1. Find the area of the shape.
10 in
9 in

The formulas  length, b₂ and height in options C and D respectively are also true

We are going to  make use of the concept subject of the formula here:

Given : A=1/2 h(b₁ + b₂ )

where A is the area of the trapezoid, h is the height, and b₁ and b₂ are the lengths of the two parallel sides

Let's make h the subject now:

A=1/2 h(b₁ + b₂ )                          Cross multiply A to the other side

2A =  h(b₁ + b₂ )                          Divide both sides by (b₁ + b₂ )  

h = 2A/(b₁ + b₂ )

Let's make b₁ the subject:

A=1/2 h(b₁ + b₂ )                          Cross multiply A to the other side

2A =  h(b₁ + b₂ )                           Divide both sides by h

(b₁ + b₂ ) = 2A/h                           Subtract b₂ from both sides

b₁ = 2A/h - b₂

Let's also make b₂ the subject:

A=1/2 h(b₁ + b₂ )                          Cross multiply A to the other side

2A =  h(b₁ + b₂ )                           Divide both sides by h

(b₁ + b₂ ) = 2A/h                           Subtract  b₁  from both sides

b₂ = 2A/h -  b₁

Since b₁ = 2A/h - b₂, b₂ = 2A/h -  b₁ and  h =  2A/(b₁ + b₂ ). Therefore, the formulas in options C and D are also true

Learn more about area of a trapezoid on:

https://brainly.com/question/12220738

#SPJ1

Answer:

In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

Step-by-step explanation:

Answer:

Sales Tax: $100.75

Total Price: $1400.75

Step-by-step explanation:

1,300 × .0775 = 100.75

1,300 + 100.75 = $1400.75

Answer:

Tax: $100.75

Total: $1,400.75

Step-by-step explanation:

1,300*0.0775 = 100.75, 1,300 + 100.75 = 1,400.75

The position vector of point P, MP, is given by MP = 6i - j.

To find the position vector of point P, which is the midpoint of NO, we can use the midpoint formula.

The midpoint formula states that the midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂) is given by:

Midpoint (Mᵖ) = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)

Let's find the position vector of point P using the given information:

Point N: N = 4i - 5j

Point O: O = 8i + 3j

Using the midpoint formula, we can find the coordinates of point P:

x-coordinate of P: (x₁ + x₂) / 2 = (4i + 8i) / 2 = 12i / 2 = 6i

y-coordinate of P: (y₁ + y₂) / 2 = (-5j + 3j) / 2 = -2j / 2 = -j

Therefore, the position vector of point P, MP, is given by:

MP = 6i - j

for such more question on vector

https://brainly.com/question/17157624

#SPJ8

Answer:

5.4

Step-by-step explanation:

square of 29 = 5.385164807

5.385164807 estimated is 5.4

The most appropriate way to model 9485 with the base ten blocks is
9 - thousand, 4 - hundred, 8- ten, and 5 - once.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Base ten block implies the number of blocks according to the digit representation,
For the given question,
The number represents there are 9485 cubes, which can be represented as 9 - thousand, 4 - hundred, 8- ten, and 5 - once.

Thus, the most appropriate way to model 9485 with the base ten blocks is 9 - thousand, 4 - hundred, 8- ten, and 5 - once.

Learn more about arithmetic here:

https://brainly.com/question/11559160

#SPJ1

The missing values in the quantitative reasoning given are : -2, 13 and 9

Given the rule :

We can deduce that :

For the left circle :

circle = -6 - (-4) = -6 + 4 = -2

For the right circle :

circle = 11 - (-2) = 11 + 2 = 13

For the left square :

square = 13 + (-4)

square = 13 -4 = 9

Therefore, the missing values are : -2, 13 and 9

Learn more on puzzle: https://brainly.com/question/27645967

#SPJ1

Answer:

-4 = k/-5

k=20

Answer:

6y - 5x = 6

Step-by-step explanation:

im a god thats how

Answer:

0

Step-by-step explanation:

Answer:

\(x=4,\\y=8\)

Step-by-step explanation:

Notice that in the diagram, opposite sides are equal. This is true for any rectangle, so even without the equal sides being marked, we'd know that each pair of opposite sides have the same length.

Therefore, we can set up the following equations and solve for \(x\) and \(y\):

\(2y=y+8,\\y=\boxed{8}\)

\(4x-8=2x,\\-8=-2x,\\x=\boxed{4}\)

The amount of force used to pull the cart from 60 N to 90 N, the new acceleration of the cart is, 1.5 m/s²

The definition of force is the pushing or pulling of anything. Push and pull are the result of two things interacting with one another. Stretch and crush are two more phrases that can be used to describe force.

Formula of force,

F = ma

Given that,

A man pulled a cart filled with stones that had a total mass of 60 kg

He increased the amount of force used to pull the cart from 60 N to 90 N

New acceleration of cart = ?

F  = ma

Old acceleration,

60  = 60a

a   =  1 m/s²

New acceleration,

90 = 60a

a   = 90/60

a   =  3/2

a   =  1.5 m/s²

Hence, the new acceleration is 1.5 m/s²

To know more about Force check:

https://brainly.com/question/13191643

#SPJ2

a. The data points are (4, 650) and (8, 400).

b. The slope of the line is -62.5.

A number that describes a line's direction and steepness is known as the slope or gradient of a line in mathematics.

How to find the slope:

To find the slope of the line, we can use the formula: slope = (y2 - y1) / (x2 - x1).

Plugging in the values from our data points, we get: slope = (400 - 650) / (8 - 4) = -250 / 4 = -62.5.

c. The slope of the line represents the change in the amount of coffee sold for each unit change in price.

In this case, a negative slope of -62.5 means that for every increase of $1 in the price, the amount of coffee sold decreases by 62.5 pounds.

d. To write the equation of the line using the point-slope form, we need a point from our data and the slope.

We'll use (4, 650) as our point and the slope of -62.5 that we found earlier.

The point-slope form is: y - y1 = m (x - x1), where m is the slope and (x1, y1) is the point.

Plugging in our values, we get: y - 650 = -62.5 (x - 4).

Rearranging, we get: y = -62.5 x + 650 + 62.5 * 4 = -62.5 x + 762.5.

e. To predict the number of coffee consumers would be willing to buy at a price of $6 per pound, we can plug in x = 6 into our equation and solve for y.

y = -62.5 x + 762.5, so y = -62.5 * 6 + 762.5 = 450.

This means that at a price of $6 per pound, consumers would be willing to buy 450 pounds of coffee.

Read more about slope here:

https://brainly.com/question/3493733

#SPJ1

Answer:

C. 5/12

Step-by-step explanation:

Finding the missing side :

Taking the tan ratio :

Answer:

1: -9, 2: 7.7, 3: -36.5, 4: 0.06

Step-by-step explanation:

They make you do a warm up? poor kid...

just multiply to solve

Answer:

The length of a side of a cubic die of volume equal to 343/4 is 4.41 inches.

Step-by-step explanation:

The volume of a cube is given by:

\( V = l^{3} \)

Where:

l: is the length =?  

V: is the volume = 343/4 in³

By solving the above equation for "l" we have:

\( l = (V)^{1/3} = (343/4 in^{3})^{1/3} = 4.41 in \)

Therefore, the length of a side of a cubic die of volume equal to 343/4 is 4.41 inches.

None of the options are correct for the given volume.

I hope it helps you!                                

hello

to answer precisely, i have to see the graphs in the question but overall, the answer should look like something like the graph in the attached file

In order to determine the number of nachos and lemonade sold, you first write the given situation in an algebraic way.

If x is the number of nachos and y the number of lemonades, then, you have:

2.50x + 2.25y = 112.50 cost of the nachos and lemonade sold

x + y = 94 nachos and lemonade sold

Next, solve the previous system.

Multiply the second equation by 2.50. Next, subtract the equation to the first one:

(x + y = 94)(2.50)

2.50x + 2.50y = 235

2.50x + 2.25y = 112.50

-2.50x - 2.50y = -235

-0.25y = -122.5

solve the previous equation for y:

y = -122.5/(-0.25)

y = 490

Next, replace the previous value of y into the expression x + y = 94 and solve for x:

x + y = 94

x + 490 =

your answer is 3.375

Answer:

Perimeter of the circle = 31.42 in(exact value) ≈ 31.40 in (approximate value)

Area of the circle = 78.55 in²

Step-by-step explanation:

Given:

Radius = 5 in

To Find:

Area & Perimeter of the circle

Solution:

We know that,

Taking π as 3.142 and substituting values,we obtain

We know that,

Answer:

1/2

Step-by-step explanation:

-3/4 + (1/10 ÷ 2/5)

1/10 ÷ 2/5 = 1/10 x 5/2 (Keep. Change. Flip. [KCF])

1/10 x 5/2 = 5/20 (or simplify to 1/4)

1/4 - 3/4 = 0.25 - 0.75 = -0.5 (or 1/2)

Answers:

5)

a.Highest- 96

Lowest-52

b.74

c. 70-80

d. 13

e. 7

6)

a. 89%

b. 51%

c. In the morning(89%)

1. An equation that represents "the amount of tax on an item of price p",

t = p x X / 100

2. Marta does pay on an item whose price is $20, $1.6

Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".

Given that,

Tax rate = 8%

1. Let's assume that the sales tax rate is X%.

Then, the equation that represents the amount of tax (t) Marta pays on an item whose price is p can be written as:

t = p x X / 100

2. If the price of the item is $20, the amount of tax Marta pays can be calculated as follows:

t = $20 x X / 100

t = $20 x 8 / 100

t = $1.6

So, Marta pays $1.6 in sales tax on an item whose price is $100.

To know more about Percentage check:

https://brainly.com/question/29306119

#SPJ1

Answer:

2 squared - 7 + -4

Step-by-step explanation:

The value of the expression 8 / m - 11 / 3m is  13 / 3m

8 / m - 11 / 3m

Therefore,

8 / m - 11 / 3m

The factor of the denominator is 3m

Therefore,

8 / m - 11 / 3m = 3(8) - 11/ 3m

3(8) - 11/ 3m = 24 - 11 / 3m

24 - 11 / 3m = 13 / 3m

learn more on fraction here: https://brainly.com/question/24161414

#SPJ1

He had 40 pencils left after he gave away 8, so originally he had 40 + 8 pencils, which is 48.

Now, he bought 4 packages, which had a total of 48 pencils, so divide 48 by 4, which is 12. He had 12 pencils in each package.

To determine the solution arithmetically, first add 8 to 40, then divide 48 by 4.

To determine the solution algebraically, set up and solve the equation 40 = 4x - 8.

Each package contained 12 pencils.

Hope this helps

Kareem has $22, Raina has $28, Eric has $88.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Raina, Kareem, and Eric have a total of $138 in their wallets.

let Kareem has x dollar.

Then Raina has (x+6) dollar

and, Eric has 4x dollar

So, x+ 4x + x + 6 = 138

6x + 6 = 138

6x = 132

x= 22

Thus, Kareem has $22.

Raina has = 22 +6 = $28

and, Eric has =4x = $88

Learn more about Algebra here:

https://brainly.com/question/24875240

#SPJ1