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Yuri [45]
2 years ago
15

The volume of a square pyramid is 50 inches. The length of the base of the pyramid is 5 inches. What is the height of the pyrami

d?
Mathematics
1 answer:
fredd [130]2 years ago
4 0

Answer: the height of the pyramid is 6 inch.

Step-by-step explanation:

V=50 inch³    a=5 inch     H=?

Formula of  volume square pyramid is:

                    \boxed {V=\frac{1}{3}*S_{base}*H },        

where:   Sbase - pyramid base area;

              H -   pyramid height.

Hence,

             H=\frac{3*V}{S_{base}}\\.

Since the pyramid is square, its base is a square.        ⇒

S_{base}=a^2\\S_{base}=(5\ inch)^2\\S_{base}=25\  inch^2\\H=\frac{3*50}{25} \\H=3*2\\H=6\ (inch).

Good luck!    

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Answer:

y+4 = -\frac{1}{3} (x-1)

Step-by-step explanation:

1) First, find the slope of the line. Use the slope formula m = \frac{y_2-y_1}{x_2-x_1} to find the slope. Substitute the x and y values of the given points into the formula and solve:

m = \frac{(-5)-(-4)}{(4)-(1)} \\m = \frac{-5+4}{4-1} \\m = \frac{-1}{3}

So, the slope is -\frac{1}{3}.

2) Use the point-slope formula y-y_1  = m (x-x_1) to write the equation of the line in point-slope form. Substitute values for m, x_1, and y_1 into the formula.

Since m represents the slope, substitute -\frac{1}{3}  in its place. Since x_1 and y_1 represent the x and y values of one point on the line, choose any one of the given points (it doesn't matter which one) and substitute the x and y values of it into the formula. (I chose (1,-4), as seen below). This gives the equation of the line in point-slope form.    

y-(-4) = -\frac{1}{3} (x-(1))\\y+4 = -\frac{1}{3} (x-1)

5 0
2 years ago
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Answer:

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  • The next and every step are below.

Explanation:

1. -3=-2x^2+2x    : Given (addition property / add - 3 to both sides)

2. -3 = - 2(x^2-x)    : Given (commom factor - 2)

3. -3-1/2=-2(x^2-x+1/4)

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Since, the terms inside the parentthesis are multiplied by - 2, you have to add - 2 (1/4) = - 1/2 to the left side of the equation.

4. Now, you have that the trinomial x² - x + 1/4 is a square perfect trinomial which is factored as (x - 1/2)² and get the expression:

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5. Divide both sides by - 2 to get the next expression:

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6. The last step is to extract squere root from both sides of the equality:

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The price of the discounted ticket is 1 - 75% = 25% = 0.25 times the normal price:

  discounted price = 0.25 × $118.00 = $29.50

The sale price is $29.50.

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