How can a frequency table or histogram help you organize and analyze data?

Answer:

Distributive property

Step-by-step explanation:

The 2 shares a product/multiplies with both the 5 and 7.

Answer:

ans is 5.

hope it will help you.

There seems to be one character missing. But I gather that f(x) needs to satisfy

• [tex]x^3[/tex] divides [tex]f(x)[/tex]

• [tex](x-1)^3[/tex] divides [tex]f(x)^2[/tex]

I'll also assume f(x) is monic, meaning the coefficient of the leading term is 1, or

[tex]f(x) = x^5 + \cdots[/tex]

Since [tex]x^3[/tex] divides [tex]f(x)[/tex], and

[tex]f(x) = x^3 p(x)[/tex]

where [tex]p(x)[/tex] is degree-2, and we can write it as

[tex]f(x)=x^3 (x^2+ax+b)[/tex]

Now, we have

[tex]f(x)^2 = \left(x^3p(x)\right)^2 = x^6 p(x)^2[/tex]

so if [tex](x - 1)^3[/tex] divides [tex]f(x)^2[/tex], then [tex]p(x)[/tex] is degree-2, so [tex]p(x)^2[/tex] is degree-4, and we can write

[tex]p(x)^2 = (x-1)^3 q(x)[/tex]

where [tex]q(x)[/tex] is degree-1.

Expanding the left side gives

[tex]p(x)^2 = x^4 + 2ax^3 + (a^2+2b)x^2 + 2abx + b^2[/tex]

and dividing by [tex](x-1)^3[/tex] leaves no remainder. If we actually compute the quotient, we wind up with

[tex]\dfrac{p(x)^2}{(x-1)^3} = \underbrace{x + 2a + 3}_{q(x)} + \dfrac{(a^2+6a+2b+6)x^2 + (2ab-6a-8)x +2a+b^2+3}{(x-1)^3}[/tex]

If the remainder is supposed to be zero, then

[tex]\begin{cases}a^2+6a+2b+6 = 0 \\ 2ab-6a-8 = 0 \\ 2a+b^2+3 = 0\end{cases}[/tex]

Adding these equations together and grouping terms, we get

[tex](a^2+2ab+b^2) + (2a+2b) + (6-8+3) = 0 \\\\ (a+b)^2 + 2(a+b) + 1 = 0 \\\\ (a+b+1)^2 = 0 \implies a+b = -1[/tex]

Then [tex]b=-1-a[/tex], and you can solve for a and b by substituting this into any of the three equations above. For instance,

[tex]2a+(-1-a)^2 + 3 = 0 \\\\ a^2 + 4a + 4 = 0 \\\\ (a+2)^2 = 0 \implies a=-2 \implies b=1[/tex]

So, we end up with

[tex]p(x) = x^2 - 2x + 1 \\\\ \implies f(x) = x^3 (x^2 - 2x + 1) = \boxed{x^5-2x^4+x^3}[/tex]

Answer:

It moved for 152.7 seconds

Step-by-step explanation:

Time taken/ period, T :

[tex]{ \sf{T = \frac{distance}{speed} }}[/tex]

substitute the variables:

[tex]{ \sf{T = \frac{8482}{(200 \times 1000)} }} \\ \\ { \sf{T =0.042 \: hours }}[/tex]

In seconds:

[tex]{ \sf{T = (0.042 \times 3600) \: s}} \\ { \sf{T = 152.7 \: seconds}}[/tex]

Answer: 68.25 hrs.

Step-by-step explanation:

200 Km. to miles = 124.274 miles

8482 mi/124.274 mi =

68.25 hours

Answer:

X>-4

Y>-18

X>-7

I hope this helps

Step-by-step explanation:

f(g(x))=(3x+1)^2 +2(3x+1) -4

=9x^2 +6x +1 +6x +2 -4

=9x^2 +12x +(-1)

Answer:

a =15, b=2

Axis of Symmetry = [tex]\frac{-b}{2a}[/tex]

[tex]=\frac{-2}{2 * 15}[/tex]

= [tex]-\frac{1}{15}[/tex]

To find the y-value for the vertex sub in the axis of symmetry for x

[tex]y=15(-\frac{1}{15} )^{2}+2(-\frac{1}{15} )-8\\\\=-\frac{121}{15}[/tex]

∴ Vertex [tex](-\frac{1}{15}, -\frac{121}{15} )[/tex]

Step-by-step explanation:

Answer:

832.4 KWH of energy

Step-by-step explanation:

Find how many KWH of energy were used by dividing the total cost by 0.12:

99.89/0.12

= 832.4

So, approximately 832.4 KWH of energy were used that month.

Answer:

The three even, consecutive integers are 72, 74, and 76.

Step-by-step explanation:

Let a be the first even integer.

Then the other two consecutive integers, b and c, will be represented by:

[tex]\displaystyle b = a + 2 \text{ and } \\ \\ c = b + 2 = (a + 2) + 2 = a + 4[/tex]

One-sixth of the smallest (that is, a) is three less than one-tenth the sum of the other two even integers (that is, b and c).

Therefore:

[tex]\displaystyle \frac{1}{6} a = \frac{1}{10}\left( b +c\right) - 3[/tex]

Solve for a. Substitute:

[tex]\displaystyle \frac{1}{6} a =\frac{1}{10}\left((a+2)+(a+4)\right) - 3[/tex]

Simplify and solve for a:

[tex]\displaystyle \begin{aligned} \frac{1}{6} a &= \frac{1}{10}(2a + 6) - 3 \\ \\ \frac{1}{6} a &= \frac{1}{5} a + \frac{3}{5} - 3\\ \\ -\frac{1}{30} a &= -\frac{12}{5} \\ \\ a &= 72\end{aligned}[/tex]

Hence, the first even integer is 72.

Therefore, the two other consecutive even integers must be 74, and 76.

In conclusion, the three even, consecutive integers are 72, 74, and 76.

The volume of a rectangular prism is the product of the prism's dimension (i.e. length, width and height). The dimension of the rectangular prism are:

[tex]Length = 3x^2\\ Width = 2x - 1\\ Height = 3x + 4[/tex]

Given that:

[tex]Volume = (18x^4 + 15x^3 - 12x^2)[/tex]

First, we factor out [tex]3x^2[/tex]

[tex]Volume = 3x^2 \times (6x^2 + 5x - 4)[/tex]

Expand

[tex]Volume = 3x^2 \times (6x^2 + 8x-3x - 4)[/tex]

Factorize

[tex]Volume = 3x^2 \times (2x(3x + 4) -1(3x + 4))[/tex]

Factor out [tex]3x + 4[/tex]

[tex]Volume = 3x^2 \times ((2x -1) (3x + 4))[/tex]

Rewrite as:

[tex]Volume = 3x^2 \times (2x -1) \times (3x + 4)[/tex]

The volume of a rectangular prism is:

[tex]Volume = Length \times Width \times Height[/tex]

So; by comparison:

[tex]Length = 3x^2\\ Width = 2x - 1\\ Height = 3x + 4[/tex]

Read more about polynomials and volumes at:

https://brainly.com/question/2141804

Answer:

3x^2 -2x + 1 =3(x^2-2/3x+1/3)=3(x-1/3)^2+2/9*3= 3(x-1/3)^2+2/3

(x-1/3)^2 is greater or equal to zero

3(x-1/3)^2 is greater or equal to zero

and 2/3 is greater than zero

So there sum is greater than zero

Proved

Step-by-step explanation:

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

Consider x^2-2/3x+1/3

Remember that (a-b)^2 =a^2-2ab+b^2

x^2=a^2

a=x

-2/3x= -2*x*b

b=1/3

S0 (x-1/3)^2= x^2-2/3x+1/9

x^2-2/3x+1/3= x^2-2/3x+1/9+1/3-1/9= (x-1/3)^2+2/9

3x^2 -2x + 1 =3(x^2-2/3x+1/3)=3(x-1/3)^2+2/9*3= 3(x-1/3)^2+2/3

(x-1/3)^2 is greater or equal to zero

3(x-1/3)^2 is greater or equal to zero

and 2/3 is greater than zero

So there sum is greater than zero

Proved

Answer:

Step-by-step explanation:

(f o g) is the same as f(g(x))

f(x) = -6x, substitute x with g(x) = -6x+5

f(g(x)) = -6g(x) = -6(-6x+5) = 36x -30

(f o g) = 36x -30

Answer:5 units

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Answer:

h= 2A/a+b

Step-by-step explanation:

you know the gig

Step-by-step explanation:

A ratio is a way to show a relationship or compare two numbers of the same kind. We use ratios to compare things of the same type.

Answer:

12

Step-by-step explanation:

36/12=3

48/12=4

Answer:

highest common factor of 36 and 48 is 12

9514 1404 393

Answer:

  AC = AB

Step-by-step explanation:

The attached diagram shows the only segments that are the same length are ...

  AC = AB

__

A and B lie on the same vertical line, 5 units apart. A and C are separated by 3 units vertically and 4 units horizontally, so AC is the hypotenuse of a 3-4-5 right triangle.

Answer:x_1= -1 or x_2= -6

Step-by-step explanation:

In the pictures

By using factorization, [tex]\[\dfrac{2x}{x + 2} = -\dfrac{6}{x + 4}.\][/tex] , values of x are -2, 3.

Factorization can be defined as the process of breaking down a number into smaller numbers which when multiplied together arrive at the original number.

These numbers are broken down into factors or divisors.

For an integer, factorization is decomposition of that integer in terms of smaller integers which when multiplied with each other give back that considered number and these composing integers are called factors of that considered integers.

Given

[tex]\[\dfrac{2x}{x + 2} = -\dfrac{6}{x + 4}.\][/tex]

Cross multiplication;

2x(x + 4) = 6(x + 2)

[tex]2x^{2} + 8x = 6x + 12\\\\2x^{2} + 8x - 6x - 12 = 0\\\\2x^{2} + 2x - 12 = 0\\\\x^{2} + x - 6 = 0[/tex]

Divide above equation by 2, we get

[tex]x^{2} + x - 6 = 0[/tex]

(x +2) (x-3)

x = -2, 3

Therefore, By using factorization, [tex]\[\dfrac{2x}{x + 2} = -\dfrac{6}{x + 4}.\][/tex] , values of x are -2, 3.

Find out more information about factorization here;

brainly.com/question/1863222

#SPJ2

Answer:

$46.20

Step-by-step explanation:

The discount of 30% brings the price down to $42, and then the sales tax would be $4.20, making the answer $46.20

Answer:

16,500

Step-by-step explanation:

thats it

Hi! I'm happy to help!

Point slope form states that y-[tex]y_{1}[/tex]=m(x-[tex]x_{1}[/tex]). m represents your slope (rise/run) and [tex]y_{1}[/tex] and [tex]x_{1}[/tex] represent your first y and x points, and y and x represent your second y and x points. We already have our equation here:

y - 4 = 1/4(x- 8)

Now, let's dive into what slope-intercept form is. Slope intercept form states that y=mx+b. m represents our slope, b represents our y intercept, y represents a y point, and x represents the corresponding x point.

Since we know our m, we can solve for b, by using our other numbers. Let's use our first set of coordinates.

4=1/4(8)+b

4=2+b

2=b

Now our second set to double check:

2=1/4(0)+b

2=0+b

2=b

We know that b must equal 2, so our equation must be y=1/4x+2, which is  option 3.

You should pick option 3.

(y-intercept is where the line hits the y-axis(when x=0). We could've used our second coordinates (0,2), where x equals 0 to know that 2 is the y-intercept (b). This shortcut only works on specific problems though.)

I hope this was helpful, keep learning! :D

Answer:

OPTION B

Step-by-step explanation:

SEE THE IMAGE FOR SOLUTION

HOPE IT HELPS

HAVE A GREAT DAY

Answer:

Remaining balance is $12.2

Step-by-step explanation:

see all steps in picture.

Answer:

Distance btw (-2, -2) and (8, -6) is (10, -4)

Step-by-step explanation:

I. Give (-2, -2) is A and (8, -6) is B

                     B - A = 8 - (-2) in x

                              = -6 - (-2) in y

                    So B - A = 10, -4

II. You can prove the answer by A.value + (10, -4) = B.value

Hope that help :D

Hi ;-)

[tex]\text{A}=(-2,-2) \ \text{and} \ \text{B}=(8,-6)\\\\|AB|=\sqrt{(8-(-2))^2+(-6-(-2))^2}\\\\|AB|=\sqrt{(8+2)^2+(-6+2)^2}\\\\|AB|=\sqrt{10^2+(-4)^2}\\\\|AB|=\sqrt{100+16}\\\\|AB|=\sqrt{116}\rightarrow\boxed{|AB|=2\sqrt{29}} \ (\text{because} \ 116=4\cdot29)[/tex]

Answer:

(a+b+c) (x+y+z)

Step-by-step explanation:

hope this helps to uh

Step-by-step explanation:

x+y+z+bx+by+bz+cx+cy+cz

Take Like terms

x+bx+cx+y+by+cy+z+bz+cz

x(b+c)+y(b+c)+z(b+c)

(x+y+z)(b+c)

hope it helps

Answer:

This is called a bisector.

Steps:-

First put the vertices on graph and find Triangle ABC .

Then Transact it the give amount i.e 5units and get A'B'C'