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2 years ago

6

Apply the 30º-60º-90º triangle theorem to find the length of the shorter leg of a triangle if the length of the hypotenuse is 20

20 cm. 103‾√103 cm 320‾‾‾√320 cm 320‾‾‾√‾‾‾‾‾√320 cm 1010 cm 20‾‾‾√20 cm

1 answer:

Brilliant_brown [7]2 years ago

5 0

YOU NEED A DIFFERENT MATH TEACHER

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Solve the proportional equation 3/r = 5/r+3

romanna [79]

Answer:

r=9/2 or 4.5

Step-by-step explanation:

First of all our goal is to get R by itself

by cross multiplying we get,

(r+3)*3=5r

by distributive property we get

3r+9=5r

substracting 3r from both sides we get

9=2r

by dividing by 2 in both sides we get

r=9/2 or 4.5

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2 years ago

Completing the square x^2 + 10x

IRISSAK [1]

Answer:

x^2 + 10x + 25

Step-by-step explanation:

(B/2) ^2

10/2 = 5

5^2 = 25

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3 years ago

Use the exponential decay model, Upper A equals Upper A 0 e Superscript kt, to solve the following. The half-life of a certai

Akimi4 [234]

Answer:

It will take 7 years ( approx )

Step-by-step explanation:

Given equation that shows the amount of the substance after t years,

$A=A_0 e^{kt}$

Where,

$A_0$ = Initial amount of the substance,

If the half life of the substance is 19 years,

Then if t = 19, amount of the substance = $\frac{A_0}{2}$ ,

i.e.

$\frac{A_0}{2}=A_0 e^{19k}$

$\frac{1}{2} = e^{19k}$

$0.5 = e^{19k}$

Taking ln both sides,

$\ln(0.5) = \ln(e^{19k})$

$\ln(0.5) = 19k$

$\implies k = \frac{\ln(0.5)}{19}\approx -0.03648$

Now, if the substance to decay to 78% of its original amount,

Then $A=78\% \text{ of }A_0 =\frac{78A_0}{100}=0.78 A_0$

$0.78 A_0=A_0 e^{-0.03648t}$

$0.78 = e^{-0.03648t}$

Again taking ln both sides,

$\ln(0.78) = -0.03648t$

$-0.24846=-0.03648t$

$\implies t = \frac{0.24846}{0.03648}=6.81085\approx 7$

Hence, approximately the substance would be 78% of its initial value after 7 years.

5 0

2 years ago

Find the height of a triangular prism with a base length of 10 yards, a base height of 20 yards, and a volume of 600 cubic yards

Artemon [7]

The volume of the triangular prism is the Area of the base times the height
the area of the base is:
$\frac{ab}{2}$
and the volume is:
$V=(\frac{ba}{2})h$

now b=10 yards, a=20 yards, and V=600 yards^3
we clean the height

$h=\frac{2V}{ab}=\frac{2\cdot 600}{10\cdot 20} = 6
$

the answer is height = 6 yards

8 0

2 years ago

Devaughn is 5 years younger than Sydney. The sum of their ages is45. What is Sydney's age?

Verizon [17]

Let the age of devaughn be x and Sydney be y.
Then,x+y=45
x+5=y
y=x+5
here,
put y=x+y in x+y=45
then,
x+y=45
x+x+5=45
2x=40
x=20
now,
y=x+5
y=20+5
y=25

5 0

3 years ago

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