Which is the slope of the line with equation 7 x − 3 y = 21 ?
A. 3 7
B. − 3 7
C. 7 3
D. − 7 3

As a result of answering the given question, we may state that As a expressions result, the pool was used by 311 children.

An expression in mathematics is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, division, exponentiation, and so on) that expresses a quantity or a value. Expressions might be simple, such as "3 + 4", or complex, such as "(3x2 - 2) / (x + 1)". They can also include functions like "sin(x)" or "log(y)". Expressions can be evaluated by substituting values for the variables and performing the mathematical operations in the order specified. For example, if x = 2, the formula "3x + 5" evaluates to 3(2) + 5 = 11. Expressions are frequently used in mathematics to express real-world situations, create equations, and simplify complex mathematical problems.

To indicate the number of children and adults who used the pool, we'll use two variables. Let:

Let x denote the number of children and y the number of adults.

We can deduce from the problem:

x + y = 402 (the total number of individuals who used the pool) (the total number of people who used the pool)

1.5x + 2y = 648.5 (the total revenue from entrance) (the total revenue from admission)

We can solve for x and y using these two equations.

\(x + y = 402\sx = 402 - y\\1.5x + 2y = 648.5 1.5(402 - y) + 2y = 648.5 603 - 1.5y + 2y = 648.5\)

The pool was visited by 91 adults. The first equation can be used to calculate the number of children:

\(x + y = 402\sx + 91 = 402\sx = 311\)

As a result, the pool was used by 311 children.

To know more about expressions visit :-

https://brainly.com/question/14083225

#SPJ1

Answer:

1/7

Step-by-step explanation:

Please write these fractions as 5/7 and 1/2.  5 7 and 1 2 are incomplete and confusing.

On Saturday the distance traveled was 5/7 of the total distance.

2/7 of that total was left for Sunday.  Half of 2/7 is 1/7.

1/7 of the total distance was traveled on Sunday.

Answer:

the answer for this problem is x^2+2x-15

Step-by-step explanation:

(x+5)(x-3)

x(x-3)+5(x-3)

x^2-3x+5(x-3)

x^2-3x+5x-15

=x^2+2x-15

Answer:

1. $15

2. $450

3. $20

Brainly plz :))

Answer:

Step-by-step explanation:

interval in mathematics stands for a set of real numbers,

denoted by [a,b] where a and b are the starting and ending real numbers both inclusive respectively.

thus, interval [a,b] is the set of real numbers starting from a to b both are real numbers and are included.

Answer:

The value of x is 30 and y is 14

Step-by-step explanation:

Here, In given triangle,

∆JLK is similar to ΔPQR

JL is corresponds to PQ.

So, we have the ratio, 21/y ...(1)

Now,

LK is corresponds to QR.

So, we have the ratio, 18/12 = 3/2 ...(2)

Now,

JK is corresponds to PR.

So, we have the ratio, x/20 ...(3)

Then, (1) = (2) = (3)

21/y = 3/2 = x/20 ...(*)

Now, Cross Multiply by (1) and (2) we get,

21 × 2/y × 3

42 = 3y

3y = 42

y = 42/3

y = 14

Here, we get the value of y is 14. So, we will put the value of y in (1) we get,

21/y = 21/14

So, by (*) we get

21/14 = 3/2 = x/20

Then, Cross Multiply with (2) and (3) we get,

3/2 = x/20

20 × 3 = 2 × x

60 = 2x

2x = 60

x = 60/2

x = 30

Thus, The value of x is 30 and y is 14

21/y = 3/2 = x/20

21/14 = 3/2 = 30/20

3/2 = 3/2 = 3/2

-TheUnknownScientist

Answer:

27/28

Step-by-step explanation:

2/7 - x =5/4

-2/7      -2/7

    x=27/28

Answer:

Step-by-step explanation:

The table shows the amount of rainfall recorded over the first 10 months of a year. Draw a line plot, if needed.

Amount of Rainfall (inches)

Part A

What is the difference between the greatest and least amounts of rainfall in a month?

Let x = the unknown.

Greatest amount= 3 1/4

Least amount = 3/4

x= 3 1/4 - 3/4 = 2 1/2 inches.

Part B

If the last 2 months of the year each have the most common amount of rainfall, how much more rain will fall for the year?

The number with the most common amount is  2 3/4.

2 3/4 + 2 3/4 = 5 1/2 inches.

Depending on whether the movement is along the x-axis or the y-axis, the ordered pair would be either (0.25, 0) or (0, 0.25).

To plot an ordered pair starting from the origin and moving 0.25, we need both an x-coordinate and a y-coordinate.

We are starting from the origin (0, 0), we can apply the movement of 0.25 to either the x-axis or the y-axis.

If we move 0.25 units on the x-axis, the x-coordinate of the ordered pair would be 0.25, and the y-coordinate would remain 0 since there is no movement on the y-axis. Therefore, the ordered pair would be (0.25, 0).

Similarly, if we move 0.25 units on the y-axis, the x-coordinate would remain 0 since there is no movement on the x-axis, and the y-coordinate of the ordered pair would be 0.25. In this case, the ordered pair would be (0, 0.25).

So, depending on whether the movement is along the x-axis or the y-axis, the ordered pair would be either (0.25, 0) or (0, 0.25).

To know more about ordered pair refer here:

https://brainly.com/question/28874341#

#SPJ11

(x+1) & (x-5) are the factors of given equation.

The given Equation is,

x3- \(3x^{3}\) - 9

Here, If we substitute x =5, in the given equation, then we find

     (5)3 - 3(5)3 - 9*5 -5 = 0

x-5 is factor of given equation to find another factor dividing given equation by x-5

    we will get =(x2+2x+1) after dividing the equation by x - 5

Hence x3- \(3x^{3}\) - 9 =(x2+2x+1) (x-5)

                            =(x+2)2 (x-5)

To learn more about Equation click the link

brainly.com/question/29657983

#SPJ4

Answer:

t = 4.875 s

h(4.875) = 686.25 ft

t ≈ 11.424 s

Step-by-step explanation:

These questions are more easily answered if the equation is written in vertex form. Subtracting the constant and dividing out -16, we get ...

h(t) -306 = -16(t^2 -9.75t)

Adding the square of half the t-coefficient inside parentheses gives ...

 h(t) -306 -380.25 = -16(t^2 -9.75t +23.765625)  

 h(t) = -16(t -4.875)^2 + 686.25

This tells us the maximum height is 686.25 ft at time t = 4.875 seconds.

__

When the rock hits the ground, h(t) = 0, so ...

0 = -16(t -4.875)^2 + 686.25

686.25/16 = (t -4.875)^2 . . . . . subtract 686.25, divide by -16

√42.890625 +4.875 = t ≈ 11.424 . . . . take the square root, add 4.875

The rock hits the ground after about 11.424 seconds.

The given expression 4 * d^(-5) / (18 * d^9) can be simplified to 4 / (18 * d^14) by moving the negative exponent to the denominator.

To simplify the given expression, let's break it down step by step:

Expression: 4 * d^(-5) / (18 * d^9)

Step 1: Simplify the numerator:

The expression 4 * d^(-5) can be rewritten as 4 / d^5 by moving the negative exponent to the denominator.

Expression becomes: 4 / (d^5 * 18 * d^9)

Step 2: Simplify the denominator:

In the denominator, we can combine the terms with the same base, d, by adding their exponents: d^5 * d^9 = d^(5+9) = d^14.

Expression becomes: 4 / (18 * d^14)

Step 3: Divide the numerator by the denominator:

To divide by a fraction, we can multiply by its reciprocal. The reciprocal of (18 * d^14) is 1 / (18 * d^14).

Expression becomes: 4 * (1 / (18 * d^14))

Step 4: Simplify the expression:

Multiplying 4 by 1 gives us 4.

Final Expression: 4 / (18 * d^14)

Therefore, the equivalent expression for 4 * d^(-5) / (18 * d^9) is 4 / (18 * d^14).

Learn more about expression here:

https://brainly.com/question/28170201

#SPJ11

Answer:

the equivalent expression for 4 * d^(-5) / (18 * d^9) is 4 / (18 * d^14).

Step-by-step explanation:

Answer:

In 5 years, you will have $1,288.48

Step-by-step explanation:

Answer Nate will have 1,288.48 in his bank after 5 years

I hope this helps but if it's wrong I'm sorry just let me know what I did wrong

Step-by-step explanation:

Hey there!

Given;

-5/6m = -60

~ Multiply "6m" and "-60".

-5 = 6m*-60

-5 = -360m

~ Divide "-5" by "-360"

m = -5/-360

m = 1/72

Therefore, the value of "m" is 1/72.

Hope it helps....

Answer:

He can find how much water he has left after watering his plants, and subtract it by how much he started with.

By using a measuring cup. This would help him find the amount of water left in the can, which then the amount of cups would be subtracted from 10.

that it is important for likert-type scale response choices to be balanced at the ends of the response continuum. This means that there should be an equal number of positive and negative response options to avoid any bias or skew in the results.

An explanation for this is that if there are too many positive or negative response options, respondents may feel pressured to choose a certain option even if it doesn't accurately reflect their true opinion. This can result in inaccurate data and can skew the results of the survey or study.

balancing the response choices on a likert-type scale is crucial for obtaining accurate and unbiased data. By having an equal number of positive and negative options, respondents are more likely to provide honest and accurate responses.

To know more about number, visit:

https://brainly.com/question/17429689

#SPJ11

Answer:

76

Step-by-step explanation:

10 * 4 + 6 ^ 2  = 40 + 36 = 76

Roughly 14 times as 20% of 70 is 14.

The car is traveling at a speed of 45 feet per second, which is approximately 30.682 kilometers per hour. The rectangular parking lot, with dimensions of 86.5 feet wide and 123 feet long, has an area of 10214.95 square meters.

To convert the speed from feet per second to kilometers per hour, we need to use the conversion factors. There are 0.3048 meters in a foot and 3600 seconds in an hour. By multiplying the given speed of 45 feet per second by (0.3048 * 3600) / 1000, we obtain the speed in kilometers per hour, which is approximately 30.682 km/h.

Comparing the converted speed with the speed limit, we find that the car is exceeding the limit. The speed limit is stated as 35 miles per hour, and since 1 mile equals 5280 feet, we can convert it to feet per second by multiplying it by 5280/3600. This gives us a speed limit of approximately 51.33 feet per second. As the car's speed is 45 feet per second, it is indeed exceeding the 35 mile per hour speed limit.

To calculate the area of the rectangular parking lot in square meters, we multiply its length (123 ft) by its width (86.5 ft). However, since the desired unit is square meters, we need to convert the result. Since 1 meter equals 3.28084 feet, we divide the product by (3.28084^2) to obtain the area in square meters. Thus, the area of the parking lot is approximately 10214.95 square meters.    

Graphically determining the resultant force can be done by creating a vector diagram. We represent force F1 (magnitude 5.50 units, direction 31.0° above the positive x-axis) and force F2 (magnitude 5.00 units, direction of the positive y-axis) as vectors starting from the origin. Drawing these vectors to scale, we can then find the vector sum by connecting the tail of F1 with the head of F2. The magnitude of the resultant force is the length of this vector, and the direction is measured counterclockwise from the positive x-axis.

Learn more about vector here:

https://brainly.com/question/30958460

#SPJ11

Answer:

\(\huge\boxed{\sf y=-\frac{3}{8} x+\frac{1}{2} }\)

Step-by-step explanation:

\(y=mx+b\)

Where m is slope and b is y-intercept

\(\displaystyle m=-\frac{3}{8} , \ b =\frac{1}{2}\)

Put in the above general equation!

So, the equation becomes:

\(\displaystyle y=-\frac{3}{8} x+\frac{1}{2}\)

Answer: y= (-3/8)x+(1/2)

Step-by-step explanation: Since you're given the slope (-3/8) and the y-intercept (1/2) it is easy to write the equation of the line. The equation of a line is defined as y=mx+b; where m is the slope (-3/8) and b is y-intercept (1/2). Therefore, the equation you are looking for is y=(-3/8)x+(1/2)

Distance from the summit of Mount Everest to the horizon, Rounded to the nearest mile, the distance from the summit of Mount Everest to the horizon is 210 miles.

Distance refers to the space between two points or the length of a line between them. It may also refer to a range, extent, or magnitude that separates one point from another. Distance may be a physical concept, such as the distance between two cities or the distance traveled by a moving object.

The distance between two points can be calculated using a number of mathematical techniques, including the Pythagorean theorem, the distance formula, and vector addition.

d = √(2Rh + h²)

where d is the distance to the horizon, R is the radius of the Earth (4000 miles), and h is the height of the observer (in this case, the height of the summit of Mount Everest, which is 29,030 feet).

We need to convert the (h) height of the summit to miles:

29,030 ft = 29,030/5280 miles ≈ 5.49 miles

Now we can plug in the values and solve for d:

d = √(2 × 4000 × 5.49 + 5.49^2) =209.64288 ≈ 210 miles

Therefore, the distance from the summit of Mount Everest to the horizon is approximately 210 miles when rounded to the nearest mile.

To know more about the "distance": https://brainly.com/question/26046491

#SPJ11

Answer:

10

Step-by-step explanation:

um I pretty sure that's the answer but i could be wrong

Answer: 6×10-4

Step-by-step explanation:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the  

10

. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

6×10-4

Families who spent less than $200 per day:

Percentage = Area to the left of z = Area to the left of -0.7833

Families who spent between $200 and $300 per day:

Percentage = Area between z1 and z2 = Area to the left of z2 - Area to the left of z1

Families who spent more than $300 per day:

Percentage = Area to the right of z = 1 - Area to the left of z

To find the percentage of families who spent a certain amount on food and lodging, we need to use the concept of z-scores and the standard normal distribution.

The formula for calculating the z-score is:

z = (x - μ) / σ

Where:

z is the z-score

x is the value we want to find the percentage for

μ is the mean (average) value

σ is the standard deviation

Let's calculate the z-scores for the given scenarios:

Families who spent less than $200 per day:

z = (200 - 247) / 60 = -0.7833

Families who spent between $200 and $300 per day:

z1 = (200 - 247) / 60 = -0.7833

z2 = (300 - 247) / 60 = 0.8833

Families who spent more than $300 per day:

z = (300 - 247) / 60 = 0.8833

Now, we can use the z-scores to find the corresponding percentage using a standard normal distribution table or a calculator.

Families who spent less than $200 per day:

Percentage = Area to the left of z = Area to the left of -0.7833

Families who spent between $200 and $300 per day:

Percentage = Area between z1 and z2 = Area to the left of z2 - Area to the left of z1

Families who spent more than $300 per day:

Percentage = Area to the right of z = 1 - Area to the left of z

You can use a standard normal distribution table or a calculator that provides the functionality to calculate these probabilities based on the z-scores.

learn more about  z-score here:

https://brainly.com/question/31871890

#SPJ11

Answer:

$495

Step-by-step explanation:

The length of the trip is useless information in this question, because you only need cost and members. You divide 2475 by 5 to see how many times it evenly goes into the cost, which brings you your total of $495

Answer:

-57.6 degrees

Step-by-step explanation:

0 is a point between 53.6 degrees and -4 degrees.

The change from 53.6 to 0 was -53.6 degrees, and that from 0 to -4 degrees was -4 degrees.  

Thus, the total change (drop) in temperature was -53.6 degrees less 4 degrees, or -57.6 degrees.

When comparing the two numbers we get that 116/9 is greater than square root of 160.

The square root of 160

= √160

= 12.6491...

≈ 12.65

The fraction number is 116/9 , converting to decimal we get:

116/9

= 12.888

≈ 12.89

Now comparing the two numbers we get:

12. 89 > 12.65

hence 116/9 > 12.65

The opposite of squaring an integer is finding its square root. Finding a number that, when squared, yields the original value will reveal the square root of a number, which is found by multiplying it by itself. If "a" is equal to "b" squared, then a = b.

Every number has four roots that are four by four, one of a positive value and one of a negative value, because the square of almost any integer always represents a positive number. For instance, the square roots of 4 are both 2 and -2. However, the square root of an integer is typically expressed using only the positive value.

To learn more about square root visit:

https://brainly.com/question/1540542

#SPJ1

Answer:

5 : 7

Step-by-step explanation:

groom's side: 40

bride's side: 56

ratio groom to bride = 40/56 = 20/28 = 10/14 = 5/7

Answer: 5 : 7

Part A: Width = 9.3 ft; Height = 16.5 ft; Area =  153.45 sq ft.

Part B: Width = 38.25 ft ; Height = 91 ft; Area =  3503.5 sq ft.

Part A: conversion factor: 1 in = 3 ft

Width = 3.1 in

Width = 3.1 x 3

Width = 9.3 ft

Height = 5.5 x 3 ft

Height = 16.5 ft

Area = Width x Height

Area = 9.3 ft x  16.5 ft

Area = 153.45 sq ft

Part B: conversion factor: 1 in = 6.5 ft

Width = 8.5 in

Width = 8.5 x 6.5

Width = 38.25 ft

Height = 14 x 6.5 ft

Height = 91 ft

Area = Width x Height

Area = 38.5 ft x  91 ft

Area =  3503.5 sq ft

To know more about the conversion factor, here

https://brainly.com/question/97386

#SPJ1