A pair of linear equations is shown: y = −3x + 5 y = x + 2 Which of the following statements best explains the steps to solve the pair of equations graphically? On a graph, find the point of intersection of two lines; the first line has y-intercept = 5 and slope = −3, and the second line has y-intercept = 2 and slope = 1. On a graph, find the point of intersection of two lines; the first line has y-intercept = −3 and slope = 5, and the second line has y-intercept = 1 and slope = 2. On a graph, find the point of intersection of two lines; the first line has y-intercept = −5 and slope = 3, and the second line has y-intercept = −2 and slope = −1. On a graph, find the point of intersection of two lines; the first line has y-intercept = 3 and slope = −5, and the second line has y-intercept = −1 and slope = −2.

The volume of the new figure is approximately 63.36 ft³.

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.

If the dimensions of a figure are multiplied by a scale factor of k, then its volume will be multiplied by a factor of k³.

In this case, the dimensions are multiplied by 2/5, which is the same as multiplying by a scale factor of 0.4 (2/5 = 0.4). Therefore, the volume of the new figure will be:

V' = (0.4)³ * V

where V is the original volume.

Substituting V = 975 ft³, we get:

V' = (0.4)³ * 975 ft³

V' ≈ 63.36 ft³

Therefore, the volume of the new figure is approximately 63.36 ft³.

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Step-by-step explanation:

To simplify the expression:

(-11r² +8rs + 4s² ) − (11r² − 4rs – 3s²), we need to perform the subtraction operation by distributing the negative sign to each term inside the parentheses:

-11r² + 8rs + 4s² - 11r² + 4rs + 3s²

Now we can combine like terms by adding or subtracting coefficients of the same variables:

(-11r² - 11r²) + (8rs + 4rs) + (4s² + 3s²)

Simplifying further, we get:

-22r² + 12rs + 7s²

Therefore, the simplified expression is -22r² + 12rs + 7s².

Answer:

2 (x + 8) + 5x.

Step-by-step explanation:

This question is to find the algebraic expression given by words. Call the unknown number x. Then the sum of it and eight is x + 8. Two sets of it means 2 (x + 8). Now that added to five times the number is 2 (x + 8) + 5x. Then, the answer is: 2 (x + 8) + 5x.

Answer: 1.0

Step-by-step explanation:

sohcahtoa means you use sine.

sin(37) = 0.6/x

xsin(37) = 0.6

x = 0.6/sin(37)

x = 0.996

x = 1.0

Answer:

Minimum--> 250

Q1--> 255

Q2--> (Median): 307

Q3--> 433

Maximum-->507

Step-by-step explanation:

To find the five-number summary of this data set, we need to determine the minimum value, maximum value, and three quartiles (Q1, Q2, Q3) which divide the data into four equal parts.

First, we need to sort the data set in ascending order:

{ 250, 253, 255, 267, 307, 425, 433, 435, 507 }

Minimum: 250

Maximum: 507

To find the quartiles, we need to find the median of the entire data set (Q2) and then the medians of the two halves of the data set, which will give us Q1 and Q3.

Q2 (Median): The median of the entire data set can be found by averaging the two middle numbers.

Q1: The median of the lower half of the data set is 255, which is the middle value of { 250, 253, 255, 267, 307 }. Therefore, Q1 = 255.

Q3: The median of the upper half of the data set is 433, which is the middle value of { 425, 433, 435, 507 }. Therefore, Q3 = 433.

Answer:

17,242 cm³

Step-by-step explanation:

Step 1:

Volume of square prism = (area of base) * height

Volume of square prism = (25 * 30) * 25

Volume of square prism = 750 * 25

Volume of square prism = 18,750 cm³

Step 2:

Volume of cylinder = (area of base) * height

Volume of cylinder = (π * (8/2)²) * 30

Volume of cylinder = 16π * 30

Volume of cylinder = 480π

Volume of cylinder ≈ 1,508 cm³

Step 3:

Volume of composite = (Volume of square prism) − (Volume of cylinder)

Volume of composite = 18,750 cm³ − 1,508 cm³

Volume of composite = 17,242 cm³

This means that the lowest goal (LCD) is 72 and that the total of 1/8 and 1/9 stated with one common denominator = 72 is 17/72.

The denominator of a fraction, which represents many spaced evenly out parts are utilized to split an object, is the smallest amount inside the fraction. The fraction is divided by it. The denominator in this situation is 4, suggesting there are four parts altogether.

The fractions mentioned have 8 and 9 as their denominators. Multiples of 8 include 8, 16, 24, 32, 40, 48, 56, 64, 72, and 80, while multiples of 9 include 9, 18, 27, 36, 45, 54, 63, 72, and 81.

It is evident that 72 will be the first common number of 8 and 9. Hence, for 1/8 and 1/9, its least common factor (LCD) is 72.

We must express every fraction with denominator 72 in order to sum the fraction with a common denominator:

1/8 Equals 9/72 (with multiplying both the numerator and the denominator by 9)

1/9 Equals 8/72 (with multiplying both the denominator and the numerator by 8)

We can now combine the fractions:

1/8 plus 1/9 = 9/72 plus 8/72

= 17/72

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After 5 hours, there will be 700 gallons of water still in the pool.

Given that, the pool has 1,200 gallons of water and can drain 100 gallons an hour.

After 5 hours, the total amount of water drained from the pool will be 100 gallons per hour times 5 hours, or 500 gallons.

= 100 gallons × 5

= 500 gallons

To find out how much water will still be in the pool, we need to subtract the amount of water drained from the original amount "y":

This forms an equation.

Amount of water still in the pool = original amount - water drained from the pool.

y = 1,200 gallons - 500 gallons

y = 700 gallons

Therefore, 700 gallons of water is still in the pool.

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To solve this problem, we can use similar triangles. Let's call the height of the building "h". Then, we have two similar triangles: one formed by Ruby, the tree, and the top of the tree; and the other formed by Ruby, the building, and the top of the building.

We know that the height of the tree is 20 feet, and the distance from the tree to Ruby is 31 feet. We also know that the distance from Ruby to the building is 190 feet.

Using these values, we can set up a proportion:

h / (190 + 31) = 20 / 31

Simplifying the proportion, we get:

h / 221 = 20 / 31

Multiplying both sides by 221, we get:

h = (20 / 31) * 221

h ≈ 143.23

Therefore, the height of the building is approximately 143 feet. Rounded to the nearest foot, the height of the building is 143 feet.

Answer:

75 degrees

Step-by-step explanation:

Since angle ABD = angle ABC + angle CBD, and we know each of those, we can add them to get the answer.

30+45=75 degrees.

There are 260 students who attend Juniper Middle School. The average daily unexcused absences increased by 25% from September to October.

a. Let's assume that the total number of students at Juniper Middle School is "x."

Given that 55% of the students are in the 8th grade, we can write:

0.55x = number of 8th grade students

And since the remaining 117 students are in 7th grade, we can write:

x - 0.55x = 117

0.45x = 117

x = 260

Therefore, there are 260 students who attend Juniper Middle School.

b. To find the percent change from September to October, we can use the formula:

percent change = ((new value - old value) / old value) x 100%

Substituting the given values, we get:

percent change = ((6 - 4.8) / 4.8) x 100%

percent change = (1.2 / 4.8) x 100%

percent change = 25%

Therefore, the average daily unexcused absences increased by 25% from September to October.

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The probability that the next piece of quartz Nora picks will be yellow is [tex]\frac{1}{9}[/tex].

What is probability?

Probability is a tool that can be used to calculate the likelihood of an event. It can only be used to assess the likelihood that an event will take place. a scale where 0 represents impossibility and 1 represents a particular occurrence.

We are given that Nora picks pieces 18 times from the box and gets 3 purple, 2 yellow, 5 white, and 8 pink quartz pieces.

So, for the event,

⇒ Probability of yellow pieces = [tex]\frac{2}{18}[/tex]

⇒ Probability of yellow pieces = [tex]\frac{1}{9}[/tex]

Hence, the probability that the next piece of quartz Nora picks will be yellow is [tex]\frac{1}{9}[/tex].

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Answer:

6 units

Step-by-step explanation:

(8, 10 ) → (8, 4 )

since the x- coordinates of each point are the same, both 8

then this is a vertical straight line

the difference is then the absolute value of the difference in the y- coordinates, that is

| 10 - 4 | = | 6 | = 6

or

| 4 - 10 | = | - 6 | = | 6 | = 6

Answer:

70 gold and bronze

Step-by-step explanation:

Add gold at 20 percent and bronze at 50 percent to get 70 percent gold and bronze.

Answer:

In 2x*3y, you must multiply each term together. 2*3=6 and x*y=xy. So, 2x*3y=6xy.

If I had $14 to spend, the park that I will choose based on the information will be park D where 6 rides cost $16.50

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

In this case, if I had $14 to spend, the park that I will choose based on the information will be park D where 6 rides cost $16.50. This is because it's the cheapest.

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Answer:

a machine in a factory makes 2 1/4 pounds of nails in 1 1/2 hours. At what rate in pounds

per hour does the machine makes nails?

The program uses the conversion factors of 2.205 pounds per kilogram and 39.37 inches per meter to convert the input values to the correct units for the formula.

To design a program in Raptor that prompts the user to enter a person's weight in pounds and height in inches, and then calculates and displays their body mass index (BMI), we can follow these steps:

Start by opening Raptor and creating a new program.

Add three input symbols to prompt the user for their weight, height, and a constant value for BMI. Label each input symbol accordingly.

Add three assignment statements to assign the input values to variables. We can use the labels we assigned to the input symbols as variable names to make the code more readable.

Add two calculation statements to calculate the person's BMI using the formula [tex]BMI = (weight in pounds * 703) / (height in inches)^2.[/tex]Assign the result to the BMI variable.

Add three output symbols to display the person's weight, height, and BMI. We can concatenate strings with the variable values to make the output more informative.

Finally, save the program and run it to test it with different input values.

Here's what the program would look like:

Start

// Prompt the user for weight, height, and BMI

Input "Enter weight in pounds:", weight

Input "Enter height in inches:", height

Input "BMI:", bmi_constant

// Calculate BMI

Set weight_in_kg = weight / 2.205 // Convert weight to kilograms

Set height_in_m = height / 39.37 // Convert height to meters

[tex]Set bmi = weight_in_kg / (height_in_m ^ 2)[/tex] // Calculate BMI

// Display results

Output "Weight: " + weight + " lbs"

Output "Height: " + height + " in"

Output "BMI: " + bmi

Stop

When the program is run, it will prompt the user to enter their weight, height, and a constant value for BMI. It will then calculate the person's BMI using the formula, convert the weight to kilograms and the height to meters, and display the results along with the original weight and height values. The program uses the conversion factors of 2.205 pounds per kilogram and 39.37 inches per meter to convert the input values to the correct units for the formula.

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Answer:

$40+99=136  For 1 week

For 3 weeks it would be $120

The parameter to describes a binomial experiment that would determine the probability that a case of 36 bottles has all bottles properly filled is x = 36, p = 0.96 and n = 36. So, the right choice for answer is option (c).

A binomial experiment is an experiment using a fixed number of independent trials with only two outcomes. These experiments'outcomes are defined as either success or failure. The following requirements for experiment are :

Water Quantity in a bottle = 20 ounces

According to bottling company, the percentage of bottle with correct amount = 96% = 0.96

so, probability of success, p = 0.96

Probability for 36 bottles has all bottles properly filled, that is x = 36. Now, looking the all choice, we conclude option(c) is correct choice.

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Answer:

25%

Step-by-step explanation:

If the cost price could be 100

Then there's A/Q

One-fourth is always 100/4 = 25%

Answer:

Step-by-step explanation:

[tex]A=\pi r^2=\pi \times 5^2=25\pi[/tex]

Solution: [tex]A=25\pi[/tex] units²

1. The function that will directly calculate the final price on an item is " a * 0.455".

2. The percentage that is actually being saved by the custumer is 54.5%.

The final price of an item after the discount and coupon can be calculated using the following function:

Final price = a * (1 - 0.35) * (1 - 0.30)

Final price = a * 0.455

This function first applies the 35% discount, which reduces the original price (a) to 65% of its value. Then, it applies the 30% coupon to the discounted price, which reduces it to 70% of its value.

Original price = $100

Sale price (35% off) = $100 * (1 - 0.35)

Sale price (35% off) = $65

Final price = $65 * (1 - 0.30)

Final price = $45.50

Savings = $100 - $45.50

Savings = $54.50

Percentage saved:

= (Savings / Original price) * 100%

= ($54.50 / $100) * 100%

= 54.5%

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Answer:

13487 ft³

Step-by-step explanation:

Volume of a Cylinder: 2πr²*h

π = 3.14

r = 9 ft

h = 53 ft

Volume = 2(3.14)(9)²*53 = 13486.86 ft³

Rounded to nearest whole number

Volume of the Cylindrical Water tank is 13487 ft³

Answer:

For an item to have measurable volume, the item must have space and must have a closed surface. Therefore, the item is the cereal box.

Step-by-step explanation:

hope its right!

Answer: The answer is -10 :)

Step-by-step explanation:

12)f(x)=2x-6

=》f(3)=2(3)-6

=》6-6=0

f(×)=2x-6

f(0)=-6

=》f(-2)=2(-2)-6

=》-4-6

=-10

13)h(3)=6(3)+2

=》18+2

=20

h(0)=0+2

h=2

(-2)=6(-2)+2

=》-12+2

=-10

Answer: the movie streaming service offers 80 children's movies

Step-by-step explanation:

     $5.05                                     15

+    $9.05                                     20

+  $13.05                                     25

+  $17.05                                      30

+  $21.05                                 +   35

   $65.25                                  125      

NUMBER OF CUPS SOLD :-125

TOTAL PROFIT:- $65.25

Step-by-step explanation:

3y is not a constant for it has a variable.

However, (2+8) = (10) is a constant