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3 years ago

Which of the following quantities are inversely proportional?

Mathematics

1 answer:

andreyandreev [35.5K]3 years ago

5 0

Option 1 and option 4 are inversely proportional.

Inversely proportional means when one variable increases the other decreases in proportion.

Option 1 is true. When the number of tractors increases, the time to plow a farm decreases.

Option 4 is also true. If height is too large, base area should be too less to equalize the area.

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The hypotenuse of an isosceles right triangle is centimeters longer than either of its legs. Find the exact length of each side.

Varvara68 [4.7K]

Question

The hypotenuse of an isosceles right triangle is 11 centimeters longer than either of its legs. find the exact length of each side.

Answer:

$Hypotenuse:37.56$

$Other\ Legs: 26.56$

Step-by-step explanation:

Let the hypotenuse be y and the other legs be x.

So:

$y = 11 + x$

Required

Determine the exact dimension of the triangle

Using Pythagoras theorem;

$y^2 = x^2 + x^2$

$y^2 = 2x^2$

This gives:

$(11+x)^2 = 2x^2$

Open bracket

$121 + 22x + x^2= 2x^2$

Collect like terms

$2x^2 - x^2 -22x - 121 = 0$

$x^2 -22x - 121 = 0$

Using quadratic formula:

$x = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}$

$x = \frac{-(-22)\±\sqrt{(-22)^2 - 4*1*-121}}{2*1}$

$x = \frac{-(-22)\±\sqrt{968}}{2*1}$

$x = \frac{22\±31.11}{2}$

Split

$x = \frac{22+31.11}{2}\ or\ x = \frac{22-31.11}{2}\\$

$x = \frac{53.11}{2}\ or\ x = \frac{-9.11}{2}$

x can not be negative.

So:

$x = \frac{53.11}{2}$

$x = 26.56$

Recall that:

$y = 11 + x$

$y = 11 + 26.56$

$y = 37.56$

Hence, the dimensions are:

$Hypotenuse:37.56$

$Other\ Legs: 26.56$

6 0

3 years ago

Pls help I’ll give 23 points

Andrew [12]

Answer:

$2594.07

Step-by-step explanation:

Principal P = $2250
Interest rate r = 2.4% = 0.024 PA compounded
Compound number n = 1 (once per year)
Time t = 6 years

<u>Future amount formula:</u>

F = P(1 + r/n)^(nt)

<u>Substitute given values:</u>

F = 2250(1 + 0.024)^6 = 2594.07

8 0

3 years ago

Is it possible for a pair of nonadjacent angles to share a vertex ?

Hoochie [10]

Yes with vertical Angles.
:) hope this helps

3 0

3 years ago

I really need help on this please

hammer [34]

The answer is letter A

7 0

3 years ago

Please help will give brainliest

Olenka [21]

Give the other person brainliest just answering so they can get it

3 0

3 years ago