[/tex]

Have a nice day!

Density should be the answer

Answer:

Density

Step-by-step explanation:

Density is the mass of a substance per unit volume. Volume is the amount of space an object occupies.

Answer:

x=1, y=-1

Step-by-step explanation:

i hope im right sorry if im not >.<

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}y=x^2-4&(1)\\y=-2x-5&(2)\end{array}\right\\\\\text{Put (1) to (2):}\\\\x^2-4=-2x-5\qquad\text{add}\ 2x\ \text{and 5 to both sides}\\\\x^2+2x+1=0\\\\x^2+x+x+1=0\\\\x(x+1)+1(x+1)=0\\\\(x+1)(x+1)=0\\\\(x+1)^2=0\iff x+1=0\qquad\text{subtract 1 from both sides}\\\\x=-1\\\\\text{put the value of}\ x\ \text{to}\ (2):\\\\y=-2(-1)-5\\\\y=2-5\\\\y=-3[/tex]

Answer: Hello there!

The system of equation given is:

y = x^2-4

y = -2x-5

And we want to solve this system:

the first step we can do is replace y in the first equation by the given in the second equation:

y = x^2-4 = -2x - 5

now we can solve it for x:

x^2-4 +2x + 5 = 0

x^2 +2x + 1 = 0

and now we can use the cuadratic equation forumla:

this is, if we have a function of the form:

ax^2 + bx + c = 0

the solutions are:

[tex]x = \frac{-b +/- \sqrt{b^2 -4ac} }{2a}[/tex]

in our equation we have a=1, b = 2 and c= 1

we replace it in the formula given, and we obtain:

[tex]x = \frac{-2 +/- \sqrt{2^2 -4*(1)} }{2} = \frac{-2 +/- \sqrt{4 - 4} }{2} = -2/2 = -1[/tex]

Now we got the value of x, and we could replace it in one of the equations and get the value of y:

y = -2x-5

y = -2*(-1) - 5 = 2 -5 = -3

then the pair is (-1, -3)

and the correct option is D.

Answer:

Craig earns $1,200 each month

Explanation:

We are given that Craig pays a total of $720 each year for his telephone service

We also know that a year has 12 months

This means that:

Craig pays [tex]\frac{720}{12}= 60[/tex] dollars each month for his telephone services

We are given that the monthly phone bill is [tex]\frac{1}{20}[/tex] of his monthly earnings

Assume that his monthly payment is x

We have:

[tex]\frac{1}{20}x = PhoneBill\\ \\ \frac{1}{20}x = 60\\ \\   x=60*20 = 1200[/tex] dollars

Hope this helps :)

Craig earns about $1200 each month and pays a total of $720 each year for his telephone service.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the amount earned each month

Hence:

(1/20)x * 12 months = 720

x = 1200

Craig earns about $1200 each month and pays a total of $720 each year for his telephone service.

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It should be 44ft high

For this case we have that the height of the stack of sheets is given by the number of sheets multiplied by the thickness of each. That is to say:

[tex]\frac {3} {16} * 14 = \frac {14 * 3} {16} = \frac {42} {16} = \frac {21} {8} = 2.625[/tex]

Thus, the height of the stack is 2,625 inches

Answer:

2.625 inches

D. x < -2

(Divide 4 by -2 to isolate x)

-4 is the slope........

Answer:

4

Step-by-step explanation:

To find slope, we will rewrite this equation into slope-intercept form, y=mx+b, where m is the slope and b is the y-intercept,

- 4x + y = -1

+ 4x         +4x

y= -1 + 4x

y=4x - 1

Answer:

H

Step-by-step explanation:

6 times 6 is 36

252/36 is seven which is h

The length of height of the box is 7 inches.

A quadrilateral is a shape with four sides, four vertices, and four angles that is only two dimensional. Convex and concave are the two main forms. Convex quadrilaterals can also be divided into a number of subgroups, including trapezoids, parallelograms, rectangles, rhombus, and squares.

Given that,

Length of box = 6 in.

Width of box   = 6 in.

Volume of box = 252 square in.

Since the length and width of box are same,

Therefore its shape is cuboid.

We know that volume of cuboid = length x width x height

Therefore,

Height of the box = volume/(length x width)

                             = 252/(6x6)

                             = 7 in.

Hence, the required height = 7in.

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answer-

he should mix 16lbs of the 7.80 mix and 8lbs of the 11.40 mix

Step-by-step explanation:

hope this helps:) btw im a student at rsm and i got this for homework so ya. your welcome also, ik the answers wrong ...s i g h...

Answer:

The merchant should mix 53.33 pounds of cheaper cacao and 26.67 pounds of costlier cacao.

Step-by-step explanation:

A merchant wants to blend 80 pounds of cacao worth $9.00 a pound from two kinds: one at $11.40 a pound and the other at $7.80 a pound.

Let the number of pounds of cheaper cacao be x

Let the number of pounds of costlier cacao be y

The merchant wants total pounds = 80

So, first equation becomes:

[tex]x+y=80[/tex] or [tex]x=80-y[/tex]

Now values of per pounds become [tex]7.80x[/tex] and [tex]11.40y[/tex]

As the merchant wants the mixture worth $9 so second equation becomes:

[tex]7.80x+11.40y=9(80)[/tex]

=> [tex]7.80x+11.40y=720[/tex]

Substituting [tex]x=80-y[/tex] in second equation, we get

[tex]7.80(80-y)+11.40y=720[/tex]

=> [tex]624-7.80y+11.40y=720[/tex]

=> [tex]3.60y=96[/tex]

[tex]y=26.67[/tex] pounds

We know, [tex]x=80-y[/tex]

=> [tex]x=53.33[/tex] pounds

So, The merchant should mix 53.33 pounds of cheaper cacao and 26.67 pounds of costlier cacao.

We can check this:

[tex]53.33(7.80)+26.67(11.40)=720.012[/tex] dollars

The answer is $0.60.

Calculate the mean of the first week

Calculate the mean of the second week

Subtract the mean for the first from the mean of the second week.

Answer:

f(1/3) = 1

Step-by-step explanation:

Given

f(n)=3n

We have to find f(1/3).

In order to find the value of the given function at a point, we put the value in the function where the variable is used.  

i.e. to find f(2) for f(x); x will be replaced by 2 in the function. Similarly to find f(1/3), we will replace n by 1/3 in the function.

So to find  

f(1/3)=3*  1/3

=1

So, the value of f(1/3) is 1 ..