Two similar triangles are shown.
to create
AXYZ was dilated, then
AQAG
translated
reflected
dilated
rotated

Answer:

V = 3534 cm^3

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h

the radius is 7.5 and the height is 20

V = pi ( 7.5)^2 * 20

V =1125 pi cm^3

Using the pi button for pi

V =3534.291735 cm^3

Rounding to the nearest whole number

V = 3534 cm^3

Answer:

b)3534 cm^3

Step-by-step explanation:

To find the area of a cylinder, you first have to find the area of the base which is in the shape of a circle. The area of a circle is given by the equation πr^2. In this case r, the radius, is 7.5 cm. So plugging in 7.5 for r you get 7.5^2 × π. Plugging in 3.1415 for π you get ~176.671. Now all you do is multiply this by the height, 20cm, and get the answer of ~3534 cm^3.

Answer:

x can take any value and are viable in this situation if and only if it is a positive number

Step-by-step explanation:

We know that the area of a rectangle is given by:

A = x * y

So if we replace we have:

12 ≤ x * y ≤ 36

We divide by y, and we have:

12 / y ≤ x ≤ 36 / y

Which means that the value of x depends on y, that is to say if y is worth 1, the inequality would be:

 12 ≤ x ≤ 36

In the event that y is equal to 2:

 12/2 ≤ x ≤ 36/2

 6 ≤ x ≤ 18

Which means, that depending on y, x can take any value and are viable in this situation if and only if it is a positive number.

The image of the function is missing, you can see it at the end of the answer.

For a rectangle of length L and width W, the area is given by:

A = L*W

We will find that the solution is: 3/2 ≤ x ≤ 11/2

Here we have:

L = 3

W = 2x + 1

Then the area equation is:

A = 3*(2x + 1) = 6x + 3

And we also have the inequality:

12 ≤ A ≤ 36

Replacing A with the equation we get:

12 ≤ 6x + 3 ≤ 36

Now we solve this for x:

12 - 3 ≤ 6x ≤ 36 - 3

9  ≤ 6x  ≤ 33

Now we divide both sides by 6.

9/6 ≤ x ≤ 33/6

3/2 ≤ x ≤ 11/2

If you want to learn more, you can read:

https://brainly.com/question/1468729

Answer:

Rational.

Step-by-step explanation:

Irrational numbers are real numbers that can't be written as fractions.

One clue is that the decimal goes on forever (doesn't terminate) without repeating. (pi)

.14 can be written as a fraction: 14/100

Answer:

It's rational

Step-by-step explanation:

Because irrational numbers cannot be written s a fraction and rational numbers can

Answer:

(2)They are perpendicular.

Step-by-step explanation:

Answer:

Equation: f(x) = -x² + 3

Step-by-step explanation:

If we want to find the roots/solve for x, we can either graph the problem or use quadratic formula to find when f(x) = 0:

To get the equation of the graph, our parent function is: f(x) = a(x - h)² + k, or f(x) = x². Since we are reflecting over the x-axis with a vertical stretch and vertically moving up to (0, 3), we are modifying a and k only.

Answer:

Second choice.

f(x) = 1/2(x - 6)^2 + 3/2.

Step-by-step explanation:

The distance of a point  (x, y) from the focus = the distance of the point from the directrix, so:

(x - 6)^2 + (y - 2)^2 = (y - 1)^2

x^2 - 12x + 36 + y^2 - 4y + 4 = y^2 - 2y + 1

x^2 -12x + 39 = 2y

y = f(x) = 1/2 (x^2 - 12x + 39)

I see you want the answer in vertex for so it is:

f(x)  = 1/2 [ (x - 6)^2 - 36)  + 39)

f(x)  = 1/2(x - 6)^2 + 3)

f(x) = 1/2(x - 6)^2 + 3/2.

A parabola is a plane that is approximately U-shaped.

The equation of the parabola is: [tex]\mathbf{y = \frac{1}{2}(x - 6)^2 + \frac 32}[/tex]

The given parameters are:

[tex]\mathbf{Focus = (6,2)}[/tex]

[tex]\mathbf{Directrix: y = 1}[/tex]

First, equate the directrix to 0

[tex]\mathbf{y - 1 = 0}[/tex]

The equation is then calculated as:

[tex]\mathbf{(x - a)^2 + (y - b)^2 = (y- 1)^2}[/tex]

Where:

[tex]\mathbf{(a,b) = (6,2)}[/tex]

So, we have:

[tex]\mathbf{(x - 6)^2 + (y - 2)^2 = (y- 1)^2}[/tex]

Expand

[tex]\mathbf{x^2 - 12x +36 + y^2 - 4y + 4 = y^2 - 2y + 1}[/tex]

Subtract y^2 from both sides

[tex]\mathbf{x^2 - 12x +36 - 4y + 4 =- 2y + 1}[/tex]

Collect like terms

[tex]\mathbf{x^2 - 12x +36 + 4 - 1 =4y - 2y}[/tex]

[tex]\mathbf{x^2 - 12x +39 =2y}[/tex]

Divide through by 2

[tex]\mathbf{y = \frac{1}{2}(x^2 - 12x +39)}[/tex]

Express 39 as 36 + 3

[tex]\mathbf{y = \frac{1}{2}(x^2 - 12x +36 + 3)}[/tex]

Factor out 3/2

[tex]\mathbf{y = \frac{1}{2}(x^2 - 12x +36) + \frac 32}[/tex]

Expand the bracket

[tex]\mathbf{y = \frac{1}{2}(x^2 - 6x - 6x +36) + \frac 32}[/tex]

Factorize

[tex]\mathbf{y = \frac{1}{2}(x(x - 6) - 6(x -6)) + \frac 32}[/tex]

Factor out x - 6

[tex]\mathbf{y = \frac{1}{2}((x - 6) (x -6)) + \frac 32}[/tex]

Express as squares

[tex]\mathbf{y = \frac{1}{2}(x - 6)^2 + \frac 32}[/tex]

Hence, the equation of the parabola is: [tex]\mathbf{y = \frac{1}{2}(x - 6)^2 + \frac 32}[/tex]

Read more about equations of parabola at:

https://brainly.com/question/4074088

Answer:

143.81

Step-by-step explanation:

Trapezoid Area

A = 2b/2 * h

A = 9 + 23/2 * 7

A = 32/2 * 7

A = 16 * 7

A = 112

Semi-circle Area

A = πr²/2

A = π4.5²/2

A = π20.25/2

A = 63.62/2

A = 38.81

Total Area

112 + 38.81

143.81

Answer:

The two inequalities are;

P ≤ 90e^(0.047t)

P ≤ 270 + 100·t

Step-by-step explanation:

The parameters given for the testing of the new growth inhibitor are;

The growth rate of the bacteria = 4.7% exponentially

The growth inhibitor lowers the growth rate

The population of bacteria after time, t = P

The increase in the number of bacteria per unit time in the 100

The maximum number of bacteria in the standard tube = 270

Therefore, the number of bacteria after the first filling of the tube is P ≤ 270 + 100·t

The equation for exponential growth is [tex]A_0 e^{kt}[/tex]

Where:

A₀ = Initial population = 90

k = Percentage growth rate as percentage

t = Time

The equation for the population of bacteria under the influence of the inhibitor is therefore;

P ≤ [tex]90 \times e^{0.047 \cdot t}[/tex] which is P ≤ 90e^(0.047t).

Answer:

P≤270+100t

P≤90e^(0.047t)

Answer:

0.07%

Step-by-step explanation:

This equation is solving for what percentage of 100 kg is 0.07 kg.

1. Set up the equation

[tex]\frac{0.07}{100}[/tex] = [tex]\frac{x}{100}[/tex]

0.07 kg out of 100 kg is equal to x out of 100 because x represents the percentage and percentages are out of 100.

2. Solve by cross multiplying

100x = 7

3. Solve for x by dividing both sides by 100

x = 0.07

The answer is 0.07%

Answer:

102.88 m

Step-by-step explanation:

Pythagorean Theorem:

a²+b²=c²

48²+91²=c²

2304+8281=10585

c²=10585

Square both sides

c= 102.88

How far the players ran:

102.88 m

Answer:

Solution,

Area of rectangle= 524.4 m^2

Length(L)= 6.9 m

Breadth(B)=?

Now,

[tex]area = length \times breadth \\ or \: 524.4 = 6.9 \times b \\ or \: 524.4 = 6.9b \\ or \: b = \frac{524.4}{6.9} \\ b = 76 \: m[/tex]

Again,

Perimeter of rectangle:

[tex]2(l + b) \\ = 2(6.9 + 76) \\ = 2 \times 82.9 \\ = 165.8 \: m[/tex]

Hope this helps...

Good luck on your assignment.....

Answer:

The perimeter of the rectangle is 165.8cm

Step-by-step explanation:

Area of a rectangle = length × width

Area = 524.4m²

length = 6.9m

524.4 = 6.9 × width

width = 524.4 / 6.9

width = 76m

Perimeter of a rectangle =

2(length ) + 2(width)

length = 6.9m

width = 76m

Perimeter = 2( 6.9) + 2(76)

= 13.8 + 152

The final answer is

= 165.8cm

Hope this helps you

Answer:

Step-by-step explanation:

A square has equal sides. Let x represent the length of each side of the square carpet. The diagram representing the room and the carpet is shown in the attached photo. Therefore, the length of the room would be (x + 2)m while the width of the room would be (x + 1)m

Since the area of the room is 56m², it means that

(x + 2)(x + 1) = 56

x² + x + 2x + 2 = 56

x² + 3x + 2 - 56 = 0

x² + 3x - 54 = 0

x² + 9x - 6x - 54 = 0

x(x + 9) - 6(x + 9) = 0

x - 6 = 0 or x + 9 = 0

x = 6 or x = - 9

Since the dimension of the carpet cannot be negative, then x = 6

The dimension of the carpet is 6m × 6m

Answer:

900L per minute

Step-by-step explanation:

1- 70 - 20 = 50

2- in this 50 min the 45000L has been drawned

3- 45000L / 50 = 900L

.. ..

Answer:

David is 12 years old.

Step-by-step explanation:

Let r = Rebecca's age

Let d = David's age

let p = Dad's age

David is 3 times as younger than his dad:

d = [tex]\frac{p}{3}[/tex]

David is 2 times older than Rebecca:

d = 2r

Rebecca is 30 years younger than the dad:

r = p-30

All three equations can be solved by a system

2r = [tex]\frac{p}{3}[/tex]

r = p-30

multiplying r = p-30 by negative 2 and adding it to 2r = [tex]\frac{p}{3}[/tex]

0 = (-2p + p/3) + 60

multiplying new equation by 3

0 = (-6p + p) + 180

5p = 180

p = 36

d = 36/3 = 12

Answer:

A y=1/2x(powerof)2+5

B 17.5

C x=√42 or x=−√42

Step-by-step explanation:

Answer:

a. y = x^2 + 10

b. when x=5,   y  = 35

c. when y = 26,   x =  +4 or -4

Step-by-step explanation:

Given

y = k (x^2/2 + 5), and

(2,14) is on the curve.

Solution:

Substitute x=2 and y=14 in the above equation

14 = k (2^2/2 + 5)

14 = k (2+5)

14 = 7k

k = 14/7 = 2

a. equation connecting x and y is

   y = 2 (x^2/2 + 5), or

   y = x^2 + 10

b. when x=5

   y = 5^2 + 10 = 25 + 10 = 35

c. when y = 26

  26 = x^2 + 10

  x^2 = 26-10 = 16

  x= sqrt(16) = +4 or -4

Answer:

a) x = 5

b) x = 4

Step-by-step explanation:

a) x:2 = 10:4

Product of extremes = Product of means

=> x*4 = 10*2

=> 4x = 20

Dividing both sides by 4

=> x = 5

b) 3:x = 6:8

Product of extremes = Product of Means

=> 3*8 = 6*x

=> 24 = 6x

Dividing both sides by 6

=> x = 4

Answer:

Solution,

[tex]a. \: \: \frac{x}{2} = \frac{10}{4} \\ \: \: or \: x \times 4 = 10 \times 2 \: ( \: cross \: multiplication) \\ \: \: or \: 4x = 20 \\ or \:x = \frac{20}{4} \\ \: \: \: x = 5[/tex]

[tex]b. \: \frac{3}{x} = \frac{6}{8} \\ or \: 6 \times x = 3 \times 8 \: ( \: cross \: multiplication) \\ or \: 6x = 24 \\ \: or \: x = \frac{24}{6} \\ x = 4[/tex]

Hope this helps...

Good luck on your assignment

Answer:

0.79

Step-by-step explanation:

This value is the most opposite of the value above R, meaning that there is an association between the variables.

Answer:

.79

Step-by-step explanation:

Bc y not

Hey there! :)

Answer:

SA = 144 cm².

Step-by-step explanation:

Find the surface area by calculating the areas of each of the lateral sides and bases:

In this instance, the bases are triangles, so the formula A = 1/2(bh) will be used:

Bases:

A = 1/2(bh)

A = 1/2(4·3)

A = 1/2(12)

A = 6 cm².

There are two bases, so:

6 × 2 = 12 cm²

Find the areas of the lateral sides using A = l × w:

5 × 11 = 55 cm²

4 × 11 = 44 cm²

3 × 11 = 33 cm²

Add up all of the areas:

12 + 55 + 44 + 33 = 144 cm².

Answer:

144 cm^2

Step-by-step explanation:

So, first find the area of the triangle. To find that you need to use the formula A = bh ÷ 2 (Area = base x height ÷ 2)

A = (4)(3) ÷ 2

A of triangle = 6

Since there are 2 triangles, you need to multiply the area by 2, which equals 12.

To find the area of the rectangles, you need to use the formula A = lw (Area = length x width)

For the first rectangle,

A = 11 x 5

A = 55

For the second rectangle,

A = 4 x 11

A = 44

For the third rectangle,

A = 3 x 11

A = 33

Now, you need to add the areas of the triangles and rectangles together to get your surface area.

12 + 55 + 44 + 33 = 144cm^2

So, the surface area of the triangular prism is 144 cm^2.

Answer:

Options 2, 4, and 5 are correct (from top to bottom)

Step-by-step explanation:

g(0)=0

g(1)=1

g(-1)=1

g(4)≠-2

g(4)=2

g(1)≠-1

g(1)=1

Options 2, 4, and 5 are correct (from top to bottom)

Answer:

x=70

z=20

y=30

Step-by-step explanation:

first find x: the sum of straight angle is 180

x+110=180

x=180-110=70

now find z: the sum of the angles of triangle is 180:

x=70, right angle=90

z+70+90=180

find y:

y+110+40=180

y=180-150=30

z=180-160=20

Answer:

x=70 degrees, y= 30 degrees, z=20 degrees

Step-by-step explanation:

110+x=180 => straight angle def.

180-110+40=y => def. of angles in triangle

x( 70 degrees) +90+z=180, z= 20 => angles in triangle

Answer:

(x + 2)

Step-by-step explanation:

When we factor the expression x² - 8x - 20, we should get (x + 2)(x - 10).

Alternatively, we can use synthetic division or long division to get our answer.

Answer:

x + 2

Step-by-step explanation:

got it right edg '22

Answer:

30 people

Step-by-step explanation:

If you start off with 1/2 a lemon for 6 people, then 1 whole would be 12. 1 1/2 would be 18 people and 2 whole lemons would be 24. so 2 1/2 is 30 people.

Answer:

4^2

Step-by-step explanation:

4^4 times 4^3 is equal to 4^7 since you just add the exponents. Then, when dividing, you subtract the exponents, so 4^7/4^5 is 4^2. I hope this is helpful!

Answer:

the answer is

Step-by-step explanation:

4 to the power of 2

you add 4 and 3 which is 7

and 7 subtract 5 which is

4 to the power of 2

Answer:

this difference indicates that the results are independent but not reliable.

Answer:a

Step-by-step explanation:

Answer:

[tex]a = 3[/tex]

Step-by-step explanation:

[tex]3 {a}^{2} = 27 \\ \frac{3 {a}^{2} }{3} = \frac{27}{3} \\ {a}^{2} = 9 \\ a = \sqrt{9} \\ a = 3[/tex]

Answer: 9

Step-by-step explanation:

First divide both sides by 3

[tex]a^2=9[/tex]

Then root both sides([tex]\sqrt{a^2}=\sqrt{9}[/tex])

a = 9

Hope it helps <3

Edit: :o this is my 250th answer

A=4[tex]\pi -8[/tex]

that is your answer :-)

Answer:

[tex]A = 4\pi - 8[/tex]

Step-by-step explanation:

ody

Answer:

162°

Step-by-step explanation:

This is a hexagon, so the sum of the angle measures will be 720°

Add up the measures

40x=720

Divide

X=18

Multiply by 9 to find angle of D

9*18=162

The measure of the interior angle at vertex D is 162°. Hence, option B. is the right choice.

Polygons are closed plane figures formed by the intersection of 3 or more non-collinear line segments.

The sum of interior angles of an n side polygon = (n-2)180°.

We are given a 6 side polygon ABCDEF.

∴ n = 2.

The sum of interior angles of polygon ABCDEF = (6-2)180° = 4*180° = 720°.

The angles are 2x, 9x, 2x, 9x, 9x, and 9x.

Their sum = 2x + 9x + 2x + 9x + 9x + 9x = 40x.

This sum = The obtained sum

or, 40x = 720°

or, x = 720°/40 = 18°.

∴ Interior angle at vertex D = 9x = 9*18° = 162°. Hence, option B. is the right choice.

Learn more about Polygons at

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Answer:

[tex]$\left(\frac{x}{2} + 3 y\right)^{4}=\frac{x^{4}}{16} + \frac{3}{2} x^{3} y + \frac{27}{2} x^{2} y^{2} + 54 x y^{3} + 81 y^{4}$[/tex]

Step-by-step explanation:

[tex]$\left(\frac{1}{2}x+3y \right)^4=\left(\frac{x}{2}+3y \right)^4\\$[/tex]

Binomial Expansion Formula:

[tex]$(a+b)^n=\sum_{k=0}^n \binom{n}{k} a^{n-k} b^k$[/tex], also [tex]$\binom{n}{k}=\frac{n!}{(n-k)!k!}$[/tex]

We have to solve [tex]$\left(\frac{x}{2} + 3 y\right)^{4}=\sum_{k=0}^{4} \binom{4}{k} \left(3 y\right)^{4-k} \left(\frac{x}{2}\right)^k$[/tex]

Now we should calculate for [tex]k=0, k=1, k=2, k=3 \text{ and } k =4;[/tex]

First, for [tex]k=0[/tex]

[tex]$\binom{4}{0} \left(3 y\right)^{4-0} \left(\frac{x}{2}\right)^{0}=\frac{4!}{(4-0)! 0!}\left(3 y\right)^{4} \left(\frac{x}{2}\right)^{0}=\frac{4!}{4!}(81y^4)\cdot 1 =81 y^{4}$[/tex]

It is the same procedure for the other:

For [tex]k=1[/tex]

[tex]$\binom{4}{1} \left(3 y\right)^{4-1} \left(\frac{x}{2}\right)^{1}=54 x y^{3}$[/tex]

For [tex]k=2[/tex]

[tex]$\binom{4}{2} \left(3 y\right)^{4-2} \left(\frac{x}{2}\right)^{2}=\frac{27}{2} x^{2} y^{2}$[/tex]

For [tex]k=3[/tex]

[tex]$\binom{4}{3} \left(3 y\right)^{4-3} \left(\frac{x}{2}\right)^{3}=\frac{3}{2} x^{3} y$[/tex]

For [tex]k=4[/tex]

[tex]$\binom{4}{4} \left(3 y\right)^{4-4} \left(\frac{x}{2}\right)^{4}=\frac{x^{4}}{16}$[/tex]

You can perform the calculations, I will not type everything.

The answer is the sum of elements calculated.

Just organizing:

[tex]$\left(\frac{x}{2} + 3 y\right)^{4}=\frac{x^{4}}{16} + \frac{3}{2} x^{3} y + \frac{27}{2} x^{2} y^{2} + 54 x y^{3} + 81 y^{4}$[/tex]

Answer:  [tex]\bold{\dfrac{1}{16}x^4 + \dfrac{3}{2}x^3y + \dfrac{27}{2}x^2y^2 +54xy^3+81y^4}[/tex]

Step-by-step explanation:

                     Binomial Tree

n=0                         1

n=1                      1      1

n=2                  1    2     1

n=3               1    3    3     1

n=4            1    4    6    4    1

Using the Binomial Theorem

[tex]\bigg(\dfrac{1}{2}x+3y\bigg)^4\\\\\\=1\bigg(\dfrac{1}{2}x\bigg)^4(3y)^0\quad \rightarrow \quad \dfrac{1}{16}x^4\\\\+4\bigg(\dfrac{1}{2}x\bigg)^3(3y)^1\quad \rightarrow \quad \dfrac{3}{2}x^3y\\\\+6\bigg(\dfrac{1}{2}x\bigg)^2(3y)^2\quad \rightarrow \quad \dfrac{27}{2}x^2y^2\\\\+4\bigg(\dfrac{1}{2}x\bigg)^1(3y)^3\quad \rightarrow \quad 54xy^3\\\\+1\bigg(\dfrac{1}{2}x\bigg)^0(3y)^4\quad \rightarrow \quad 81y^4[/tex]

______________________

[tex]= \dfrac{1}{16}x^4 + \dfrac{3}{2}x^3y + \dfrac{27}{2}x^2y^2 +54xy^3+81y^4[/tex]

Answer:

factor: 5(2x'y'+3xy)

Step-by-step explanation:

thats for factoring, i didnt know what you needed

Answer:

25xy

Step-by-step explanation:

collect like terms