The formula for the length of the hypotenuse in a right triangle is \sqrt{a^2+b^2} a 2 +b 2 square root of, a, squared, plus, b, squared, end square root where aaa and bbb are the lengths of the triangle's sides (this formula is derived from the Pythagorean theorem). From the side, a certain ramp has a right-triangular shape. Its height is 303030 centimeters and its horizontal length is 333 meters. What calculation will give us the estimated length of the ramp in meters? Choose 1 Choose 1 (Choice A) A \sqrt{\dfrac{30^2}{100^2}+3^2} 100 2 30 2 +3 2 square root of, start fraction, 30, squared, divided by, 100, squared, end fraction, plus, 3, squared, end square root (Choice B) B \sqrt{30^2+3^2\cdot 100^2} 30 2 +3 2 ⋅100 2 square root of, 30, squared, plus, 3, squared, dot, 100, squared, end square root (Choice C) C \sqrt{30^2\cdot 100^2+3^2} 30 2 ⋅100 2 +3 2 square root of, 30, squared, dot, 100, squared, plus, 3, squared, end square root (Choice D) D \sqrt{30^2+\dfrac{3^2}{100^2}} 30 2 + 100 2 3 2 square root of, 30, squared, plus, start fraction, 3, squared, divided by, 100, squared, end fraction, end square root

a

step-by-step explanation:

when a number is between two straight lines it means the absolute value.

to find absolute value you need to know how many numbers is that number away from 0.

when finding absolute value the number will always come out positive

so absolute value of -3 is 3

absolute value of 3/2 is 3/2

absolute value of -2 is 2

absolute value of 3.5 is 3.5

absolute value of -1 is 1

now put these numbers in order:

a)   |-1|, |3/2|, |-2|, |-3|, |3.5|

second option

step-by-step explanation:

the measures of a triangle equal 180. use that to find x.

2x+3x+4x=180

9x=180

9x/9=180/9

x=20

now you know x, you know angle a is 40°, angle b is 60°, angle c is 80°.

because angle a is 40°, the first option doesn't work.

because angle b is 60°, the second option does work.

when you add angle a and b, you get 100°. complementary means it equals 90°, so the third option doesn't work.

when you add angle a and c, you get 120°, which is not 100.

(a) {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …}

(b) $59 398

step-by-step explanation:

(a) the annual sequence of profits

aₙ = a₁rⁿ⁻¹

the model for the sequence of profits is {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …} .

(b) profit after 15 yr

  a₁ = $ 30 000

  r = 1.05

a₁₅ = 30 000 × 1.05¹⁴

a₁₅ = 30 000 × 1.979 93

a₁₅ = $59 398

the profit in year 15 will be $59 398.

hi there!

the answer is: 2 and -2

step-by-step explanation:

case 1: an absolute value of positive number will still be a positive number

so absolute value of 2 is 2

case 2: an absolute value of negative number will be positive number so absolute value of -2 is 2