Evaluate the expression

Answer:

See below.

Step-by-step explanation:

So, we have the zeros -4 with a multiplicity of 1, zeros 2 with a multiplicity of 3, and f(0)=64.

Recall that if something is a zero, then the equation must contain (x - n), where n is that something. In other words, for a polynomial with a zero of -4 with a multiplicity of 1, then (x+4)^1 must be a factor.

Therefore, (x-2)^3 (multiplicity of 3) must also be a factor.

Lastly, f(0)=64 tells that when x=0, f(x)=64. Don't simply add 64 (like what I did, horribly wrong). Instead, to keep the zeros constant, we need to multiply like this:

In other words, we will have:

[tex]f(x)=(x+4)(x-2)^3\cdot n[/tex], where n is some value.

Let's determine n first. We know that f(0)=64, thus:

[tex]f(0)=64=4(-2)^3\cdot n[/tex]

[tex]64=-32n, n=-2[/tex]

Now, let's expand:

Expand:

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

[tex]f(x)=(x^2+2x-8)(x^2-4x+4)(-2)[/tex]

[tex]f(x)=(x^4-4x^3+4x^2+2x^3-8x^2+8x-8x^2+32x-32)(-2)[/tex]

[tex]f(x)=-2x^4+4x^3+24x^2-80x+64[/tex]

This is the simplest it can get.

Answer:

0

Step-by-step explanation:

3^2 is 9, and (-3)^2 is 9.

so, 9-9=0

Answer:

3

Step-by-step explanation:

Use this equation

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] substitute

-6-3/0-3 subtract

-9/-3 simplify

-3/-1 two negitives cansle out

3/1=3

Hope this helpes, if it did, please consider giving me brainliest, it will help me a lot. If you have any questions, feel free to ask.

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Answer:

3

Step-by-step explanation:

To find the slope, we use the slope formula

m= ( y2-y1)/(x2-x1)

   = ( -6 -3)/(0 -3)

    = -9/-3

    = 3

Answer:

x = 1/2

Step-by-step explanation:

2(4x+2) = 4x - 12(x-1)

Distribute

8x +4 = 4x - 12x +12

Combine like terms

8x + 4 = -8x +12

Add 8x to each side

8x+4+8x = -8x+12 +8x

16x+4 = 12

Subtract 4 from each side

16x +4-4 = 12-4

16x = 8

Divide by 16

16x/16 =8/16

x = 1/2

Answer:

x = 1/2

Step-by-step explanation:

2(4x+2) = 4x - 12(x-1)

Expand brackets.

8x + 4 = 4x - 12x + 12

Subtract 4 on both sides.

8x = 4x - 12x + 12 - 4

Subtract 4x and add 12x on both sides.

8x - 4x + 12x = 12 - 4

Combine like terms.

16x = 8

Divide both sides by 16.

x = 8/16 = 1/2

Answer:

  $2192.60

Step-by-step explanation:

March 4 is day 63 of the year. So, the amount of tax that Kelly needs to refund to Mason is the tax for the remaining 365 -63 = 302 days of the year.

Kelly will owe Mason ...

  (302/365)($2650) = $2192.6027 ≈ $2192.60

Answer:

P = 110N + 1,900.

$4,540.

Step-by-step explanation:

Her base salary is $1,900, so your constant/y-intercept for the equation is $1,900.

She makes an additional $110 for each copy, so your slope is $110.

P (the total pay) = 110 * the number of copies sold + 1,900

P = 110N + 1,900.

She sells 24 copies.

P =  110 * 24 + 1,900

P = 2,640 + 1,900

P = 4,540.

So, her total pay is $4,540.

Hope this helps!

Answer:

The probability that the person is between 65 and 69 inches is 0.5403

Step-by-step explanation:

Mean height = [tex]\mu = 66[/tex]

Standard deviation = [tex]\sigma = 2.5[/tex]

We are supposed to find What is the probability that the person is between 65 and 69 inches i.e.P(65<x<69)

[tex]Z=\frac{x-\mu}{\sigma}[/tex]

At x = 65

[tex]Z=\frac{65-66}{2.5}[/tex]

Z=-0.4

Refer the z table for p value

P(x<65)=0.3446

At x = 69

[tex]Z=\frac{69-66}{2.5}[/tex]

Z=1.2

P(x<69)=0.8849

So,P(65<x<69)=P(x<69)-P(x<65)=0.8849-0.3446=0.5403

Hence the probability that the person is between 65 and 69 inches is 0.5403

Answer:

Step-by-step explanation:

Let the measure of third angle be X

The sum of interior angle of triangle = X

Let's create an equation

[tex]x + 32 + 90 = 180[/tex]

Add the numbers

[tex]x + 122 = 180[/tex]

Move constant to R.H.S and change its sign

[tex]x = 180 - 122[/tex]

Subtract the numbers

[tex]x = 58[/tex] °

Hope this helps...

Best regards!!

Answer:

11 / 12 or 0.9167

Step-by-step explanation:

Given:

3/4 + 1/6

Find:

Value with expression

Computation:

"3/4 added to number 1/6"

3/4 + 1/6

By taking LCM

[9 + 2] / 12

11 / 12 or 0.9167

Answer:

a. $849.45

Step-by-step explanation:

In the above question, we are given the following information

Coupon rate = 10%

Face value = 1000

Maturity = n = 20 years

t = number of periods = compounded semi annually = 2

Percent yield = 12% = 0.12

Bond Value formula =

C/t × ([1 -( 1/ 1 + r/t)-^nt ÷] r/t) +( F/ (1 + r/t)^nt)

C = coupon rate × face value = 10% × 1000 = 100

Bond value:

= 100/2 × ( [1 - (1 /1 + 0.12/2)^-20×2]÷ 0.12/2)+ (1000/( 1 + 0.12/2)^20×2

= 50 × ( [1 - (1 /1 + 0.06) ^40] ÷ 0.06) + ( 1000/ (1 + 0.06) ^40

= 50 × ( [1 - (1/ (1.06) ^40] ÷ 0.06 ) + (1000/(1.06)^40)

= 50 × 15.046296872 + 97.222187709

= $849.45

Bond value = $849.45

Answer:

15 pt

Step-by-step explanation:

to convert qt to pt you multiply by 2 so 7 and 1/2 times 2 is 15

Answer:

2√2−3

Step-by-step explanation:

Simplify each term.

Since there are no imaginary terms, the complex conjugate is the same as the simplified expression.

Hope this can help

Answer:

number of children ticket sold = 70

number of adult ticket sold = 70 × 3 = 210

number of student ticket sold = 500 - 4(70) = 500 - 280 = 220

The number of Adult's ticket sold = 270, Children's ticket sold = 90 and Student's ticket sold = 140.

We have a local theatre that sells out for their show. They sell all 500 tickets for a total purse of $8,040.00. The tickets were priced at $15 for students, $12 for children, and $18 for adults.

Adult's ticket = [y]

Children's ticket = [x]

Student's ticket = [z]

and

y = 3x

Now -

x + y + z = 500

x + 3x + z = 500

4x + z = 500       ....[1]

and

12x + 18y + 15z = 8040

12x + 18(3x) + 15z = 8040

12x + 54x + 15z = 8040

66x + 15z = 8040     ....[2]

On solving [1] and [2], we get -

x = 90 and z = 140

and

y = 3x = 3 x 90 = 270

y = 270

Therefore, the number of Adult's ticket sold = 270, Children's ticket sold = 90 and Student's ticket sold = 140.

To solve more questions on Equations, Equation Modelling and Expressions visit the link below -

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A - No

B - No

C - Yes

D - Yes

.

C and D are alternate exterior angles

If it has a single zero that means it has to be just touching the x-axis with its tip.

We know that if it has only one zero, the discriminant equals 0.

So,

[tex]D=b^2-4ac=0\implies (-k)^2-4(1)(9)=0[/tex]

Solving for k,

[tex]k=\pm\sqrt{36}=\boxed{\pm{6}}[/tex].

Hope this helps.

Answer:

60 cm

Step-by-step explanation:

You need to use ratios to solve.  If the scale is 1:30 then the wheel is 2:(?).  Cross-multiply the fractions and solve for x.

1/30 = 2/x

1x = 30*2

x = 60

The wheel is 60 cm in diameter.

Answer:

60 centimeters

Step-by-step explanation:

The scale is 1:30. The wheel diameter is 2 while the actual size of the wheel is unknown. Therefore, the scale for the wheel is 2:x

Let’s set up a proportion.

1/30=2/x

First, cross multiply. Multiply the numerator of the first fraction by the denominator of the second. Then, multiply the numerator of the second by the denominator of the first.

1*x= 2*30

1x=20*30

x=20*30

x=60

Add appropriate units, in this case centimeters (cm).

x= 60 cm

The actual diameter of the wheel is 60 centimeters.

Answer:

3 is not a solution

Step-by-step explanation:

6x – 7 = 12?

Substitute 3 in for x and see if the equation is true

6*3 - 7 = 12

18-7 = 12

11 =12

This is false so 3 is not a solution

Greetings from Brasil...

The equation is:

putting COS X for the 2nd member

- √(1 - 3.COS² X) = - COS X     ×(- 1)

√(1 - 3.COS² X) = COS X          everything squared

[√(1 - 3.COS² X)]² = (COS X)²

1 - 3.COS² X = COS² X

1 - 3.COS² X - COS² X = 0

1 - 4.COS² X = 0

making Y = COS X

1 - 4Y² = 0

- 4Y² = - 1     ×(- 1)

4Y² = 1

Y² = 1/4

Y = ±√1/4

Y = ± 1/2    

so, as we saw above

Y = COS X

1/2 = COS X   and   - 1/2 = COS X

so to get COS X = ± 1/2, then

X = π/3 = 60         (cos +)

X = 2π/3 = 120      (cos -)

X = 4π/3 = 240    (cos -)

X = 5π/3 = 300     (cos +)

So the only option that includes + and - its:

60° + n360° , 120° + n360°

4x+21+3x-5=121

7x+16=121

x=15

angle ABD =4(15)+21=81

Concepts:

Answer:

First option and fifth option

-2x-1=3^(-x) and 2^(-x)+2= -5^x + 3 don't intersect.

Therefore, the graphs have no solution.

Answer:

Step-by-step explanation:

Given,

Radius ( r ) = 10

Height ( h ) = 6

pi ( π ) = 3.14

now, let's find the volume of given cone:

[tex]\pi {r}^{2} \frac{h}{3} [/tex]

Plug the values

[tex] = 3.14 \times {10}^{2} \times \frac{6}{3} [/tex]

Evaluate the power

[tex] = 3.14 \times 100 \times \frac{6}{3} [/tex]

Calculate

[tex] = 628 \: {units}^{3} [/tex]

Hope this helps..

Best regards!!

Answer:

The answer is 200π units³ .

Step-by-step explanation:

Given that the formula of volume of cone is V = 1/3×π×r²×h where r represents radius and h is height. Then, you have to substitute the value of radius and height into the formula :

[tex]v = \frac{1}{3} \times \pi \times {r}^{2} \times h[/tex]

[tex]let \: r = 10 \: , \: h = 6[/tex]

[tex]v = \frac{1}{3} \times \pi \times {10}^{2} \times 6[/tex]

[tex]v = \frac{1}{3} \times \pi \times 600[/tex]

[tex]v = 200\pi \: {units}^{3} [/tex]

Answer:

Look for perpendicular lines or corresponding angles or alternate interior angles.

Step-by-step explanation:

When you want to show that a quadrilateral is a parallelogram you need to show that the oposite sides are parallel. In order to show that two segments are parallel there are various theorems and definitions you can use.

1 -  Remember that two lines perpendicular to the same segment are parallel.

2 - When two lines are cut by a secant and their alternate interior angles are congruent, then the resulting lines are parallel, I will attach a drawing to illustrate what I am saying.

3 - When two lines are cut by a secant and their CORRESPONDING angles are congruent, then the resulting lines are parallel, I will also attach a drawing to illustrate what I am saying.

Answer:7

Step-by-step explanation:

Answer:

X=7

Step-by-step explanation:

made a 100 on my quiz but i dont feel like puting my work in here and typing it

Answer: The concentration will be 8 milligrams per liter at 2 hours and 4 hours.

Step-by-step explanation:

GIven: The concentration of a certain painkiller supplied by serum varies in its effectiveness over time according to the following function, [tex]C (t) = - t^2 + 6t[/tex] where C is the concentration of the painkiller in the serum measured in milligrams per liter so that it takes effect during t hours.

Put C(t)=8, then we get

[tex]8=-t^2+6t\\\\\Rightarrow\ t^2-6t+8=0\\\\\Rightarrow\ t^2-2t-4t+8=0\\\\\Rightarrow\ t(t-2)-4(t-2)=0\\\\\Rightarrow\ (t-2)(t-4)=0\\\\\Rightarrow\ t=2,4[/tex]

At t=2, [tex]C(t)=-(2)^2+6(2)=-4+12=8[/tex]

At t=4, [tex]C(t)=-(4)^2+6(4)=-16+24=8[/tex]

Hence, the concentration will be 8 milligrams per liter at 2 hours and  4 hours.

Answer: 12-i

               12-(√-1)

Step-by-step explanation:

[tex]18-\sqrt{-25}[/tex]   Original Question

[tex]18-(\sqrt{25} * \sqrt{-1} )[/tex]   Split

[tex]18-5*(\sqrt{-1} )[/tex]   Solve for square root

[tex]12-\sqrt{-1}[/tex]   Subtract

You can substitute [tex]\sqrt{-1}[/tex] for i

[tex]12-i[/tex]   Substitute

Answer:

18-5i

Step-by-step explanation:

Answer:

b. the approx time it takes an investment to double in value

Answer:

We accept H₀

p-value = 0,1618

Step-by-step explanation:

We are going to solve a one tail proportion-test ( right tail)

We assume Normal distribution

Sample population 1000

Political strategist to test  wants to test:

Null hypothesis                             H₀           p = p₀       or   p = 26 %

Alternate hypothesis                    Hₐ           p > p₀        or  p > 26%

We assume CI  90 % then

α = 10 %     α = 0,1    and  z score for α = 0,1  is critical value

z = 2,32          ( note  2,32 is z score for α = 0,1017 "good approximation")

To compute z(s)

z(s)  =  ( p -p₀ ) / √ p₀q₀/n

z(s)  =  ( 0,29 - 0,26 ) /√ 0,26*0,74/1000

z(s)  = 0,03 / 0,014

z(s) = 2,14

We compare z(s) and z(c)

z(s) < z(c)

2,14 < 2,32

z(s) is in the acceptance region we accept H₀

The p-value for z(s) is from z-table

p-value = 0,1618

Answer:

[tex]\boxed{\frac{1}{8} }[/tex]

Step-by-step explanation:

[tex]\frac{5}{4} / 10[/tex]

Changing "division" into multiplication and inverting the term after it:

[tex]\frac{5}{4} * \frac{1}{10}[/tex]

=> [tex]\frac{1*1}{4*2}[/tex]

=> 1/8

Answer:

1/8

Step-by-step explanation:

Well to do 5/4 ÷ 10 let's set up the following.

[tex]\frac{5}{4} / \frac{10}{1}[/tex]

Then we use the keep, change, and flip rule.

So keep 5/4 change the / to a * and flip the 10/1 ro a 1/10.

[tex]\frac{5}{4} * \frac{1}{10}[/tex]

Now we multiply them to get,

5/40

simplified

1/8

Thus,

the answer is 1/8.

Hope this helps :)