161,743 vinyl records were sold in 1967.

Answer:

corresponding angles . the answer

Answer:

corresponding angles

Step-by-step explanation:

its called the corresponding angles and are equal value

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:

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)

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:

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

Answer:

29

Step-by-step explanation:

5x5=25

25+4=29

First for 5 times 5 u do 5x5=25 and for (5x5) plus four u add 4 to the answer of 5 times five which makes 29.

Answer:

The answer is 29

Step-by-step explanation:

5 times 5 plus 4

5 × 5 + 4

Use BODMAS

(Bracket of Division, Multiplication, Addition and Subtraction)

(5 × 5) + 4 = 25 + 4 = 29

Thus, The answer is 29

-TheUnknownScientist 72

Answer:

[tex]\textsf{c)} \quad |3x+12|=\begin{cases}3x+12 \; &\text{if}\;x > -4\\0 \; &\text{if} \; x=-4\\-3x-12\; &\text{if}\;x < -4\end{cases}[/tex]

[tex]\textsf{d)} \quad |(x-19)+11|=\begin{cases}x-8\; &\text{if}\;x > 8\\0 \; &\text{if} \; x=8\\8-x \; &\text{if}\;x < 8\end{cases}[/tex]

[tex]\textsf{e)} \quad |14-(x-6)|=\begin{cases}x-20 \; &\text{if}\;x > 20\\0 \; &\text{if} \; x=20\\20-x \; &\text{if}\;x < 20\end{cases}[/tex]

[tex]\textsf{f)} \quad |14-(6-x)|=\begin{cases}x+8 \; &\text{if}\;x > -8\\0 \; &\text{if} \; x=-8\\-x-8 \; &\text{if}\;x < -8\end{cases}[/tex]

Step-by-step explanation:

The absolute value parent function, f(x) = | x |, is defined as:

[tex]f(x)=\begin{cases}x \; &\text{if}\;x > 0\\0 \; &\text{if} \; x=0\\-x\; &\text{if}\;x < 0\end{cases}[/tex]

Therefore:

Its graph is V-shaped and has the following properties:

Given absolute value expression:

[tex]|3x+12|[/tex]

Simplify the given expression:

[tex]\implies |3x+12|=|3(x+4)|=3|x+4|[/tex]

Set the simplified absolute value expression to zero and solve for x:

[tex]\begin{aligned}\implies 3|x+4|&=0\\|x+4|&=0\\x+4&=0\\x&=-4\end{aligned}[/tex]

Therefore, the vertex of the graph of the given absolute expression is (-4, 0).

Therefore, the slope of the expression will be positive for values of x greater than -4, and negative for values of x less than -4.  Set the expression inside the absolute value sign to positive and negative to find the two expressions with positive and negative slopes:

[tex]|3x+12|=\begin{cases}3x+12 \; &\text{if}\;x > -4\\0 \; &\text{if} \; x=-4\\-3x-12\; &\text{if}\;x < -4\end{cases}[/tex]

Given absolute value expression:

[tex]|(x-19)+11|[/tex]

Simplify the given expression:

[tex]|(x-19)+11|=|x-19+11|=|x-8|[/tex]

Set the simplified absolute value expression to zero and solve for x:

[tex]\begin{aligned}\implies |x-8|&=0\\x-8&=0\\x&=8\end{aligned}[/tex]

Therefore, the vertex of the graph of the given absolute expression is (-8, 0).

Therefore, the slope of the expression will be positive for values of x greater than 8, and negative for values of x less than 8. Set the expression inside the absolute value sign to positive and negative to find the two expressions with positive and negative slopes:

[tex]|(x-19)+11|=\begin{cases}x-8\; &\text{if}\;x > 8\\0 \; &\text{if} \; x=8\\8-x \; &\text{if}\;x < 8\end{cases}[/tex]

Given absolute value expression:

[tex]|14-(x-6)|[/tex]

Simplify the given expression:

[tex]|14-(x-6)|=|14-x+6|=|20-x|[/tex]

Set the simplified absolute value expression to zero and solve for x:

[tex]\begin{aligned}\implies |20-x|&=0\\20-x&=0\\x&=20\end{aligned}[/tex]

Therefore, the vertex of the graph of the given absolute expression is (20, 0).

Therefore, the slope of expression will be positive for values of x greater than 20, and negative for values of x less than 20. Set the expression inside the absolute value sign to negative and positive to find the two expressions with positive and negative slopes:

[tex]|14-(x-6)|=\begin{cases}x-20 \; &\text{if}\;x > 20\\0 \; &\text{if} \; x=20\\20-x \; &\text{if}\;x < 20\end{cases}[/tex]

Given absolute value expression:

[tex]|14-(6-x)|[/tex]

Simplify the given expression:

[tex]|14-(6-x)|=|14-6+x|=|x+8|[/tex]

Set the simplified absolute value expression to zero and solve for x:

[tex]\begin{aligned}\implies |x+8|&=0\\x+8&=0\\x&=-8\end{aligned}[/tex]

Therefore, the vertex of the graph of the given absolute expression is (-8, 0).

Therefore, the slope of expression will be positive for values of x greater than -8, and negative for values of x less than -8.  Set the expression inside the absolute value sign to positive and negative to find the two expressions with positive and negative slopes:

[tex]|14-(6-x)|=\begin{cases}x+8 \; &\text{if}\;x > -8\\0 \; &\text{if} \; x=-8\\-x-8 \; &\text{if}\;x < -8\end{cases}[/tex]

Answer:

C&E

Step-by-step explanation:

Answer:

C and E

Step-by-step explanation:

given a quadratic in standard form

y = ax² + bx + c ( a ≠ 0 ) , then

• if a > 0 then the graph opens upward

• if a < 0 then the graph opens downward

----------------------------------------------------------------

A y = - x² + 9x with a < 0 then opens downward

B y = 10x - 5x² with a < 0 then opens downward

C y = (2x - 1)² = 4x² - 4x + 1 with a > 0 then opens upward

D y = (1 - x)(2 + x) = 2 - x - x² with a < 0 then opens downward

E y = x² - 8x - 7 with a > 0 then opens upward

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:

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.

Answer:

160

Step-by-step explanation:

First, create an equation to show the number of books per hour.

6x=96

Divide each side by 6

x=16

Then, multiple 16 by 10 to get the total cartons packed in 10 hours.

16x10=160

#A

Produced energy

[tex]\\ \rm\Rrightarrow 3.9(10^33)(2.45)(10^5)=9.56(10^38) ergs[/tex]

#B

7.4×10^4mm

shorter is more preferable

Answer:

3/7

Step-by-step explanation:

there are a total of 14 crayons in the box.

The probability of choosing a red crayon is 4/14 and the probability of choosing a yellow crayon is 2/14

The probability of choosing either red or yellow is the sum of those two fractions which gets you 6/14 which equals 3/7

Answer:

x=13

Step-by-step explanation:

3x=2x+21−8

3x=2x+13

3x−2x=13

x=13

Answer:

x = 13

Step-by-step explanation:

3x + 8 = 2x + 21

x + 8 = 21

x = 13

Answer:

3x - 35 = 130

Step-by-step explanation:

Vertically opposite angles are congruent.

3x - 35 = 130

hope it helps ~

Answer:

A. (-3,1)

Explanation:

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

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: y=-4x+2

Step-by-step explanation:

Answer:

  A) x = 2; y = 2; (m, n) = (1/2, 0); (p, q) = (-3/2, 12)

  B) K; A and E

  C) 11

Step-by-step explanation:

With the exception of the vertical line, the equations of the lines can be written in terms of their slope and y-intercept. The slope is the ratio of "rise" to "run". The "rise" is the vertical change between points, and the "run" is the horizontal change between the same points. Changes to the right or up are taken as positive. The change amounts can be read from the graph by counting grid squares, or by subtracting coordinate values.

The regions described by an inequality will be to the right of a boundary line for x > (boundary), and above the boundary line for y > (boundary). When these inequalities are reversed, the region will be left or below the boundary, respectively.

__

The slope-intercept equation for a line is ...

  y = mx +b . . . . where m is the slope, and b is the y-intercept

(i) x = 2 . . . . . . points on the vertical line have an x-value of 2

(ii) y = 2 . . . . . 0 slope, y-intercept of 2

(iii) m = 1/2, n = 0 . . . . rise = 1 for run = 2; y-intercept = 0

(iv) p = -3/2, q = 12 . . . . rise = -3 for run = 2; y-intercept = 12

__

(i) Region K is to the right of the vertical line, and above the two slanted lines

(ii) Regions A and E are below y=2 and the two slanted lines

__

The maximum value of x+y will be found at the point on the line x+y=c, where c is the largest possible value. That is, it will lie on the line ...

  y = -x +c . . . . a line with a slope of -1

such that the line is as far as possible from the origin.

For region G, the point that maximizes "c" in the above equation is point (2, 9), so ...

 c = x +y = 2 +9 = 11

The maximum value of (x+y) in region G is 11.

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.

Answer:

12ft.

If the real length was 15 but is 5 down in the drawing that means the scale is 3ft to every inch. (15/5 =3).

With that said the width of the drawing is 4 inches. 4 x 3 = 12..

The width of the real pool would be 12 ft.

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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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.

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 perimeter of the rectangle is 46[tex]\frac{1}{3}[/tex] yds.

Perimeter is the total distance around an object.

To calculate the perimeter of the rectangle, we use the formula below.

Formula:

Where:

From the diagram in the question,

Given:

Substitute these values into equation 1

Hence, The perimeter of the rectangle is 46[tex]\frac{1}{3}[/tex] yds.
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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:

156

Step-by-step explanation:

A problem like this can be solved using multiplication. If each row has 13 seats and there are 12 rows you can get the total amount of seats by multiplying 13x12.