Find the volume. Use 3.14 for π where necessary. Round the answer to two decimal places.

[tex]g(x) =8x^5 + ax^4 +5x +20 \\\\\text{If}~ x +4 ~ \text{is a factor of g(x) then,}~ \\\\g(-4)=0\\\\\implies 8(-4)^5 +a(-4)^4+5(-4) +20 = 0\\\\\implies 256a -8192 = 0\\\\\implies a = \dfrac{8192}{256} = 32[/tex]

Answer:

Beach parking lot is the right answer.

Step-by-step explanation:

the beach parking is near the beach refreshment stand.

pls mark branliest.

[tex]\\ \rm\rightarrowtail y=(x-3)(x+3)=x^2-9[/tex]

Zeros are x intercepts

#2

#3

Axis of symmetry=x=0

#4

Answer:

Given quadratic equation:  y = (x - 3)(x + 3)

Zeros (x-intercepts)

The zeros of a quadratic equation are the points where the graph of the quadratic equation crosses the x-axis.  So the x-intercepts (zeros) are when y = 0

⇒ (x - 3)(x + 3) = 0

⇒ (x - 3) = 0  so  x = 3

⇒ (x + 3) = 0  so  x = -3

Therefore, the x-intercepts are at (3, 0) and (-3, 0).

y-intercept

The y-intercept is the point where the graph crosses the y-axis.  So the y-intercept is when x = 0

⇒ (0 - 3)(0 + 3) = -9

Therefore, the y-intercept is at (0, -9)

Vertex

Expand the equation so that it is in standard form y = ax² + bx + c:  

⇒ y = x² - 9

x-value of vertex is -b / 2a ⇒ -0 / 2 = 0

substitute the found value of x into the equation to find y:

⇒ y = (0)² - 9 = -9

Therefore, the vertex is (0, -9)

Axis of symmetry

Axis symmetry of a quadratic equation is x = a where a is the x-value of the vertex.

Therefore, the axis of symmetry is x = 0

The unknown number which is two times the quantity of a number increased by one is the same as four more than the same number be is 3

let

x = unknown number

2x + 1 = 4 + x

2x - x = 4 - 1

solve

x = 3

Therefore, the unknown number is 3

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The one thing wrong with the answer is option B. The minus signs should be plus signs.

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

Given quadratic is 4x²+12x+9

Taking common 4

4(x²+3x) + 9

=4(x² + 3x + 9/4) + 9 - 9

=4(x + 3/2)²

=(2x+3)²

=(2x+3)(2x+3)

So, the minus sign must be a plus sign. option B is correct.

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Answer:

[D]

Step-by-step explanation:

Graph using the end point and a few selected points.

x          y

0          0

1          2

2     2.83

Graph also below:

[RevyBreeze]

First Part

Given that

[tex]Volume = \frac{4}{3} \pi r^{3}[/tex]

We have that

[tex]Volume = \frac{4}{3} \pi r^{3} = \frac{4}{3} \pi (\frac{Diameter}{2})^{3} = \frac{4}{3} \pi 9^{3} = 972\pi cm^{3} \approx 3053.63 cm^{3}[/tex]

Second Part

Given that

[tex]Volume = \frac{4}{3} \pi r^{3}[/tex]

If the Diameter were reduced by half we have that

[tex]Volume = \frac{4}{3} \pi r^{3} = \frac{4}{3} \pi (\frac{r}{2}) ^{3} = \frac{\frac{4}{3} \pi r^{3}}{8}[/tex]

This shows that the volume would be [tex]\frac{1}{8}[/tex] of its original volume

First Part

Gather Information

[tex]Diameter = 18cm[/tex]

[tex]Volume = \frac{4}{3} \pi r^{3}[/tex]

Calculate Radius from Diameter

[tex]Radius = \frac{Diameter}{2} = \frac{18}{2} = 9[/tex]

Use the Radius on the Volume formula

[tex]Volume = \frac{4}{3} \pi r^{3} = \frac{4}{3} \pi 9^{3}[/tex]

Before starting any calculation, we try to simplify everything we can by expanding the exponent and then factoring one of the 9s

[tex]Volume = \frac{4}{3} \pi 9^{3} = \frac{4}{3} \pi 9 * 9 * 9 = \frac{4}{3} \pi 9 * 9 * 3 * 3[/tex]

We can see now that one of the 3s can be already divided by the 3 in the denominator

[tex]Volume = \frac{4}{3} \pi 9 * 9 * 3 * 3 = 4 \pi 9 * 9 * 3[/tex]

Finally, since we can't simplify anymore we just calculate it's volume

[tex]Volume = 4 \pi 9 * 9 * 3 = 12 \pi * 9 * 9 = 12 * 81 \pi = 972 \pi cm^{3}[/tex]

[tex]Volume \approx 3053.63 cm^{3}[/tex]

Second Part

Understanding how the Diameter reduced by half would change the Radius

[tex]Radius =\frac{Diameter}{2}\\\\If \\\\Diameter = \frac{Diameter}{2}\\\\Then\\\\Radius = \frac{\frac{Diameter}{2} }{2} = \frac{\frac{Diameter}{2}}{\frac{2}{1}} = \frac{Diameter}{2} * \frac{1}{2} = \frac{Diameter}{4}[/tex]

Understanding how the Radius now changes the Volume

[tex]Volume = \frac{4}{3}\pi r^{3}[/tex]

With the original Diameter, we have that

[tex]Volume = \frac{4}{3}\pi (\frac{Diameter}{2}) ^{3} = \frac{4}{3}\pi \frac{Diameter^{3}}{2^{3}}\\\\ = \frac{4}{3}\pi \frac{Diameter^{3}}{2 * 2 * 2} = \frac{4}{3}\pi \frac{Diameter^{3}}{8}\\\\[/tex]

If the Diameter were reduced by half, we have that

[tex]Volume = \frac{4}{3}\pi (\frac{Diameter}{4}) ^{3} = \frac{4}{3}\pi \frac{Diameter^{3}}{4^{3}}\\\\ = \frac{4}{3}\pi \frac{Diameter^{3}}{4 * 4 * 4} = \frac{4}{3}\pi \frac{Diameter^{3}}{4 * 2 * 2 * 4} = \frac{4}{3}\pi \frac{Diameter^{3}}{8 * 8} = \frac{\frac{4}{3}\pi\frac{Diameter^{3}}{8}}{8}[/tex]

But we can see that the numerator is exactly the original Volume!

This shows us that the Volume would be  [tex]\frac{1}{8}[/tex] of the original Volume if the Diameter were reduced by half.

Answer:

20 lb of 31 cent candy, 30 lb of 46 cent candy

Step-by-step explanation:

sorry don't have one

here is a smiley face for you

:D

The amount of each type of candy (in pounds) that are mixed for the considered condition is: 20 pounds of first type of candy and 30 pounds of second type of candy.

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.

For this case, we can assume the separate weights of each type of candies to be represented by variables.

Let we have:

x pounds of first type of candy is mixed with y pounds of second candy.

The weight of the mixture = x + y = 50 pounds

The cost of the mixture = 40 cents per pound  = [tex]40 \times 50 = 2000[/tex] cents

Cost of the mixture = cost of x pounds of first candy+ cost of y pounds of second candy = [tex]31x + 46y[/tex]
Thus, we get [tex]31x + 46y =2000[/tex]

Therefore, we got a system of two linear equations as:

[tex]x +y = 50\\31x + 46y =2000[/tex]

From first equation, we get:

[tex]x = 50 -y[/tex]

Substituting this value in second equation, we get:

[tex]31(50-y) + 46y =2000\\1550 + 15y = 2000\\15y = 450\\\\y = 450/15 = 30[/tex]

Putting this value of y in equation for x, we get:

[tex]x = 50-y = 50-30 = 20[/tex]

Thus, the amount of each type of candy (in pounds) that are mixed for the considered condition is: 20 pounds of first type of candy and 30 pounds of second type of candy.

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Answer:

Is a solution

Step-by-step explanation:

Just do the division [tex]\frac{52}{13}[/tex]

Answer:

366 possible outcomes

Step-by-step explanation:

just took a test on edge

Step-by-step explanation:

[tex] = 7 \times \frac{3}{5} - 6 \times \frac{3}{5} \\ = \frac{7 \times 5 + 3}{5} - \frac{6 \times 5 + 3}{5} \\ = \frac{38}{5} - \frac{33}{5} \\ = \frac{38 - 33}{5} \\ = \frac{5}{5} [/tex]

Now convert into lowest term

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

1/1 is the answer ....

The probability that the next person will purchase exactly one costume is given by: 68/399

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

The total number of visitors to the website is 314 + 68 + 17 = 399.

Out of these 399 visitors, 68 purchased exactly one costume.

Therefore, the probability that the next person will purchase exactly one costume is given by:

68/399

This fraction cannot be simplified any further, so the final answer is:

68/399.

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Answer:

yw

Step-by-step explanation:

makin a chart :)

Answer:

720

Step-by-step explanation:

n*180

n

the answer is 720

The number of times that the clock was skipping every 30 minutes from Friday noon to Monday 6 pm is; 3 seconds

We know that from time conversion;

1 day = 24 hours

1 hour = 60 minutes = 2 × (30 minutes)

1 day = 24 hours × 2 × (30 minutes)

1 day = 48 × (30 minutes)

Thus, there are 48 times of 30-minutes in a day. However on Friday, we start counting at noon, which is half of the day.

Thus, on Monday, the mark is only up to 6 pm, which is three-fourths of the day. Thus;

Friday = 48 × (3/4)  = 24

Saturday = 48

Sunday = 48

Monday = 48 × (3/4)  = 36

Total times = 24 + 48 + 48 + 36 = 156

Thus, it means that there was 156 times of  30-minutes that have passed during the time period.

x = 468 seconds ÷ 156

x = 3 seconds  

Therefore, the clock was skipping 3 seconds every 30 minutes from Friday noon to Monday 6 pm.

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Answer:

' =9 93/107 days

Step-by-step explanation:

1/11+1/24

one day =35/264

35/264 -1/32

=107/ 1056- fraction of rem in a day

1 day= 107/1056

x = 1

=107/1056x=1

x=1÷107/1056

1056÷107

=9 93/107 days

Answer:

Mean = 8

Step-by-step explanation:

add all the numbers

2+3+5+6+8+11+11+12+14 = 72

then divide by how many number there are which is 9

72 / 9 = 8

area of trapezoid: 153 units²

Here given information:

trapezium area = [tex]\sf \frac{1}{2}[/tex] * ( side 1 + side 2 ) * height

[tex]\hookrightarrow \sf \dfrac{1}{2} * ( 10 + 24) * 9[/tex]

[tex]\hookrightarrow \sf 153 \ units^2[/tex]

Answer:

804

Step-by-step explanation:

603/9 x 12

67 x 12

804

Answer:

804 miles in 12 hours

Step-by-step explanation:

603/9 which = 67

67*12 which equal 804

don't forget the unit (mph)

Answer:

76%

Step-by-step explanation:

Given:

If 24% of the Skittles in the bag are red, what percentage of the Skittles are not red?

Solve:

Percent - Out of 100

100 - 24 = 76

Hence, 76% of the skittles are not red.

~~Lenvy~~

Answer:

76% are not red

Formula:

(Total Skittle %)-(Red Skittle %)=(Non-Red Skittle %)

Work:

100%-24%=76%

Answer:

Step-by-step explanation:

Let a = tan⁻¹(x), so tan(a) = x,

[tex]\sin(a)=\frac{x}{\sqrt{1+x^2}}, \cos(a)=\frac{1}{\sqrt{1+x^2}},[/tex]

Let b = tan⁻¹(y), so tan(b) = y,

[tex]\sin(b)=\frac{y}{\sqrt{1+y^2}}, \cos(b)=\frac{1}{\sqrt{1+y^2}},[/tex]

sin( tan⁻¹(x) +  tan⁻¹(y)) = sin(a + b)

= sin(a) cos(b) + cos(a)sin(b)

= [tex]\frac{x}{\sqrt{1+x^2}}\times\frac{1}{\sqrt{1+y^2}}+ \frac{y}{\sqrt{1+y^2}}\times\frac{1}{\sqrt{1+x^2}}[/tex]

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

Answer:

what the heck question is this

Hey there!

ORIGINAL EQUATION:
|x + 2| = 3

TRANSLATE:

x + 2 = 3 or x + 2 = -3

SOLVING for: x + 2 = 3

SUBTRACT 2 to BOTH SIDES

x + 2 - 2 = 3 - 2

CANCEL out: 2 - 2 because it give you 1

KEEP: 3 - 2 because help solve for the current x-value

NEW EQUATION: x = 3 - 2

SIMPLIFY IT!
x = 1

Thus, your answer is: x = 2

/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\

SOLVING for: x + 2 = -3

SUBTRACT 2 to BOTH SIDES

x + 2 - 2 = -3 - 2

CANCEL out: 2 - 2 because it give you 0

KEEP: -3 - 2 because it help solve for the current x-value

NEW EQUATION: x = -3 - 2

SIMPLIFY IT!
x = -5

Thus, your answer is: x = -5

/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\

Therefore, your answer is: x = 1 or x = -5

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

The average daily balance of the transactions given for the billing period will be $1798.

From the complete question, the average daily balance is completed below:

Billing date = 2645.92 × 5 = $13229.6

Repayment on June 6 = $1345.92 × 2 = $2691.84

June 8 = $1381.85

June 9: = $1518.53 × 8 = $12148.24

Gas = $1560.90

Groceries = $1687.37 × 10 = $16873.70

Clothing = $1902.49 × 4 = $7609.96

Total = $53935.19

Therefore, the average daily balance will be:

= $53935 / 30

= $1798

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Answer:

the largest Angle has a measure of 360 degrees

Answer:

B. 90 in²

Area of white triangle

3×4/2

12/2 = 6 in²

Area of blue triangle

12×16/2

192/2= 96in²

96in² - 6in² = 90 in²

Answer:

given ,

two points A ( -1 , 2 ) and B ( 0 , -14 )

______________________________________

[tex]\fbox\pink{Solution -}[/tex]

let the midpoint be P ( x , y )

using midpoint formula ,

[tex]P(x,y) = ( \frac{ x_{1} + x_{2} }{2} , \frac{ y_{1} + y_{2} }{2} ) \\ \\ P(x,y) = ( \frac{ - 1 + 0}{2} , \frac{2 + ( - 14)}{2} ) \\ \\ (x,y) = ( \frac{ - 1}{2} , \frac{ - 12}{2} ) \\ \\ x = \frac{ - 1}{2} \\ \\ y = \frac{ - 12}{2} => - 6[/tex]

thus ,

the coordinates of the midpoint are

[tex]\red{P( \frac{ - 1}{2} , - 6)} \\ \\ or \\ \\ \red{P( -0.5 , - 6 )} [/tex]

hope helpful :D

Answer:

Step-by-step explanation:

A(-1,2)  x₁ = -1  &  y₁ = 2

B(0 ,-14)   x₂ = 0  & y₂ = -14

[tex]\text{ \sf Midpoint = $\left(\dfrac{x_{1}+x_{2}}{2} ,\dfrac{y_{1}+y_{2}}{2}\right)$ }[/tex]

              [tex]= \left (\dfrac{-1+0}{2} ,\dfrac{2+[-14]}{2} \right) \\\\\\=\left(\dfrac{-1}{2}, \dfrac{-12}{2}\right)\\\\\\=\left( -0.5 , -6 \right)[/tex]