A polynomial has been factored, as shown below:
f(x) = (x - 3)(x + 8)(x - 11)
What are the zeros of the polynomial?
3, 8, 11
3,-8, 11
-3, 8, -11
-3,3, -8,8, -11, 11

Answer:

A) 15 hours

B) 108 hours

C) 2073.45 miles

Step-by-step explanation:

The earth rotates fully 1 time in 24 hours. Fully rotate means that it goes through 360 degrees in 24 hours.

A)

For this, we can set up unit ratio to solve.

"If earth rotates 360 degrees in 24 hours, 225 degrees take how much time (let it be x)?"

[tex]\frac{360}{24}=\frac{225}{x}\\360x=24*225\\360x=5400\\x=\frac{5400}{360}\\x=15[/tex]

So , it takes 15 hours.

B)

Here, the rotation is given in radian, NOT degrees. We know that  2π radians is 360 degrees, thus we can say:

"If earth rotates 2π radians in 24 hours, 9π radians take how much time (let it be y)?"

[tex]\frac{2\pi}{24}=\frac{9\pi}{y}\\2\pi y=9\pi * 24\\2\pi y = 216\pi\\y=\frac{216\pi}{2\pi}\\y=108[/tex]

So, it take 108 hours.

C)

The point on the equator is on the "outside" of the earth. So we need to figure out the circumference of the earth, given diameter is approximately 7920.

Circumference formula is  C = 2πr, where C is the circumference, r is the radius (half of diameter, which is 7920/2 = 3960)

Hence

C = 2πr = 2π(3960) = 7920π

Hence, is 24 hours, a point travels  7920π  miles. 2 hours is 1/12th of 24 hours, so in 2 hours the point will travel 1/12th the distance is travels in 24 hours. So:

[tex]\frac{7920\pi}{12}=2073.45[/tex]

Thus, it will travel 2073.45 miles in 2 hours.

Answer:

A). 15 hours

B). 108 hours

C). 2074.28 miles

Step-by-step explanation:

A). The Earth completely rotates on its axis once every 24 hours.

It means the Earth takes 24 hours to complete 360° or 2π radians

Per hour rotation of the Earth will be = [tex]\frac{\text{Angle rotated in one rotation}}{\text{Time taken for one rotation}}[/tex]

= [tex]\frac{360}{24}=15[/tex] degree per hour

or [tex]\frac{2\pi }{24}=\frac{\pi }{12}[/tex] radians per hour

Now we have to calculate the time taken in 225° rotation.

∵ In 15° rotation was time taken = 1 hour

∴ In 1° rotation time taken by the Earth = [tex]\frac{1}{15}[/tex]

∴ In 225° time spent by the Earth = [tex]\frac{(1)(225)}{15}=15[/tex] hours

B). ∵ [tex]\frac{\pi }{12}[/tex] radians rotation was completed in the time = 1 hour

∴ 1 radian rotation was completed in time = [tex]\frac{1}{\frac{\pi }{12}}=\frac{12}{\pi }[/tex]

∴ 9π radians rotation will be completed in time = [tex]\frac{12(9\pi )}{\pi }= 108[/tex] hours

Therefore, time taken in 9π rotation will be 108 hours.

C). If the diameter of the earth is 7920 miles then we have to calculate angle of rotation of a point on equator in 2 hours.

Since Length of arc = radius × angle of rotation

Since angle of rotation in 1 hour = [tex]\frac{\pi }{12}[/tex] radians

So angle of rotation in 2 hours = [tex]\frac{2\pi }{12}=\frac{\pi }{6}[/tex]

Now we put these values in the formula

Length of arc = [tex]\frac{7920}{2}(\frac{\pi }{6})=660\pi[/tex] miles

                      = 660(3.1428)

                      = 2074.28 miles

To solve the equation 3/(y - 5) = 15/(y + 4) for the value of y, cross multiply to eliminate the fractions. Then collect the y terms on one side and the constant terms on the other side. Finally, divide both sides by the coefficient of y to find the value of y.

To solve the equation 3/(y - 5) = 15/(y + 4) for the value of y, we first cross multiply to eliminate the fractions.

This gives us 3(y + 4) = 15(y - 5). Expanding this equation, we have 3y + 12 = 15y - 75.

Next, we collect the y terms on one side and the constant terms on the other side. Simplifying the equation, we get 12 + 75 = 15y - 3y.

Combining like terms, we have 87 = 12y. Finally, we divide both sides of the equation by 12 to solve for y.

Therefore, the value of y is 7.25.

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Formula for volume of cone:

V = [tex]\pi r^{2}  \frac{h}{3}[/tex]

r = 6 km

h = 12 km

V = [tex]\pi 6^{2} \frac{12}{3}[/tex]

V = [tex]\pi 36*4[/tex]

V = [tex]\pi 144[/tex]

V = 452.389 km^3 <----------------------Using the calculators pi button

V = 452.16 km^3 <-------------------------Using 3.14 for pi

Hope this helped!

~Just a girl in love with Shawn Mendes

To find the number of minutes at which the costs of the two plans will be equal, we set up an equation and solve for x. The costs will be equal after 250 minutes of calls.

To find the number of minutes of calls at which the costs of the two plans will be equal, we can set up an equation. Let's denote the number of minutes as x. For the first plan, the total cost is given by:

Total Cost = $13 + $0.17x.

For the second plan, the total cost is given by:

Total Cost = $23 + $0.13x.

Setting these two equations equal to each other, we have:

$13 + $0.17x = $23 + $0.13x.

Simplifying this equation, we get:

$0.17x - $0.13x = $23 - $13.

$0.04x = $10.

Dividing both sides by $0.04, we get:

x = $10/$0.04 = 250 minutes.

Therefore, the costs of the two plans will be equal after 250 minutes of calls.

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Answer:

Option C.

Step-by-step explanation:

From the graph we can find the points (2,3) for first straight line (blue) and (2,2) for second straight line (red). These points Andre satisfied by option C.

x+2y=8

2+2×3=8

8=8.

Again, 2x+4y=12

2×2+4×2=12

12=12

The correct answer is Option C.

x + 2y = 8

2x + 4y = 12

In its simplest format in algebra, the definition of an equation exists as a mathematical statement that indicates that two mathematical expressions exist equal. For instance, 3x + 5 = 14 exists an equation, in which 3x + 5 and 14 exist two expressions separated by an 'equal' sign.

Equation of line in Two point form

When we know any two points on a line lets say [tex](a_1,b_1)[/tex] and [tex](a_2,b_2)[/tex], we can write its equation as:

[tex]y-b_1=m(x-a_1)[/tex]

where

[tex]m=\dfrac{b_2-a_2}{b_1-a_1}[/tex]

Here we have points of red line:( from graph) (0,3) and (6,0)

Equation of line: y-3=m(x-0)

m=0-3/6-0=-1/2

Equation:2y-6=-1(x)

               2y+x=6

Now from graph, we can see that the blue line is parallel to red line, therefore their slopes are same

The equation of blue line is as follows

y=mx+c

Point on blue line :(0,4)

4=(-1/2)*(0)+c

c=4

The equation is x+2y=8.

Therefore, it matches with option C.

x + 2y = 8

2x + 4y = 12

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I don't really understand the 3 5. Are you talking about 3.5? Same with the 1 4 are you talking about 1.4 or 14 or what? I'll be willing to help if  you could help me with that! :)

Answer:

The "mode" is the value that occurs most often. If no number in the list is repeated, then there is no mode for the list.

Step-by-step explanation:

Answer:

914

I think it's the only answer

Hello There!

The answers are 916 and 914

HAVE A GREAT REST OF YOUR DAY!

12.5 percent is the percent decrease.

Answer:

A is the best answer.

Step-by-step explanation:

A is. It can be written as y [ or v] = -2(x + 3)^2 + 7 which is the pure form of a vertex equation.

C doesn't work since that is a linear function. Nothing is squared.

D doesn't work. That is just the way an ordinary quadratic is written. (Standard form).

B doesn't work. The quadratic is written in factored form.

ANSWER

[tex]y - 7= - 2 {(x + 3)}^{2} [/tex]

EXPLANATION

The vertex form of a quadratic function is given by:

[tex]y = a {(x - h)}^{2} + k[/tex]

From the given options, the first choice is

[tex]y - 7= - 2 {(x + 3)}^{2} [/tex]

[tex]y=- 2 {(x + 3)}^{2} + 7[/tex]

where a=-2, h=-3, and k=7.

Therefore the vertex is (-3,7)

Hence the first choice is the correct option.

Answer:

62 square units

Step-by-step explanation:

The area of a rectangular prism is the sum of the areas of its six faces. Opposite faces have the same area, so it is the sum of 3 pairs of faces. The area of one face of each pair is the product of the dimensions of that face. Those three areas are ...

• L·W

• W·H

• H·L

so the total surface area is ...

A = 2(LW +WH +HL)

For hand calculation, this can be simplified a bit to ...

A = 2(LW +H(L+W)) . . . . . requires one less multiplication

For your prism, the area is ...

A = 2(5·2 + 3(5+2)) = 2(10 +21) = 62 . . . square units

A rectangular prism is a three-dimensional shape with six faces. The opposite faces are equal in length. It has twelve sides and six vertices

The formula for the surface area of a rectangular prism = SA=2lw+2lh+2hw

Where:

l = length

w = width

h  = height

Surface area = (2 x 5 x 2) + (2 x 5 x 3) + (2 x 3 x 2)

= 20 + 30 + 12

= 62 square units

Please find attached an image of a rectangular prism. A similar question was solved here: https://brainly.com/question/21226782?referrer=searchResults

Answer:

Part 27) Option D. 89.12°

Part 28) Option B. 66.42°

Step-by-step explanation:

Part 27)

we have

tan(x)=65

so

using a calculator

x=arctan(65)=89.12°

Part 28)

we have

cos(x)=2/5

so

using a calculator

x=arccos(2/5)=66.42°

Answer:

Option D. 89.12°

Option B. 66.42°

Step-by-step explanation:

tan(x)=65

x=arctan(65)=89.12°

Part 28)

cos(x)=2/5

x=arccos(2/5)=66.42°

Answer:

They are 3, 11 and 55.

Step-by-step explanation:

x +y + z = 69

y = x - 8

z = 5x

Substitute z = 5x in the first equation:

x + y + 5x = 69

6x + y = 69.........(1)

From the second equation

-x + y = -8.........(2)

Subtract equations (1) - (2):

7x = 77

x = 11

So z = 5x = 5*11 = 55 and

y =  x - 8 = 11 - 8 = 3..

Answer:

x = 11, y = 3 and z = 55

Step-by-step explanation:

Let the three numbers be x, y and z.  Then x + y + z = 69

Then y = x - 8, and z = 5x.  Substituting these expressions in x into

x + y + z = 69, we get:  x + x - 8 + 5x = 69, or

7x = 77, so that x = 11.

If x = 11, then:

y = x - 8 = 11 - 8 = 3, and:

z = 5x = 5(11) = 55

Then x = 11, y = 3 and z = 55.

Check:  Do these three numbers add up to 69?  11 + 3 + 55 = 69?  YES

Answer:

Step-by-step explanation:Let us find points of intersection of line  

3

x

+

4

y

−

k

=

0

and circle  

x

2

+

y

2

=

16

. We can do this by putting value of  

y

from first equation i.e.  

y

=

k

−

3

x

4

and we get

x

2

+

(

k

−

3

x

)

2

16

=

16

or  

16

x

2

+

k

2

+

9

x

2

−

6

k

x

=

256

i.e.  

25

x

2

−

6

k

x

+

k

2

−

256

=

0

This would give two values of  

x

and corresponding two values of  

y

i.e. two points. But tangent cuts the circle in only at one point. This will be so when discriminant is zero i.e.

(

−

6

k

)

2

−

4

⋅

25

⋅

(

k

2

−

256

)

=

0

or  

−

64

k

2

+

25600

=

0

or  

k

=

±

20

graph{(x^2+y^2-16)(3x+4y-20)(3x+4y+20)=0 [-10, 10, -5, 5]}

Answer:

-1, 7

Step-by-step explanation:

Equation of the circle:

x² + (y − k)² = 16

When the circle intersects y = 3:

x² + (3 − k)² = 16

x² + 9 − 6k + k² = 16

x² = 7 + 6k − k²

x = ±√(7 + 6k − k²)

For the circle to be tangent to the line, it can only intersect at one point.  If x has only one value, then:

√(7 + 6k − k²) = -√(7 + 6k − k²)

2√(7 + 6k − k²) = 0

7 + 6k − k² = 0

k² − 6k − 7 = 0

(k − 7) (k + 1) = 0

k = -1, 7

The two values of k are -1 and 7.

(c)A bowler’s scorecard shows he threw a strike on one-fifth of his throws that night. Descriptive statistics describe an event that happens over time, for example, a batting average would be a descriptive statistic or a win/loss ratio.

Answer:

[tex]JK=2.25\ units[/tex]

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional, and this ratio is called the scale factor

so

[tex]\frac{JK}{ST}=\frac{KL}{TU}[/tex]

substitute the given value and solve for JK

[tex]\frac{JK}{1.5}=\frac{6}{4}[/tex]

[tex]JK=(1.5)\frac{6}{4}[/tex]

[tex]JK=2.25\ units[/tex]

Answer:

D. 1024 π units²

Step-by-step explanation:

We have sphere, with a radius of 16 units.

The surface area of a sphere is given by the following formula:

Surface Area of a sphere = 4 π r²

We already know r, which is 16.  So,

SA = 4 * π * 16² = 256 * 4 * π  = 1024 π  units²

That's enough for our answer, which matches answer D from the list.

If we want to have an actual number.... we would have to multiply 1024 by π.

SA = 1024 * π = 3217 units²

Answer:

option D

1024π units²

Step-by-step explanation:

Given in the question that radius of a sphere = 16 unit

Formula to use to calculate the surface area of the sphere

here r is the radius of the sphere

4 π (16)²

4 π (256)

1024π units²

Surface area of a sphere with radius 16 units = 1024π units²

Answer:

91 degrees.

Step-by-step explanation:

This is a parallelogram (a quadrilateral with 2 pairs of parallel sides).

The 2 interior adjacent angles add up to 180 degrees in a parallelogram so

m < DAB = 180 - 89 = 91 degrees.

Answer: The measure of ∠DAB is 91°.

Step-by-step explanation:

Since we have given that

AB = CD

AD = BC

So, ABCD is a parallelogram.

m∠D=89°

and we know that

∠A and ∠D are adjacent angles.

So, their sum would be supplementary.

Now, it becomes,

[tex]89^\circ+\angle A=180^\circ\\\\\angle DAB=180^\circ-89^\circ\\\\\angle DAB=91^\circ[/tex]

Hence, the measure of ∠DAB is 91°.

Answer: Second Option

[tex]g(x)=-\frac{5}{7}(\frac{3}{5})^{-x}[/tex]

Step-by-step explanation:

The function  [tex]g(x)=(\frac{3}{5})^x[/tex] is an exponential function.

Functions of this type have a range that goes from (0, ∞)

When multiplying the function by a negative coefficient  [tex]-\frac{5}{7}[/tex], now all the values of g(x) will be negative and the range of  [tex]g(x)=-\frac{5}{7}(\frac{3}{5})^x[/tex] will be: (-∞, 0)

Then we must search among the options a function with range (-∞, 0)

Since the exponential functions of the form [tex](a) ^ x[/tex], where [tex]a>0[/tex] always have range (0, ∞)  Then the correct option will be the one with a negative coefficient.

The correct option is the second option

The function [tex]h(x) = -\frac{5}{7}\cdot \left(\frac{3}{5} \right)^{-x}[/tex]same range of [tex]f(x) = - \frac{5}{7}\cdot \left(\frac{3}{5} \right)^{x}[/tex].

In this question we must determine a second function whose range is equal to the range of the first one. In geometry, a rigid transformation is a transformation experimented by a function such that euclidean distance is conserved. The range is the set of values of [tex]h(x)[/tex] associated to the function.

If we apply a reflection around the y-axis, then the range is conserved but relationship between the range and the domain is changed in rigid manner. The reflection around the y-axis follows the following formula:

[tex]h(x) = f(-x)[/tex]    (1)

If we know that [tex]f(x) = - \frac{5}{7}\cdot \left(\frac{3}{5} \right)^{x}[/tex], then the resulting function is:

[tex]h(x) = -\frac{5}{7}\cdot \left(\frac{3}{5} \right)^{-x}[/tex]

The function [tex]h(x) = -\frac{5}{7}\cdot \left(\frac{3}{5} \right)^{-x}[/tex] has the same range of [tex]f(x) = - \frac{5}{7}\cdot \left(\frac{3}{5} \right)^{x}[/tex]. [tex]\blacksquare[/tex]

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Reciprocal means to flip it, so in this case swap the numerator and denominator and the answer will be:

[tex] - \frac{5}{3} \: \: or \: \: - 1 \frac{2}{3} [/tex]

I would choose A

Answer:

325 cents per pound

Step-by-step explanation:

Answer:

325 cents per pound

Step-by-step explanation:

Answer:

The given statement is true.

Step-by-step explanation:

In order to inscribe a circle in a triangle, the circle's center must be placed at the incenter of the triangle.

This statement is true.

The INCENTER is the center of the circle that is inscribed in the triangle. Like the centroid, the incenter is always inside the triangle.

Answer:

true

Step-by-step explanation:

Answer:

The lengths of the other sides is equal to 10 units

Step-by-step explanation:

we know that

An equilateral triangle is a triangle that have three equal sides and three equal interior angles (each internal angle measure 60 degrees)

so

If the triangle has two interior angle measures of 60° and 60°, then the measure of the third interior angle must be equal to 60 degrees (remember that the sum of the interior angles in a triangle must be equal to 180 degrees)

Therefore

The triangle is an equilateral triangle and the length of the three sides is equal to 10 units

Answer:

10 and 10

Step-by-step explanation:

I took it on edge

Answer:

Part 1) The central angle is equal to ∠EOD+∠DOG or the central angle is equal to 360°-∠EOG

Part 2) The central angle is equal to ∠KOL

Part 3) The arc made by the ∠4 is the arc LI

Part 4) The arc made by the ∠2 is the arc FG

Step-by-step explanation:

Part 1) Name the central angle of the given arc

Arc EDG

The central angle is equal to ∠EOD+∠DOG

or

The central angle is equal to 360°-∠EOG

Part 2) Name the central angle of the given arc

Arc KL

The central angle is equal to ∠KOL

Part 3) Name the arc made by the given angle

∠4

The arc made by the ∠4 is the arc LI

Part 4) Name the arc made by the given angle

∠2

The arc made by the ∠2 is the arc FG

1 yard = 3 feet

The foundation is 2/3 yard wide, by 1 yard deep by 10 yards long.

Volume is Length x width x height.

Volume = 2/3 x 1 x 10 = 6.66 cubic yards.

The answer is B.

Answer:

Step-by-step explanation:

sec(-x) − sin(-x) tan(-x)

So the first step is often to write everything in terms of sine, cosine, or tangent.  So let's rewrite using sec x = 1 / cos x:

1/cos(-x) − sin(-x) tan(-x)

Now we need to deal with those -x angles.  For that, we use reflection identities:

sin(-x) = -sin x

cos(-x) = cos x

tan(-x) = -tan x

Therefore:

1/cos(x) − sin(x) tan(x)

Now let's rewrite tan(x) as sin(x) / cos(x):

1/cos(x) − sin²(x)/cos(x)

Factoring:

(1 − sin²(x)) / cos(x)

Using Pythagorean identity: sin²(x) + cos²(x) = 1.  So 1 − sin²(x) = cos²(x).

cos²(x) / cos(x)

And finally, we divide.

cos(x)

Answer:

The perimeter of the new pentagon is [tex]27\ cm[/tex]

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its perimeters is equal to the scale factor

so

To find the perimeter of the new pentagon, multiply the perimeter of the original pentagon by the scale factor

Let

z ----> the scale factor

[tex]z=3/2=1.5[/tex]

The perimeter of the new pentagon is equal to

[tex](18)*1.5=27\ cm[/tex]

Answer: $58.00

Step-by-step explanation:

Answer:

The yearly rate of appreciation of the comic book is r=0.017 or r=1.7%

Step-by-step explanation:

we have

[tex]v(t)=1,350(1.017)^{x}[/tex]

This is a exponential function of the form

[tex]f(x)=a(b)^{x}[/tex]

where

a is the initial value

b is the base

In this problem

a=$1,350

b=1.017

Remember that

b=1+r

so

1+r=1.017

r=1.017-1=0.017

therefore

The yearly rate of appreciation of the comic book is r=0.017 or r=1.7%

Answer:

The yearly rate of appreciation of the comic book is r=0.017 or r=1.7%

Step-by-step explanation:

we have

This is a exponential function of the form where

a is the initial value

b is the base

In this problem

a=$1,350

b=1.017

Remember that

b=1+r

so

1+r=1.017

r=1.017-1=0.017

therefore

The yearly rate of appreciation of the comic book is r=0.017 or r=1.7%