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The length of each side of an equilateral triangle is increased by 20%, resulting in triangle ABC. If the length of each side of

kompoz [17]

Answer: Area of ΔABC is 2.25x the area of ΔDEF.

Step-by-step explanation: Because equilateral triangle has 3 equal sides, area is calculated as

$A=\frac{\sqrt{3} }{4} a^{2}$

with a as side of the triangle.

Triangle ABC is 20% bigger than the original, which means its side (a₁) measures, compared to the original:

a₁ = 1.2a

Then, its area is

$A_{1}=\frac{\sqrt{3} }{4}(1.2a)^{2}$

$A_{1}=\frac{\sqrt{3} }{4}1.44a^{2}$

Triangle DEF is 20% smaller than the original, which means its side is:

a₂ = 0.8a

So, area is

$A_{2}=\frac{\sqrt{3} }{4} (0.8a)^{2}$

$A_{2}=\frac{\sqrt{3} }{4} 0.64a^{2}$

Now, comparing areas:

$\frac{A_{1}}{A_{2}}= (\frac{\sqrt{3}.1.44a^{2} }{4})(\frac{4}{\sqrt{3}.0.64a^{2} } )$

$\frac{A_{1}}{A_{2}} =$ 2.25

The area of ΔABC is 2.25x greater than the area of ΔDEF.

7 0

2 years ago

Could I get some help? QUESTION: This table shows the profit for a company (in millions of dollars) in different years.

Pani-rosa [81]

Answer:

17 million

Step-by-step explanation:

-0.34( $8^{2}$ ) + 4.43(8) + 3.46

-21.76 + 35.44 + 3.46

13.68 + 3.46

17.14

Answer: C 17 million

Have an amazing day!

PLEASE RATE!

7 0

2 years ago

Which of the following rational functions is graphed below?

IrinaVladis [17]

Answer:

Option (D)

Step-by-step explanation:

The given graph represents a rational function having,

1). Vertical asymptote → x = 2

2). Horizontal asymptote → y = 0

Parent function representing the rational function will be in the form of,

F(x) = $\frac{1}{x^{2} }$

Since, vertical asymptote of the function is x = 2, denominator of the function will be in the form of (x - 2)².

Since, horizontal asymptote of the function is y = 0, highest exponent term in the numerator will be 0.

Therefore, numerator of the fraction will be x⁰.

The rational function given in the graph will be,

F(x) = $\frac{x^{0}}{(x-2)^2}$

F(x) = $\frac{1}{(x-2)^2}$

Option (D) will be the answer.

6 0

3 years ago

PLEASE HELP!!! ILL MARK A HIGH POINT COUNT, GIVE BRAINLIEST, FIVE STARS, AND GIVE THANKS TO WHOEVER ANSWERS CORRECTLY!!!!

Westkost [7]

Each letter of the alphabet is worth two times as much as the one before it, implying that the value of each letter rises in mathematical progression. The formula for finding the nth term of an arithmetic progression would be used. I am written as

a + (n - 1)d = Tn

Where

The number of terms in the arithmetic sequence is represented by n.

The common difference of the terms in the arithmetic sequence is represented by d.

The first term of the arithmetic sequence is represented by a.

Tn stands for the nth word.

Based on the facts provided,

n = 26 characters1 Equals a

3 minus 1 equals 2 (difference between 2 letters)

Therefore,

1 + (26 - 1)2 = T26

51 = T26

The formula for calculating the sum of an arithmetic sequence's n terms

is as follows:

[2a + (n - 1)d] Sn = n/2

As a result, S26 is the sum of the first 26 terms.

S26 = 20/2[2 1 + (26 - 1)2] S26 = 20/2

[2 + 50] S26 =

676 = S26 = 13 52

3 0

1 year ago

I think it’s the third one

Zigmanuir [339]

It’s third to the one

7 0

2 years ago

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