The formula for a trapezoid relates the area A, the two bases, a and b, and the height, h.
Solve for a.
Answers
multiply both sides by 2 to get
2A = (a+b)*h
divide both sides by h
to get 2A/h = a+b
subtract b from both sides to get a = 2A/h -b
3rd choice is correct
Option C - a = [tex]$\frac{2A-bh}{h}[/tex] is the correct alternative.
We have the formula for a trapezoid that relates the area - A, the two bases - a and b and the height - h as follows -
[tex]$A=\frac{(a+b)}{2} h[/tex]
We have to solve for ' a '.
Solve for x : x ( 1 + 2 + 3 + .... + n) = πOn solving -
x( 1 + 2 + 3 + .... + n) = π
[tex]\frac{xn(n+1)}{2} =\pi[/tex]
[tex]x =\frac{2\pi }{n(n+1)}[/tex]
According to the question, we have -
[tex]$A=\frac{(a+b)}{2} h[/tex]
2A = (a + b)h
2A = ah + bh
2A - bh = ah
a = [tex]$\frac{2A-bh}{h}[/tex]
Hence, Option C is the correct alternative.
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Related Questions
Angela lives in the United States. She went on a trip, flying first to London, then to Paris, then back to the United States. Assume that currency rates remained constant during her trip.a. If the currency rate was $1.67 per English pound, about how many pounds did she receive in exchange for $500 cash? Show your work or explain your reasoning.
Answers
The number of pounds that she received in exchange for $500 cash will be 299.40 pounds.
What are ratio and proportion?A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.
Angela lives in the United States. She went on a trip, flying first to London, then to Paris, then back to the United States. Assume that currency rates remained constant during her trip. If the currency rate was $1.67 per English pound.
The dollar is directly proportional to the pound.
Let p be the number of the pound.
p / 500 = 1 / 1.67
p = 500 / 1.67
p = 299.40 pounds.
The number of pounds that she received in exchange for $500 cash will be 299.40 pounds.
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Write and English phrase that would translate into the following mathematical expression. 5z-8.
Which of the following is equivalent to the expression 5z-8?
Answers
8 less then the product of 5 and a number z <== this is equivalent
do I still have to write an English phrase ?....if so,
the product of 5 and a number z, decreased by 8
To mail a first class letter, the U.S Postal Service charges $.34 for the first ounce and $.21 for each additional ounce. It cost $1.18 to mail your letter. How many ounces does your letter weigh?
Answers
a food store makes a 11-pound mixture of peanuts, almonds, and raisians. The cost of peanuts is $1.50 per pounds, almonds cost $3.00 per pound, and raisins cost $1.50 per pound. The mixture calls for twice as many peanuts as almounds. The total cost of the mixture is $21.00. How much of each ingredient did the store use.
Answers
Eddie purchased 4 packages of light bulbs and received a 15% discount. He also paid $4.85 in taxes on his purchase. Write an algebraic expression to represent the total amount Eddie paid. Let x represent the cost of each package purchased.
Answers
Which expression is the best estimate of the product of 7/8 and 1/10
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Jonah is arranging books on a shelf. The order of the books matters to him. There are 336 ways he can arrange the books. Choose True or False for each statement.
Answers
The sum of the probabilities of any event and its complement is always 1.
The student's question involves probability and arrangement of objects, which falls under the subject of mathematics. More specifically, the problem relates to permutations and the fundamental counting principle, combined with basic probability concepts.
Statement 36: The sample space is the set of all possible outcomes that can occur. Since there are 12 different books, the sample space consists of these 12 unique titles, where 8 are fiction (F1 to F8) and 4 are nonfiction (N1 to N4). The sample space is therefore: {F1, F2, F3, F4, F5, F6, F7, F8, N1, N2, N3, N4}.
Statement 37: The sum of the probabilities of an event and its complement is always 1. This is because an event and its complement together cover all possible outcomes in the sample space.
What can child-care homes and facilities do to help families and reduce the risk of child abuse?
Answers
They can review staff behavior expectations, have special considerations for very young children and make sure child case spaces are designed well.
Hope This Helps You!
Good Luck :)
Answer:
If a staff member notices behavioral changes in the child it could improve the situation if a staff member subtly questioned the child not alarming anything and if the child is aware of abuse the staff member could quickly respond and seek help from a higher person.
if 4x +5=9x-2,then x=
Answers
9x - 4x = 5 + 2
5x = 7
x = 7/5
x = 1.4
Isabella's ballet class is preforming a spring recital for which they need butterfly costumes. Each butterfly costume is made from 3 3/5 yards of fabric. Use Distributive Property to find the number of yards of fabric needed for 5 costumes. (Hint: A mixed number can be written as the sum of an integer and a fraction.)
Answers
We are given that:
fabric required = 3 3/5 yards
costumes = 5
We can write fabric required as a fraction in the form of:
(3 * 5) + 3 = 18
fabric required = 18 / 5 yards
So total fabric required is = (18 / 5 yards) * 5 = 18 yards
Answer:
18 yards
The area of one face of a cube is 25 cm2 . what is the surface area of the cube
Answers
If the area of one side of a cube is 25 cm², then
surface area of the cube = 25 * 6 = 150 cm²
If the area of one face of a cube is 25 cm2 . what the surface area of the cube will be is: 150cm²
Let x represent the surface area of the cube
Hence:
Surface area of a cube of edge x =6x²
Surface area of the cube =6(25cm)²
Surface area of the cube=150cm²
Inconclusion if the area of one face of a cube is 25 cm2 . what the surface area of the cube will be is: 150cm²
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What is the simplified form of cos C ?
A. √2/2
B. 1
C. √2
D. √5/2
Answers
cosC = 5/(5√2)
5/5 is equal to 1, so they cancel each other out to leave just √2.
The simplified form of cos C is sqrt(2)/2.
What is cos ?"Cos is the cosine function of a right triangle in trigonometry. Cos function is the ratio of adjacent side and hypotenuse. It helps us to find the length of the sides of the triangle, irrespective of given angle.
Suppose we have a right triangle and α is the angle between adjacent side and hypotenuse, then as per the cos function, we can write
Cos α = Adjacent Side/Hypotenuse"
Here, given the base of the triangle is = 5
and hypotenuse is = 5sqrt2
So, [tex]cos C = 5/5\sqrt2 = 1/\sqrt2[/tex]
Multiplying both numerator and denominator by sqrt2
We get [tex]\sqrt2/2[/tex].
Hence, the value of cos C is [tex]\sqrt2/2[/tex]
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Rotating a polygon in Quadrant II 270° clockwise is the same as
A) rotating it 90° clockwise.
B) rotating it 180° clockwise.
C) rotating it 90° counterclockwise.
D) rotating it 270° counterclockwise.
Answers
Answer:
90°
Step-by-step explanation:
Hi! A and B are definitely not the right answers, because that’s basically rotating it forward even more. Rotating a polygon in Quadrant II 370 degrees clockwise is like rotating it 99 degrees counterclockwise, because the next 90 degrees you were to rotate it, it would be in it’s original position. The answer is C.
You have $20 to spend on taxi fare. The ride costs $5 plus $2.50, per mile.
Answers
In this situation a good method would be to make an equation.
Let x represent the number of miles traveled.
The ride costs $2.50 per mile, so the cost of the total trip is equal to 2.5x + 5. (the 5 is the base 5$ cost)
Set this equation equal to 20 as you have $20 to spend.
So, we get
2.5x + 5 = 20
Subtract 5 on both sides to get:
2.5x = 15
Divide by 2.5 on both sides to find x.
x = 6
You can travel 6 miles in the taxi.
Talia is packing a moving box. She has a square-framed poster with an area of 9 square feet. The cube-shaped box has a volume of 30 cubic feet. Will the posture lie flat in the box?
Answers
length of the poster = sqrt (9 ft^2) = 3 ft
length of the cube = cbrt (30 ft^3) = 3.11 ft
Since, the length of the cube is longer compared to the length of the poster then, the poster will lie flat on the cube.
Answer: Yes, the posture will be lie flat in the box.
Step-by-step explanation:
since we have given that
Area of square framed poster = 9 sq. feet
Volume of cube shaped box = 30 cubic feet.
As we know the formula for "volume of cube":
[tex]Volume=30\\\\a^3=30\\\\a=\sqrt[3]{30}=3.10\ feet[/tex]
So, Area of cube shaped box would be
[tex]6a^2=6\times (3.1)^2=57.9\ ft^2[/tex]
Since the cube box is large enough so that the posture will lie flat in the box.
if f(x) = 2x-5, which expression represents f(x+1)
Answers
Insert the value of x which is x+1 ->
F(x+1)= 2(x+1)-5
Distribute ->
F(x+1)=2x+2-5
Then, add like terms->
F(x+1)=2x-3
Answer: The required expression for f(x+1) is 2x-3.
Step-by-step explanation: We are given the following function :
[tex]f(x)=2x-5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We are to find the expression for f(x+1).
To find the expression for f(x+1), we need to substitute x+1 in place of x in (i).
So, we get from expression (i) that
[tex]f(x+1)\\\\=2(x+1)-5\\\\=2x+2-5\\\\=2x-3.[/tex]
Thus, the required expression for f(x+1) is 2x-3.
Devin brought his snail collection to school.He has 10 snails.How could he put them into 2 tanks so two classes could see them?Write equation for all the possible ways.One of the way is given. Explain how you have found all the ways.
Answers
To make a greeting card Bryce used 1/8 sheet of red paper,3/8 sheet of green paper and 7/8 sheet of white paper. How much paper did Bryce use
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Find the area of the trapezoid.
144 square units
72 square units
88 square units
44 square units
Answers
area = 13+9=22
22/2 = 11
11x 4 = 44 square units
Answer:
44 square units
Step-by-step explanation:
Area of the trapezoid formula is [tex]\frac{base1 + base2}{2} \cdot height[/tex]
To find the base and the height we count the number of units in the graph
Base 1= 13
Base 2= 9 and height = 4
Now plug in all the values in the formula and find the area of the trapezoid
Area of the trapezoid=[tex]\frac{base1 + base2}{2} \cdot height[/tex]
=[tex]\frac{13+9}{2} \cdot 4[/tex]
=[tex]\frac{22}{2} \cdot 4[/tex]
=44 square units
The probability that concert tickets are available by telephone is 0.91. for the same event, the probability that tickets are available through a web site is 0.96. assume that these two ways to buy tickets are independent. what is the probability that someone who tries to buy tickets both through the internet and by the telephone will obtain at least one ticket? round your answer to four decimal places (e.g. 98.7654).
Answers
Final answer:
The probability of obtaining at least one concert ticket through both the internet and by telephone is 0.9984.
Explanation:
The probability that someone who tries to buy tickets both through the internet and by telephone will obtain at least one ticket is 0.9984.
To calculate this, we first find the probability of not getting any tickets through either method: P(no tickets) = P(no tickets by phone) * P(no tickets online). Then, subtract this probability from 1 to get the probability of obtaining at least one ticket: P(at least one ticket) = 1 - P(no tickets).
By default, the normal style places ____ points of blank space after each paragraph. 8 10 12 14
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The normal style places 10 points of blank space after each paragraph.
In Microsoft word when we want to start a new paragraph we press enter from the keyboard and the new paragraph will start. We can also use a dialog box to write, show or highlight the paragraph.
If a distribution is normal with mean 8 and standard deviation 2, then the median is also 8. True or false?
Answers
I hope this is correct :)
if a number is a natural number, then it is also a whole number? what is the Inverse, the Converse, the Contrapositive, and the Bi-Conditional? and what is the Truth value for each one?
Answers
The original statement, 'If a number is a natural number, then it is also a whole number' is true because every natural number falls into the set of whole numbers. However, its converse is not true, as whole numbers include 0, which is not a natural number, making the inverse and the bi-conditional false. The contrapositive of the statement is true, maintaining logical consistency.
Explanation:If a number is a natural number, then it is indeed also a whole number. The relationship between natural numbers and whole numbers is an inclusive one, where all natural numbers (1, 2, 3, ...) are also whole numbers (0, 1, 2, 3, ...). The original statement can be expressed in logical form as: If P, then Q, where P is 'a number is a natural number,' and Q is 'it is also a whole number.'
Here is how the other forms of the statement look:
The inverse negates both the hypothesis and the conclusion: If not P, then not Q. So, 'If a number is not a natural number, then it is not a whole number.'
The converse switches the hypothesis and the conclusion: If Q, then P. For our statement, 'If a number is a whole number, then it is also a natural number.'
The contrapositive negates and switches the hypothesis and conclusion: If not Q, then not P. Therefore, 'If a number is not a whole number, then it is not a natural number.'
The bi-conditional states that P if and only if Q: A number is a natural number if and only if it is a whole number.'
The truth value of the original statement is true since all natural numbers are whole numbers. However, the converse is not true because whole numbers also include 0, which is not a natural number. Consequently, the inverse and the bi-conditional are false. The contrapositive is true because if it is not a whole number, then it can't be a natural number (considering that whole numbers include all natural numbers).
The following is Michael Jordan’s baseball stats. Year Avg Gm AB R H TB 2B 3B HR 1994 0.202 127 436 46 88 116 17 1 3 Research baseball statistics online to determine what each label represent in the baseball world. How can you use the given information to determine how many singles Jordan hit during his baseball career?
Answers
Using mathematical operations, the total no. of singles Jordan hit during his baseball career = 67.
What are mathematical operations?Understanding the distinction between Operators and Operands will be made easier if we are aware of the differences between and purposes for Numbers/Values, Symbols, and Functions.
Understanding mathematical operations will be aided by being aware of the distinction between Operators and Operands as well as their function.
In the given statistics,
The number of Home Runs = 3
The number of Doubles = 17
The number of Triples = 1
The total no. of hits = 88
Now, to calculate the total no. of singles hit = 88 - (3+17+1)
= 67
Therefore, the total no. of singles Jordan hit during his baseball career = 67.
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The number of miles driven varies directly with the number of hours in the car. Billy drives 171 miles in 3 hours, so he could drive _____ miles in 4.5 hours.
Answers
Billy drives 171 miles in 3 hours, so he could drive 256.5 miles in 4.5 hours.
What is speed?The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.
We know that the speed formula
Speed = Distance/Time
The number of miles driven varies directly with the number of hours in the car.
Billy drives 171 miles in 3 hours.
Then the number of miles he can drive in 4.5 hours will be
Let x be the number of miles covered in 4.5 hours.
The speed remains constant.
Then we have
x / 4.5 = 171 / 3
x = 256.5 miles
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Billy could drive 256.5 miles in 4.5 hours.
Explanation:To find the number of miles Billy could drive in 4.5 hours, we will use the concept of direct variation. Direct variation states that when two variables are directly proportional, their ratio is constant.
Given that Billy drives 171 miles in 3 hours, we can set up a proportion:
Miles driven / Hours in the car = Miles driven / Hours in the car
Using the given values, we have:
171 / 3 = x / 4.5
To solve for x, cross multiply:
3x = 171 * 4.5
Divide both sides by 3:
x = (171 * 4.5) / 3
Simplifying the right side of the equation gives us:
x = 256.5
Therefore, Billy could drive 256.5 miles in 4.5 hours.
Find the slope of each of the lines below:
Answers
The slope is "Undefined".
The area of a sale is 40.5 ft.² the base and height of the sail equal what is the height of the cell
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Which graph represents the solution set of the system of inequalities?
{−2x+y≤4
y>x+2
Answers
The correct graph is:
First graph
Step-by-step explanation:The first inequality is:
[tex]-2x+y\leq 4[/tex]
The graph of this inequality is a straight solid line ( since the inequality is a inequality with a equality sign i.e. not strict ) which passes through (-2,0) and (0,4) and the shaded region is towards the origin as it passes the zero point test.
The second inequality is:
[tex]y>x+2[/tex]
is a dotted straight line (since the inequality is strict) which passes through (-2,0) and (0,2) and the shaded region is away from the origin as it fails the zero point test.
Hence, the correct graph is the first graph.
How do you find the coordinates of the midpoint of segment VW with the end points of V(-2,-6) and W(x+2, y+3)
Answers
The coordinates of the midpoint of segment VW are (x/2, (y-3)/2).
Explanation:To find the coordinates of the midpoint of segment VW, we can use the midpoint formula.
The midpoint formula states that the x-coordinate of the midpoint is the average of the x-coordinates of the endpoints, and the y-coordinate of the midpoint is the average of the y-coordinates of the endpoints.
Given the endpoints V(-2, -6) and W(x+2, y+3), we can find the x-coordinate of the midpoint by taking the average of the x-coordinates: (-2 + (x+2))/2.
Similarly, we can find the y-coordinate of the midpoint: (-6 + (y+3))/2.
So the coordinates of the midpoint are (x/2, (y-3)/2).
solve for z 15 points
Answers
[tex]Step^1:[/tex] we have to [tex]simplify[/tex] your factions
[tex]Like: [/tex] [tex]z - \frac{4}{9} - \frac{1}{3} = \frac{5}{9} [/tex]
[tex]Replace[/tex] the [tex]subtraction [/tex] symbol to the [tex]additional [/tex] symbol since [tex]adding[/tex] is the opposite of [tex]subtraction [/tex] (since we changed the symbols the first two fractions numerators becomes a negative)
Our problem becomes: [tex] z + \frac{-4}{9} + \frac{-1}{3} = \frac{5}{9} [/tex]
Let's gather all of our "[tex]like-terms[/tex]" (if we have any in this question/problem)
[tex]Like: [/tex] [tex]z + \frac{-4}{9} + \frac{-1}{3} \\ = \frac{5}{9} [/tex]
The step we just did when we [tex]solved [/tex] it gave us: [tex]z + \frac{-7}{9} = \frac{5}{9} [/tex]
For our last step: Let's [tex]Add [/tex] by the number/fraction [tex] \frac{7}{9} [/tex] on each of your sides that we're working with!
[tex]Like:[/tex] [tex]z + \frac{-7}{9} + \frac{7}{9} (Cancel) \\ = \frac{5}{9} + \frac{9}{9} (Keep) [/tex]
Therefore, we have came to our [tex]answer[/tex] , which is: [tex]z = \frac{4}{3} [/tex]
Good luck on your assignment and enjoy your day!
[tex]MeIsKaitlyn:)[/tex]
Sorry, I was late to answering your question :(