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3 years ago

If FG || BC, which equation is necessarily true?

Mathematics

1 answer:

vazorg [7]3 years ago

7 0

First, let's prove that triangle ABC and AFG are similar.

Line segment FG and BC are parallel to each other, that's a given.
With this information, we can state that these sides are similar to each other since you can transform BC on to FG using only rigid transformations and dilations.

Another thing is that both of these triangles share angle A, that's a given. Therefore, using the SA similar theorem, we can conclude that these triangles are similar.

Now that we know that triangle ABC and AFG are similar we may start going to the answer box.

We can eliminate the first three answer choices for having sides we cannot make full conclusions due to limited knowledge.

The only answer remaining is the fourth choice.

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ozzi

Answer:

Step-by-step explanation:

Using the rule of exponents

$(a^nb^n)^{m}$ = $a^{(mn)}$ $b^{(mn)}$ , hence

( $a^{\frac{1}{2} }$ $b^{\frac{1}{3} }$ )^( $\frac{1}{2}$ )

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4 0

4 years ago

A square was altered so that one side is increased by 9 inches in the other side is decreased by 2 inches. The area of the resul

nevsk [136]

Answer:

area of the original square = 36 in²

Step-by-step explanation:

given data

one side is increased = 9 inches

other side is decreased = 2 inches

area of the resulting rectangle = 60 in²

solution

we consider here x as the length of any one side

and

longer side of the resulting rectangle = x + 9

and

the shorter side x - 2

so that area of this rectangle is (s+9) × (s-2) = 60 in²

standard form of equation is x² + 7x - 18 = 60 .....................1

it will be

x² + 7x - 78 = 0

(s+13) (s-6) = 0

so that here x = -13

and x = 6

here we Discard x = -13 because the side length cannot be negative.

so x = 6

and area of the original square = 36 in²

5 0

3 years ago

Please help with this problem.

Serhud [2]

Answer:

Explanation:

According to the Unit Circle, <em>sin</em> π\6 is ½, so we plug this into the cosine function to get this:

cos π\6 - π\6 → cos 0 >> 1

If you are ever in need of assistance, do not hesitate to let me know by subscribing to my You-Tube channel [USERNAME: MATHEMATICS WIZARD], and as always, I am joyous to assist anyone at any time.

**I do not have Unit Circle video uploaded yet, but if I need to, just notify me in the comments or on of course, You-Tube.

*** Plus, we need to make sure that the x-value falls in between 0 and π\2, which it did, so no need to worry.

3 0

3 years ago

:) y = (3 - x)(x + 2)

valentina_108 [34]

Answer:

-x² + x + 6

Step-by-step explanation:

Hey there!

To solve this, you have to use foil...

( 3 - x ) ( x + 2 )

3 ( x + 2 ) = 3x + 6

-x ( x + 2 ) = -x² - 2x

3x + 6 - 2x - x²

-x² + x + 6

Hope this helps :)

8 0

3 years ago

The area of a rectangular patio is 2 13/16 square yards. if the patio is 7/8 of a yard, long then how wide is the patio

Lera25 [3.4K]

Answer 3 3/14

(7/8) times (45/14)= 45/16. Got 45/16 from 2 13/16

8 0

4 years ago

If FG || BC, which equation is necessarily true?​

If FG || BC, which equation is necessarily true?