1: In Rectangle ABCD, AC is 5x - 12, and BD is 2x + 15. Find x.

Two equivalent fractions for 20/100 are 1/5 and 2/10. These are found by simplifying the fraction 20/100 by dividing by 20 and 10, respectively. Setting up proportions in different contexts often uses the principle that multiplication and division are related through reciprocals.

To find two equivalent fractions for 20/100, we can simplify the fraction by dividing the numerator and the denominator by the same number. Since both 20 and 100 are divisible by 20, we can divide them both by 20 to get the first equivalent fraction, which is 1/5. To find a second equivalent fraction, we might choose another common divisor, like 10, which gives us 2/10 as another equivalent fraction to 20/100.

Converting percents to fractions involves writing the percentage as a fraction with a denominator of 100 and then simplifying. For instance, 20% would become 20/100 which simplifies to 1/5. To set up a proportion in other contexts, you could follow examples like setting scales in drawings or units in ratios equal to one another, and in doing so, you're often utilizing the concept that multiplication and division are related through the use of reciprocals.

Answer:hey

Step-by-step explanation:

Answer:

The number of general admission tickets sold was 21 and the number of VIP tickets sold was 12

Step-by-step explanation:

Let

x ----> the number of general admission tickets sold

y ----> the number of VIP tickets sold

we know that

[tex]x+y=33[/tex] ---> equation A

[tex]70x+105y=2,730[/tex] ----> equation B

Solve the system of equations by graphing

Remember that the solution is the intersection point both lines

using a graphing tool

The solution is the point (21,12)

see the attached figure

therefore

The number of general admission tickets sold was 21 and the number of VIP tickets sold was 12

Final answer:

To solve how many general admission and VIP tickets John sold, a system of equations is formed and solved, revealing that John sold 21 general admission tickets and 12 VIP tickets.

Explanation:

John is selling tickets to an event with two different pricing options, general admission tickets at $70 and VIP tickets at $105. He sold a total of 33 tickets resulting in revenue of $2730. To determine how many of each type of ticket he sold, we will use a system of equations.

Let x represent the number of general admission tickets sold and y represent the number of VIP tickets sold. We can then form the following two equations based on the information provided:

x + y = 33 (equation 1: total number of tickets sold)

70x + 105y = 2730 (equation 2: total revenue from ticket sales)

To solve this system, we can use the method of substitution or elimination. Here, we'll use substitution for simplicity. First, solve equation 1 for x:

x = 33 - y

Substitute this expression for x in equation 2:

70(33 - y) + 105y = 2730

Simplify and solve for y:

2310 - 70y + 105y = 2730

35y = 420

y = 12

Since y = 12, substitute y back into equation 1 to find x:

x = 33 - 12 = 21

Therefore, John sold 21 general admission tickets and 12 VIP tickets.

Answer:

Your final answer will be 2x^2 + 5x -3

Step-by-step explanation:

Answer:

85.44 miles apart

Step-by-step explanation:

According to the question;

We are supposed to determine how far apart are the airports.

That is;

c² = 80² + 30²

    = 6400 + 900

    = 7300

c = √7300

  = 85.44

Thus, the airports are 85.44 miles apart

The circumference and the area of the circular flower bed is 14π feet

The formula for calculating the circumference of a circle is expressed as:

C = 2πr

Given the following parameeters

diamter = 14ft

radius = 14/2  = 7ft

Susbtitute

C = 2π(7)

C = 14π feet

A  = π(7)^2
A = 49 π square feet

Hence the circumference and the area of the circular flower bed is 14π feet

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Distance between 2 points formula: √(x2 − x1)² + (y2 − y1)²

= √(7 - (-3))² + (-1 - 5)²

= √10² + -6²

= √100 + 36

= √136

≈ 11.662 (Note that this number is rounded because its a a non-terminating decimal).

Best of Luck!

Answer:

15.5 seconds.

Step-by-step explanation:

From the time the driver activated the brakes until he stopped, he travelled 76 - 14 = 62 meters.

During this time the car slowed  down from 8 m/s to 0 m/s.

Assuming the deceleration was constant during this time we can apply one of the equations of motion for constant  acceleration:

s = (u + v)t / 2   where u = initial velocity, v = final velocity, s = distance and t = the time, so:-

62 = (8 + 0)t/ 2

62 = 8t/2

4t = 62

t = 15.5 seconds.

The inequality 12x+9 ≥ 21  represents the minimum rate Chanita have to swim on second day to complete the distance.

Step-by-step explanation:

Given,

Length of English Channel = 21 miles

Distance covered on first day = 9 miles

Time to complete remaining distance on second day = 12 hours

Let,

x be the distance covered per hour on second day.

Time to cover distance * Distance covered per hour + Distance on first day ≥ Total distance

12x+9 ≥ 21

The inequality 12x+9 ≥ 21  represents the minimum rate Chanita have to swim on second day to complete the distance.

Keywords: addition, inequality

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Answer:

The answer is in the picture below. :)

Step-by-step explanation:

Answer:

The tire's weight in 1.146 pounds.

Step-by-step explanation:

Given:

There are 453.592 grams in one pound.

A semi-slick, Kevlar tire weighs about 520 grams.

Now, to find the tire's weight in pounds.

As, given 1 pound is 453.592 grams.

The weight of tire = 520 grams.

So, to get the tire's weight in pounds by using conversion factor:

1 pound = 453.592 grams.

Thus, 520 grams is:

[tex]\frac{520}{453.592}[/tex]

[tex]=1.146\ pounds.[/tex]

Therefore, the tire's weight in 1.146 pounds.

Answer:

13/6

Step-by-step explanation:

2 5/6=17/6

w+2/3=17/6

w=17/6-2/3

w=17/6-4/6

w=13/6

Answer:

x is greater than StartFraction 1 Over 6 EndFraction.

Step-by-step explanation:

–2(8x – 4) < 2x + 5

⇌  –16x + 8 < 2x + 5

⇌ 3 < 18x

⇌ 1/6 < x

⇌ x > 1/6

Answer:

A

Step-by-step explanation:

The slope of the line that passes through (–3, 3) and (1, –5) is –2

Solution:

Given slope of the line passes through two points (–3, 3) and (1, –5).

Formula for the slope of the line passes through two points is

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Here, [tex]x_1=-3, x_2=1, y_1=3,y_2=-5[/tex]

Substitute these in the slope formula, we get

⇒ [tex]m=\frac{(-5)-3}{1-(-3)}[/tex]

⇒ [tex]m=\frac{-5-3}{1+3}[/tex]

⇒ [tex]m=\frac{-8}{4}[/tex]

⇒ [tex]m=-2[/tex]

Hence, the slope of the line that passes through (–3, 3) and (1, –5) is –2.

Answer:

A customer earns one free night per 10 nights stayed.

Step-by-step explanation:

A hotel offers a reward program based on the number of nights stayed. The function f(x) represents the number of free nights earned as a function of x, the number of nights stayed.

Here, [tex]f(x) = \frac{x}{10}[/tex] ........... (1)

In the above equation if we put x = 10 nights then f(10) = 1 night.

From, the equation (1) we get that a customer earns one free night per 10 nights stayed. (Answer)

The correct option is A. a customer will earn 1 free night per 10 night stayed.

Given,

[tex]f(x)=\dfrac{x}{10}[/tex]..........equation (1) .

Since the hotel offers a reward program based on the number of nights stayed. The function [tex]f(x)[/tex] represents the number of free nights earned as a function of [tex]x[/tex], the number of nights stayed.

From equation (1), it is clear that  f(x) is the one- tenth times  of x. it means the customer will earn 1 free night per 10 night stayed.

Hence the correct option is A. a customer will earn 1 free night per 10 night stayed.

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Answer:

3

Step-by-step explanation:

42 divided by 2 equals 21

21 divided by 8 equals 2.625

therefore, sharon must buy 3 packets of cheese.

Answer:

X = -15

Step-by-step explanation:

Divide -60 by 4

Answer:

[tex]8(68) + 20[/tex]

[tex]8 \times 68 + 20[/tex]

[tex]544 + 20[/tex]

[tex]x = 564[/tex]

Answer:

170

Step-by-step explanation:

8/20=x/y

simplify. 2/5

2/5=68/y

68*5/2=y

68*5=340

340/2=170

y=170

Answer:

[tex]y = \frac{3}{4}x + \frac{19}{4}[/tex]

Step-by-step explanation:

We have to get the equation of the straight line through the points (3,7) and (-1,4).

Now, we know that the two-point formula of a straight line passing through the two points [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] is given by

[tex]\frac{y - y_{1} }{y_{1} - y_{2}} = \frac{x - x_{1} }{x_{1} - x_{2}}[/tex].

So, in our case, the equation of the straight line will be

[tex]\frac{y - 7}{7 - 4} = \frac{x - 3}{3 + 1}[/tex]

⇒ 4(y - 7) = 3(x - 3)

⇒ 4y - 28 = 3x - 9

⇒ 4y = 3x + 19

⇒ [tex]y = \frac{3}{4}x + \frac{19}{4}[/tex] (Answer)

Answer:i8lil

Step-by-step explanation:

loo;;o;o;oo;

Answer:

you Go up to who ever teaches you cuz it’s 8 and u should know This

Answer:

x=-1, y=1. (-1, 1).

Step-by-step explanation:

5y-6=x

y=-x

-----------

5(-x)-6=x

-5x-6=x

-5x-x=6

-6x=6

x=6/-6

x=-1

y=-(-1)=1

Answer:

the answer is b

Step-by-step explanation:

Answer:

B. 0.38

Step-by-step explanation:

Answer: 64g

Step-by-step explanation: added 20 by 20 and then add the 4.

Answer:it stays the same

Step-by-step explanation: because if it different letters it can’t combine

Answer:

Julie Spends $5.62, Micah spends $28.10 and Jeremy Spends $34.82

Step-by-step explanation:

If Micah spends 5 times as much as Julie, that is $28.10 because 5.62 x 28.10 = 28.10. If Jeremy spends 6.72 more than Micah, you would do 28.10 + 6.72, which is 34.82

I think I did the math correct but I may be wrong

Answer:

reeeeee

Step-by-step explanation:

ererrrrrrrrrrrrrrrr

Answer:

1.55 × 10^24

Step-by-step explanation:

The answer is A aka 1.55 x 10 to the power of 24

Answer:

1664 boys

Step-by-step explanation:

3200×0.52=1664 boys

Answer:

1664

Step-by-step explanation:

Multiply 3200 by the 52% as a decimal, which is 0.52, and 3200 times 0.52 gives you the answer 1664.

Answer:

The actual answer is C) 2, -3/400

Step-by-step explanation:

I hope this can help, I checked for the answer after the quiz.

Step-by-step explanation:

Given  expression

Number of insect                  Number of mayflies

         x                                                    [tex]\frac{3}{14}x[/tex]

According to problem

[tex]\frac{3}{14}x[/tex][tex]=15[/tex]

⇔[tex]x = \frac{15 \times 14}{3}[/tex]

⇔[tex]x = 70[/tex]

Answer:

see attached picture please

Last Option: "The division property is used to create step 4" is the correct answer

Step-by-step explanation:

Given equation is:

[tex]6(3x-4)-26 = 40[/tex]

Step 1: Distributive property

[tex]18x-24-26 = 40\\[/tex]

Step 2: Simplifying

[tex]18x-50 = 40[/tex]

Step 3: Addition Property of Equality

[tex]18x-50+50 = 40+50\\18x = 90[/tex]

Step 4: Division Property of Equality

[tex]\frac{18x}{18} = \frac{90}{18}\\x = 5[/tex]

Hence,

Last Option: "The division property is used to create step 4" is the correct answer

Keywords: Linear equation, variables

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Answer:

23.902

Step-by-step explanation: