MATHEMATICS MIDDLE SCHOOL

A square pyramid is made up of a base with a side length of 10 inches and faces that are triangles with a height of 12 inches. What is the surface area of the square pyramid? A. 120 square inches

B. 125 square inches

C. 240 square inches

D. 340 square inches

Answers

Answer 1

Answer:

Answer:

The correct option is D

D) 340 inch²

Step-by-step explanation:

The base of the pyramid is a square with side 10 inch

Area of square base = Length · Width = 10 · 10

Area of square base = 100 inch²

Height of triangle = 12 inches

Base of triangle = 10 inches

Area of triangle = (1/2)(Height)(Base) = (1/2)(12)(10)

Area of triangle = 60 inch²

Total number of triangles in a pyramid = 4

Total Area of 4 triangles = 4 · 60 inch²

Total Area of 4 triangles = 240 inch²

Surface Area = Area of 4 triangle + Area of the square base

Surface Area = 240 inch² + 100 inch²

Surface Area = 340 inch²

Answer 2

Answer:

Answer:

The Answer would be D

Step-by-step explanation:

This Answer would also apply to E2020 test/exam

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Can someone help me with this problem... #20

Is 2/3 greater than 7/8

Answers

For this question you should know:
7/8 is equal to 21/24
and
2/3 is equal to 16/24
so now you can see that 21/24 is greater than 16/24 so 7/8 is greater than 2/3 :)))
I hope this is helpful
have a nice day

Yes, 2/3 is greater than 7/8, because if you cross multiply 2x8=16 and then 3x7=21. The 2/3 is the 21 and the 7/8 is the 16

Simplify:-4(w + 1) + 5w
A. -9w + 4
B. -9w – 4
C. w + 4
D. w – 4

Answers

Answer:

Step-by-step explanation:

D. W - 4

Answer:

The answer is D. W-4

Step-by-step explanation:

A 30-30-120 isosceles triangle has two legs of length 4 units. If it is rotated around an axis that contains one leg, what is the volume of the solid of revolution?

Answers

Volume of the solid of revolution is 127.47 cubic units

What is Isosceles triangle?

An isosceles triangle is a triangle that has two sides of equal length.

What is Volume?

Volume is a scalar quantity expressing the amount of three-dimensional space enclosed by a closed surface.

What is Solid of revolution?

A solid of revolution is a solid figure obtained by rotating a plane curve around some straight line that lies on the same plane

Angles of the given isosceles triangle = 30-30-120 triangle

Length of the leg = 4 units

Length of the Third side c = $\sqrt{a^(2)+b^(2)-2ab cos C }$

Where a and b are the length of the leg and C is the vertex angle

Then,

Length of the third side c= $\sqrt{4^(2)+4^(2)-2(4)(4)cos120 } =4√(3)$

It is rotated around an axis that contains one leg

Draw the figure,

From the figure we can say that we have to subtract the volume of the big cone from the volume of the small cone to find the required volume of the cone

Volume of big cone = $(1)/(3)\pi r^(2)\sqrt{l^(2).r^(2) }$

where, r is the radius and l is the slant length

r = $(4√(3) )/(2)=2√(3)$ unit

l= $4√(3)$ unit

Volume of the big cone = $(1)/(3)\pi (2√(3))^(2)\sqrt{(4√(3))^(2). (2√(3))^(2) }$ =301.59 cubic unit

Volume of small cone = $(1)/(3)\pi r^(2)\sqrt{l^(2).r^(2) }$

r = $(4√(3) )/(2)=2√(3)$ unit

l= 4 unit

Volume of the small cone = $(1)/(3)\pi (2√(3))^(2)\sqrt{(4^(2) . (2√(3))^(2) }$ =174.12 cubic unit

Volume of required region = Volume of big cone - Volume of small cone

=301.59 - 174.12

=127.47 cubic unit

Hence, volume of the solid of revolution is 127.47 cubic unit

Learn more about Isosceles triangle, Volume and Solid of revolution here

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i think i know how to solve it but i would take a couple of minutes

Which compound inequality could this graph be the solution of?

Answers

Answer:

B. 2x + 3 ≥ 11 or 4x - 7 ≤ 1

Step-by-step explanation:

Given compound inequality,

In option A,

2x + 3 ≥ 11 and 4x - 7 ≤ 1

⇒ 2x ≥ 8 and 4x ≤ 8

⇒ x ≥ 4 and x ≤ 2

$\implies [4,\infty)\cap (-\infty, 2]$

$=\phi$

2x + 3 ≥ 11 and 4x - 7 ≤ 1 can not be the correct inequality,

In option B,

2x + 3 ≥ 11 or 4x - 7 ≤ 1

⇒ 2x ≥ 8 or 4x ≤ 8

⇒ x ≥ 4 or x ≤ 2

$\implies [4,\infty)\cup (-\infty, 2]$

Which is shown in the given graph,

Thus, 2x + 3 ≥ 11 or 4x - 7 ≤ 1 is the correct compound inequality,

In option C,

2x + 3 > 11 or 4x - 7 < 1

⇒ 2x > 8 or 4x < 8

⇒ x > 4 or x < 2

$\implies (4,\infty)\cup (-\infty, 2)$

So, which is not shown in the graph,

2x + 3 > 11 or 4x - 7 < 1 can not be the correct compound inequality,

In option D,

2x + 3 ≥ 11 or 4x - 7 ≥ 1

⇒ 2x ≥ 8 or 4x ≥ 8

⇒ x ≥ 4 or x ≥ 2

$\implies [4,\infty)$

Which is not shown in the graph,

2x + 3 ≥ 11 or 4x - 7 ≥ 1 is not the correct compound inequality.

B.. 4 is less than or equal to x, 2 is greater or equal to x

What is 1/6 divide by 2/6

Answers

1/6 divided by 2/6

reciprocal of 2/6 is 6/2

1/6*6/2= 1/2

$(1)/(6) / (2)/(6) \n\n (1)/(6) * (6)/(2) \n\n=\boxed{ (1)/(2) }$

Tom has read the first 40 pages of a book. He plans to read another 12 pages each day Write an equation that represents the relationship between the total number of pages, p, and the number of days he has been reading , d.