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3 years ago

Select the correct answer.

Mathematics

1 answer:

Pani-rosa [81]3 years ago

6 0

Answer:

its probably division property if equality

Step-by-step explanation:

because it has division in it

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Please Help? A circle has an arc length of 5π in. The central angle for this arc measures π/3 radians. What is the area of the a

Zielflug [23.3K]

Answer:

The area of the associated sector is $\frac{25}{24}\pi \ in^{2}$

Step-by-step explanation:

step 1

Find the radius of the circle

we know that

The circumference of a circle is equal to

$C=2\pi r$

we have

$C=5\pi\ in$

substitute and solve for r

$5\pi=2\pi r$

$r=2.5\ in$

step 2

Find the area of the circle

we know that

The area of the circle is equal to

$A=\pi r^{2}$

we have

$r=2.5\ in$

substitute

$A=\pi (2.5^{2})=6.25\pi\ in^{2}$

step 3

Find the area of the associated sector

we know that

$2\pi\ radians$ subtends the complete circle of area $6.25\pi\ in^{2}$

by proportion

Find the area of a sector with a central angle of $\pi/3\ radians$

$\frac{6.25\pi }{2\pi} =\frac{x}{\pi/3}\\x=6.25*(\pi/3)/2\\ \\x=\frac{25}{24}\pi \ in^{2}$

8 0

3 years ago

Rhett is solving the quadratic equation zero equals X2 minus 2X -3 using the quadratic formula which shows the correct substitut

Alina [70]

X^2-2x -3 =0
a =1 b =-2 and c = -3

x = - (-2) +/- sqrt (-2)^2 - 4(1)(-3)
--------------------------------------
2(1)

x = + 2 +/- sqrt [(4) - 4(-3)]
-------------------------------
2

x = +2 +/- sqrt [4 + 12]
--------------------------
2
x = +2 +/- sqrt[16]
-------------------
2

x = +2 +/- (4)
-------------
2

x = 2 + 4 or 2 -4
------- ------
2 2

x = 6/2 or -2/2

x = 3 or x = -1

8 0

2 years ago

Two trains left the station traveling in opposite directions. The distance Train A traveled is modeled by the function d(t)=81t

stira [4]

Answer:

Option A - The distance Train A traveled in 1 h is equal to the distance Train B traveled in 1 h.

Step-by-step explanation:

Given : The distance Train A traveled is modeled by the function $d(t)=81t$

where d represents distance in miles and t represents time in hours.

To find : How does the distance Train A traveled in 1 hour compare to the distance Train B traveled in 1 hour?

Solution :

Distance traveled by Train A in 1 hour is

$d(t)=81t$

$d(t)=81(1)=81$

Distance traveled by Train B in 1 hour is

$d(t)=81t$

$d(t)=81(1)=81$

or for B, we have 324 miles in 4 hours. If that is at a constant speed, it travels 324/4 = 81 miles in one hour

Therefore, The distance Train A traveled in 1 h is equal to the distance Train B traveled in 1 h.

Hence, Option A is correct.

8 0

2 years ago

Apply Crammer's Rule to find the solution to the following quations .2x + 3y = 1, 3x + y = 5

Bond [772]

Answer:

The solution to the equation system given is:

<u>x = 2</u>
<u>y = -1</u>

Step-by-step explanation:

First, we must know the equations given:

2x + 3y = 1
3x + y = 5

Following Crammer's Rule, we have the matrix form:

$\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] =\left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}1\\5\end{array}\right]$

Now we solve using the determinants:

$x=\frac{\left[\begin{array}{ccc}1&3\\5&1\end{array}\right]}{\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] } =\frac{(1*1)-(5*3)}{(2*1)-(3*3)} = \frac{1-15}{2-9} =\frac{-14}{-7} = 2$

$y=\frac{\left[\begin{array}{ccc}2&1\\3&5\end{array}\right]}{\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] } =\frac{(2*5)-(3*1)}{(2*1)-(3*3)}=\frac{10-3}{2-9} =\frac{7}{-7}=-1$

Now, we can find the answer which is x= 2 and y= -1, we can replace these values in the equation to confirm the results are right, with the first equation:

2x + 3y = 1
2(2) + 3(-1)= 1
4 - 3 = 1
1 = 1

And, with the second equation:

3x + y = 5
3(2) + (-1) = 5
6 - 1 = 5
5 = 5

4 0

2 years ago

What is -11/8 + -11/4

madam [21]

Answer:

-4and1/8

Step-by-step explanation:math

8 0

3 years ago

Read 2 more answers