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Maurinko [17]
3 years ago
14

I need help on this I don’t understand how to do this

Mathematics
1 answer:
stepan [7]3 years ago
8 0

Answer:

Hi there!

The correct answer to this question is: The <u>side length</u> of the square base is 18 inches and the <u>height</u> of the pyramid is 9 inches.

Step-by-step explanation:

The equation to find the volume of a square pyramid is V= (b^2)(h/3)

we are given the volume to be 972 inches cubed, additionally we know that the base of the square is x inches, the height is x/2

then we plug in and we get 972= (x^2)(x/2/3)

then you simplify to 972 = x^3 / 6 then you multiply six on both sides and  you get x^3 = 5832

cube root on both sides and you get x = 18 that means the base is 18 inches and the height is x/2 then you plug 18 in and you get the height to be 9 inches.

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3 years ago
Read 2 more answers
A radio station signal covers a circular area out from the signal tower. It gets weaker the farther away your are. The local sta
valentinak56 [21]

Answer:

1. We would hear better at Dunkin's since its distance from the radio station is the shortest.

2. McDonald's is out of range of the radio station since its distance is greater than the range of the radio station.

Step-by-step explanation:

1) Will we hear it better at Zaxby's (2,-4), McDonalds (4, -4), or Dunkin' (-3,3). Show work to support your decision and explain your reasoning.

We need to find the distance of each point from the tower.

The shorter the distance from the radio station the better the signal.

The distance between two points (x₁, y₁) and (x₂, y₂) is given by d = √[(x₂ - x₁)² + (y₂ - y₁)²].

With (x₁, y₁) = (0, 0) the location of local station WDHS

For Zaxby's distance located at (2, -4) = (x₂, y₂)

So, d₁ = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(2 - 0)² + (-4 - 0)²]

= √[(2)² + (-4)²]

= √[4 + 16]

= √20

= √(5 × 4)

= √5 × √4

= 2√5

= 4.47 miles

For McDonald's distance located at (4, -4) = (x₂, y₂)

So, d₂ = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(4 - 0)² + (-4 - 0)²]

= √[(4)² + (-4)²]

= √[16 + 16]

= √32

= √(16 × 2)

= √16 × √2

= 4√2

= 5.66 miles

For Dunkin's distance located at (-3, 3) = (x₂, y₂)

So, d₃ = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(-3 - 0)² + (-3 - 0)²]

= √[(-3)² + (-3)²]

= √[9 + 9]

= √18

= √(9 × 2)

= √9 × √2

= 3√2

= 4.24 miles

<u>Since Dunkin's distance, d₃ = 4.24 is the least distance from the radio station and is within range of 5 miles, we would hear better at Dunkin's.</u>

2) Are any of these location outside the range of the radio station? If so, which one(s). Defend your decision mathematically.

The radio station is outside of range if its distance is greater than 5 miles. That is, d > 5 miles.

So, we calculate the distance of each point from the radio station.

With (x₁, y₁) = (0, 0) the location of local station WDHS

For Zaxby's distance located at (2, -4) = (x₂, y₂)

So, d₁ = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(2 - 0)² + (-4 - 0)²]

= √[(2)² + (-4)²]

= √[4 + 16]

= √20

= √(5 × 4)

= √5 × √4

= 2√5

= 4.47 miles

For McDonald's distance located at (4, -4) = (x₂, y₂)

So, d₂ = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(4 - 0)² + (-4 - 0)²]

= √[(4)² + (-4)²]

= √[16 + 16]

= √32

= √(16 × 2)

= √16 × √2

= 4√2

= 5.66 miles

For Dunkin's distance located at (-3, 3) = (x₂, y₂)

So, d₃ = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(-3 - 0)² + (-3 - 0)²]

= √[(-3)² + (-3)²]

= √[9 + 9]

= √18

= √(9 × 2)

= √9 × √2

= 3√2

= 4.24 miles

<u>So, for each of the distances calculated above, only McDonald's distance, d₂ = 5.66 miles > 5 miles. </u>

<u>So, McDonald's is out of range of the radio station.</u>

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What additional information will allow you to prove the triangles congruent by the HL Theorem?
marissa [1.9K]

Answer:

The correct option is 3.

Step-by-step explanation:

The HL theorem states that 'if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.'

From the given figure it is noticed that triangle ABC and triangle EDC. In triangle  ABC and triangle EDC, hypotenuses of triangles are AB and DE respectively.

To use HL hypotenuse and one leg of triangles must be equal.

AB=DE                             (hypotenuse)

AC=DC                             (leg)

BC=EC                              (leg)

Therefore the additional information  AC=DC  will allow you to prove the triangles congruent by the HL Theorem. Option 3 is correct.

8 0
3 years ago
Read 2 more answers
The net of a square pyramid is shown: What is the surface area of the figure? (A)0.7625 square inch
aniked [119]

Answer:

C. 0.6625 square inches

Step-by-step explanation:

To get the area of the net of a square pyramid;

We need to find the are of the square base and the area of the four triangles;

Area of the square base = s²

                                         = (0.25 in)²

                                         = 0.0625 in²

Area of one triangle = 0.5 × b × h

                                 = 0.5 × 0.25 in × 1.2 in

                                 = 0.15 in²

Area of the four triangles = 0.15 in² × 4

                                          = 0.6 in²

Therefore;

Area of the net square pyramid = 0.0625 in² + 0.6 in²

                                                     = 0.6625 square inches

6 0
3 years ago
To find the difference of 7- 3 5/12 how do yu rename the 7
Alchen [17]
Since we need them to be fractions, 7 could be 7/1. but now we need a common denominator, so lets find one!

7*12 = 84
1*12 = 12

Answer: 84/12


6 0
3 years ago
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