Solve 35 / 2 using an area model. Use long division and the distributive property to record your work

Answer: Please see explanation column for answer.

x= -36

Step-by-step explanation:

Step 1

from the attachment, Carlo solving is given as

1/3 (1/2x- 9) = 1/2 (x+18)

1/6x-3= 1/2x+9

1/4x-3=9

1/4x=12

x=48

Carlos error started when he subtracted wrongly 1/2 x from 1/6x which gave him 1/4 x instead of - 1/3 x.

Solving correctly, we have that

1/3(1/2x-9) = 1/2(x+18)

1/6x -3= 1/2x+ 9

taking like terms to like terms

1/6x-1/2x= 9+3

(1-3)/6x= 12

-2/6x= 12

-1/3x= 12

multiplying both sides by -3

-1/3x X -3 = 12 X -3

x= -36

Answer: The answer is 5x-8.

Step-by-step explanation: The equation we have is (8x-9)-(3x-1). The first step is to write the equation as shown:

8x-9-(3x-1)

After that step, next is to apply the distributive law:

8x-9-3x+1

Then, group/combine like terms:

8x-3x-9+1

Then adding similar elements:

5x-9+1

And finally, solving:

5x-8

Answer: C

Step-by-step explanation:

The length of the PR would be 82.

Option (A) is correct.

What is an expression?

An expression is a combination of numbers, variables, and mathematical operations that represents a value or a computation. Expressions can be simple or complex and can include constants, variables, and various mathematical operations such as addition, subtraction, multiplication, and division. Expressions are often used to represent mathematical operations in algebraic, trigonometric, and calculus problems. They can be evaluated to find a numerical value or simplified to reveal underlying mathematical relationships.

In the given figure, the length of both line segments is equal, hence

PR = 10x + 842

PQ + QR = 10x + 842

8x + 678 + 12 = 10x + 842

First we can subtract 12 from both sides of the equation:

8x + 678 = 10x + 830

Then we can subtract 8x from both sides of the equation:

678 = 2x + 830

Then we can subtract 830 from both sides of the equation:

-152 = 2x

Then we can divide both sides of the equation by 2:

x = -76

So PR = 8x + 678 + 12

PR = 8(-76) + 678 + 12

PR = -608 + 678 + 12

PR = -608 + 690

PR = 82

Hence, the length of the PR would be 82.

Option (A) is correct.

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The required equation is x × 3 = 528.75 - 60.

The cost of the labor per hour is $156.25

How do equations work?

The definition of an equation is a mathematical statement with at least two terms that contain variables or equal numbers.

Let x be the cost of the labor per hour.

We know that

x × 3 = labor cost

60 + x × 3 = total cost

We also know that the total cost is $528.75

So we can write the equation:

60 + x × 3 = 528.75

Solving for x:

x × 3 = 528.75 - 60

x × 3 = 468.75

x = 468.75/3

x = 156.25

Therefore, the cost of the labor per hour is $156.25

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Answer:

10,37

Step-by-step explanation:

for EF= [tex]\sqrt{17^{2} -14^{2} } =10[/tex]

for D= we have 2 knowns which are 53 and 90, so we need to minus them from each other to get D.  90-53=37

Answer:

170 miles

Step-by-step explanation:

Use 80 miles and 150 miles as the legs of a right triangle, and find the length of the hypotenuse using the Pythagorean theorem.

a² + b² = c²

80² + 150² = c²

6400 + 22500 = c²

c = √28900

x = 170

Answer: 170 miles

Answer:

x = p(m-n)

Step-by-step explanation:

we can eliminate the 'p' in the denominator by multiplying each side of the equation by 'p' to get:

mp = np + x

now we can subtract 'np' from each side to get:

mp - np = x

we can further simplify it as:

p(m-n) = x

Answer:

X=n-p×m

Step-by-step explanation:

m=n-x/p

p×m=n-x

n-p×m=n+x-n

X=n-p×m

The final balace in Tracy's bank account is $ 361.80.

In this question we must pay attention to every movement in a bank account and determine final balance within. The hint is having an active reading in the meaning of translating every Tracy's movement in additions and subtractions, First, we translate very sentence into numbers and signs:

Tracy's checking account: + $ 300.00

Tracy bought new sneakers: - $ 63.00

Tracy deposited a paycheck: + $ 43.25

Tracy wrote a check: - $ 17.75

Tracy wrote a check: - $ 9.45

Tracy made a withdrawal at her bank: - $ 20.00

Tracy deposited a paycheck: + $ 43.25

Tracy wrote a check: - $ 18.00

Tracy made a withdrawal at another bank: - $ 20.00 - $ 1.50

Tracy deposited her birthday money: + $ 125.00

Second, calculate the final balance in Tracy's account:

x = 300.00 - 63.00 + 43.25 - 17.75 - 9.45 - 20.00 + 43.25 - 18.00 - 20.00 - 1.50 + 125.00

x = 361.80

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These two lines intercept on a graph on the coordinate X(0, 1) Y(9, 7).

The term "intercept" refers to the location where a line or curve intersects an axis on a graph. An object's x-intercept is defined as where a point crosses the x-axis. The term "y-intercept" refers to a point that crosses the y-axis. The intersection of the x-axis and the y-axis is what is meant by a line's intercept.

step1

y=-2x+9

graph the line using the slope and y intercept or two points

y=-2x+9

X(0,1) Y(9,7)

step2

y=3x-6

slope 3 y intercept (0,-6)

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Answer:

- 14

Step-by-step explanation:

the bars around 2t , indicate the absolute value of 2t

the absolute value function always gives a positive value , that is

| - a | = | a | = a

so for example

| - 4 | = | 4 | = 4

given

[tex]\frac{2}{3}[/tex] p - | 2t | - s² ( substitute values for p, t and s into the expression )

= [tex]\frac{2}{3}[/tex] × 12 - | 2(- 3) | - (- 4)²

= 2 × 4 - | - 6 | - 16

= 8 - 6 - 16

= 2 - 16

= - 14

The model to solve t + 4 = 5 is that John hast number of oranges and got 4 more making 5 oranges.

A mathematical model is an abstract, mathematically based description of a physical system. Mathematical modeling is the process of creating a mathematical model.

To make a prediction or offer insight, mathematical modeling is the process of creating a mathematical representation of a real-world scenario.

The equation t + 4 = 5 can be solved by subtracting 4 from both sides of the equation:

t + 4 = 5

t = 5 - 4

t = 1

So t = 1 is the solution to the equation

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Answer:

The correct answer is C. 1

Answer: I believe it is A

Answer:

12ft  x 9ft

Step-by-step explanation:

1/6" equals 1' actual ==> 1"=6'actual.

1.5" = 9'

2" = 12'

By utilizing the given scale of 1/6 inch equals 1 foot, the actual length of the bathroom is calculated to be 9 feet and width is 12 feet, from the given measurements of the drawing.

The mentioned math problem is based on scale conversion, specifically in the realm of measurement. Given that every 1/6 inch on the scale drawing equals 1 foot in reality, the first step to solving this problem is to convert the measurements of the drawing into scale inches. To convert the length of 1 1/2 inches to the actual length, multiply 1.5 by 6 (as 1 inch is 6 times of 1/6 inch). This equals to 9 feet. Similarly, for the width of 2 inches, multiply 2 by 6 to get 12 feet.

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Answer:

Always start with the first number. The one in 1.47 is less than the 4 in 4.01, so 1.47 is less than 4.01.

Least to greatest is 1.4, 1.47, 4.01, and 4.1

=============================================

Explanation:

I appreciate you showing your work so far, and your thought process.

Your steps are correct because the events [tex]A \cup B[/tex] and [tex](A \cup B)'[/tex] are complementary, aka opposite. One or the other must happen. It's like a coin flip heads vs tails.

The last thing you need to do really is simplify 1-0.5-0.5+0.25 to get the final answer 0.25

-------------------

This is what I would do as an approach.

P(A u B) = P(A) + P(B) - P(A n B)

P(A u B) = 0.5 + 0.5 - 0.25

P(A u B) = 0.75

So,

P( (A u B)' ) = 1 - P(A u B)

P( (A u B)' ) = 1 - 0.75

P( (A u B)' ) = 0.25

-------------------

Another approach:

Imagine we had 100 people.

50 are in set A to give P(A) = 50/100 = 0.50

50 are in set B to give P(B) = 0.50

25 are in both A and B to get P(A n B) = 25/100 = 0.25

50+50-25 = 75 people are in either A, or B, or both

That leaves 100-75 = 25 in neither set

25/100 = 0.25

I recommend to draw out the Venn Diagram.

In this case, the marked price of 220 is the cost price and discount of 20% is announced on sales, so the selling price is 176.

The t-shirt costs $166.5 to purchase. To do this, multiply the listed price (220) by the discount rate (20%) stated as a decimal. This will give you the amount of the discount (0.20).

220*0.20 =44

The selling price is then determined by deducting the discount (44) from the marked price (220):

220-44 =176

Before applying any markups or reductions, the retailer paid the item's cost price, commonly referred to as the wholesale price. The price a consumer pays to purchase an item is known as the selling price. The selling price will be less than the advertised price if a discount is being offered, and the difference between the two represents the discount.

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y = 32 home runs will Mario hit during his ninth season.

Now, According to the question:

Linear models describe a continuous response variable as a function of one or more predictor variables. They can help you understand and predict the behavior of complex systems or analyze experimental, financial, and biological data. Linear regression is a statistical method used to create a linear model.

According to the graph, we have

The equation is:

y = 3x + 5

Put the value of x = 9

We get:

y = 3 × 9 + 5

y = 32

(Figure out the function of the image, and then bring the value of 'x' into it.)

Hence, y = 32 home runs will Mario hit during his ninth season.

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Answer:

Step-by-step explanation:

a)
0.5 x (a + b) x h
0.5 x (5 + 30) x 30
Area = 525

b) Overestimate

The height of the bullet after 3 second is 640m

Motion under gravity refers to the movement of an object whose vertical motion is affected by the presence of gravity. The force that attracts objects downwards is gravity. In fact, gravity works towards the centre of the Earth.

When an object is thrown up, the height of the object is calculated as h = v²/2g

where v is the velocity and g is the acceleration due to gravity.

v = -16t²+ 256(t)

when t = 3s

v = -16( 3)²+ 256

v = -144+256

v = 112m/s

therefore the height attained by the bullet =

h = 112²/2×9.8

h = 640m

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Answer:

2.50x + 1.25y ≤ 30

x + y ≥ 14

x ≤ 10 and y ≤ 24

Step-by-step explanation:

we can by elimination if we multiply the second inequality by -2.5, we get:

-2.50x - 2.5y ≥ -35

if we add the first inequality to the above we get:

   2.50x + 1.25y ≤ 30

+  -2.50x - 2.5y ≥ -35

-1.25y = -5

divide each side by -1.25 to get:

y = 4

therefore, x = 10

if you graph each system you must look for the area where the shading of each inequality overlaps

upon graphing, the solution is x ≥ 10 and y ≤ 24

Each of the given statements are interpreted in context below.

What is the quadratic equation?

A quadratic equation is a polynomial equation of the form ax^2 + bx + c = 0, where x is the variable and a, b, and c are constants. The solutions of the equation are the values of x that make the equation true.

a. N(1) = 11: This statement represents that 1 hour after the food truck opens, there are 11 people in line.

b. N(0) = N(3): This statement represents that at the time the food truck opens, the number of people in line is the same as 3 hours after the food truck opens.

c. N(4) > N(6): This statement represents that at 4 hours after the food truck opens, the number of people in line is greater than at 6 hours after the food truck opens.

d. N(R) = 34: This statement represents that the number of people in line at an unspecified time R is 34. The letter "R" can be any value for time, it is only a placeholder for any arbitrary value.

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An inequality representing c, the total number of 150-kilogram crates that can be loaded into the shipping container: c ≤ 98

We know that an inequality is a mathematical statement that represents the inequalities between two algebraic expressions with two variables .

It is an unequal relation between two algebraic expressions.

Here, the greatest weight that can be loaded into the container = 26,000 kilograms

the weight of each crate = 150 kilogram

and the weight of other shipment = 11300 kilograms

Let c be the total number of 150-kilogram crates that can be loaded.

So, we get an inequality:

150 c + 11300 ≤ 26,000

150 c ≤ 26,000 - 11300

150 c ≤ 14700

c ≤ 98

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The quotient and remainder, when written as partial fractions, of 8x²³-21²-67x-24 is represented by 2x²-x-21.

(8x³-21²-67x-24) = (2x²-x-21) + (6x¹-42)

This is done by dividing 8x²³-21²-67x-24 by 2x² and using long division to find the remainder.

The result of the division is a quotient of 4x²-33x+12 and a remainder of 2x²-x-21.

The result is 4x².

Then, subtract 4x² from 8x²³ to get the remainder of 4x³.

Next, divide 4x² into 21².

The result is 33x.

Then, subtract 33x from 4x³ to get the remainder of 4x²-33x.

Finally, divide 4x²-33x into 67x.

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The marginal column total for the given data is option D: 39; 16.

What is marginal total?

A set of marginal totals is produced when the cell frequencies of a (multidimensional) contingency table are added over one or more of the classifying variables. The row and column totals are the marginal totals for a two-dimensional table.

The sum of the row entries or the sum of the column entries are called the marginal totals. Marginal distributions are computed by dividing the row or column totals by the overall total.

The number of men who prefer to eat fish = 11

The number of women who prefer to eat fish = 6

The number of men who prefer to eat red meat = 28

The number of women who prefer to eat red meat = 10

So, the marginal column total for the number of men who prefer to eat fish and red meat collectively is -

11 + 28 = 39

The marginal column total for the number of women who prefer to eat fish and red meat collectively is -

6 + 10 = 16

Therefore, the marginal total is 39, 16.

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let f = father's present age, let s = son's

:

write an equation for each statement, simplify

:

Three years ago a father was thrice as old as his son

f - 3 = 3(s-3)

f - 3 = 3s - 9

f = 3s - 9 + 3

f = 3s - 6

in 5 years time the father will be twice as his son

f + 5 = 2(s+5)

f + 5 = 2s + 10

f = 2s + 10 - 5

f = 2s + 5

replace f with 3s - 6, from the 1st statement

3s - 6 = 2s + 5

3s - 2s = 5 + 6

s = 11 yrs is the son's age

find the fathers age

f = 3(11) - 6

f = 33 - 6

f = 27 yrs is the father's age

:

what will be the sum of their age in four years

27+4 + 11+4 = 46

The value of 21•15 equals (20+1)•15. This is true.

An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.

The value of 21•15 will be:

= 21 × 15

= 315

Also (20+1)•15 will be:

= 21 × 15

= 315

Therefore, they're equal.

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Complete question

The value of 21•15 equals (20+1)•15. True or false?

Answer:

no.................,.............

The time taken by both the workers working together, which is 2 days.

The time taken to build a house by two workers working together can be calculated using the formula T = (1/W1 + 1/W2)^-1, where W1 and W2 are the working speeds of each worker. In this case, W1 = 2 days and W2 = 3 days. So, the time taken to build a house by both workers together is calculated as follows:

T = (1/2 + 1/3)^-1 = (3/6)^-1 = 6/3 = 2 days

Therefore, both the workers working together will take 2 days to build a house. This is because when two workers work together, the total work done in a given time is equal to the sum of the work done by each worker separately in that given time. In this case, both the workers will take 2 days and 3 days respectively to build the house when working separately, so when they work together the total work done in a given time will be 5 days. This is equal to the time taken by both the workers working together, which is 2 days.

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The problem involving exponents (1/5 x 5)⁵ is calculated to get 1

Information made available in the question is an equation of the form

= (1/5 x 5)⁵

The math question is solved using the idea of PEMDAS which is an acronym for order of arrangement of mathematical operations as

the full meaning include

P - parenthesis

E  - exponents

M - multiplication

D - division

A - addition

S - subtraction

applying the sequence the problem is solved using parenthesis first

= (1/5 x 5)⁵

= (1)⁵

Then exponents

= (1)⁵

= 1 * 1 * 1 * 1 * 1

= 1

The solution is 1

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