(04.02 LC)
The graph below shows the numbers of cups of grape juice that are mixed with cups of lemon-lime soda to make servings of grape soda:

A graph is shown. The values on the x-axis are 0, 1, 2, 3, 4, 5. The values on the y-axis are 0, 2, 4, 6, 8, 10. Points are shown on ordered pairs 0, 0 and 1, 2 and 2, 4 and 3, 6 and 4, 8. These points are connected by a line. The label on the x-axis is Lemon lime Soda in cups. The title on the y-axis is Grape Juice in cups.
What is the ratio of the number of cups of grape juice to the number of cups of lemon-lime soda?

By setting up a proportion based on the similar triangles created by the streetlight and the building, we can find that Melanie is standing 48 feet away from the building.

To solve the problem of determining how far Melanie is standing from the building using the shadows, we can use similar triangles. We are given a 25-foot streetlight that casts a 20-foot shadow and a 60-foot tall building. The goal is to find the length of the shadow cast by the building, which will tell us how far Melanie is from the building.

By setting up a proportion based on the similar triangles, we have:

Therefore, Melanie is standing 48 feet away from the building.

To solve the equation 5x(x+6) = -50 by completing the square, we first isolate the quadratic term and then add the square of half the coefficient of x to both sides of the equation. Taking the square root gives us the solution x = -3 + i and x = -3 - i.

To solve the equation by completing the square, we first need to isolate the quadratic term on one side of the equation. So, let's distribute the 5x to get 5x^2 + 30x = -50. Next, we move the constant term to the other side and divide the equation throughout by the leading coefficient to get x^2 + 6x + 10 = 0.

Now, we can complete the square by adding the square of half the coefficient of x (which is 3) to both sides of the equation. This gives us (x + 3)^2 + 10 - 9 = 0, which simplifies to (x + 3)^2 + 1 = 0.

Taking the square root of both sides, we get x + 3 = ±√(-1), which means x = -3 ± i. Hence, the solution to the equation is x = -3 + i and x = -3 - i.

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The triangles ABC and DEF are similar

If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.

Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides

Given data ,

Let the first triangle be represented as ΔABC

Let the second triangle be represented as ΔDEF

Now , the measure of ∠ABC = 35°

So , the measure of ∠ACB = 55° ( given ∠BAC = 90° )

And , the measure of ∠EFD = 55°

So , the measure of ∠DEF = 35°

And , the corresponding sides of similar triangles are in the same ratio

Hence , they are similar triangles

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Answer:

48

Step-by-step explanation:

it is c and d (edge)

To solve the inequality –3x – 4 < 2, subtract 4 from both sides and then divide by -3, we get x > -2. The values that satisfy this inequality are -4, 0, and 3.

To solve the inequality –3x – 4 < 2, we need to isolate the variable x. First, we subtract 4 from both sides of the inequality: –3x < 6. Next, we divide both sides of the inequality by –3, but since we are dividing by a negative number, we need to flip the inequality sign: x > -2. Therefore, the values that are solutions to the inequality are greater than -2. Among the options provided, the values that are greater than -2 are -4, 0, and 3. Therefore, you should check the boxes next to -4, 0, and 3.

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y = amount left so y = 67

rewrite the equation as:

67 = -24x+379

subtract 379 from both sides

-312 = -24x

 divide both sides by -24

x = -312 / -24

x = 13

the answer is 13 weeks

Answer:

April 10

Step-by-step explanation:

EOM (End Of Month) to receive a discount attached to the invoice when paying before the payment is due.

In this case, 1/10 means that there will be a 1% discount if the invoice is paid within 10 days of receipt.

But since the terms of credit are EOM, the 10 days are counted from the end of March, that brings us to April 10.

Therefore, an invoice dated March 28 with terms 1/10, E.O.M. results at the end of the credit period on April 10.

Hope this helps!

To determine which fraction is greater, convert each to its decimal form. The comparison shows 27/35, which is approximately 0.7714, is greater than 17/30, which is approximately 0.5667.

When comparing the fractions 17/30 and 27/35, it's helpful to find a common denominator or convert each to its decimal equivalent. To compare without finding a common denominator, you can convert each fraction to a decimal:

17/30 is approximately 0.5667,
27/35 is approximately 0.7714.

By comparing the decimal values, it's clear that 27/35 is greater than 17/30. Therefore, 27/35 is the greater fraction.

The expression 3.14 x 10³ is scientific notation for B. 3,140.

Scientific notation is a way of writing a large number or small number with many digits in a simpler form using the power of 10.

For example, 30,000 can be written as 3 × 10⁴.

So the given number is 3.14 x 10³.

The power of 10 has the number 3.

Hence the decimal point has to moved 3 decimal places to the right.

When it is moved to 1 place, it becomes 31.4.

When it is moved to 2 decimal places, it becomes 314.

When it is moved to 3 decimal places, it becomes 3140.

Hence the given expression is equivalent to 3140.

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The number of music lessons must a member and a non-member take so the cost for each is the same will be 15.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

PEMDAS rule means the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

It costs $150 to be a member of a music club. A member of the club pays $5 per music lesson. A nonmember pays $15 per music lesson.

Let x be the number of music. Then the equation is given as,

15x = 5x + 150

Simplify the equation, then we have

15x - 5x = 150

10x = 150

x = 15

The number of music lessons must a member and a non-member take so the cost for each is the same will be 15.

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The correct option is d. 8 oz. can of juice is most convenient to meet this requirement.

First, let's convert 240 milliliters to ounces because the answer choices are in ounces.

1 milliliter is approximately equal to 0.0338 ounces.

So, 240 milliliters is approximately \( 240 \times 0.0338 \) ounces, which is about 8.112 ounces.

Now, let's examine the options:

a. 5 oz. can of juice: Not enough juice. It's less than the required 8.112 ounces.

b. 4 oz. can of juice: Not enough juice. It's less than the required 8.112 ounces.

c. 12 oz. can of juice: More than enough juice. It's more than the required 8.112 ounces.

d. 8 oz. can of juice: Exactly the amount needed. It matches the required 8.112 ounces, which is the closest to the calculated amount of 8.112 ounces.

Therefore, the 8 oz. can of juice is the most convenient option to meet the requirement of having 240 milliliters of juice every 2 hours.

To solve 649 x 53, use the standard algorithm by multiplying each digit and adding the results.

To solve the multiplication problem 649 x 53 using the standard algorithm, follow these steps:

Therefore, 649 x 53 = 34, 3 9.

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Both companies will charge the same amount in 32 hours

From the information given, the equation to solve the question will be:

376 + (12 × h) = 280 + 15(h)

376 + 12h = 280 + 15h

Collect like terms

15h - 12h = 376 - 280

3h = 96

Divide both side by 3.

3h/3 = 96/3

h = 32

The amount charged will be:

376 + 12h = 376+12(32)

= 376 + 384

= 760

The amount charged will be $760

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Answer:

Sela's piano class will end at 5 : 15 pm

Step-by-step explanation:

Sela's piano lesson starts at 4 : 45 pm.

If we have to calculate the time when her lesson ends we will add the duration of the class in minutes.

After 30 minutes time will be

4 : 45 + 00 : 30 = 4 : 75

Now we know 00 : 75 or 75 minutes means 1 hour 15 minutes

therefore, 4 : 75 will become 5 : 15 pm

Sela's piano class will start at 4 : 45 pm and end at 5 : 15 pm

Adam can fill 2 glasses of water completely with the 5/7 liter of water he has, as each glass holds 2/7 liter.

The student asked how many glasses of water Adam could fill if he had 5/7 liter of water and each glass has a capacity of 2/7 liter.

To find out the number of glasses Adam can fill, we need to divide the total amount of water he has by the amount that each glass can hold. The calculation is as follows:

Total water (5/7 L) ÷ Capacity of one glass (2/7 L) = Number of glasses

5/7 L ÷ 2/7 L = 5/2 or 2.5. This means Adam can completely fill 2 glasses with a little water leftover, as we cannot have a half glass in a practical scenario.

Adam filled 2.5 glasses of water.

To find the number of glasses Adam filled, we need to divide the total amount of water he had (5/7 liter) by the capacity of each glass (2/7 liter). So, we divide 5/7 by 2/7 to get the answer. To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. Therefore, (5/7) ÷ (2/7) = (5/7) x (7/2) = 35/14 = 2.5 glasses. So, Adam filled 2.5 glasses of water.

Answer:

The correct option is C.

Step-by-step explanation:

It is given that gross pay is a function of the number of hours that you work.

Let y represents the gross pay and x represents the number of hours. So, the value of x and y can be negative.

Hourly wage = $8 per hour.

The weekly gross pay function is

[tex]y=8x[/tex]              .... (1)

Domain is the set of inputs and ranges is the set of outputs.

It is given that you work 40 hours per week. It means the value of x lies between 0 to 40.

Domain = [0,8]

Substitute x=40 in equation (1), to find the gross pay when number of hours is 40.

[tex]y=8(40)=320[/tex]

Range = [0,320]

The practical domain is 0 through 40. The practical range is 0 through 320.

Therefore the correct option is C.

The practical domain for the function representing gross pay is the range of hours worked, 0 to 40 hours. The practical range is the corresponding gross pay, from $0 to $320, based on an $8 per hour wage for up to 40 hours of work. So correct answer  is option C.

To determine the practical domain and range of the function that represents your gross pay based on an hourly wage of $8 per hour, we must consider the possible number of hours you can work in a week and the corresponding earnings. Given that you work 40 hours per week, the practical domain (which represents the number of hours worked) would be any value from 0 to 40 hours, since you cannot work negative hours and we're assuming a standard full-time workweek.

The practical range (which represents the gross pay) is calculated by multiplying the number of hours worked by the hourly wage. Therefore, the range would be 0 (if you work 0 hours) to $320 (if you work 40 hours), because 40 hours times $8 per hour equals $320.

So, the correct answer from the given options is Option C.

Practical domain: 0 through 40.

Practical range: 0 through 320.