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Y_Kistochka [10]

2 years ago

8

A triangular pyramid has a surface area of 174 square feet. It is made up of equilateral triangles with side lengths of 10 feet.

What is the slant height?

1 answer:

emmainna [20.7K]2 years ago

6 0

Answer:

Slant height = 7.07 ft to nearest hundredth.

Step-by-step explanation:

The slant height = height of one of the triangular sides

Using Pythagoras:

S^2 = 1/2 * 10^2 + 10^2 = 50 ft.

S = √50 = 7.071

You might be interested in

Is 5 5/6 + 1 3/4=5 1/12 reasonable

ira [324]

Answer:

No, it is unreasonable.

Step-by-step explanation:

5/5/6+1/3/4=35/6+7/4

=70/12+21/12

=91/12

=7 7/12

4 0

2 years ago

The symphonic choir and the jazz choir are recording songs for an album. The album can be no more than 72 minutes long. The jazz

zimovet [89]

Answer:

The symphonic choir can record a maximum of 14 songs.

Step-by-step explanation:

We know that the album cannot be more than 72 minutes long, and the jazz choir records a total of $7 (3min) = 21$ song minutes.

If we call $c$ the number of songs the symphonic choir records , and each song is 3.5 minute long, then the song minutes for the symphonic choir are $3.5c$ ; therefore, we have the inequality

$3.5c+21\leq 72$ <em> (this says the song minutes for jazz choir plus song minutes for symphonic choice cannot exceed 72 minutes )</em>

We solve this inequality by subtracting 21 from both sides and then dividing by 3.5:

$3.5c\leq 51$

$c\leq \frac{51}{3.5}$

$c\leq 14.47$

The maximum integer value $c$ can take is 14; therefore, the maximum number of songs the symphonic choir can record is 14 songs.

3 0

3 years ago

A box in the shape of a rectangular prism has a dimension of 30 meters x 27 meters x 28 meters what is the surface area of the b

erastovalidia [21]

Your answer would be <span> 4812 m².</span>

5 0

2 years ago

Sin theta+costheta/sintheta -costheta+sintheta-costheta/sintheta+costheta=2sec2/tan2 theta -1

sleet_krkn [62]

$\dfrac{sin\theta + cos\theta}{sin\theta-cos\theta}+\dfrac{sin\theta-cos\theta}{sin\theta+cos\theta}=\dfrac{2sec^2\theta}{tan^2\theta-1}$

From Left side:

$\dfrac{sin\theta + cos\theta}{sin\theta-cos\theta}\bigg(\dfrac{sin\theta+cos\theta}{sin\theta+cos\theta}\bigg)+\dfrac{sin\theta-cos\theta}{sin\theta+cos\theta}\bigg(\dfrac{sin\theta-cos\theta}{sin\theta-cos\theta}\bigg)$

$\dfrac{sin^2\theta+2cos\thetasin\theta+cos^2\theta}{sin^2\theta-cos^2\theta}+\dfrac{sin^2\theta-2cos\thetasin\theta+cos^2\theta}{sin^2\theta-cos^2\theta}$

NOTE: sin²θ + cos²θ = 1

$\dfrac{1 + 2cos\theta sin\theta}{sin^2\theta-cos^2\theta}+\dfrac{1-2cos\theta sin\theta}{sin^2\theta-cos^2\theta}$

$\dfrac{1 + 2cos\theta sin\theta+1-2cos\theta sin\theta}{sin^2\theta-cos^2\theta}$

$\dfrac{2}{sin^2\theta-cos^2\theta}$

$\dfrac{2}{\bigg(sin^2\theta-cos^2\theta\bigg)\bigg(\dfrac{cos^2\theta}{cos^2\theta}\bigg)}$

$\dfrac{2sec^2\theta}{\dfrac{sin^2\theta}{cos^2\theta}-\dfrac{cos^2\theta}{cos^2\theta}}$

$\dfrac{2sec^2\theta}{tan^2\theta-1}$

Left side = Right side <em>so proof is complete</em>

8 0

3 years ago

Read 2 more answers

Given that (5,-8) is on the graph of f(x), find

My name is Ann [436]

Answer:

The corresponding point for the function f(x + 2) is (3 , -8)

Step-by-step explanation:

* Lets talk about the transformation

- If the function f(x) translated horizontally to the right by h units,

then the new function g(x) = f(x - h)

- If the function f(x) translated horizontally to the left by h units,

then the new function g(x) = f(x + h)

* Lets solve the problem

- There is a graph of f(x)

- Point (5 , -8) lies on the graph of f(x)

- The graph of f(x) change to f(x + 2)

∵ f(x) ⇒ f(x + 2)

∵ If the function f(x) translated horizontally to the left by h units,

then the new function g(x) = f(x + h)

∴ f(x) translated horizontally 2 units to the left

∴ Any point on the graph its x-coordinate translated 2 units

to the left

∴ The x-coordinate of any point on the graph is subtracted by 2

∵ Point (5 , -8) lies on the graph

∴ Its corresponding point is (5 - 2 , -8) = (3 , -8)

* The corresponding point for the function f(x + 2) is (3 , -8)

7 0

3 years ago