What is equelivlent to 3 to the 5th power

The shorter leg of a right triangle is 7cm shorter than the longer leg. The hypotenuse is 7cm longer then the linger leg. What i

Gelneren [198K]

The shorter leg is 21cm, longer leg is 28 cm and hypotenuse is 35cm.

Step-by-step explanation:

Let,

The longer leg = x

The shorter leg = x-7

Hypotenuse = x+7

Using Pythagoras theorem;

$a^2+b^2=c^2\\(x-7)^2+(x)^2=(x+7)^2\\x^2-14x+49+x^2=x^2+14x+49\\2x^2-14x+49-x^2-14x-49=0\\x^2-28x=0\\x(x-28)=0\\$

Either,

x= 0

Or,

x-28=0 =>x=28

As length cannot be zero, therefore,

Longer side = 28cm

Shorter side = x-7 = 28-7 = 21cm

Hypotenuse = x+7 = 28+7 = 35cm

The shorter leg is 21cm, longer leg is 28 cm and hypotenuse is 35cm.

Keywords: triangle, pythagoras theorem

Learn more about triangles at:

#LearnwithBrainly

5 0

3 years ago

The expression 2a+1.5b 2a+1.5b gives the cost (in dollars) for a a cupcakes and b b cookies at a bake sale

zepelin [54]

Is there a question here? I can't see it!

5 0

3 years ago

The graph h = −16t^2 + 25t + 5 models the height and time of a ball that was thrown off of a building where h is the height in f

Thepotemich [5.8K]

Answer:

part 1) 0.78 seconds

part 2) 1.74 seconds

Step-by-step explanation:

step 1

At about what time did the ball reach the maximum?

Let

h ----> the height of a ball in feet

t ---> the time in seconds

we have

$h(t)=-16t^{2}+25t+5$

This is a vertical parabola open downward (the leading coefficient is negative)

The vertex represent a maximum

so

The x-coordinate of the vertex represent the time when the ball reach the maximum

Find the vertex

Convert the equation in vertex form

Factor -16

$h(t)=-16(t^{2}-\frac{25}{16}t)+5$

Complete the square

$h(t)=-16(t^{2}-\frac{25}{16}t+\frac{625}{1,024})+5+\frac{625}{64}$

$h(t)=-16(t^{2}-\frac{25}{16}t+\frac{625}{1,024})+\frac{945}{64}\\h(t)=-16(t^{2}-\frac{25}{16}t+\frac{625}{1,024})+\frac{945}{64}$

Rewrite as perfect squares

$h(t)=-16(t-\frac{25}{32})^{2}+\frac{945}{64}$

The vertex is the point $(\frac{25}{32},\frac{945}{64})$

therefore

The time when the ball reach the maximum is 25/32 sec or 0.78 sec

step 2

At about what time did the ball reach the minimum?

we know that

The ball reach the minimum when the the ball reach the ground (h=0)

For h=0

$0=-16(t-\frac{25}{32})^{2}+\frac{945}{64}$

$16(t-\frac{25}{32})^{2}=\frac{945}{64}$

$(t-\frac{25}{32})^{2}=\frac{945}{1,024}$

square root both sides

$(t-\frac{25}{32})=\pm\frac{\sqrt{945}}{32}$

$t=\pm\frac{\sqrt{945}}{32}+\frac{25}{32}$

the positive value is

$t=\frac{\sqrt{945}}{32}+\frac{25}{32}=1.74\ sec$

8 0

3 years ago

8. It took Sharon 85 minutes to wash three cars. She spent x minutes on each car and 10 minutes

Yuliya22 [10]

Answer:

c. 25 minutes

Step-by-step explanation:

3x + 10 = 85

3x = 85 - 10

3x = 75

x = 25

8 0

3 years ago

A headline in a major newspaper read, "Breast-fed youth found to do better in school."a. Do you thinkthis statement was based on

Maurinko [17]

Answer:

Randomized experiment

Step-by-step explanation:

Such a statement is said to be Randomized experiment as the kids in the school have been selected at random and their performances are observed and recorded. Later it is inquired if they are breast fed or not. This information is later assessed and a conclusion is reached. This type of research or experiment is Randomized experiment.

Considering that the experiment is Randomized, the statement should be "Link found between breast-feeding and school performances". This statement does not restrict the performances of the student specifically on breast-feeding but shows a probable affect of it.

3 0

2 years ago