Sketch the quadratic function f(x) = -2x2 + 4x + 6. Which key feature of the graph is not true?
A) maximum (1, 8)
B) y-intercept (0, 6)
C) x-intercept (3, 0)
D) x-intercept (-2, 0)

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:

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:

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

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.

Answer: [tex]tan(x)=\±\frac{3}{4}[/tex]

Step-by-step explanation:

You know that [tex]sin(x)=\frac{3}{5}[/tex] and you can identify that. Then:

[tex]sin^2(x)=(\frac{3}{5})^2[/tex]

[tex]sin^2(x)=\frac{9}{25}[/tex]

Remember that:

[tex]cos^2(x)=1-sin^2(x)[/tex]

Then [tex]cos^2(x)[/tex] is:

[tex]cos^2(x)=1-\frac{9}{25}\\\\cos^2(x)=\frac{16}{25}[/tex]

Apply square root to both sides to find cos(x):

[tex]\sqrt{cos^2(x)}=\±\sqrt{\frac{16}{25}}\\cos(x)=\±\frac{4}{5}[/tex]

Remember that:

[tex]tan(x)=\frac{sin(x)}{cos(x)}[/tex]

Then, this is:

[tex]tan(x)=\frac{\frac{3}{5}}{\±\frac{4}{5}}[/tex]

[tex]tan(x)=\±\frac{3}{4}[/tex]

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:

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:

m = 1/3

Step-by-step explanation:

When you multiply by a fraction it's actually dividing.

:)

The variable m equals 1/3 for the equation 2 = 6m obtained by dividing both sides by 6.

The given equation is 2=6m.

m is the variable in the equation.

To determine the value of m in the equation 2 = 6m, we need to isolate the variable m.

Divide both sides of the equation by 6:

2/6 = (6m)/6

1/3 = m

Therefore, m equals 1/3.

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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

[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:

- 13

Step-by-step explanation:

To evaluate h(j(2)) substitute x = 2 into j(x) then substitute the value obtained into h(x)

j(2) = - 2 × 2 = - 4, then

h(- 4) = (3 × - 4) - 1 = - 12 - 1 = - 13

Hence h(j(2)) = - 13

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:

The top-right graph.

Step-by-step explanation:

Because f(-2) = 0.

The graph which represents the non-linear function with power 1/3 is similar graph in right side of upper option. Thus, the option B is correct.

When the graph of the function represents the straight line, then it is called the linear function.

The graph of a function in which the power of variable is more than one is called the non-linear graph.

The function given in the problem is,

f(x)=∛(x+2)

It is a non-linear function. This function can be written as,

[tex]f(x)=(x+2)^\dfrac{1}{3}[/tex]

The graph of this function is attached below. This graph passes from the point (-2,0) and (0,1.26) and looks similar to the option B (right side of upper option).

Hence, the graph which represents the non-linear function with power 1/3 is similar graph in right side of upper option. Thus, the option B is correct.

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Answer:

the answer is c

Step-by-step explanation:

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}

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:

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:

it would be b

Answer: 40 per square mile

Step-by-step explanation: 800/20

Answer: $92.53

Step-by-step explanation:

95 x 0.026 = 2.47

95 - 2.47 = $92.53

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:

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

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.

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]

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Answer:

1) y = 12

2) x = 4

3) w = -3

4) k = -35

Step-by-step explanation:

Answer:

Question 1: y = 12

Question 2: x = 4

Question 3: w = -3

Question 4: k = -35

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:

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:431⁄500

Step-by-step explanation:

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

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{1}~,~\stackrel{y_1}{-7})\qquad \stackrel{center}{(\stackrel{x_2}{-6}~,~\stackrel{y_2}{-4})}\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{radius}{r}=\sqrt{[-6-1]^2+[-4-(-7)]^2}\implies r=\sqrt{(-6-1)^2+(-4+7)^2} \\\\\\ r=\sqrt{(-7)^2+3^2}\implies r=\sqrt{58} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{-6}{ h},\stackrel{-4}{ k})\qquad \qquad radius=\stackrel{\sqrt{58}}{ r}\\[2em] [x-(-6)]^2+[y-(-4)]^2=(\sqrt{58})^2\implies (x+6)^2+(y+4)^2=56[/tex]

To find the equation of the circle with a given point (1,-7) and center (-6,-4), calculate the radius using the distance formula to find that the radius is √58, then substitute the center coordinates and radius into the standard circle equation to get (x + 6)² + (y + 4)² = 58.

To write the equation of the circle given a point on the circle at (1,-7) and the center at (-6,-4), we will use the standard form of the circle's equation (x-h)² + (y-k)² = r², where (h, k) is the center of the circle and r is the radius. First, we calculate the radius of the circle using the distance formula: r =
√[(x_2-x_1)² + (y_2-y_1)²]. Plugging in our values, we get r = √[(1 - (-6))² + (-7 - (-4))²] = √[49 + 9] = √58. Therefore, the equation of the circle with center (-6,-4) and passing through the point (1,-7) is (x + 6)² + (y + 4)² = 58.