If the circumference of a circle is 62.8 feet, what is the radius of the circle
Use 3.14 for pie

The total ratio is 5

The number of comedy movies watched is 12

The number of other movies watched is 18

Ratio is a comparison of two or more numbers that indicates their sizes in relation to each other. Therefore,

He has watched 2 comedy movies for every 3 other movies. The total movies he has watched is 30. Therefore,

Ratio of comedy to total movies is as follows:

number of comedy movies watched = 2 / 5 × 30 = 60 / 5 = 12

number of other movies watched = 3 / 5 × 30 = 90 / 5 = 18

Therefore,

total ratio = 5

number of comedy movies watched = 12

number of other movies watched = 18

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Comedy movies- 2   (12)

Other movies- 3       (18)

Total movies- (5)       30

Answer:

[tex]\displaystyle Substitution[/tex]

Explanation:

Elimination and Substitution are two methods to use when solving systems of equations in two and three variables [tex]\displaystyle [z, y, and\:x].[/tex]With Elimination, you decide on which pair of variables you want to eradicate so they are set to zero, whereas Substitution is mainly used when one variable is automatically isolated. If not, then you must manually decide on which variable to isolate as well as the equation you want to wourk.

I am joyous to assist you at any time.

The radius of the given circle with a central angle of 7π/10 and arc length of 33cm is 15cm.

It is given that

The central angle of the given circle = 7π/10 radians

Length of arc = 33cm

Arc length = central angle* radius

From the above formula

Radius = Arc length/Central Angle

Radius = [tex]\frac{33}{(7\pi)/10 }[/tex]

Radius = 15cm

Therefore, radius of the given circle is 15cm.

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Answer:

15 cm or B on egde

Step-by-step explanation:

Answer:

5x^2 - 8x - 32

Step-by-step explanation:

Area of rectangle = base x height

Area of larger rectangle = (3x - 8)(2x + 4)

                                        = 6x^2 - 4x - 32

Area of smaller rectangle = (x + 4)x

                                           = x^2 + 4x

Area of shaded region = area of larger rectangle - area of smaller rectangle

                                      = (6x^2 - 4x - 32) - (x^2 + 4x)

                                      = 5x^2 - 8x - 32

Answer:

If [tex]sin x = 0[/tex] we get [tex]2 (0) (\pm1) = 0[/tex] which is true. so we have a first set of solutions given by

[tex]x= 0; x = \pi[/tex];

Else, if [tex]sin x \ne 0[/tex] we can divide both sides by it and we get

[tex]2 cos x = \frac 1 {cos x} \rightarrow 2cos^2x =1 \rightarrow cos^2x =\frac12\\cos x= \pm \frac{\sqrt2}2[/tex]

Which gives us a second set of solutions given by [tex]x= \frac{\pi}4;x= \frac{3\pi}4; x= \frac{5\pi}4;x= \frac{7\pi}4[/tex];

We can group all solutions (doesn't matter, but it's more elegant!) by writing

[tex]x= k\frac{\pi}4; k\in \{0,1,3,4,5,7\}[/tex]

Answer:

if it is area of triangle it would be 49

Step-by-step explanation:

Answer:

C. 1200 yds

Step-by-step explanation:

Each cm equals 10 yards, so start by multiplying the 3cm and 8 cm by 10. Then all you do is insert those numbers into the equation for the area of a triangle which is 1/2BH

1/2*80*30=1200

Answer:

C. 1,200 yds

Step-by-step explanation:

To find the area of a triangle, you must use the triangle area formula, [tex]A = \frac{1}{2}(b*h)[/tex].

Since 1 cm = 10 yards, then 8 cm = 80 yards and 3 cm = 30 yards. You can use 80 yards as your base and 30 yards as your height to find the area:

[tex]A=\frac{1}{2} (80*30)[/tex]

[tex]A=\frac{1}{2} (2400)[/tex]

[tex]A=1200[/tex]

Therefore, the answer is C. 1,200 yards.

I hope this helps!

Answer:

Step-by-step explanation:

When we say "y varies inversely as x", we mean that y is proportional to the inverse of x: y = k·(1/x). This relation is usually written ...

  y = k/x

It can be solved for the other values:

  xy = k . . . . multiply by x

  x = k/y . . . divide by y

If you are given the equation, the value of k can be read directly from it: it is the constant in the numerator.

__

  k = xy = 5·6 = 30; the equation is y = 30/x

  y = k/x = 36/4 = 9; the equation is y = 36/x

 k = 50 (read from the equation); x = k/y = 50/20 = 5/2

  k = 24 (read from the equation); y = k/x = 24/12 = 2

The angle of refraction is 15.6 deg.

We have given that An incident ray strikes a piece of diamond at an angle of 40. 5 degrees.

When a ray of light passes from medium 1 to medium 2, the refractive index of medium 2 with respect to 1 is the ratio of the absolute refractive index of medium 2 and medium 1

[tex]1n_{2}=\frac{^{n_{1}}}{n_{2}}[/tex]

When light passes from air into diamond, with the given values of refractive indices,

[tex]an_{d}=\frac{^{n_{d}}}{n_{a}}=\frac{2.42}{1.0003} =2.4193[/tex]

According to Snell's law,

[tex]an_{d}=\frac{^{sini}}{sin r}[/tex]

[tex]< br/ > sinr=an_{d}=\frac{^{sini}}{sin r}=\frac{sin(40.5)}{2.41930} =0.2684[/tex]

[tex]< br/ > r=arcsin(0.2684)=15.57 deg[/tex]

The angle of refraction is 15.6 deg

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Answer:

42 sq ft

Step-by-step explanation:

L x W x H

3 x 7 x 2

21 x 2

42 sq ft

Answer:x=-1

add 1 to 3 to get 4, add 3 to -7 to get -4, divide both sides by -4

Answer:

[tex] \: [/tex]

Step-by-step explanation:

Given Equation,

[tex] \\ {\longrightarrow \qquad{ \sf{-3x+3=-7x-1}}}\\ \\ [/tex]

Adding 7x to both sides we get,

[tex]{\longrightarrow \qquad{ \sf{-3x+3 + 7x=-7x-1 + 7x}}}\\ \\ [/tex]

[tex]{\longrightarrow \qquad{ \sf{4x+3=-1}}}\\ \\ [/tex]

Subracting -3 from sides we get,

[tex] \\ {\longrightarrow \qquad{ \sf{4x+3 - 3=-1 - 3}}}\\ \\ [/tex]

[tex]{\longrightarrow \qquad{ \sf{4x=-4}}}\\ \\ [/tex]

Dividing both sides by 4 we get,

[tex] \\ {\longrightarrow \qquad{ \sf{ \frac{4x}{4} = \frac{ - 4}{4} }}}\\ \\ [/tex]

[tex]{\longrightarrow \qquad{ \sf{x=-1}}}\\ \\ [/tex]

n/3-2 = 2

n/3 = 4

n = 12

The solution to the algebraic equation, n/3 - 2 = 2, is: n = 12.

If given an algebraic equation, such as n/3 - 2 = 2, to solve for n, you have to isolate n as shown below:

n/3 - 2 = 2

Add 4 to both sides of the equation

n/3 = 2 + 2

n/3 = 4

Multiply both sides by 3

n = (4)(2)

n = 12

Therefore, the solution to the algebraic equation, n/3 - 2 = 2, is: n = 12.

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The inequalities that must be true if m is greater-than-or-equal-to n are given as:

Only those operations are allowed which are sure to not modify the inequality between the expressions in the statement.

Some operations that are sure not to modify the inequalities are:

Addition, Subtraction, multiplication by positive real numbers, division by positive real numbers etc.

Example, if 5 > 2, then you can do whatever which keeps the term on the side of 5 bigger than the terms formed on side of 2.

Thus, 5 + 1  > 2 + 1 is correct, (it was addition of 1, a real number).

For the considered case, we're given that:

[tex]m \geq n[/tex]

Checking all the options sequentially, we get:

It must be true, since the multiplication is done by 2.1, which is > 0

It must be true since -4 is a real number, and addition or subtraction of any real number (if done on all the sides of the statement) doesn't change the inequality

From [tex]m \geq n[/tex], addition or subtraction is guaranteed to not change the inequality only if they are of same quantity on all the sides of the inequality. Thus, this inequality is not necessary to be true.
Example, if we take m = 5, n =3, then,

[tex]5 \geq 3[/tex] but [tex]5 - 3=0 \: \rm and \: 3 + 3= 6 \implies 5-3 < 3 + 3[/tex]

It must be true if given that [tex]m \geq n[/tex] since multiplication of equal positive real number on both the sides of  [tex]m \geq n[/tex] was done.

one-half of 6 = 3, thus, this inequality means [tex]3m \geq 9m[/tex]

Dividing both the sides by 3, we get:

[tex]m \geq 3n[/tex]

It is not  necessary to be true if  [tex]m \geq n[/tex]. Example

[tex]3 \geq 2\\but\\ 3 < 3 \times 2 = 6[/tex]

Thus, the inequalities that must be true if m is greater-than-or-equal-to n are given as:

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Rami's family will pay less if they use savings instead of credit.

Step-by-step explanation:

Took the test 8th grade K12

Answer:

[tex]\sf x=2+\sqrt{6},\:x=2-\sqrt{6}[/tex]

Explanation:

[tex]\sf y = x^2 -4x[/tex]

given that y = 2

[tex]\sf x^2 -4x = 2[/tex]

[tex]\sf x^2 -4x -2 = 0[/tex]

using quadratic formula:

[tex]\sf x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \ \ \ when \ ax^2 + bx + c = 0[/tex]

[tex]\rightarrow \sf x_{1,\:2}=\dfrac{-\left(-4\right)\pm \sqrt{\left(-4\right)^2-4\cdot \:1\cdot \left(-2\right)}}{2\cdot \:1}[/tex]

[tex]\rightarrow \sf x_1=\dfrac{-\left(-4\right)+2\sqrt{6}}{2\cdot \:1},\:x_2=\dfrac{-\left(-4\right)-2\sqrt{6}}{2\cdot \:1}[/tex]

[tex]\rightarrow \sf x=2+\sqrt{6},\:x=2-\sqrt{6}[/tex]

in decimals:

[tex]\rightarrow \sf x=4.45 , \ -0.45[/tex]

The volume of the cylinder is [tex]\pi r^{2}h[/tex]

Volume = [tex]\pi 3^{2} * 4=113.097[/tex] cubic inches (approximated)

Hope that helped!

Answer:

3x - 35 = 130

Step-by-step explanation:

Vertically opposite angles are congruent.

3x - 35 = 130

hope it helps ~

160 i believe. to find the area of a triangle act like its a square and divide in half. for squares multiply base by height.

take the area of each shape and add it up

Answer:

A. (-3,1)

Explanation:

if you invert the point over the Y-axis, then it will switch the x point to negative.

Answer:

y^12/5 aka the first option

Step-by-step explanation:

(9x^5y^16)/(45x^5y^4)

rules of exponents say youll do 5-5 because when dividing with exponents you subtract them

you get x^0 which is equal to 1 due to another rule of exponents

youll do 16-4 next and get 12 so y^12

now 9/45=5

the answer is (y^12)/5 (the first option)

Answer:

Tm = 6 - Ts

Step-by-step explanation:

If I am incorrect in my reasoning, please let me know so that I can plan better for my future answers. Have an amazing day.

Answer:1) 1/12 2)21/5 3) 9/25.

Step-by-step explanation:

5x1/12x5 is 5/60, which is 1/12. 4 2/3 is 14/3. 14x9/3x10 is 126/30, or 21/5. 36 percent is 36/100. Divide by 2. 18/50. Divide by two again, 9/25.

Answer:

Step-by-step explanation:

First of all, you have to set up the equation

2x^2 + x -1 = 2               Subtract 2 from both sides

2x^2 + x - 1 - 2 = -2+2   Combine

2x^2 + x - 3 = 0             This factors.

(2x + 3)(x -1 ) = 0

Either

2x + 3 = 0                       Subtract 3 from both sides

2x = - 3                           Divide by 2

2x/2 = - 3/2                    

x = - 3/2                         which you already know

or

x - 1 = 0                          Add 1

x - 1 + 1 = 1

x = 1

the other answer is x = 1

Answer:

Step-by-step explanation:

d(t) = 4t + 382 - 16t²

where d is the distance (in feet) between the rock and ground t seconds after thrown. Ground is 0 feet.  As a note, I'm not clear why the "4t" term is in this equation.  It has the effect of adding an increase in height at the rate of 4 feet/sec.  I'll assume this is to accommodate any increase in height due to the throw, but it is a bit curious.  

a.  How long after the rock is thrown is it 370 feet from the ground?

The 382 in the equation represents the starting height of the rock (382 feet).  To find the time to reach 370 feet:

370 = 4t + 382 - 16t²

Solve using the quadratic equation.  There will be two answers, one negative, which we'll discard until we can go backwards in time.  The positive value is 1, which would mean the rock will be at 370 feet in 1 second after throwing.

b. After how many seconds will the rock reach the ground?

Ground is 0 feet:

0 = 4t + 382 - 16t²

t = 5 seconds

c. What is the height of the rock when it is halfway to the ground?

The initial height is 382 feet, as per the equation, since when t = o (initial), d(t) is 382 feet.  Halfway to the ground would be (382/2) or 191 feet.