A film set designer is using white and colored tiles in a pattern to create paths of different lengths. If x is the length of the path in feet, the number of colored tiles needed to make it is calculated using the rule

(8x2y2)(3xy)

where y represents the number of white tiles.

Which simplified expression represents the number of colored tiles used for a path of length x feet?

24x3y3
11x3y3
24x2y2
11x2y2

ANSWER

(f.g)(x)

EXPLANATION

From the table we can observe the following patterns:

f(-6)=12

g(-6)=-6

h(-6)=-72=12×-6

f(0)=3

g(0)=0

h(0)=0=3×0

f(6)=-6

g(6)=6

h(6)=-36=-6×6

Hence the h(x) is obtained by multiplying f(x) by g(x).

h(x)=(f.g)(x)

Answer:

B

Step-by-step explanation:

This quadratic factors.

x^2 - 15x + 56

= (x - 7)(x - 8)

x - 7 = 0

x = 7

=====

x - 8 = 0

x = 8

====

{7,8}

Answer:

2 cake donuts

Step-by-step explanation:

This is a question on probability, which means that we can find:

# of wanted outcomes/total outcomes.

Wanted outcomes: Vicky ate 3 cake donuts, so our value is 3.

Total outcomes: Vickey ate 3 + 4 + 8 = 15 donuts, so our value is 15.

Plug in: 3/15

Simplify: 1/5

So 1/5 of donuts Vicky eats will probably be cake donuts.

1/5 * 10 = 2

Answer: $92.53

Step-by-step explanation:

95 x 0.026 = 2.47

95 - 2.47 = $92.53

Answer:

Step-by-step explanation:

Euler's formula is

V - E + F = 2

Givens

V = 15

E = 15

F = ?

Solution

15 - 15 + F = 2

F = 2

I'm not sure this makes sense, but it is what the formula gives you.

The student can calculate the number of edges in a polyhedron by using Euler's formula for polyhedra. Given the number of faces and vertices, both being 15, we solve for edges and find that the polyhedron would have 28 edges.

The student wants to calculate the missing number of edges in a geometrical shape given the number of faces and vertices. This can be solved in mathematics using Euler's formula for polyhedra which is Faces + Vertices - Edges = 2. In the current situation, where the shape has 15 faces and 15 vertices, you can solve for edges. Inserting these values into Euler's equation yields: 15 (faces) + 15 (vertices) - Edges = 2. As a result, Edges = 15 + 15 - 2 = 28 edges.

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Answer:431⁄500

Step-by-step explanation:

Answer:

x =34

Step-by-step explanation:

The sum of the angles of a triangle add to 180

The two angles in the middle are vertical angles to they are both 56 degrees

56+x+90 = 180

Combine like terms

146 +x = 180

Subtract 146 from each side

146-146 +x = 180-146

x = 34

ANSWER

B.[tex] (x + 6)^{4} [/tex]

EXPLANATION

The given functions are:

f(x)=x+6

and

[tex]g(x)= {x}^{4} [/tex]

We want to find

[tex]g(f(x)) = g(x + 6)[/tex]

This is the composition of functions, where one function becomes the input of the second function.

We plug in x+6 into the expression for g(x) to obtain,

[tex]g(f(x)) = (x + 6)^{4} [/tex]

The correct answer is B.

43/60 would be the probability

The required estimation is [tex]P(A)=\frac{43}{60}[/tex]

Important information:

Number of observation=60

Number of expected outcomes =43

Probability: Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed between zero and one. So, the formula probability is,

P(A)=Expected observation/number of observations

Now, substituting the given values into the above formula we get,

[tex]P(A)=\frac{43}{60}[/tex]

Learn more about the topic probability:

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Answer: $1,950 explanation: 1500 x 0.05 =75 75 x 6 years = 450. 1500+450=1950

assuming simple interest.

[tex]\bf ~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$1500\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\dotfill &6 \end{cases} \\\\\\ A=1500[1+(0.05)(6)]\implies A=1500(1.3)\implies A=1950[/tex]

Answer:

(5,-6)

Step-by-step explanation:

When you write the equation of a circle in the form

[tex](x-x_0)^2+(y-y_0)^2=r^2[/tex]

Then the center of the circle will be [tex](x_0,y_0)[/tex] and the radius will be [tex]r[/tex].

Answer:  The center of the given circle is (5, -6).

Step-by-step explanation:  We are given to find the center of the circle represented by the following equation :

[tex](x-5)^2+(y+6)^2-4^2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We know that

the STANDARD equation of a circle with center (h, k) and radius r units is given by

[tex](x-h)^2+(y-k)^2=r^2.[/tex]

From equation (i), we have

[tex](x-5)^2+(y+6)^2=4^2\\\\\Rightarrow (x-5)^2+(y-(-6))^2=4^2.[/tex]

Comparing with the standard form, we get that the center of the given circle is (h, k) = (5, -6).

Thus, the center of the given circle is (5, -6).

Answer:

[tex]LW=17.5\ units[/tex]

Step-by-step explanation:

we know that

In the right triangle LAY

Find the measure of side LY applying the Pythagoras Theorem

[tex]LY^{2} =3.5^{2}+ 7.0^{2} \\ \\ LY^{2} =61.25\\ \\ LY=\sqrt{61.25}\ units[/tex]

Find the cosine of angle ALY

[tex]cos(<ALY)=\frac{LA}{LY}[/tex]

[tex]cos(<ALY)=\frac{3.5}{\sqrt{61.25}}[/tex] -----> equation A

In the right triangle LWY

[tex]cos(<ALY)=\frac{LY}{LW}[/tex]

[tex]cos(<ALY)=\frac{\sqrt{61.25}}{LW}[/tex] -----> equation B

equate equation A and equation B and solve for LW

[tex]\frac{3.5}{\sqrt{61.25}}=\frac{\sqrt{61.25}}{LW}[/tex]

[tex]LW=(\sqrt{61.25})(\sqrt{61.25})/3.5[/tex]

[tex]LW=17.5\ units[/tex]

Answer:

There

Step-by-step explanation:

Answer:

-2040

Step-by-step explanation:

[tex]S_n=a_1\dfrac{r^n-1}{r-1} \qquad\text{for first term $a_1$ and common ratio r}\\\\S_8=-8\dfrac{2^8-1}{2-1}=-2040[/tex]

The sum of the first 8 terms is -2040.

Answer:

The remainder is 0 ⇒ 3rd answer

Step-by-step explanation:

* In the synthetic calculation we use the coefficient of the dividend

  with the value of x when the divisor = 0

∵ x - 1 = 0 ⇒ add 1 to both sides

∴ x = 1  

Step 1 : Write down the coefficients of the f(x) , put x = 1 at the left  

                         1        1     0     -1     1     -1    

                                ________________

Step 2 : Bring down the first coefficient to the bottom row.

                        1         1      0    -1     1    -1    

                               ________________

                                   1

Step 3 : Multiply it by 1, and carry the result into the next column.

                       1         1      0    -1     1    -1    

                               ____ 1_________

                                  1  

Step 4 : Add down the column

                       1        1       0    -1     1    -1    

                                ____1__________

                                 1      1

Step 5 : Multiply it by 1, and carry the result into the next column

                       1        1      0     -1     1     -1    

                              _____1___1_______

                                 1       1

Step 6 : Add down the column

                      1         1       0    -1      1     -1    

                                ____1___1______

                                 1       1      0

Step 7 : Multiply it by 1, and carry the result into the next column

                    1        1       0    -1      1     -1    

                               ___1___1___0______

                              1      1      0

Step 8 : Add down the column

                    1         1     0      -1      1      -1  

                          _____1____1__0_____

                              1      1       0      1

Step 9 : Multiply it by 1, and carry the result into the next column

                  1         1     0      -1       1      -1  

                          ____1____1___0___1___

                            1     1        0      1        

Step 10 : Add down the column

                  1         1     0      -1       1      -1  

                          ____1____1___0___1___

                            1     1        0      1         0

∴ The quotient is (x³ + x² + 1 ) and the remainder is 0

* The remainder is 0

Answer:

14 five-dollar bills

Step-by-step explanation:

Let

x-----> the number of five-dollar bills

y----> the number of twenty-dollar bills

we know that

x+y=32 ----> y=32-x ----> equation A

5x+20y=430 ----> equation B

Substitute equation A in equation B and solve for x

5x+20(32-x)=430

5x+640-20x=430

20x-5x=640-430

15x=210

x=14 five-dollar bills

Find the value of y

y=32-x ----> y=32-14=18 twenty-dollar bills

ANSWER

[tex]x \: < \: - 8[/tex]

EXPLANATION

The given inequality is

[tex]3 - (2x - 5) \: < \: - 4(x + 2)[/tex]

Expand:

[tex]3 - 2x + 5 \: < \: - 4x - 8[/tex]

Group similar terms, to obtain:

[tex] - 2x + 4x\: < \: - 8 - 5 - 3[/tex]

Combine similar terms:

[tex]2x\: < \: - 16[/tex]

Divide both sides by 2 to get,

[tex]x \: < \: - 8[/tex]

Answer: 40 per square mile

Step-by-step explanation: 800/20

Find the difference between 45 and 55:

55-45 = 10

Find the difference between the mpg for 45 and 55:

35 - 34.1 = 0.9

Divide the difference in mpg by the difference in x:

0.9 / 10 = 0.09

The answer is B.

Answer:

Option B: 0.09 mpg/mph

Step-by-step explanation:

You divide the delta (=difference) in F by the delta in x:

delta F is 35.0-34.1 = 0.9

delta x = 55-45 = 10

so rate of change is 0.9/10 = 0.09, answer B

Answer:

Step-by-step explanation:

[tex]\log_ab=c\iff a^c=b\\\\Domain:\ x+2>0\to x>-2\\\\\log_3(x+2)-8=-2\qquad\text{add 8 to both sides}\\\\\log_3(x+2)=6\iff x+2=3^6\\\\x+2=729\qquad\text{subtract 2 from both sides}\\\\x=727\in D[/tex]

The answer is is x=727 ^^

Answer:

see explanation

Step-by-step explanation:

Subtract [tex]\frac{2}{3x}[/tex] from both sides

[tex]\frac{1}{6}[/tex] = [tex]\frac{4}{3x}[/tex] - [tex]\frac{2}{3x}[/tex] = [tex]\frac{4-2}{3x}[/tex] = [tex]\frac{2}{3x}[/tex]

Cross- multiply

3x = 12 ( divide both sides by 3 )

x = 4

As a check

Substitute x = 4 into the equation and if both sides are equal then it is the solution.

left side

[tex]\frac{2}{12}[/tex] + [tex]\frac{1}{6}[/tex] = [tex]\frac{1}{6}[/tex] + [tex]\frac{1}{6}[/tex] = [tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]

right side

[tex]\frac{4}{12}[/tex] = [tex]\frac{1}{3}[/tex]

Both sides are equal hence x = 4 is the solution

ANSWER

[tex]x = 11[/tex]

EXPLANATION

According to the exterior angle theorem, the sum of remote interior angles equal an exterior angle.

This implies that,

[tex](7x + 7) \degree + 66 \degree =(1 2x + 18) \degree[/tex]

We group the similar terms to get:

[tex]7 + 66 - 18 = 12x - 7x[/tex]

[tex]55= 5x[/tex]

Divide both sides by 5.

[tex]x = \frac{55}{5} [/tex]

[tex]x = 11[/tex]

Answer:

No answer

Step-by-step explanation:

I don't think this equation has an answer.

Normally, you'd try to combine like terms

3 3/4 = 2 + 3/4

3 3/4 = 2 3/4

3 and 3/4 is not equal to 2 and 3/4.

So, I believe this equation has no answer

Answer:

x-1

Step-by-step explanation:

(3)(2)+5x-(5)(2)-4x+5-2

=6+5x-10-4x+5-2

=x-1

Answer:

-2x2+x+3

Step-by-step explanation:

you have to combine like terms

-5x2+ 3x2= -2x2

5x-(-4x)= x

5-2=3

-2x2+x+3

on the twelfth day because 3-6-9-12 and 12

Billy will have both swimming and piano lessons on the same day every 12th day.

To determine when Billy will have both swimming and piano lessons on the same day, we need to find the least common multiple (LCM) of the two schedules. Billy has swimming lessons every 3rd day and piano lessons every 12th day.

The LCM of 3 and 12 is the smallest number that both 3 and 12 can divide into without leaving a remainder. The prime factorization of 12 is [tex](2^2 \times 3\))[/tex], and the prime factorization of 3 is simply 3 . To find the LCM, we take the highest powers of all prime factors that appear in the factorization of both numbers:

For 3: [tex]\(3^1\)[/tex]

For 12: [tex]\(2^2 \times 3^1\)[/tex]

The LCM is [tex]\(2^2 \times 3^1 = 4 \times 3 = 12\)[/tex].

Since the LCM of 3 and 12 is 12, Billy will have both lessons on the same day every 12th day. This is because every 12th day is a day when both his 3-day swimming lesson cycle and his 12-day piano lesson cycle align.

Answer:

It's B. 1/6^9

Step-by-step explanation:

It is simplified to 6^-9 which is equal to 1/6^9.

Answer:

Step-by-step explanation:

[tex]\csc B=\dfrac{1}{\sin B}\\\\-1\leq\sin B\leq1,\ \text{therefore}\ \csc B\leq-1\ or\ \csc B\geq1\\\\-1.75\leq-1\\\\0.5\to \bold{ANSWER}\\\\1\geq1\\\\1.05\geq1[/tex]

By definition, the cosecant is the inverse of the sine:

[tex]\csc(x) = \dfrac{1}{\sin(x)}[/tex]

Since the sine is never more than 1, the cosecant can never be smaller than 1.

So, the only impossible option is 0.5.

Answer:

the answer is c

Step-by-step explanation:

Answer:

The angles are 65° and 115°

Step-by-step explanation:

Let

x,y ----> the two side interior angles of two parallel lines

we know that

x+y=180° ----> equation A

x-y=50° ----> equation B

Adds equation A and equation B

x+x=180°-50°

2x=130°

x=65°

Find the value of y

x+y=180° -----> 65°+y=180° ----> y=180°-65°=115°

therefore

The angles are 65° and 115°

Answer:

The baton will not fit in the rectangular box

Step-by-step explanation:

step 1

Find the diagonal of the base of the  rectangular base and then compare with the length of the baton

Applying the Pythagoras Theorem

Let

x ----> the length of the diagonal base of rectangular box

we know that

[tex]x^{2}=13^{2}+35^{2} \\ \\x^{2} =1,394\\ \\x= 37.3\ in[/tex]

[tex]38\ in > 37.3\ in[/tex]

therefore

The baton will not fit in the rectangular box