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2 years ago

What is the length of the hypotenuse in the 30 60 90 triangle shown below

Mathematics

1 answer:

andreyandreev [35.5K]2 years ago

6 0

Answer:

Step-by-step explanation:

In a 30-60-90, the hypotenuse is twice the length of the short side. If the short side is 6, the long side is 12

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The sum of a number and its reciprocal is 41/20. Find the number. smaller value larger value

Natali [406]

Step-by-step explanation:

Let the number is x. Its reciprocal will be 1/x. According to given condition, we get :

$x+\dfrac{1}{x}=\dfrac{41}{20}\\\\\dfrac{x^2+1}{x}=\dfrac{41}{20}\\\\20x^2+20=41x\\\\20x^2-41x+20=0$

It is a quadratic equation. The values of x are :

$20x^2-25x - 16x+ 20 =0\\\\5x(4x - 5) -4( 4x - 5) = 0\\\\(5x-4)(4x-5)=0\\\\5x-4=0\ \text{and}\ (4x-5)=0\\\\x=\dfrac{4}{5}\ \text{and}\ x=\dfrac{5}{4}$

The smaller number is 4/5 and the larger number is 5/4.

6 0

3 years ago

Select ALL the correct answers.

jolli1 [7]

Answer:

(4x+5)(-3x-1) = -12x²-19x-5

Option A:

(-16x² + 10x - 3) + (4x² - 29x - 2) = -12x²-19x-5

Option A is correct.

Option B:

3(x - 5) - 2(6x² + 9x + 5) = -12x²-15x-25

Option B is wrong.

Option C:

2(x - 1) - 3(4x² + 7x + 1) = -12x²-19x-5

Option C is correct.

Option D:

(2x² - 11x - 9) - (14x² + 8x - 4) = -12x²-19x-5

Option D is correct.

4 0

2 years ago

Kelly and Greta are asked to write an equation for the scenario below. "One person was able to plant 4 trees in the same amount

Alina [70]

Answer:

$y=\dfrac{1}{4}x$

Kelly is correct.

Step-by-step explanation:

One person is able to plant 4 trees

Let x be the number of people

y be the number of trees

The situation is represented by

$1x=4y\\\Rightarrow y=\dfrac{1}{4}x$

5 people are able to plant 20 trees

$5x=5(4y)\\\Rightarrow 5x=20y\\\Rightarrow y=\dfrac{5x}{20}\\\Rightarrow y=\dfrac{1}{4}x$

So, the situation is represented by $y=\dfrac{1}{4}x$

Hence, Kelly is correct.

6 0

2 years ago

Read 2 more answers

0.2y=0.5x+0.1 please solve with math thank you

Cerrena [4.2K]

<span>"Simplifying 0.2y = 0.5x + 0.1
Reorder the terms: 0.2y = 0.1 + 0.5x Solving 0.2y = 0.1 + 0.5x Solving for variable 'y'.
Move all terms containing y to the left, all other terms to the right.
Divide each side by '0.2'. y = 0.5 + 2.5x Simplifying y = 0.5 + 2.5x"</span>

7 0

3 years ago

1/5r+ 8/15 when r=1/3

ZanzabumX [31]

Answer:

3/5

Step-by-step explanation:

1/5r + 8/15

~Substitute

1/5(1/3) + 8/15

~Simplify

1/15 + 8/15

~Add

9/15

~Simplify

3/5

Best of Luck!

5 0

3 years ago