Use two different methods to find and explain a formula for the area of a trapezoid
that has parallel sides of length a and b and height h. Consider these ideas or others: (a)
Combine two copies of the trapezoid to make a parallelogram. (b) Subdivide the trapezoid
into two triangles, one with base b and one with base a.
Answers
The two possible ways to find the area are -
A = (1/2) × {a + b} × {h}A = {b x h} - (1/2) x {(b - a} x h}What is trapezoid?
A trapezoid, also known as a trapezium, is a flat closed shape having 4 straight sides, with one pair of parallel sides.
Area : ½ x (sum of the lengths of the parallel sides) x perpendicular distance between parallel sidesPerimeter : sum of lengths of sides of trapezoidNumber of vertices : 4Number of edges : 4Properties : Convex polygonType : QuadrilateralSum of interior angles : 360°We have a trapezoid.
Now, we can find the area in two ways -
[1] -
A = (1/2) × {a + b} × {h}
[2] -
A = {b x h} - (1/2) x {(b - a} x h}
Therefore, the two possible ways to find the area are -
A = (1/2) × {a + b} × {h}A = {b x h} - (1/2) x {(b - a} x h}To solve more questions on trapezoids, visit the link below -
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Related Questions
**WILL MARK BRAINLIEST AND GIVE 20 POINTS**
Graph the equations y=-1/2x+3 and y=2x-2 in the applet below.
1) After you graph the two lines, be sure to take a screenshot of your work and include it in your answer below.
2) What is the solution to the system of equations?
3) Prove that the answer you provided in part 2 is correct, by substituting the solution into the original equations. Be sure to show all your work.
Answers
the solution is (2,2)
step by step explanation:
y=-1/2x+3 : go up 3 on the y-axis, then go down 1 and the the right 2 and repeat.
y=2x-2 : go down 2 the y-axis, then got up 2 and to the right 1 and repeat.
where ever point the two linear lines intersect in the solution point.
Please help im desperate and its a 8th grade question only please
Answers
Answer:
a. 31/6; 33/6; 35/6
b. + 2/6
c. 37/6; 39/6; 41/6
d. 49/6
Step-by-step explanation:
First we need to find the first three terms.
To do so solve the equations in the boxes.
When dividing by a fraction you multiply by the reciprocal so the equations are now as follows:
2 * 31/12
3 * 11/6
5 * 7/6
Solve these to get
62/12 = 31/6
33/6
35/6
The term to term rule as shown above is adding 2/6 or 1/3.
To find the next three terms in the sequence add 2/6 to the term.
35/6 + 2/6 = 37/6
37/6 + 2/6 = 39/6
39/6 + 2/6 = 41/6.
To find the 10th term you need to write out the arithmetic sequence equation.
an = a1 + (n-1)d
an is the term you want to find and n is the term number in this case that is 10. D is the common difference which in this case is 2/6. Plug these into the equation. A1 is the first term in the equation which in this case is 31/6.
31/6 + (10-1) 2/6
31/6 + (9)2/6
31/6 + 18/6 = 49/6
Find the missing angle
RPQ= __________
Answers
The value of angle RPQ in the circle is 115 degrees.
How to find the angle in the circle?Using angles of intersecting chord theorem, If two chords intersect inside a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.
Therefore,
∠RPQ = 1 / 2 (arc angle RQ + arc angle SA)
arc angle RQ = 175 degrees
arc angle SA = 55 degrees
Hence,
∠RPQ = 1 / 2 (175 + 55)
∠RPQ = 1 / 2 (230)
∠RPQ = 115 degrees.
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Answer: 115 degrees
Step-by-step explanation:∠
RPQ = 1 / 2 (175 + 55)
∠RPQ = 1 / 2 (230)
∠RPQ = 115 degrees.
7. If the following triangle is isosceles, solve for x. Just type the number
only, the answer is a positive whole number.
(5x − 7)°
(8x - 55)
Answers
The required value of x for a given isosceles triangle is 16.
What is an isosceles triangle?
A triangle with two sides that have the same length is said to be an isosceles. When two sides of an isosceles triangle are equal, the angles across from those two sides likewise match up and are always equal.
Given that, the isosceles triangle then
two angles are equal
So, (5x-7)° = (8x-55)°
or, 8x - 5x = 55-7
or, 3x = 48
or, x = 48/3 = 16
Hence, the required value of x is 16.
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8x - 3y = 12
-8x+3y=5.
Answers
Answer:
No solution-------------------------
Given system:
8x - 3y = 12,- 8x + 3y = 5.We see constants are same with opposite sign.
To make them same multiply both sides of the second equation by -1:
( -1 )( -8x + 3y) = ( - 1)*5 ⇒ 8x - 3y = - 5Now we have two equations with same left sides but different right sides:
12 = - 5This is false and hence the system has no solution.
Drive-A-Lot Cars runs a promotion for three years of interest-free payments on sedans. The cost of a new sedan is $22,968 (including tax). What is the average monthly payment a customer will make if they pay off the car during the interest-free period? Type your answer in the box.
Answers
The average monthly payment made by the customer is $638.
How to calculate the average?In order to calculate average, divide the total sum of the data to the total number of data. An average is a standard number for a given data whose value can both be more or less than it.
Given that,
The cost of Sedan for three years is $22,968.
The time in months can be calculated as,
3 × 12 = 36 months
The average payment per month can be found by dividing the total amount by total number of months as follows,
Average monthly payment = 22968/36
= 638
Hence, the average monthly payment made by a customer in the interest-free period is $638.
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If Alex earns $380/week. How much would he make per year, and per month? Explain
Answers
Answer:
$19,760 per year
$1,520 per month
Step-by-step explanation:
There are 4 weeks in 1 month, so multiply $380 by 4:
380 x 4 = $1,520 per month.
1 year = 52 weeks:
380 x 52 = $19,760 per year.
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If a = -2i and b = 5-5i, then find the value of the a³b in fully simplified form.
Answers
Answer:80
Step-by-step explanation:
Which expression represents each mathematical phrases
add 12 and a number
subtract a number from 12
divide a number by 12
multiply 12 by a number
Answers
add 12 and a number : 12 + c
Subtract a number from 12 : 12 - c
Divide a number by 12: c over 12
Multiply 12 by a number: 12c
Step-by-step explanation:
Add 12 and a number:
Let c = any number then the statement "add 12 and a number" will be: 12 + c
Similarly,
As a number has to be subtracted from 12. Subtracting a number from 12 will be: 12 -c
The number has to be divided by 12 so the number will be the numerator and 12 will be the denominator.
Multiplication simply means 12*c OR 12c
4.1 Number Talk: Division
Find each quotient mentally.
645 divided by 100
645 divided by 50
48.6 divided by 30
48.6 divided by x
Answers
645/50= 12.9
48.6/30 = 1.62
48.6/x = 48.6/x
The coldest temperature ever recorded in Mathville was - 16 deg * E This happened on January 30th, 1978. The normal low for that day is 19^ * E. How much colder was the record temperature than the normal low temperature?
Answers
I hope this helps!
Which expressions are equivalent to this expression?
3(n+4)
Select each correct answer.
Responses
3n + 4
3n−12
12 + n + n + n
2n + 12 + n
Answers
We need to figure out what is given in the question.
Given:
[tex]3(n + 4)[/tex]
Options:
---------------------
[tex]3n + 4\\3n−12\\12 + n + n + n\\2n + 12 + n[/tex]
---------------------
It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
Answer:
[tex]2n + 12 + n = 3n + 12 = 3(n + 4)[/tex]
Therefore, the correct options are 12 +n+n+n and 2n + 12+n
A Question 1 (1 point) Retake question
Solve.
5(a − 1) - 15 = 3(a + 2) + 4
Answers
Answer:
A=11
Step-by-step explanation:
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The mean of 4 numbers is 16.5. What would the new mean be if the number 16 is added to the data set?
A.
16.4
B.
12.4
C.
32.5
D.
20.5
Answers
Answer:
Its b
Step-by-step explanation:
B
20 points!!Use what we know about the pythagorean theorem
to determine if this triangle is a right triangle. Write a
statement explaining why this is or is not a right
triangle. Show your work to justify your answer.
Answers
The triangle is a not right triangle because it does not follow the Pythagoras theorem
How to determine if the triangle is a right triangle?From the question, we have the figure that represents the parameter that can be used in our computation:
The sides of the triangles are
6, 8 and 9
For a triangle to be a right triangle, the side lengths must follow the Pythagoras theorem
The Pythagoras theorem states that
Longest side² = Sum of the squares of the other sides
So, we have
9² = 6² + 8²
Evaluate
81 = 100
The above equation is false
Hence, the triangle is not a right triangle
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F and H are sets of real numbers defined as follows.
F = { v l v < 4}
H = { v l v ≥ 7}
Write F ∩ H and F ∩ H using interval notation. If the set is empty, write ∅.
Answers
For the two sets F = {v | v < 4} and H = {v | v ≥ 7}, F∩H = Ф and
F∪H = {v | v ∈ R} - {4, 5, 6}.
What are sets and subsets?A set is a collection of well-defined objects.
A subset contains all the elements or a few elements of the given set.
The improper subset is when it contains all the elements of the given set and the proper subset is when it doesn't contain all the elements of the given set.
Given, Are two sets F = {v | v < 4} and H = {v | v ≥ 7}.
Now, F∩H are those elements of the sets that are common to both here none of the elements are coom so F∩H is Ф.
F∪H are those elements that are either in F or in H or in both.
∴ F∪H = {v | v < 4 or v ≥ 7} Or F∪H = {v | v ∈ R} - {4, 5, 6}
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Given (x – 7)2 = 36, select the values of x.
Answers
For the given equation, [tex](x-7)2=36[/tex] the value for [tex]x=25[/tex].
Calculating the value of the unknown variable while keeping the equation balanced on both sides is the process of solving equations.
A condition on a variable is an equation when it ensures that two expressions in the variable have the same value. The equation's solution is the amount of the variable for which the condition is met.
Initially, the equation [tex](x-7)2=36[/tex] must be made simplified to find [tex]x[/tex].
[tex](x-7)2=36[/tex]
By using distributive law,
⇒ [tex](x-7)2=36[/tex]
⇒ [tex]2x-14=36[/tex]
Now add 14 on both sides,
⇒ [tex]2x-14+14 =36+14[/tex]
⇒ [tex]2x =36+14[/tex]
⇒ [tex]2x =50[/tex]
As the next step, divide both sides by 2,
⇒ [tex]\frac{2x }{2} =\frac{50}{2}[/tex]
⇒ [tex]x=25[/tex]
Therefore, after solving the equation step-by-step, [tex]x=25[/tex].
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contractor bought 10.8 ft2 of sheet metal. He has used 2.3 ft2 so far and has $170 worth of sheet metal remaining. The equation 10.8x−2.3x=170 represents how much sheet metal is remaining and the cost of the remaining amount. How much does sheet metal cost per square foot?
Answers
The cost of sheet metal per square foot is $20.
What is a expression? What is a mathematical equation? What is Equation Modelling? What is the general equation of a straight line? What is the significance of slope of line?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. The general equation of a straight line is -
y = mx + c
[m] is called slope and it tells the unit rate of change in [y] with respect to [x].
We have a contractor bought 10.8 ft² of sheet metal. He has used 2.3 ft² so far and has $170 worth of sheet metal remaining.
The equation 10.8x − 2.3x = 170 represents how much sheet metal is remaining and the cost of the remaining amount.
We have the following equation -
10.8x − 2.3x = 170
8.5x = 170
x = 170/8.5
x = 20
Therefore, the cost of sheet metal per square foot is $20.
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Which values of x are solutions to the equation below?
Check all that apply.
4x²2²-30=34
A. X = √√8
B. X=-4
C. X= 4
D. X = 8
E. X = -8
OF. X = -√8
Answers
Answer:
Step-by-step explanation:
D
Which ordered pair could represent another vertex of the image? (0, –1) (2, 6) (4, 0) (6, 1)
Answers
Answer:
Step-by-step explanation:
t says that's 4 units distant from the another vertex. So, if a square is formed by 4 equal sides and 4 right angles, then you just have to add 4 units on x or y.
-> (2, 1) -> + 4 units on X
-> = (6, 1)
or
-> (2, 1) -> +4 units on Y
-> = (2, 5)
(2, 5) isn't an answer so the unique possible answer is (6, 1)
Answer: (6, 1)
HELP ME OUT THANKS SO MUCH
Answers
Answer:
52 = 13h
Step-by-step explanation:
Gasoline costs $2.75 a gallon. At most, how many gallons can be boughts for $22.00.
Answers
15.2 gallons of gasoline will cost:
15.2 * 2.75 =$41.8
9.5 gallons of diesel will cost:
9.5 * 3.02= $28.69.
The total amont Grabiel will spend on gasoline and diesel:
$41.8 +28.69= $70.49
Answer:
8
Step-by-step explanation:
2.75x8=22
or
22.00÷2.75=8
(not sure)
There are 20 slices of bread in a loaf. How
many 2-slice sandwiches can you make
with 1 loaf? Write a multiplication fact
and a division fact you could use to solve
this problem.
Answers
Answer:
Step-by-step explanation: All you have to do would just separate the bread into groups of 2, and then count how many groups you have, and that would give you the answer.
SOLVE F FOR FFF
1 + 8f = -6+ 7f
F =
Answers
Answer:
f = -7
Step-by-step explanation:
1 + 8f = -6 + 7f
Add 6 on both sides
7 + 8f = 7f
Subtract 8f on both sides
7 = -1f
Divide by -1 to make f positive
f = -7
what is 18 1/2 - 6.6 ?
Answers
Answer: The answer to your question is 83.9
(When rounded, the answer is 84)
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The coordinates of the vertices of a polygon are (-3, 1), (-3, 3), (-1, 5), (2, 4), and (2, 1).
What is the perimeter of the polygon to the nearest tenth of a unit?
A. 16.0 units
B. 17.2 units
C. 15.4 units
D. 18.8 units
Answers
Using the coordinates of the vertices of a polygon (-3, 1), (-3, 3), (-1, 5), (2, 4), and (2, 1) the perimeter of the polygon is 16.0 units
How to find the perimeter of the polygonThe perimeter is calculated by summing the sides
The length of line in an ordered pair is calculated using the formula
d = √{(x₂ - x₁)² + (y₂ - y₁)²}
where
d = distance between the points
x₂ and x₁ = points in x coordinates
y₂ and y₁ = points in y coordinates
(-3, 1) and (-3, 3) =√{(-3 - -3)² + (3 - 1)²} = 2
(-3, 3) and (-1, 5) = √{(-1 - -3)² + (5 - 3)²} = 2√2
(-1, 5) and (2, 4) = √{(2 - -1)² + (4 - 5)²} = √10
(2, 4) and (2, 1) = √{(2 - 2)² + (1 - 4)²} = 3
(2, 1) and (-3, 1) = √{(-3 - 2)² + (1 - 1)²} = 5
The perimeter = 2 + 2√2 + √10 + 3 + 5
The perimeter = 15.9907
The perimeter = 16.0 units
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NO LINKS!! Determine if the figures have line, point, and/or rotational symmetry. Check all that apply. Part 2
Answers
Recall properties of symmetry:
Line - reflection mirror,Rotational - you can rotate it about its center and it will overlap with the initial shape after minimum of 180 degrees rotation,Point - the center is acting as a midpoint of the segment formed by opposite points. Rotational symmetry of even order is also a point symmetry.Using the properties we can state that:
#5It has rotational (of order 2) and point symmetry.#6It has no symmetry.#7It has rotational (of order 3) symmetry.#8It has rotational (of order 6) and point symmetry.Step-by-step explanation:
6.25 points
Find the GCF for the list.
10m4, 40m⁹
10m5
40m4
10m4
6.25 points
list
One antifreeze solution is 41% alcohol and another is 11% alcohol. How much of each mixture should be added to make 30 L of a solution that is 29% alcohol?
Answers
Answer:
18 liters of 41% alcohol and 12 liters of 11% alcohol.
Step-by-step explanation:
.41x + .11(30-x) = .29(30) I am going the clear the decimal by multiply all the way through by 100
41x + 11(30 -x ) = 29(30)
41x + 330 -11x = 875 Combine like terms
30x +330 = 875 Subtract 330 from both sides
30x = 540 Dived both sides by 30
x = 18
30 - 18 = 12
Amount Percent Total
x .41 .41x
30 - x .11 .11(30 - x)
30 .29 .29(30)
Look at the total column
.41x + .11(30-x) = .29(30)
True or False
Determine if the ratios are equivalent.
4/5 and 15/20
Group of answer choices
True
False
Answers
Answer:
False
Step-by-step Explanation:
15:20=5×3 5×4 =3 4=3:4 So it is not equivalent to 4 : 5.
Answer:
this my alt account
Step-by-step explanation:
The parabola y=x^2 is reflected across the x-axis and then scaled vertically by a factor of 1/8. What is the equation of the new parabola?
Answers
The equation of the new parabola, that is, the image of the parabola f(x) = x² is g(x) = - (1 / 8) · x².
What is the equation of the image of a parabola?
In this problem we must determine the image of the parabola f(x) = x², which is the result of a sequence of two rigid transformations: (i) Reflection across the x-axis, (ii) Dilation. Each kind of rigid transformation is described below:
Reflection across the x-axis
f'(x) = - f(x)
Dilation
g(x) = k · f'(x), where k is the scale factor.
Now we proceed to determine the equation of the new parabola:
Step 0
f(x) = x²
Step 1
f'(x) = - x²
Step 2
g(x) = - (1 / 8) · x²
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