the function a(b) relates The area of a trapezoid with a given height of 12 and one base length of 9 with the length of its other base
Answers
The equation that represents the function B(a) as the length of the side parallel to the base is B(a) = a/6 - 9, as per the area of a trapezoid.
What is the area of a trapezoid?If the length of two parallel sides of a trapezoid is 'a', 'b' and the height of that trapezoid is 'h', then the area of a trapezoid can be represented as
= [(a + b)h]/2
Given, the base of the trapezoid is 9 and the height of the trapezoid is 12.
Therefore, 'b' is the parallel side of the base.
The given function that represents the area of the trapezoid is:
A(b) = [12(b + 9)]/2
Let, A(b) = a.
Therefore, a = [12(b + 9)]/2
⇒ 2a = 12(b + 9)
⇒ a = 6(b + 9)
⇒ a = 6b + 54
⇒ 6b = a - 54
⇒ b = (a - 54)/6
⇒ b = a/6 - 9
If we assume the length of the side parallel to the base 'b' = B(a), therefore, the equation will be:
B(a) = a/6 - 9
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Related Questions
The rays or segments that form angles are called________.
A. Points
B. Vertices
C. Sides
D. Endpoints
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Consider the parabola represented by the equation -2y2 = 4x. This parabola will open to the . The equation of the directrix of the parabola is . The focus of the parabola is . NextReset
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then you integrate, by using the line as the upper area, then subtracting the lower area parabola between 0 and 2 int(-1/2x + 4 - (x^2 - 2x + 3)) = -1/4x^2 + 4x -x^3/3 + x^2 - 3x replace 2 for x and you will get -1 + 8 - 8/3 + 4 - 6 12 - 29/3 = 7/3
what percent of 150 is 350
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2.33 * 100
233%
Hope this helps!
is = 350
of = 150
% = x
350/150 = x/100
cross multiply because this is a proportion
(150)(x) = (350)(100)
150x = 35000
x = 35000/150
x = 233.33% or 233 1/3%
The sum of three consecutive odd integers is 219. What is the largest of these integers?
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3a+6 = 219
3a = 213
a=71
a+2=73
a+4= 75
therefore the highest number is 75.
I hoped I helped and good luck if you have a test or a quiz!
A glass tabletop is supported by a rectangular pedestal. if the tabletop is 8 inches wider than the pedestal on each side, what is the perimeter of the glass tabletop
Answers
When adding make sure you add 4 sides worth of calculations. You have to consider the left and right side (for length) and front and back for the width.
The solution for this problem is:
Side 1 (8+36+8)
+
Side 2 (8+48+8)
+
Side 3 (8+36+8)
+
Side 4 (8+48+8)
= 232
The perimeter of the glass tabletop is 232 inches. The option (E) is correct.
To find the perimeter of the glass tabletop, we need to determine its dimensions first. According to the problem, the glass tabletop is 8 inches wider than the pedestal on each side.
Dimensions of the Pedestal:
- Width: 36 inches
- Length: 48 inches
Since the tabletop extends 8 inches beyond the pedestal on each side, we add 16 inches (8 inches on each side) to both the width and the length of the pedestal.
Width of the glass tabletop:
[tex]\[ \text{Width} = 36 \, \text{inches} + 16 \, \text{inches} = 52 \, \text{inches} \][/tex]
Length of the glass tabletop:
[tex]\[ \text{Length} = 48 \, \text{inches} + 16 \, \text{inches} = 64 \, \text{inches} \][/tex]
The perimeter [tex]\( P \)[/tex] of a rectangle is given by:
[tex]\[P = 2 \times (\text{Length} + \text{Width})\][/tex]
Substituting the dimensions:
[tex]\[P = 2 \times (64 \, \text{inches} + 52 \, \text{inches})\\P = 2 \times 116 \, \text{inches} = 232 \, \text{inches}\][/tex]
The correct perimeter of the glass tabletop is [tex]\( 232 \)[/tex] inches.
The complete question is:
A glass tabletop is supported by a rectangular pedestal. If the tabletop is 8 inches wider than the pedestal on each side, what is the perimeter of the glass tabletop?
A) 92 inches
B) 116 inches
C) 176 inches
D) 184 inches
E) 232 inches
Building a is 160 feet shorter than building
b. the total height of the two buildings is 1490 feet. find the height of each building.
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How do you do the cube of x plus 5
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3t(t+2)-(3t^2+5t) when t=19
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3t(t+2)-(3t^2+5t) when t=19
3(19)(19+2)-(3(19)²+5(19) =(57)(21)-(1083+95) =1197-1178 =19
Mr. haigwood is shopping for a school picnic . veggie burgers comes in packages of 15 and buns come in packages of 6. he wants to serve veggie burgers on buns and wants to have no items left over. Mr. haighwood says that he will have to buy at least 90 of each item 6 x 15 =90. Do you agree with his reasoning
Answers
LCM = 30,
so they need to buy atleast 30 of each item.
Answer:
Mr. haigwood is not right.
Step-by-step explanation:
The veggie burgers comes in packages of 15 and buns come in packages of 6.
Mr. haigwood wants to serve veggie burgers on buns and wants to have no items left over.
Now, to find the least number of burgers and buns needed so nothing is left over, we will find the LCM of 15 and 6.
15 = 3 x 5
6 = 2 x 3
LCM = 2 x 3 x 5 = 30
As given, Mr. haighwood says that he will have to buy at least 90 of each item 6 x 15 =90.
This is not right. He needs to buy at least 30 of each item so that nothing is left over.
What is the maximum number of communication paths for a team of twenty people?
Answers
so, A/Q
20*(20-1)/2
=190
190 is the maximum communication paths for a team of twenty people.
Did I do the problem -2x+10=-2(x+5) ? If not plz explain and answerthxx
Answers
So now the answer would be 10 = -10.
Which leads me to believe that this question wasn't written correctly because 10 does not equal -10 for sure.
A boat traveled 252 miles downstream and back. The trip downstream took 12 hours. The trip back took 84 hours. What is the speed of the boat in still water? What is the speed of the current?
Answers
The required speed of the current is given as 9 miles per hour.
Given that,
A boat traveled 252 miles downstream and back. The trip downstream took 12 hours. The trip back took 84 hours. What is the speed of the boat in still water is to be determined.
Speed is defined as when an object is in motion, the distance covered by that object per unit of time is called speed.
Here,
let the speed of the current be y, and the speed of the boat at still water be x,
According to the question,
Downstream speed,
252 / 12 = x + y - - - -(1)
upstream speed,
252 / 84 = x - y - - - (2)
Adding equations 1 and 2
21 + 3 = 2x
x = 24 / 2
x = 12 miles/hour
Now,
3 = 12 - y
y = 9 miles/ hour
Thus. the required speed of the current is given as 9 miles per hour.
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Final answer:
To find the speed of the boat in still water and the current, we used the relation of speed, distance, and time for downstream and upstream travel to set up equations. We solved these to determine that the boat's speed in still water is 12 miles per hour, and the current's speed is 9 miles per hour.
Explanation:
The question asks to determine the speed of the boat in still water and the speed of the current given the distances and times for traveling downstream and upstream. Using the given data, we can set up two equations based on the speed-distance-time relationship:
Downstream speed = Speed of boat in still water + Speed of current
Upstream speed = Speed of boat in still water - Speed of current
Let v represent the speed of the boat in still water, and c represent the speed of the current. We have the equations:
(v + c) = 252 miles / 12 hours = 21 miles/hour (downstream)
(v - c) = 252 miles / 84 hours = 3 miles/hour (upstream)
Adding these two equations gives us:
2v = 24 miles/hour
Dividing by 2:
v = 12 miles/hour
Substituting v in either equation to find c:
c = 21 miles/hour - v = 21 miles/hour - 12 miles/hour
c = 9 miles/hour
Therefore, the speed of the boat in still water is 12 miles/hour, and the speed of the current is 9 miles/hour.
In May, Liam and Charlie had the same amount of money in their savings accounts. In June, Liam deposited $140 into his account. Charlie said he increased the money in his account by 5%. When they compared their balances, they found that they were still equal.
How much money did they both have in their accounts in May?
Answers
Answer:2,800.00
Step-by-step explanation:
Find the distance between the points (8,9) and (1,4). round decimals to the nearest tenth.
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The concession stand at a ballpark makes $0.43 profit from each hot dog sold. It also makes a profit of $0.65 from each pretzel sold and $1.31 from each drink sold. Which expression represents the total profit, in dollars, that the stand will make on a day when they sell h hot dogs, p pretzels, and d drinks?
Answers
explanation:
h stands for hotdogs, p for pretzels, and d for drinks. c represents the total cost.
each price next to the variable describes the profit per item.
hope this helps! :D
Answer:
P = 0.43h + 0.65p + 1.31d represents the total profit, in dollars that the stand will make on a day when they sell h hot dogs, p pretzels, and d drinks
Step-by-step explanation:
Given : The concession stand at a ballpark makes $0.43 profit from each hot dog sold. It also makes a profit of $0.65 from each pretzel sold and $1.31 from each drink sold
We have to find an expression that represents the total profit, in dollars that the stand will make on a day.
Let the stand sells h hot dogs, p pretzels, and d drinks on a day
Since profit of one hot dog is $ 0.43
So , profit of h hot dogs is $ 0.43h
also, profit of one pretzels is $ 0.65
So , profit of p pretzels is $ 0.65p
also, profit of one drink is $1.31
So , profit of d drinks is $ 1.31d
Total profit of a day is the total profit he earned from selling each item.
thus, total profit is given by equation
P = 0.43h + 0.65p + 1.31d
Thus, P = 0.43h + 0.65p + 1.31d represents the total profit, in dollars that the stand will make on a day when they sell h hot dogs, p pretzels, and d drinks
Given: x+2y=-6. Solve for y. y=x-6/2
Answers
Answer:
y = (-x -6)/2
Step-by-step explanation:
You want to solve x +2y = -6 for y.
Isolate the variableThe first step here is to get the y-term by itself on one side of the equal sign. We can do that by subtracting x from both sides of the equation.
x +2y -x = -6 -x
2y = -6 -x
Now, we divide by the coefficient of y to get y by itself.
2y/2 = (-6 -x)/2
y = (-x -6)/2
We can also write this as ...
y = -x/2 -3
Answer:
The expression represents [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex] is [tex]\( y = \frac{-6 - x}{2} \)[/tex]
Explanation:
To solve the equation [tex]\(x + 2y = -6\)[/tex] for [tex]\(y\)[/tex], follow these steps:
1. Subtract [tex]\(x\)[/tex] from both sides of the equation to isolate the term containing [tex]\(y\)[/tex]:
[tex]\[2y = -6 - x\][/tex]
2. Divide both sides of the equation by [tex]\(2\)[/tex] to solve for [tex]\(y\):[/tex]
[tex]\[y = \frac{-6 - x}{2}\][/tex]
So, the solution for [tex]\(y\) is \(y = \frac{-6 - x}{2}\).[/tex]
What is the smallest integer that can be added to -2m^3-m+m^2+1 to make it completely divisible by m+1?
Answers
-2m^3+m^2-m+1=(m+1)(-2m^2+3m-4)+5
The smallest integer to add is -5.
someone please help me with this problem
Answers
so the rectangular prism, or that box, is really just 6 rectangles stacked up to each other at the edges, notice
front and back are just two 9x5 rectangles
left and right are just two 5x4 rectangles
top and bottom are just two 9x4 rectangles
get the area of all 6, sum them up, and that's the area of the box.
(2x4+x3−4x2+3)+(4x4−2x3−x2+10x+2)
Express the answer in standard form.
Enter your answer in the box.
Answers
Answer: The required sum is [tex]6x^4-x^3-5x^2+10x+5.[/tex]
Step-by-step explanation: We are given to find the following sum:
[tex]S=(2x^4+x^3-4x^2+3)+(4x^4-2x^3-x^2+10x+2).[/tex]
To find the sum, we need to add the coefficients of the same exponents of the unknown variable x.
The summation is as follows:
[tex]S\\\\=(2x^4+x^3-4x^2+3)+(4x^4-2x^3-x^2+10x+2)\\\\=(2+4)x^4+(1-2)x^3+(-4-1)x^2+10x+(3+2)\\\\=6x^4+(-1)x^3+(-5)x^2+10x+5\\\\=6x^4-x^3-5x^2+10x+5.[/tex]
Thus, the required sum is [tex]6x^4-x^3-5x^2+10x+5.[/tex]
Vector u has its initial point at (14, -6) and its terminal point at (-4, 7). Write the component form of u and find its magnitude.
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[tex]\bf u\implies \begin{cases} (14,-6)\\ (-4,7) \end{cases}\implies (-4-14)~,~(7-(-6)) \\\\\\ (-18) ~,~(7+6)\implies \stackrel{\textit{component form}}{\ \textless \ -18~,~13\ \textgreater \ } \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ||u||=\sqrt{a^2+b^2}\implies ||u||=\sqrt{(-18)^2+13^2}\implies ||u||=\sqrt{493}[/tex]
The component form of vector u is (-18, 13) and its magnitude is approximately 22.2.
Explanation:The subject of this question is vector algebra, specifically finding the component form and magnitude of a vector. The component form of a vector is found by subtracting the coordinates of the initial point from the terminal point. Thus, the component form of vector u with initial point at (14, -6) and terminal point at (-4, 7) is (-4-14 , 7-(-6)) = (-18, 13).
To find the magnitude of a vector, you use the formula which is the square root of the sum of the squares of the components. So for vector u, the magnitude is found by calculating √((-18)² + 13²) = √ (324 + 169) = √493, which is approximately 22.2.
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Deshaun makes 9 dollars for each hour of work. write an equation to represent his total pay p after working h hours.
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Why do we reverse the direction of the inequality symbol when multiplying or dividing by a negative number?
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the vertex of a parabola is (-2,-20), and it's y intercept is (0,-12). what is the equation of the parabola?
(y=__x^2 +__x+__)
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to find a:-
when x = 0 y = -12 so:-
-12 = a(2)^2 - 20
4a = 20-12 = 8
a = 2
so we have
y = 2(x + 2)^2 - 20
y = 2x^2 + 8x + 8 - 20
y = 2x^2 + 8x - 12 is the answer.
The equation of the graphed line is x + 2y = 5. What is the x-intercept
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hope this helps
An ice cream factory makes 170 quarts of ice cream in 2 hours. how many quarts could be made in 12 hours? what was that rate per day?
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∠E and ∠F are vertical angles with m∠E = 8x + 8 and m∠F = 2x + 38. What is the value of x?
Answers
Answer: The value of x = 5
Step-by-step explanation:
Given : ∠E and ∠F are vertical angles m∠E = 8x + 8 and m∠F = 2x + 38.
We know that the vertical angles are congruent.
It means [tex]\angle{E}\cong\angle{F}[/tex]
[tex]\Rightarrow\ m\angle{E}=\ m\angle{F}[/tex]
[tex]\Rightarrow\ 8x+8=2x+38[/tex]
Subtract 2x and 8 from both sides , we get
[tex]6x=30[/tex]
Divide both sides by 6 , we get
[tex]x=5[/tex]
Hence, the value of x = 5
Find two consecutive even integers whose sum is 126, please show your work.
Answers
x+x+2= 126
combine like terms
2x+2=126
subtract 2 from each side
2x=124
divide both sides by 2
x=62
the first integer is 62
because the second integer is represented by x+2, it is equal to 64
to check work
62+64 = 126
The two consecutive even integers whose sum is 126 are 62 and 64.
Let's represent the first even integer as x. Since the next consecutive even integer would be the next even number, we can represent it as x + 2.
The problem states that the sum of these two consecutive even integers is 126. We can set up the equation:
x + (x + 2) = 126
Now, let's solve for x by simplifying and combining like terms:
2x + 2 = 126
Subtract 2 from both sides of the equation:
2x + 2 - 2 = 126 - 2
2x = 124
Divide both sides of the equation by 2 to isolate x:
(2x) / 2 = 124 / 2
x = 62
Now that we have found the value of x, we can find the second consecutive even integer:
x + 2 = 62 + 2 = 64
Therefore, the two consecutive even integers whose sum is 126 are 62 and 64.
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how to find the sum of 2+4+6....+40?
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a, is the first term. d is difference.
Since this is an arithmetic progression, I use this formula.
Un = nth term
Sn = sum of terms.
First find the number of terms, which is 20.
Then use the second formula to find the sum.
PLEASE HELP!!!!
How do I describe the distribution of this graph???
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Please help me thank you.
Answers
4 + 4 + 7 + 7
8 + 14
22
Hope this helped!
7(2)+4(2)