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2 years ago

What is the surface area of the regular pyramid below

Mathematics

2 answers:

creativ13 [48]2 years ago

8 0

Answer:

B. $700\text{ inches}^2$ .

Step-by-step explanation:

We have been given an image of a pyramid. We are asked to find the total surface area of the given pyramid.

$\text{Surface area of pyramid}=A+\frac{1}{2}*ps$ , where,

A = Area of base of pyramid.

p = Perimeter of base,

s = Slant height,

Upon substituting our given values, we will get:

$\text{Surface area of pyramid}=14^2+\frac{1}{2}*4*14*18$

$\text{Surface area of pyramid}=196+2*14*18$

$\text{Surface area of pyramid}=196+504$

$\text{Surface area of pyramid}=700$

Therefore, the total surface area of given pyramid is 700 square inches and option B is the correct choice.

Alenkinab [10]2 years ago

5 0

$S=14\times14+4(\frac{14}{2}\times18) \\S=196+4(7\times18) \\S=196+4\times126 \\S=196+504 \\S=\boxed{700}$

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2 years ago

Read 2 more answers

Squaring both sides of an equation is irreversible. Is Cubing both sides of an equation reversible? Provide numerical examples t

nikitadnepr [17]

Answer:

<h2>Cubing both sides of an equation is reversible.</h2>

Step-by-step explanation:

Squaring both sides of an equation is irreversible, because the square power of negative number gives a positive result, but you can't have a negative base with a positive number, given that the square root of a negative number doesn't exist for real numbers.

In case of cubic powers, this action is reversible, because the cubic root of a negative number is also a negative number. For example

$\sqrt[3]{x} =-1$

We cube both sides

$(\sqrt[3]{x} )^{3} =(-1)^{3} \\x=-1$

If we want to reverse the equation to the beginning, we can do it, using a cubic root on each side

$\sqrt[3]{x}=\sqrt[3]{-1} \\\sqrt[3]{x}=-1$

There you have it, cubing both sides of an equation is reversible.

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1 year ago

Which translation maps the vertex of the graph of the function f(x) = x2 onto the vertex of the function g(x) = x2 – 10x +2?

zhuklara [117]

Answer:

<em>The translation that maps the vertex of the graph of the function f(x) = x² onto the vertex of the function g(x) = x² - 10x + 2 is </em><u>5 units to the right and 23 units down.</u>

Explanation:

<u>1) </u><u>Vertex form</u><u> of the function that represents a parabola.</u>

The general form of a quadratic equation is Ax² + Bx + C = 0, where A ≠ 0, and B and C may be any real number. And the graph of such equation is a parabola with a minimum or maximum value at its vertex.

The vertex form of the graph of such function is: A(x - h)² + k

Where, A a a stretching factor (in the case |A| > 1) or compression factor (in the case |A| < 1) factor.

<u>2) Find the vertex of the first function, f(x) = x²</u>

This is the parent function, for which, by simple inspection, you can tell h = 0 and k = 0, i.e. the vertex of f(x) = x² is (0,0).

<u>3) Find teh vertex of the second function, g(x) = x² -10x + 2</u>

The method is transforming the form of the function by completing squares:

Subtract 2 from both sides: g(x) - 2 = x² - 10x

Add the square of half of the coefficient of x (5² = 25) to both sides: g(x) - 2 + 25 = x² - 10x + 25

Simplify the left side and factor the right side: g(x) + 23 = (x - 5)²

Subtract 23 from both sides: g(x) = (x - 5)² - 23

That is the searched vertex form: g(x) = (x - 5)² - 23.

From that, using the rules of translation you can conclude immediately that the function f(x) was translated 5 units horizontally to the right and 23 units vertically downward.

Also, by comparison with the verex form A(x - h)² + k, you can conclude that the vertex of g(x) is (5, -23), and that means that the vertex (0,0) was translated 5 units to the right and 23 units downward.

5 0

2 years ago

Find the solution of 3.75x +15 = 63.75

gizmo_the_mogwai [7]

Answer:

The answer is x = 13.

Step-by-step explanation:

first, move the constant to the right and change its sign, (+15)

3.75 x = 63.75 -15

next, subtract the numbers, (65.75 -15)

3.75x = 48.75

then, divide both sides of the equation by 3.75,

final answer, x = 13

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2 years ago

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In parallelogram ABCD , diagonals AC⎯⎯⎯⎯⎯ and BD⎯⎯⎯⎯⎯ intersect at point E, AE=x2−16 , and CE=6x .

MAXImum [283]

Answer:

<h3>AC=96 units.</h3>

Step-by-step explanation:

We are given a parallelogram ABCD with diagonals AC and BD intersect at point E.

$AE=x^2-16.$ , and CE=6x .

<em>Note: The diagonals of a parallelogram intersects at mid-point.</em>

Therefore, AE = EC.

Plugging expressions for AE and EC, we get

$x^2-16=6x.$

Subtracting 6x from both sides, we get

$x^2-16-6x=6x-6x$

$x^2-6x-16=0$

Factoriong quadratic by product sum rule.

We need to find the factors of -16 that add upto -6.

-16 has factors -8 and +2 that add upto -6.

Therefore, factor of $x^2-6x-16=0$ quadratic is (x-8)(x+2)=0

Setting each factor equal to 0 and solve for x.

x-8=0 => x=8

x+2=0 => x=-2.

We can't take x=-2 as it's a negative number.

Therefore, plugging x=8 in EC =6x, we get

EC = 6(8) = 48.

<h3>AC = AE + EC = 48+48 =96 units.</h3>

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2 years ago