find the vertex : f(x)=3x^2-18x+10

Answer:

The answer is 12. There are 12 pens in each pack.

Step-by-step explanation:

The constant of proportionality between the number of packs and the number of pens that Frank buys is 12 pens per pack, calculated by dividing the total pens by the number of packs in both given scenarios.

The student asks about the constant of proportionality between the number of packs of pens and the number of pens. To find this, we divide the number of pens by the number of packs for each given scenario to ensure the ratio is consistent.

Given Frank buys three packs and ends up with 36 pens, we divide 36 pens by 3 packs to get 12 pens per pack.

When he buys five packs and has 60 pens, we again divide 60 pens by 5 packs and get the same result, 12 pens per pack. Therefore, the constant of proportionality is 12 pens per pack.

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

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%

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)

12.5 percent is the percent decrease.

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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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: 36 in²

Step-by-step explanation:

You can calculate the area of this right prism by adding the area of its faces.

You can observe that the faces of the right prism are:  Three different rectangles and two equal triangles.

The formula for calculate the  area of a rectangle is:

[tex]A=lw[/tex]

 Where "l" is the lenght and "w" is the width.

The formula for calculate the  area of a triangle is:

[tex]A=\frac{bh}{2}[/tex]

Where "b" is the base and "h" is the height.

 You can observe that the hypotenuse of the each triangle is the length of the larger rectangle, then , you can find its value with the Pythagorean Theorem:

[tex]a=\sqrt{b^2+c^2}[/tex]

Where "a" is the hypotenuse and "b" and "c" are the legs of the triangle.

Then, this is:

[tex]a=\sqrt{(4in)^2+(3in)^2}=5in[/tex]

Therefore, you can add the areas of the faces to find the area of the right prism (Since the triangles are equal, you can multiply the area of one of them by 2). This is:

[tex]A=(2in)(5in)+(3in)(2in)+(4in)(2in)+2(\frac{3in*4in}{2})=36in^2[/tex]

Answer:

8 bags

Step-by-step explanation:

The area of the path is equal to the area of the overall square minus the area of the garden.

Area of a square is the side length squared:

A = s²

The overall square has a side length of 11 feet.  The side length of the garden is 11 - 2 - 2 = 7 feet.  So the area of the path is:

A = 11² - 7²

A = 121 - 49

A = 72

The area of the path is 72 ft².  If one bag of gravel covers 9 ft², then the number of bags needed is:

72 ft² × (1 bag / 9 ft²) = 8 bags

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.

(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: $58.00

Step-by-step explanation:

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:

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°

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

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:

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:

π

Step-by-step explanation:

The standard form of the sine function is

y = a sin(bx + c)

where a is the amplitude, period = [tex]\frac{2\pi }{b}[/tex] and

phase shift = - [tex]\frac{c}{b}[/tex]

here b = [tex]\frac{1}{2}[/tex], c = - [tex]\frac{\pi }{2}[/tex]

phase shift = - [tex]\frac{-\frac{\pi }{2} }{\frac{1}{2} }[/tex]

= [tex]\frac{\pi }{2}[/tex] × 2 = π

Answer:

See attachment

Step-by-step explanation:

The given equation is:

[tex]3x^2+3y^2=75[/tex]

We divide through by 3 to obtain;

[tex]x^2+y^2=25[/tex]

This is rewritten as:

[tex]x^2+y^2=5^2[/tex]

This is the equation of a circle centered at the origin with radius 5 units.

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:

  6w³ cubic units

Step-by-step explanation:

The volume of a right rectangular prism is the product of its dimensions:

  V = LWH

  = (2w)(w)(3w) = 6w³ . . . . cubic units

Answer:

6*W^3 cubic units

Step-by-step explanation:

Right rectangular prism volume (V) is calculated as

V = L*W*H

where L is length, W is width and H is height

The height is three times the width of the base means

H = 3*W

The length of the base is twice the width means

L = 2*W

Replacing in volume formula

V = 2*W*W*3W

V = 6*W^3

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: 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]

To learn more on functions, we kindly invite to check this verified question: https://brainly.com/question/5245372

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:

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

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: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.

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:

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