1. Marco and Drew stacked boxes on a shelf. Marco lifted 9 boxes and Drew lifted 14 boxes. The boxes that Drew lifted each weighed 8 lb less than the boxes Marco lifted.

Let m represent the weight of the boxes that Marco lifted.

Which expression represents the total number of pounds Drew lifted?

A. 9(m+8)

B. 112m

C. m−8

D. 14(m−8)



2. Two stores sell the same refrigerator for the same original price. Store A advertises that the refrigerator is on sale for 15% off the original price. Store B advertises that it is reducing the refrigerator’s price by $150. When Stephanie compares the sale prices of the refrigerator in both stores, she concludes that the sale prices are equal.

Let p represent the refrigerator’s original price.

Which equation models this situation?

A. 0.15p=p−150

B. 0.15p=p+180

C. 0.85(p−150)=p

D. 0.85p=p−150


3. Two cars traveled equal distances in different amounts of time. Car A traveled the distance in 2 h, and Car B traveled the distance in 1.5 h. Car B traveled 15 mph faster than Car A.

How fast did Car B travel?

(The formula R⋅T=D , where R is the rate of speed, T is the time, and D is the distance can be used.)

Enter your answer for the box.

? mph


4. Louann and Carla received equal scores on a test made up of multiple choice questions and an essay. Louann got 14 multiple choice questions correct and received 24 points for her essay. Carla got 16 multiple choice questions correct and received 14 points for her essay.

How many points was each multiple choice question worth?

Enter your answer in the box.

? points


5. In May, Liam and Charlie had the same amount of money in their savings accounts. In June, Liam deposited $140 into his account. Charlie said he increased the money in his account by 5%. When they compared their balances, they found that they were still equal.

How much money did they both have in their accounts in May?

Enter your answer in the box.

$?

The factored form of the given expression 5x² - 7x + 2 is equal to (5x - 2)(x - 1).

To factor the quadratic expression 5x² - 7x + 2,

find two binomials in the form (ax + b)(cx + d) whose product gives us the original expression.

The general form of a quadratic expression is ax² + bx + c, where:

a = 5

b = -7

c = 2

To factor the expression, look for two numbers whose product is ac (5× 2 = 10) and whose sum is b (-7).

The two numbers are -5 and -2 because:

-5 × -2 = 10

-5 + (-2) = -7

Now,  rewrite the middle term (-7x) using these two numbers:

5x² - 5x - 2x + 2

Next, we group the terms and factor them by grouping:

(5x² - 5x) + (-2x + 2)

Factor out the greatest common factor from each group:

5x(x - 1) - 2(x - 1)

Now,  factor out the common binomial factor (x - 1):

(5x - 2)(x - 1)

Therefore, the factored form of 5x² - 7x + 2 is (5x - 2)(x - 1).

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Division and multiplication are reciprocal operators.

Dividing the positive number by 1/4 will make the positive number bigger.

From the question, we understand that:

1/4 makes the positive number smaller, when it is multiplied to the positive number.

Because division and multiplication are reciprocals,

Dividing the positive number by 1/4 will make the positive number bigger.

Hence, what division does to the positive number is that: It makes it bigger

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The unit rate appropriate for describing the amount of rainfall over time is centimeters per day. Therefore, option C is the correct answer.

Unit rate can be defined as the ratio between two measurements with the second term as 1. It is considered to be different from a rate, in which a certain number of units of the first quantity is compared to one unit of the second quantity.

Here,

Rainfall amount is expressed as the quotient of a unit of height and a unit of time.

The way to choose the most appropriate is the relation between both quantities.

For example, "meters per second" is a way too high unit for the height (which is usually inches or millimeters, instead of meters) and way too low for the time unit (which is usually per day, not seconds). This unit would have a really small number for any rain.

The most common unit is "centimeters per day"

Then, we should find a unit rate with a small unit for height and a large unit for time.

Therefore, option C is the correct answer.

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Answer: D . [tex]((y+2)=-2(x-5)[/tex]

Step-by-step explanation:

The equation of a line passing through two points (a,b) and (c,d) in point-slope form is given by :-

[tex](y-d)=\dfrac{d-b}{c-a}(x-c)[/tex]

From the given graph ,it can be seen that the line is passing through two points A(1,6) and B(5,-2).

Then the equation for the line AB in point-slope form would be :-

[tex](y-(-2))=\dfrac{-2-6}{5-1}(x-5)[/tex]

[tex]\Rightarrow\ (y+2)=\dfrac{-8}{4}(x-5)[/tex]

[tex]\Rightarrow\ (y+2)=-2(x-5)[/tex]

Hence, the equation is a point slope form equation for line AB :

[tex](y+2)=-2(x-5)[/tex]

A graph of the linear function y = 3/5(x) is shown in the image attached below.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + b

Where:

Since the given linear function y = 3/5(x) is in slope-intercept form, we would start by plotting the y-intercept:

y = 3/5(x)

y = 3/5(0)

y = 0

Next, we would use an online graphing tool to plot the given linear function for the values in its domain using table, as shown in the graph attached below.

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The correct answer would be y + 2 = - 3/2 ( x - 2 )

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Answer: [tex]\dfrac{1}{90}[/tex]

Step-by-step explanation:

Given : The total number of companies = 720

The number of companies won = 8

Now, the probability of a company winning is given by ;-

[tex]\text{P(winning)}=\dfrac{\text{Number of company wins}}{\text{ Total companies}}\\\\\Rightarrow\ \text{P(winning)}=\dfrac{8}{720}\\\\\Rightarrow\ \text{P(winning)}=\dfrac{1}{90}[/tex]

Hence, the probability of a company winning  is [tex]\dfrac{1}{90}[/tex].

Answer:

the graph in the attached figure

Step-by-step explanation:

we have

[tex]y=-x+3[/tex]

we know that

The slope of the line is negative [tex]m=-1[/tex]

The y-intercept of the line is the point [tex](0,3)[/tex] (value of y when the value of x is equal to zero)

The x-intercept of the line is the point [tex](3,0)[/tex] (value of x when the value of y is equal to zero)

therefore

the graph in the attached figure

Answers So it's just A

Step-by-step explanation:

Answer:

24.8

Step-by-step explanation:

Answer:

The answer is C.

Step-by-step explanation:

I learned about it.

Answer:d

Step-by-step explanation:

To write down 4-digit odd and even numbers using the digits 7, 5, 4, and 8, there are 4 possible odd numbers and 2 possible even numbers.

In order to write down all possible 4-digit odd and even numbers using the digits 7, 5, 4, and 8, we need to consider the following:

The work is provided in the image attached.

Answer:

The expression [tex]18-3x[/tex] describe the number of tokens Nadeen has left.

Step-by-step explanation:

Consider the provided information

Nadeen is at an arcade. She started with 18 tokens. Each game costs 3 tokens.

The cost of each game is 3 tokens

Suppose x is the number of games played by Nadeen

Thus, the cost of x games is 3x tokens

it is given that Nadeen started with 18 tokens.

So, token left = [tex]18-3x[/tex]

Therefore, the expressions [tex]18-3x[/tex] can be used to describe the number of tokens Nadeen has left.

The weight of the cheesy popcorn is 5/8 pounds.

To find the weight of the cheesy popcorn, we will calculate two-thirds of the total weight of the popcorn box, which weighs 15/16 pounds. Since the box contains two types of popcorn, buttered and cheesy, with the cheesy popcorn making up two-thirds of the box, we will simply multiply the total weight of the box by 2/3 to find our answer.

The calculation is as follows:

Total weight of the box = 15/16 pounds

Cheesy popcorn weight = (2/3) * (15/16)

Cheesy popcorn weight = (2 * 15) / (3 * 16)

Cheesy popcorn weight = 30 / 48

When simplified, this gives us 5/8 pounds

Therefore, to find the weight of the cheesy popcorn in a 15/16 pound box, calculate two-thirds of the box's total weight, which results in 5/8 pounds for the cheesy popcorn.

Answer:

Julie received $134.4 when she cashed her paycheck .

Step-by-step explanation:

Let the amount of paycheck be x

She paid $10 to her brother

She then spent $30 on fuel for her car

So, She left with amount = x-40

Now She spent half of the remaining money on a new tent for camping

Spent on camping = [tex]\frac{1}{2}(x-40)[/tex]

Remaining =  [tex](x-40)-\frac{1}{2}(x-40)[/tex]

She bought a pair of running shoes for $29.45

So, Remaining =  [tex](x-40)-\frac{1}{2}(x-40)-29.45[/tex]

We are given that She had $17.75 left.

So,  [tex](x-40)-\frac{1}{2}(x-40)-29.45=17.75[/tex]

[tex]x=134.4[/tex]

Hence Julie received $134.4 when she cashed her paycheck .