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Helga [31]
3 years ago
8

A leg of a right triangle measures 84 units, and the hypotenuse measures 85 units. What is the length of the remaining side roun

ded to the nearest hundredth unit?
Mathematics
1 answer:
kondaur [170]3 years ago
7 0

Answer:

13 units

Step-by-step explanation:

pythagorean theorem: a²+b²=c²

c= 85

b= 84

a²+(84)²=85²

a²+7056=7225

a²=169

square root of a² = square root of 169

a=13

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The initial population of a town is 2600, and it grows with a doubling time of 10 years. Determine how long it will take for the
choli [55]

Answer:

It will take the 20 years for the population to quadruple.

Step-by-step explanation:

Exponential population growth:

An exponential model for population growth has the following model:

P(t) = P(0)(1+r)^t

In which P(0) is the initial population and r is the growth rate, as a decimal.

It grows with a doubling time of 10 years.

This means that P(10) = 2P(0). We use this to find r. So

P(t) = P(0)(1+r)^t

2P(0) = P(0)(1+r)^10

(1+r)^10 = 2

\sqrt[10]{(1+r)^10} = \sqrt[10]{2}

1+r = 2^{\frac{1}{10}}

1 + r = 1.0718

So

P(t) = P(0)(1+r)^t

P(t) = P(0)(1.0718)^t

Determine how long it will take for the population to quadruple.

This is t for which P(t) = 4P(0). So

P(t) = P(0)(1.0718)^t

4P(0) = P(0)(1.0718)^t

(1.0718)^t = 4

\log{(1.0718)^t} = \log{4}

t\log{1.0718} = \log{4}

t = \frac{\log{4}}{\log{1.0718}}

t = 20

It will take the 20 years for the population to quadruple.

5 0
3 years ago
(-12)÷6+2 pls help math is hard for me
SVEN [57.7K]

The Answer is -3/2

Below is how I got that answer

(-12) / 6+2

-12/ 8  (Simplify the problem by adding 6 and 2, remove the parenthesis).

-3/2 (Simplify -12/8 by dividing it by 4)

4 0
3 years ago
Find the solution to the system of equations y=−7x+3y=−x−3​
babunello [35]

Answer:

x=1, y=-4. (1, -4).

Step-by-step explanation:

y=-7x+3

y=-x-3

-------------

-7x+3=-x-3

-7x-(-x)+3=-3

-7x+x=-3-3

-6x=-6

6x=6

x=6/6

x=1

y=-1-3=-4

3 0
3 years ago
How can this model be used to determine 2.4−0.15 ?<br><br> Enter your answers in the boxes.
Harlamova29_29 [7]
2.25! Just do 2.4- 0.15= 2.25, im sorry if its not what you wanted!
8 0
2 years ago
What is the standard form of y = 6(x - 2)2 - 3?
AveGali [126]

Answer I think A

Step-by-step explanation:

4 0
3 years ago
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