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3 years ago

Find the area of this trapezoid. Include the correct unit in your answer.

Mathematics

1 answer:

NemiM [27]3 years ago

4 0

Answer:

$\displaystyle A _{ \text{trapezoid}} = 70 {m}^{2}$

Step-by-step explanation:

we are given a trapezoid

we want to figure out the area

remember that,

$\displaystyle A _{ \text{trapezoid}} = \frac{a + b}{2} h$

where a and b represent the parallel lines and h represents the height

we get from the pic that a and b are 5 and 15 respectively and h is 7

so substitute:

$\displaystyle A _{ \text{trapezoid}} = \frac{5 + 15}{2} \times 7$

simplify addition:

$\displaystyle A _{ \text{trapezoid}} = \frac{20}{2} \times 7$

simplify division:

$\displaystyle A _{ \text{trapezoid}} = 10\times 7$

simplify multiplication:

$\displaystyle A _{ \text{trapezoid}} = 70$

since we multiply two same units we of course have to use square unit

hence,

$\displaystyle A _{ \text{trapezoid}} = 70 {m}^{2}$

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Find the smallest of two consecutive even integers if the square is 10 more than the larger

djverab [1.8K]

I think your answers are 4 and 6

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3 years ago

I need the mid point

Anestetic [448]

Answer:

$(14,\frac{-7}{2})$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Midpoint Formula: $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

Step-by-step explanation:

Step 1: Define

Point (18, 13)

Point (10, -20)

Step 2: Find Midpoint

Simply plug in your coordinates into the midpoint formula to find midpoint

Substitute [MF]: $(\frac{18+10}{2},\frac{13-20}{2})$
Add/Subtract: $(\frac{28}{2},\frac{-7}{2})$
Divide: $(14,\frac{-7}{2})$

7 0

3 years ago

Read 2 more answers

A town is planning a playground. It wants to fence in a rectangular space using an existing wall. What is the greatest area it c

777dan777 [17]

Answer:

1250 $ft^{2}$

Step-by-step explanation:

We are given that the playground is fenced on three sides of the playground and the four side has an existing wall.

Let the length of the rectangle be 'X' feet and width be 'Y' feet.

As the fencing is done using 100 feet of fence. We get the relation between the sides and the fence as, X + 2Y = 100.

As, X + 2Y = 100 → X = 100 - 2Y

Now, the area of the rectangle = XY = X × ( 100 - 2Y ).

i.e Area of the rectangle = $-2Y^{2} +100Y$ .

The general form of a quadratic equation is $y=ax^{2}+bx+c$ .

The maximum value of a quadratic equation is given by $x=\frac{-b}{2a}$ .

Therefore, the greatest value of $-2Y^{2} +100Y$ is at Y = $\frac{-100}{2 \times -2}$ = $\frac{-100}{-4}$ = 25.

Thus, Y = 25 and X = 100 - 2Y → X = 100 - 2 × 25 → X = 50.

Hence, the area of the rectangle is XY = 50 × 25 = 1250 $ft^{2}$ .

3 0

4 years ago

Simplify 9x^2-3x(2x-4)-6x

Vinvika [58]

The answer is
$3 x^{2} +6x$ 
Remember to combine like terms.
Hop this helps. c:

3 0

3 years ago

For the scenarios presented in Problems 9–17, identify a problem worth studying and list the variables that affect the behavior

Nastasia [14]

Answer:

Problem: A company with a fleet of trucks faces increasing maintenance costs as the age and mileage of the trucks increase

Identify a problem worth studying : Yes, this problem is worth studying as it illustrate the classical optimization problem where to either minimize or maximize the outcome given some constraints. In this problem we need to maximize our profit by minimizing our maintenance cost give the age of trucks.

List the variables that affect the behavior you have identified: Lease expense, license, taxes, insurance, number of trucks, number of mechanics, type of fuel, maintenance and repair, labor, number of breakdowns, wait time to repair, loss of revenue and delay penalties, drivers retention and attrition, and number of customer reviews (negative and positive) the service.

Which variables would be neglected completely: Unless there are plans to relocate to different state with different regulations, the following variables can neglected completely: Lease expense, licenses and permits, taxes, insurance, number of trucks, number of mechanics, type of fuel.

Which might be considered as constants initially: Assuming that our mechanics are full time employees, the labor cost can be considered constant. However, the parts and materials associated with the labor are not constant. And any one time cosmetic fixes can be considered constants such as a small paint job or seat cleaning.

Can you identify any sub models you would want to study in detail?: The sub model that I want to study in more detail is as follow:

Truck ownership cost=truck depreciation+truck Return on Investment (ROI)

As the truck depreciation is constant, the main focus will be on truck Return on Investment (ROI).

Truck Return on Investment (ROI)=(the gain from the truck−Cost of investment)/cost of investment.

Hence the detailed subsystem can be as follow:

Cost of investment=(Fuel cost +maintenance cost +breakdown cost+wait cost).

Identify any data you would want collected: The data you would want collected is maintenance cost and type of maintenance and specifically the tracks and truck parts that break down the most. The wait time needed to fix and maintain the trucks. And finally customer reviews. In other words, I would collect any data that directly or indirectly impact revenues. With the collected data, I would well informed about the best time to decide replacing trucks that are performing very poorly and negatively impacting the bottom-line of the company.

Step-by-step explanation:

The specific problem is selected above and it is worth analyzing and studying because is is similar to a classical optimization problem. This is because the desired output can be either maximized or minimized by adjusting the values of certain constraints such as maintenance cost, trucks parts and other necessary parameters.

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3 years ago