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madam [21]
3 years ago
14

Suppose you are covering your desk (shape below) with paper and want to know how many square inches of paper you need.

Mathematics
1 answer:
zavuch27 [327]3 years ago
3 0

Answer:

a. Divide the figure into two rectangles, find the area of each rectangle and add them (See the picture attached).

b. 279\ in^2

c. The total area of the figure is 279 square inches.

Step-by-step explanation:

a. Divide the figure into two rectangles (See the picture attached), then find the area of each rectangle and finally, add the areas calculated in order to get the total area of the given figure,

b. The area of a rectangle can be found using this formula:

A=lw

Where "l" is lenght  and "w" is the width.

 Area of Rectangle A

You can identify that:

l_A=19\ in\\\\w_A=11\ in

Then, its area is:

A_A=(19\ in)(11\ in)=209\ in^2

Area of Rectangle B

You can identify that:

l_B=10\ in\\\\w_B=18\ in-11\ in=7\ in

Then, its area is:

A_B=(10\ in)(7\ in)=70\ in^2

Total area

A_T=209\ in^2+70\ in^2=279\ in^2

c. The total area of the figure is 279 square inches.

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wlad13 [49]

Answer:

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8 0
3 years ago
Please solve with explanation I’ve been asking all day (this is not a multiple choice question)
Anastaziya [24]

Answer:

a) SA = 522.9~cm^2

b) V_{cone} = 670.2~cm^3

c) V_{empty} = 1340.4~cm^3

Step-by-step explanation:

a)

For a cone,

SA = \pi r (L + r)

where L = slant height

L = \sqrt{r^2 + h^2}

We have r = 8 cm; h = 10 cm

L = \sqrt{(8~cm)^2 + (10~cm)^2}

L = \sqrt{164~cm^2}

SA = (\pi)(8~cm)(\sqrt{164~cm^2} + 8~cm)

SA = 522.9~cm^2

b)

V_{cone} = \dfrac{1}{3}\pi r^2 h

V_{cone} = \dfrac{1}{3}(\pi)(8~cm)^2(10~cm)

V_{cone} = 670.2~cm^3

c)

V_{cylinder} = \pi r^2 h

empty space = volume of cylinder - volume of cone

V_{empty} = V_{cylinder} - V_{cone}

V_{empty} = \pi r^2 h - \dfrac{1}{3}\pi r^2 h

V_{empty} = (\pi)(8~cm)^2(10~cm) - \dfrac{1}{3}(\pi)(8~cm)^2(10~cm)

V_{empty} = 1340.4~cm^3

3 0
3 years ago
Triangles O N M and S R Q are shown. Angles O N M and S R Q are congruent. The length of side N M is 10 and the length of side S
valina [46]

Answer:

Option C.

Step-by-step explanation:

In △ONM and △SRQ,

\angle ONM\cong \angle SRQ

NM=10

SR=20

NO=8

QR=x

We need to find the value of x that will make △ONM similar to △SRQ by the SAS similarity theorem.

According to SAS similarity theorem, two triangle are similar if two corresponding sides in both triangles are proportional and the included angle in both are congruent.

It is given that \angle ONM\cong \angle SRQ. So, both triangles are similar by SAS if

\dfrac{NO}{NM}=\dfrac{SR}{QR}

Substitute the given values.

\dfrac{8}{10}=\dfrac{20}{x}

8\times x=20\times 10

8x=200

Divide both sides by 8.

x=\dfrac{200}{8}

x=25

Therefore, the correct option is C.

7 0
3 years ago
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What is the distance between 5,4 and -1,1
spayn [35]

Answer:

3\sqrt{5}

Step-by-step explanation:

Calculate the distance d using the distance formula

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with (x₁, y₁ ) = (5, 4) and (x₂, y₂ ) = (- 1, 1)

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   = \sqrt{(-6)^2+(-3)^2}

   = \sqrt{36+9}

   = \sqrt{45}

   = 3\sqrt{5} ← exact value

   ≈ 6.71 ( to 2 dec. places )

8 0
3 years ago
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