# A right triangle has sides measuring 5 inches, 12 inches, and 13 inches. What is the area, in square inches, of this triangle ?

2 months ago

## Solution 1

Guest #3894
2 months ago
Please look up and apply Heron's Formula.  Start by calculating s, where
a  +  b  +  c
s = -------------------
2

Then calculate A:

A = sqrt[ s(s-a)(s-b)(s-c) ]

## 📚 Related Questions

Question
Please please please someone help me no one on this site will help me. i so confused. please help. PLEASE SOMEONE HELP ME!!!!! ILL GIVE BRAINLIEST 1. A model rocket is launched from a roof into a large field. The path of the rocket can be modeled by the equation y = –0.04x2 + 8.3x + 4.3, where x is the horizontal distance, in meters, from the starting point on the roof and y is the height, in meters, of the rocket above the ground. How far horizontally from its starting point will the rocket land? A. 208.02 m B. 416.30 m C. 0.52 m D. 208.19 m 2. A catapult launches a boulder with an upward velocity of 184 ft/s. The height of the boulder (h) in feet after t seconds is given by the function h= -16t^2 + 184t + 20. How long does it take the boulder to reach its maximum height? What is the boulder's maximum height. A. Reaches a maximum height of 11.6 feet after 5.75 seconded. B. Reaches a maximum height of 549 feet after 11.5 seconds. C. Reaches a maximum height of 549 feet after 5.75 seconds. D. Reaches a maximum height of 23.2 feet after 11.6 seconds. 3. A ball is thrown into the air with an upward velocity of 32 ft/s. Its height (h) in feet after t seconds is given by the function h= -16t^2 + 32t + 6. How long does it take the ball to reach its maximum height? What is the ball’s maximum height? Round to the nearest hundredth, if necessary. A. Reaches a maximum height of 22 feet after 1.00 second. B. Reaches a maximum height of 22 feet after 2.00 seconds. C. Reaches a maximum height of 44 feet after 2.17 seconds. D. Reaches a maximum height of 11 feet after 2.17 seconds.
Solution 1
Problem One
The rocket will hit ground level when y = 0. The plan is is to set y =0 and solve the quadratic. Be careful how you go about to this. It is an odd way to represent this kind of problem. The question does say that y defines how far off the ground the rocket is at the beginning. Therefore the height of the building does not matter (or shouldn't). All that matters is that y is ground level when y = 0.

a = - 0.04
b = 8.3
c = 4.3

From here you should be able to calculate the answer. One of them is -0.52 which is not the one you use. Minus heights do not matter in these problems yet. The other root is your answer.

Problem Two

Problem two is the usual way to express what happens to a projectile in the air. It again is going to be solved by the quadratic equation.

There are two ways to do this problem. If you know physics, you can solve it using the projectile formulas. If you don't , then you can use the trick in the previous problem. You can calculate how long it takes to hit the ground (h will then be zero).

This problem is rather nasty for someone who has not taken physics. There is another trick. You have to divide the time you get from the previous step by 2. When you solve the quadratic for h = 0, you get 11.6 seconds. But that is the time it takes to hit the ground. Half time is when the boulder will be at it's highest point. t = 11.6 / 2 = 5.8 (which your answers record as 5.75).

h = 0

a= -16

b = 184

c = 20

The answer from this equation is t = 11.6

The time you want is t = 5.75. You can calculate the maximum height by putting 5.75 in for t.

Problem 3

Problem 3 is done exactly the same way as problem two. You just have different numbers. When h = 0 the time taken to reach zero = 2.17 seconds. Therefore the time you want to put into the original equation for the maximum height is 1/2 of 2.17 seconds. From there you can find the maximum height.

Note: there is a lot of math in here. I have gotten you past the physics. I have also alluded to the answers. I think you should be able to carry out the rest.

Question
What is the volume of a sphere if the radius is 9?
Solution 1

Step-by-step explanation: To find the volume of a sphere, start with the formula for the volume of a sphere.

Notice that our sphere has a radius of 9 units so we can plug 9 into our formula.

Now, let's simplify the exponent. 9 units³ is equal to 9 units × 9 units × 9 units or 729 units³.

Notice that we can cross cancel in and to and

Solution 2
V=4/3pi r^3
Question
What is the input to a trigonometric function? a ratio the x position of a point on the circle a central angle of a circle the y position of a point on the circle
Solution 1

Answer: A central angle of a circle

Step-by-step explanation:

The trigonometric functions are also known as circular functions.

The two fundamental trigonometric functions are defined as the coordinates of a any point A  travelling around on the unit circle of radius  1 .

The input variable in trigonometric functions is the central angle of the circle 'x' such that we get sin x and cos x which give the x and y coordinates of A.

Hence, the input to a trigonometric function is a central angle of a circle.

Solution 2
The input to a trig function is definitely an angle (whether in degrees or expressed in radians).  That angle is also "a central angle of a circle."

Question
PLEASE SOMEONE HELP ME!!!!! ILL GIVE BRAINLIEST 1. A model rocket is launched from a roof into a large field. The path of the rocket can be modeled by the equation y = –0.04x2 + 8.3x + 4.3, where x is the horizontal distance, in meters, from the starting point on the roof and y is the height, in meters, of the rocket above the ground. How far horizontally from its starting point will the rocket land? A. 208.02 m B. 416.30 m C. 0.52 m D. 208.19 m 2. A catapult launches a boulder with an upward velocity of 184 ft/s. The height of the boulder (h) in feet after t seconds is given by the function h= -16t^2 + 184t + 20. How long does it take the boulder to reach its maximum height? What is the boulder's maximum height. A. Reaches a maximum height of 11.6 feet after 5.75 seconded. B. Reaches a maximum height of 549 feet after 11.5 seconds. C. Reaches a maximum height of 549 feet after 5.75 seconds. D. Reaches a maximum height of 23.2 feet after 11.6 seconds. 3. A ball is thrown into the air with an upward velocity of 32 ft/s. Its height (h) in feet after t seconds is given by the function h= -16t^2 + 32t + 6. How long does it take the ball to reach its maximum height? What is the ball’s maximum height? Round to the nearest hundredth, if necessary. A. Reaches a maximum height of 22 feet after 1.00 second. B. Reaches a maximum height of 22 feet after 2.00 seconds. C. Reaches a maximum height of 44 feet after 2.17 seconds. D. Reaches a maximum height of 11 feet after 2.17 seconds.
Solution 1
1. When it hit the ground=>y = 0
=>By y = –0.04x^2 + 8.3x + 4.3
=>0.04x^2 - 8.3x - 4.3 = 0
=>x = [-(-8.3) +/- √{(-8.3)^2 - 4 x 0.04 x (-4.3)}]/[2 x 0.04]
=>x = [8.3 +/- 8.34]/[0.08]
=>x = 208.02 m

2. A. Reaches a maximum height of 11.6 feet after 5.75 seconded.

3. B. Reaches a maximum height of 22 feet after 2.00 seconds.

Question
A student invests \$500 for 3 years in a savings account that earns 4% interest per year. No further deposits or withdrawals were made during this time. Which does NOT yield the correct balance in the account at the end of the 3 years? Please show work for the answer! A)500(1.04)^3 B)500(1-.04)^3 C)500(1+.04)(1+.04) D)500+500(.4)+520(.04)+540.8(04)
Solution 1
To get the balance after 3 years we use the formula:
A=P(1+r/100)^n
where:
A=future amount
r=rate
n=time
thus plugging in the values we obtain:
A=500(1+4/100)^3
A=500(1+0.04)^3
A=500(1.04)^3
The correct choices are A and B

The wrong choices are C and D

Solution 2

he`s right its a or b

i'm going with b

Step-by-step explanation:

Question
Use the graph below to answer the question that follows: graph of the curve that passes through the following points, 0, 3; pi over 2, 5; pi, 3; 3 pi over 2, 1; 2 pi, 3. What is the rate of change between the interval of x = 0 and x = pi over two? 2 over pi pi over two pi over four four over pi
Solution 1

The rate of change is 4/π which is the correct answer would be option (D)

### What is a graph?

A graph can be defined as a pictorial representation or a diagram that represents data or values.

### What is the slope of the line?

The slope of a line is defined as the angle of the line. It is denoted by m

Slope m = (y₂ - y₁)/(x₂ -x₁ )

Consider two points on a line—Point 1 and Point 2. Point 1 has coordinates (x₁,y₁) and Point 2 has coordinates (x₂, y₂)

The coordinates of the endpoints of the range can be used to determine the rate of change using the slope formula: m = dy / dx.

The coordinates are

x₁=0, y₁=3

x₂=π/2, y₂=5

So rate of change = (y₂ - y₁)/(x₂ -x₁ )

Rate of change = (5-3)/(π/2-0)

Rate of change = 4/π

brainly.com/question/2234422

#SPJ5

Solution 2
X1=0, y1=3
x2=pi/2, y2=5

rate of change = (y2-y1)/(x2-x1)
=(5-3)/(pi/2-0)
=4/pi

ans is D. four over pi

Question
A cylinder has a radius of 5 feet and a height of 8 feet. Which of the following can be used to calculate the volume of a cone that fits exactly inside the cylinder? A. (3.14)(5^2)(8) B. 1/3(3.14)(5^2)(8) C. (3.14)(8^2)(5) D. 1/3(3.14)(8^2)(5)
Solution 1
The formula is pi*r^2*h/3
Question
Tanisha is planning a backyard party. She will serve hamburgers, potato salad, strawberry shortcake, and lemonade. Including Tanisha, 28 people will be at the party. Use this information to help Tanisha plan her party. Tanisha expects that each person will drink two 8−ounce glasses of lemonade at the party, and makes 448 ounces of lemonade. Tanisha's mother buys 38 lemons. They know it takes 8 lemons to make 80 ounces of lemonade. Does Tanisha need more lemons?
Solution 1
For this case we can make the following rule of three:
8 lemons --------> 80 ounces of lemonade
38 lemons ------> x
Clearing x we have:
x = (38/8) * (80)
x = 380 ounces
We observed that:
380 <448
Therefore, more lemons are needed.

Yes, Tanisha needs more lemons
Question
PLS HELP! Tanisha is planning a party. She will serve hamburgers, potato salad, strawberry shortcake, and lemonade. Including Tanisha, 28 people will be at the party. Tanisha expects that each person will drink two 8−ounce glasses of lemonade at the party, and makes 448 ounces of lemonade. Tanisha's mother buys 38 lemons. They know it takes 8 lemons to make 80 ounces of lemonade. Does Tanisha need more lemons?
Solution 1
Shee needs 448 ounces of lemonade.

448 ÷ 80 =5.8
⇒ There are 5.6 80-ounce of lemonade.

80 ounces of lemonade needed 8 lemons.
448 ounces of lemonade needed 8 x 5.6 = 44.8 lemons.

Tanisha has 38 lemons.
She does not have enough lemons.
She needs 44.8 - 38 = 7 more lemons.

Answer: Tanisha needs more lemons. She needs 7 more.
Solution 2

Step-by-step explanation:

Since she needs 448 ounces of lemonade you have to divide which is 5.6 . As a result there are 5.6 80 ounces of lemonade. 80 ounces needs 8 lemons.  448 ounces of lemonade are needed 8 x 5.6 = 44.8 lemons.  Tanisha only has 38 lemons, which isn't enough. 44.8 - 38 =  is about 7 more lemons.

Question
Solution 1
-3x - 3x = -24

Combine like terms:
- 6x = -24

Divide both side by -6:
x = 4

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