MATHEMATICS HIGH SCHOOL

A rectangular paperboard measuring 26 in long and 20 in
wide has a semicircle cut out of it.

Find the area of the paperboard that remains. Use the value 3.14
for π, and do not round your answer. Be sure to include the correct unit in your answer.

Answers

Answer 1

Answer:

Answer:

The remaining area of the paperboard is 363 square inches.

Step-by-step explanation:

The length of the rectangular board = 26 inches

The width of the rectangular board = 20 inches.

Now, the area of the board = $26*20=520$ square inches

Now, a semicircle has been cut out of it.

Let is assume that the diameter of the semicircle be 20 inches.

So, radius will be = 10 inches

Area of semicircle is = $(1)/(2) \pi r{2}$

So, we get : Area = $(1)/(2)*3.14*10*10$

= 157 square inches.

Now after cutting the semi circle, the area remained = $520-157=363$ square inches.

Therefore, the remaining area of the paperboard is 363 square inches.

Answer 2

Answer:

Answer:

See below.

Step-by-step explanation:

Find the area of the rectangle using A = l*w = 26*20 = 520.

Now find the area of the semi circle using A = 1/2 πr². Since the instructions do not say the diameter of the semi circle assume it is 20 or 26.

If it is 20: r = 10 and the area is A = 1/2 π10²=50π = 157.

If it is 26: r = 13 and the area is A = 1/2π13² = (84.5)π = 265.33.

The area of the paperboard that remains will be the area of the rectangle minus the area of the semi circle.

If the diameter of the semi circle is 20 then 520 - 157 = 363.

If the diameter of the semi circle is 26 then 520 - 254.67.

Related Questions

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What multiplies to equal 50, but adds to equal 12?
If f(x) = 1 – x, which value is equivalent to |f(i)|?a. 0 b. 1 c. √2 d. √-1
How many real number solutions does the equation have?-8x^2-8x-2=01 2 no solutions or infinitely many solutions solve the equation by completing the square. round to the nearest hundredth. x^2+6x=-7 4.41,1.59 -4.41,1.59 -4.41,-1.59 4.41,-1.59 and the last one is solve the systems of equations algebraically. show all of your steps. y=x^2+2x y=3x+20

X = y - 3x + 3y = 13

What is the solution to the system of equations?

A) (1, 4)

B) (4, 1)

C) (7, 4)

D) (2.5, 5.5)

Answers

If you would like to solve the system of equations, you can do this using the following steps:

x = y - 3
x + 3y = 13 ... y - 3 + 3y = 13
___________
y - 3 + 3y = 13
4y = 13 + 3
4y = 16
y = 4

x = y - 3 = 4 - 3 = 1

(x, y) = (1, 4)

The correct result would be A) (1, 4).

You have 6 pints of glaze. It takes 7/8 of a pint to glaze a bowl and 9/16 of a pint to glaze a plate.a. how many bowls could you glaze
b. how many plates can you glaze
c. how much glaze will be left over?

Answers

Part a) how many bowls could you glaze

we know that

You have $6$ pints of glaze. It takes $7/8$ of a pint to glaze a bowl

To find the number of bowls divide $6$ by $7/8$

$(6)/((7/8))} =(48)/(7) =6.86\ bowls$

therefore

the answer part a) is equal to

$6\ bowls$

Part b) how many plates can you glaze

You have $6$ pints of glaze. It takes $9/16$ of a pint to glaze a plate

To find the number of plates divide $6$ by $9/16$

$(6)/((9/16))} =(96)/(9) =10.67\ plates$

therefore

the answer part b) is equal to

$10\ plates$

Part c) how much glaze will be left over?

In the Part a)

$6-6 *(7)/(8) =6-(42)/(8) =(48)/(8) -(42)/(8)= (3)/(4)\ pint\ of \ glaze\ left$

In the Part b)

$6-10 *(9)/(16) =6-(45)/(8) =(48)/(8) -(45)/(8)= (3)/(8)\ pint\ of \ glaze\ left$

A. 6 = 48/8, now / (7/8) 6 bowlsB. 6 = 96/16, now / (9/16) 10 platesC. After 6 bowls you would have 6/8 glaze left, After 10 plates you would have 6/16 glaze left

Can anybody help by forming and solving this equation (plz Show steps and worhing)A train has 180 passengers At the fist stop X get off and 24 get on At the second stop half get off and 40 get on There are now 134 passengers How many passengers got off at the 1st stop (X)

thks 4 any help

Answers

so a the start 180 passengers are on the train
at the first stop x get off and 24 get on or
180-x+24=204-x

at the second stop half get off and 40 get on or
204-x-([204-x]/2)+40 or
204-x-102+x/2+40
104-1/2x+40
144-1/2x
there are now 134 passengers
144-1/2x=134
subtract 134 from both sides
10-1/2x=0
add 1/2x to both sides
10=1/2x
mutliply both sides by 2/1 to make 1/2x=1/1x
20=x
20 got off at the first stop

Form an equation using information given
180 - x - 24 + 40 = 134
then simplify and solve
196 - x = 134
196 - 134 = x
62 = x
therefore 62 people got off at the first stop

Let f(x)=(4x^2-11)^3 and g(x)=4x^2-11. given that f(x)=(h^o g)(x), find h(x).

Answers

So, f(x) is a composite function. This means that g(x) is inside of h(x); in other words, you would substitute g(x) for x in h(x).

Something happened to g(x) (in the form of h(x)) to turn it into f(x). You should notice that f(x) is simply g(x) raised to the third power.

Therefore, h(x) = x^3

You can check this by working it backwards.

Start with: h(x) = x^3
Substitute: x = g(x) = 4x^2-11
Now you have: h(x) = (g(x))^3 = (4x^2-11)^3

Hope this helps!

Answer:

this is the answer

Step-by-step explanation:

A rectangular field is 80 meters wide and 125 meters long.Give the length and width of another rectangular field that has the same perimeter but a smaller area.

Answers

Perimeter of the rectangle is 2*(80+125)=410
The rectangle having the biggest area given the same perimeter is a square. So we need to go "the other way" -- find the rectangle with larger side ratio. 200 m and 5 m is a good example.

The area of the first rectangle: $80 m * 125 m =10000 m^2$
The area of the second rectangle : $200 m * 5 m = 1000 m^2$ (10 times smaller).

A new toy store is giving away 20 modelairplanes; 9 are blue, 6 are red, and 5 are
black. An airplane is selected at random and
given to a customer. If the airplane is red,
what is the probability that the next airplane,
selected at random, is also red?