Hello.
You would write the equation like this: [tex]\frac{2}{3} c - 2[/tex]
Let me know if that was what you were looking for.
A water trough has two congruent isosceles trapezoids as ends and two congruent rectangles as sides.
The exterior surface area of the trough is ________.
The volume of the trough is _____.
If a trough is emptied until the water level is even with the midsegment of the trapezoidal ends there will be ______ cubic feet of water left in the trough.
Answer:
Part a) The exterior surface area is equal to [tex]160\ ft^{2}[/tex]
Part b) The volume is equal to [tex]240\ ft^{3}[/tex]
Part c) The volume water left in the trough will be [tex]84\ ft^{3}[/tex]
Step-by-step explanation:
Part a) we know that
The exterior surface area is equal to the area of both trapezoids plus the area of both rectangles
so
Find the area of two rectangles
[tex]A=2[12*5]=120\ ft^{2}[/tex]
Find the area of two trapezoids
[tex]A=2[\frac{1}{2}(8+2)h][/tex]
Applying Pythagoras theorem calculate the height h
[tex]h^{2}=5^{2}-3^{2}[/tex]
[tex]h^{2}=16[/tex]
[tex]h=4\ ft[/tex]
substitute the value of h to find the area
[tex]A=2[\frac{1}{2}(8+2)(4)]=40\ ft^{2}[/tex]
The exterior surface area is equal to
[tex]120\ ft^{2}+40\ ft^{2}=160\ ft^{2}[/tex]
Part b) Find the volume
We know that
The volume is equal to
[tex]V=BL[/tex]
where
B is the area of the trapezoidal face
L is the length of the trough
we have
[tex]B=20\ ft^{2}[/tex]
[tex]L=12\ ft[/tex]
substitute
[tex]V=20(12)=240\ ft^{3}[/tex]
Part c)
step 1
Calculate the area of the trapezoid for h=2 ft (the half)
the length of the midsegment of the trapezoid is (8+2)/2=5 ft
[tex]A=\frac{1}{2}(5+2)(2)=7\ ft^{2}[/tex]
step 2
Find the volume
The volume is equal to
[tex]V=BL[/tex]
where
B is the area of the trapezoidal face
L is the length of the trough
we have
[tex]B=7\ ft^{2}[/tex]
[tex]L=12\ ft[/tex]
substitute
[tex]V=7(12)=84\ ft^{3}[/tex]
Put in 39.6 <,> or = 39.61
Answer: 39.6<39.61
Step-by-step explanation: 39.6 is equal to 39.60 and 60 is greater than 1.
Answer:
39.6 is less than 39.61
Step-by-step explanation:
How Would I Find The Answer ?
Answer: B. 34°
Step-by-step explanation:
∠RQS + ∠SQT = ∠RQT
[tex]\bigg(\dfrac{1}{2}x+4\bigg)+\bigg(\dfrac{3}{4}x-6\bigg)=2x-47\\\\\\.\qquad\qquad\qquad\dfrac{5}{4}x-2=2x-47\\\\\\.\qquad\qquad\qquad\quad -2=\dfrac{3}{4}x-47\\\\\\.\qquad\qquad\qquad\qquad 45=\dfrac{3}{4}x\\\\\\.\qquad\qquad\qquad\qquad 180=3x\\\\\\.\qquad\qquad\qquad\qquad 60=x[/tex]
[tex]\angle RQS=\dfrac{1}{2}x+4\\\\.\qquad=\dfrac{1}{2}(60)+4\\\\.\qquad=30+4\\\\.\qquad=34[/tex]
Examine the linear equation. 8x – y = –6 Choose the slope-intercept form of the equivalent equation:
Step-by-step explanation:
The slope-intercept form can be obtained by solving for y.
8x-y=-6
-8x
-y=-8x-6
divide by negative 1 to turn y positive.
y=8x+6
Answer:
y=8x+6
Step-by-step explanation:
just took the prac. on edge
may somebody help me please
Plz help me!!!!!!!!!!
Answer: [tex]b)\quad \dfrac{4x^6z^4}{9y^4}[/tex]
Step-by-step explanation:
[tex].\quad \dfrac{16x^{4}y^{-3}z^{4}}{36x^{-2}y^{1}z^0}\\\\\\=\dfrac{4(4)\cdot x^{4+2}\cdot y^{-3+3}\cdot z^{4}}{4(9)\cdot x^{-2+2}\cdot y^{1+3}\cdot 1}\\\\\\=\dfrac{4x^6z^4}{9y^4}[/tex]
Write y = x + 7 in standard form using integers.
3x – 2y = 21
–2x – 3y = 21
–2x + 3y = 7
–2x + 3y = 21
Answer:
[tex]-2x+3y=21[/tex]
Step-by-step explanation:
The equation was given to us in slope-intercept form.
Thus;
[tex]y=\frac{2}{3}x+7[/tex]
We multiply each term by 3 to obtain;
[tex]3y=2x+21[/tex]
We add [tex]-2x[/tex] to both sides to obtain;
[tex]-2x+3y=21[/tex]
This equation is in the form;
[tex]ax+by=c[/tex] (standard form).
The correct choice is D.
Answer:
-2x+3y = 21
Step-by-step explanation:
We have given a equation in slope-intercept form .
y = 2/3x+7
We have to rewrite above equation in standard form.
The standard form of equation is :
Ax+By = C
Multiplying by 3 to both sides of above equation, we have
3y = 3(2/3x+7)
3y = 2x+21
Adding -2x to both sides of above equation, we have
-2x+3y = -2x+2x+21
-2x+3y = 21 which is standard form of given equation.
Use the graphing method to solve the system of linear equations:
y = -x + 3 and y = x - 1
A) (-1,2)
B) (0,3)
C) (1,0)
D) (2,1)
(AWNSWER GETS 80 POINTS)
Answer:
the asnwer will be 2,1
Step-by-step explanation:
The solution of the equations is (2,1)
What is graphing method?Finding the point of intersection of equations by plotting on the graph paper is called solving by graphing method.
How to solve the given equations?In the attached graph below,
The red line represents the equation y = -x + 3 The blue line represents the equation y = x - 1The point of intersection is clearly visible which is (2,1). This is the solution of the equations.The solution of the equations is (2,1)
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4400 dollars is placed in an account with an annual interest rate of 8.25%.how much will be in the account after 22 years, to the nearest cent?
Final answer:
To find out how much will be in the account after 22 years with an annual interest rate of 8.25%, the compound interest formula [tex]A = P(1 + r/n)^{nt}[/tex] is used, resulting in approximately $21739.63.
Explanation:
To calculate how much money will be in the account after 22 years with an annual interest rate of 8.25%, we will use the compound interest formula:
[tex]A = P(1 + r/n)^{nt}[/tex]
Where:
A is the amount of money accumulated after n years, including interest.
P is the principal amount (the initial amount of money).
r is the annual interest rate (decimal).
n is the number of times that interest is compounded per year.
t is the time the money is invested for, in years.
In this case:
P = $4400
r = 8.25% or 0.0825
n = 1 (since it's compounded annually)
t = 22 years
We plug these values into the compound interest formula:
[tex]A = 4400(1 + 0.0825/1)^{1*22}[/tex]
After calculating:
[tex]A = 4400(1 + 0.0825)^{22}[/tex]
[tex]A = 4400(1.0825)^{22}[/tex]
A comes out to approximately $21739.63, which is the total amount in the account to the nearest cent after 22 years.
Use formula p=2l+2w find the perimeter of a rectangle with a length 8.3 ft and width of 15.8 ft
Answer:
p = 48.2
Step-by-step explanation:
p = 2L + 2w
p = 2(8.3) + 2(15.8)
p = 16.6 + 31.6
p = 48.2
Answer:
P = 48.2 ft
Step-by-step explanation:
P =2l+2w
Given: l = 8.3 ft and w = 15.8 ft
Plug in
P =2(8.3) + 2(15.8)
P = 16.6 + 31.6
P = 48.2 ft
add 5 to me. Then divide by 7. If you add 12 and then subtract 7, you get 10. What number am I?
30 is the answer :))))
7..........:.........
Answer:
option B
4 a^4 /b
Step-by-step explanation:
Given in the question an expression
√(16 a^8 b^-2)
This expression can also be written as
√16 . √a^8 . √b^-2
Now as we know that
√16 = √4² = 4
√a^8 = √(a². a² . a² . a²) = √a².√ a².√ a².√ a² = a . a . a . a = a^4
√b^-2 = √1/b² = √1 ÷ √b² = 1 ÷ b = 1/b
Rearranging them
4 a^4 1/b = 4 a^4/b
Simplified form of √(16 a^8 b^-2) is 4 a^4/b
The simplified form of √(16 a^8 b^-2) is indeed 4a^4/b, which is equivalent to the original expression. therefore, option b. 4a^4/b is correct.
The given expression, √(16 a^8 b^-2), can be simplified as follows:
√(16 a^8 b^-2) = √16 * √(a^8) * √(b^-2)
Breaking it down:
√16 = √(4^2) = 4
√(a^8) = √(a^4 * a^4) = √(a^4) * √(a^4) = a^4 * a^4 = a^8
√(b^-2) = √(1/b^2) = 1/b
Now, rearranging these results:
4 * a^8 * (1/b) = 4a^8/b
So, the simplified form of √(16 a^8 b^-2) is indeed 4a^4/b, which is equivalent to the original expression. This simplified form retains the same meaning as the original expression.
for such more question on simplified form
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Can someone please help.
The answer is b: 15 m, 20m, 25m
X^2 +x -4=O solve using the Quadratic formula. First what are the valubes of a,b,c?
A=1 B=1 C=-4 , you look at the numbers in order ! X is always going to be a 1.
A right pyramid has a rectangular base that is 3 inches by 5 inches if the height of the pyramid is 8 inches, what is it’s volume ? HELP FAST PLEASE
Answer:
A) 40 in.^3
Step-by-step explanation:
volume = (1/3)(LWh)
volume = (1/3)(5 in.)(3 in.)(8 in.)
volume = 40 in.^3
Answer:
40.^3
Step-by-step explanation:
took the test
Is 2.924017738 a rational number
So Not A rational Number
I think :)
Good Luck:)))
Please help, I need these done today TT
1) Hilda is putting new tile in an area of her home. Part of the space is rectangular with a length of 10 feet and a width of 6 feet, and part of the space is triangular with a base of 4 feet and a height of 2 feet.
How many square feet of tile will Hilda need to cover the space?
2) Francine bought a TV that is 31 inches tall and 57 inches wide. She is going to mount it on the wall in her living room. The wall is 8 feet wide and 9 feet tall.
How many square inches of the wall will not be covered by the TV once it is mounted?
Answer:
Hilda needs 64 ft² of tile
8601 in² will be uncovered post mounting
Step-by-step explanation:
Ar=10•6=60 ft²
At=[4•2]/2=8/2=4 ft²
total area=Ar+At=60+4=64ft²
......
Atv=31•57=1767 in²
Aw=(12•8)•(9•12)=10368 in²
Au=Aw-Atv=10368-1767=8601 in²
Hilda will need 64 square feet of tile to cover the space. Francine will have 8601 square inches of the wall not covered by the TV once it is mounted.
To determine how many square feet of tile Hilda will need, let's calculate the area of both the rectangular and triangular parts separately and then sum them up. The area of the rectangle can be found by multiplying the length and the width, so we have:
10 feet * 6 feet = 60 square feet.
Next, we calculate the triangular area using the formula for the area of a triangle (A = base * height / 2), giving us:
4 feet * 2 feet / 2 = 4 square feet.
Adding both areas gives us a total of:
60 square feet + 4 square feet = 64 square feet needed for tiling.
For Francine's TV and the uncovered wall area, we first convert the wall measurements to inches (1 foot = 12 inches):
8 feet = 96 inches wide
9 feet = 108 inches tall
Then we calculate the area of the wall and subtract the TV's area:
Wall area: 96 inches * 108 inches = 10368 square inches
TV area: 31 inches * 57 inches = 1767 square inches
Uncovered wall area:
10368 square inches - 1767 square inches = 8601 square inches.
A pitcher of lemonade was 7/8 full. Since then, they have sold 1/2 of a pitcher of lemonade. What fraction of a pitcher do they have left?
Answer:
3/8
Step-by-step explanation:
another way of writing 1/2 is 4/8, so now it should be easy. if you have 7/8 and sell 4/8 that leaves 3/8
Answer: 3/8
Step-by-step explanation:
75% of b is 12?????????
Answer:
b=16
Step-by-step explanation:
12*100=1200
1200/75
------------------
16
Check
16*0.75=12
Which diagram shows the percent equivalent to 3/5
Answer:
The correct one would be A
Step-by-step explanation:
Because 6/10 is equivalent to 3/5
The answer is the first one, or A.
The revenue from selling xshirts is r(x) 15x The cost of buying x shirts is c(x) 7x + 20. The profit from selling xshirts is px) x) (x) What is p(x)?
Final answer:
The profit function p(x) for selling x shirts is p(x) = 8x - 20, which is found by subtracting the cost function c(x) from the revenue function r(x).
Explanation:
Profit Function
To find the profit function p(x), we subtract the cost function c(x) from the revenue function r(x). Given that r(x) = 15x and c(x) = 7x + 20, the profit function is calculated as follows:
p(x) = r(x) - c(x)
p(x) = 15x - (7x + 20)
Simplifying the equation, we combine like terms:
p(x) = 15x - 7x - 20
p(x) = 8x - 20
Thus, the profit from selling x shirts is p(x) = 8x - 20.
Plz help me!!!!!!!!!
[tex]\sqrt[3]{x^2y^2} = (x^2y^2)^{\frac 1 3} = x^{\frac 2 3}y ^{\frac 2 3}[/tex]
Answer: [tex]\bold{x^{\frac{2}{3}}y^{\frac{2}{3}}}[/tex]
Step-by-step explanation:
[tex]\sqrt[3]{x^2y^2}=\sqrt[3]{(xy)^2}=(xy)^{\frac{2}{3}}=x^{\frac{2}{3}}y^{\frac{2}{3}}[/tex]
rewrite 3 x 6/8 as the product of a unit fraction and a whole number
3×6/8 reduce is 3× 3/4= 3/1×3/4=9/4 or 2 1/4
Final answer:
To rewrite 3 x 6/8 as the product of a unit fraction and a whole number, simplify 6/8 to 3/4, and then express 3/4 in terms of the unit fraction 1/4 multiplied by 9, resulting in the expression 9 x 1/4.
Explanation:
To rewrite 3 x 6/8 as the product of a unit fraction and a whole number, we first look at the fraction 6/8. The fraction can be simplified by dividing both the numerator and the denominator by the common factor which is 2. This gives us the simplified fraction of 3/4. Now, a unit fraction is a fraction where the numerator is 1. To turn 3/4 into a unit fraction, we can multiply it by the whole number 3, because 3 x 3/4 equals 9/4. However, 9/4 is not a unit fraction. Therefore, to represent this expression as a product of a unit fraction and a whole number, we see that each 3/4 in the total of 3 times 3/4 can be expressed as 1 times the whole number 3, making the unit fraction 1/4. The correct expression would then be 9 x 1/4.
Please help me with this and thank you
6/(1/3)= 18
6(3)=18
the answer would be c
Answer:
option C
18 Flowerpots
Step-by-step explanation:
6 ÷ 1/3
6 × 3/1 = 18/1 = 18
How many liters equal 1052cm3?
Answer:
[tex]\large\boxed{1,052\ cm^3=1.052\ liters}[/tex]
Step-by-step explanation:
[tex]1Liter=1dm^3\\\\1dm=10cm\to1dm^3=(10cm)^3=1,000cm^3\\\\1052\ cm^3=\dfrac{1,052}{1,000}dm^3=1.052\ dm^3=1.052\ Liters[/tex]
HELP AND PLZZZ EXPLAIN!
18 + 3 |6 - 25| - 11
WHAT WOULD BE THE AMSWER?
Simplify 6 - 25 to -19
18 + 3| -19 | - 11
Simplify | -19 | to 19
18 + 3 × 19 - 11
Simplify 3 × 19 to 57
18 + 57 - 11
Simplify
= 64
if a clothing sale marks items 85% off, what is the numerator of the fraction which represents this discount (assume the denominator is 100)?
Answer:
85/100
Step-by-step explanation:
Find the midpoint between −18 and 52.
Which equation best models the relationship between x and y
Answer:
y = x + x or y+mx+b
Step-by-step explanation:
The first shows the relation in many different problems. But the second is used more for graphs of proportional value. You can use both in either case. But the y=x+x you would substitute the x with real numbers according to the problem.
what is the name of line segment an on the circle below
Answer:
C
Step-by-step explanation:
Let's break down the definitions.
diameter = a line across the circle that crosses the center
radius = a line from the center of the circle to any edge
chord = a line with both endpoints on the edge of the circle
arc = the outside part of the circle
Since this line has both endpoints on the edge of the circle and does not cross the center, the line is a chord.