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3 years ago

A right triangle has leg lengths 8 and x. The hypotenuse length is (x + 2). What is the length of the hypotenuse?

Mathematics

1 answer:

umka2103 [35]3 years ago

4 0

Answer:

17 is the length of the hypotenuse.

Step-by-step explanation:

The pythagora theorem tells us a²+b²=c², where C is hypotenuse.

Replace the given info into the formula:

8² + x² = (x+2)²

64 + x² = x² + 4x + 4

64 - 4 = 4x

60 = 4x

x = 60/4

x = 15

Hypotenuse length is 15+2=17

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Pleasantburg has a population growth model of P(t)=at2+bt+P0 where P0 is the initial population. Suppose that the future populat

yulyashka [42]

Answer:

The population will reach 34,200 in February of 2146.

Step-by-step explanation:

Population in t years after 2012 is given by:

$P(t) = 0.8t^{2} + 6t + 19000$

In what month and year will the population reach 34,200?

We have to find t for which P(t) = 34200. So

$P(t) = 0.8t^{2} + 6t + 19000$

$0.8t^{2} + 6t + 19000 = 34200$

$0.8t^{2} + 6t - 15200 = 0$

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$ .

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})$ , given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}$

$\bigtriangleup = b^{2} - 4ac$

In this question:

$0.8t^{2} + 6t - 15200 = 0$

So $a = 0.8, b = 6, c = -15200$

Then

$\bigtriangleup = 6^{2} - 4*0.8*(-15100) = 48356$

$t_{1} = \frac{-6 + \sqrt{48356}}{2*0.8} = 134.14$

$t_{2} = \frac{-6 - \sqrt{48356}}{2*0.8} = -141.64$

We only take the positive value.

134 years after 2012.

.14 of an year is 0.14*365 = 51.1. The 51st day of a year happens in February.

So the population will reach 34,200 in February of 2146.

6 0

3 years ago

At cheng’s bike rental cost $40 to rent a bike for seven hours how many dollars does it cost per hour of bike use

Alchen [17]

40$. 7hrs
X$. 1hr
X=40•1/7
X~5.71 $ per hour

3 0

3 years ago

BC is parallel to DE<br> What is AC?

DaniilM [7]

ΔABC ~ ΔADE
AC/AE = AB/AD
AC/(AC+15) = 8/18
18AC = 8(AC+15)
18AC = 8AC + 120
18AC - 8AC = 120
10AC = 120
AC = 120/10
AC = 12

3 0

3 years ago

Read 2 more answers

Add.

lidiya [134]

The answer is c:
87.872

5 0

3 years ago

Is AFGH ~ AJKL? If so, identify the similarity postulate or theorem that

ad-work [718]

Answer: B. Cannot be determined

Explanation:

We can't use SAS since we don't have two pairs of proportional sides. We only know one pair of sides. This also rules out SSS as well since we'd need 3 pairs of proportional sides.

We can't use AA because we don't have two pairs of congruent angles.

Currently, we simply don't have enough information to determine if the triangles are similar or not.

5 0

3 years ago