Select the answer choices that show two fractions that are equal. (Select two)..

Mathematics

1 answer:

Kruka [31]3 years ago

5 0

Problem 1

Answers: Choice A, choice D

The formula you use is

a & c/d = (a*d+c)/d

To convert from mixed number form to improper fraction form.

So,

6 & 2/3 = (6*3+2)/3 = (18+2)/3 = 20/3

And also,

8 & 1/5 = (8*5+1)/5 = (40+1)/5 = 41/5

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Problem 2

Answer: Reflection

Think of how mirrors cause a reflection and this should help you remember the term better. If we reflect point A over some line L, to get point A', then the distance from A to L is the same from A' to L also.

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Insert a rational number and an irrational number between -2/5 and 1/2

qwelly [4]

Answer:

Step-by-step explanation:

if you can pick any numbers you want then:

rational could be: 0.25 or 1/4

irrational could be: 2/7

6 0

3 years ago

a regular rectangular pyramid has a base and lateral faces that are congruent equilateral triangles. it has a lateral surface ar

Margarita [4]

A pyramid is regular if its base is a regular polygon, that is a polygon with equal sides and angle measures.
(and the lateral edges of the pyramid are also equal to each other)

Thus a regular rectangular pyramid is a regular pyramid with a square base, of side length say x.

The lateral faces are equilateral triangles of side length x.

The lateral surface area is 72 cm^2, thus the area of one face is 72/4=36/2=18 cm^2.

now we need to find x. Consider the picture attached, showing one lateral face of the pyramid.

by the Pythagorean theorem:

$h= \sqrt{ x^{2} - (x/2)^{2}}= \sqrt{ x^{2}- x^{2}/4}= \sqrt{3x^2/4}= \frac{ \sqrt{3} }{2}x$

thus,

$Area_{triangle}= \frac{1}{2}\cdot base \cdot height\\\\18= \frac{1}{2}\cdot x \cdot \frac{ \sqrt{3} }{2}x\\\\ \frac{18 \cdot 4}{ \sqrt{3}}=x^2$

thus:

$x^2 =\frac{18 \cdot 4}{ \sqrt{3}}= \frac{18 \cdot 4 \cdot\ \sqrt{3} }{3}=24 \sqrt{3}$ (cm^2)

but $x^{2}$ is exactly the base area, since the base is a square of sidelength = x cm.

So, the total surface area = base area + lateral area = $24 \sqrt{3}+72$ cm^2

Answer: $24 \sqrt{3}+72$ cm^2