Answer:No
Step-by-step explanation:
Given system of equation is:
2x + 3 = y
2x + y = 15
To check whether (2,7) is solution to this system or not, we will put x=2 and y=7 in both equations.
Putting x=2 and y=7 in Eqn 1
2(2) + 3 = 7
4 + 3 = 7
7 = 7
Thus the ordered pair satisfies the equation
Putting x=2 and y=7 in Eqn 2
2(2) + 7 = 15
4 + 7 = 15
11 ≠ 15
The ordered pair do not satisfy the second equation.
Hence,
(2,7) is not a solution to the given system of equations.
Answer:
Juan runs 7/10 of a mile every hour
Step-by-step explanation:
First find out how much he ran every 1/7 of an hour
2/5 x 1/4 = 4/7 x 1/4
1/10 = 1/7
1/10 x 7 = 1/7 x 7
7/10 = 1
Answer:
Step-by-step explanation:
1/4 of the 300 skiers are beginners......1/4 of the 260 snowboarders are beginners..
so we want the total number of beginners..
the distributive property in this situation would be :
1/4(300 + 260) .......to solve this, u first have to get rid of the parenthesis. To do this, u multiple the number directly to the left of the parenthesis, by everything in the parenthesis.....u distribute it.
1/4(560).....now we multiply
560/4 = 140
OR
this way
1/4( 300 + 260) = 1/4(300) + 1/4(260) = 300/4 + 260/4 = 75 + 65 = 140
The average rate of change over the interval
is 2.17
Explanation:
Given that the cost of a floral bouquet after a discount is given by the function ![f(x)=2.17x-10.00](https://tex.z-dn.net/?f=f%28x%29%3D2.17x-10.00)
We need to determine the average rate of change over the interval ![(12,24)](https://tex.z-dn.net/?f=%2812%2C24%29)
The average rate of change can be determined using the formula,
![\frac{f(b)-f(a)}{b-a}](https://tex.z-dn.net/?f=%5Cfrac%7Bf%28b%29-f%28a%29%7D%7Bb-a%7D)
where
and ![b=24](https://tex.z-dn.net/?f=b%3D24)
Substituting the value of a and b in the function, we get,
![f(12)=2.17(12)-10.00](https://tex.z-dn.net/?f=f%2812%29%3D2.17%2812%29-10.00)
![=26.04-10.00](https://tex.z-dn.net/?f=%3D26.04-10.00)
![=16.04](https://tex.z-dn.net/?f=%3D16.04)
![f(24)=2.17(24)-10.00](https://tex.z-dn.net/?f=f%2824%29%3D2.17%2824%29-10.00)
![=52.08-10.00](https://tex.z-dn.net/?f=%3D52.08-10.00)
![=42.08](https://tex.z-dn.net/?f=%3D42.08)
Hence, substituting these values in the formula, we get,
![\frac{f(b)-f(a)}{b-a}=\frac{42.08-16.04}{24-12}](https://tex.z-dn.net/?f=%5Cfrac%7Bf%28b%29-f%28a%29%7D%7Bb-a%7D%3D%5Cfrac%7B42.08-16.04%7D%7B24-12%7D)
Simplifying, we get,
![\frac{f(b)-f(a)}{b-a}=\frac{26.04}{12}](https://tex.z-dn.net/?f=%5Cfrac%7Bf%28b%29-f%28a%29%7D%7Bb-a%7D%3D%5Cfrac%7B26.04%7D%7B12%7D)
Dividing, we have,
![\frac{f(b)-f(a)}{b-a}=2.17](https://tex.z-dn.net/?f=%5Cfrac%7Bf%28b%29-f%28a%29%7D%7Bb-a%7D%3D2.17)
Thus, the average rate of change over the interval
is 2.17
3x^2-5x-24=0
3x^2-5x=24
x^2-5x/3=8
x^2-5x/3+25/36=8+25/36
(x-5/6)^2=313/36
x-5/6=±√(313/36)
x=5/6±√(313/36)
x=(5±√313)/6
p=(5+√313)/6
q=(5-√313)/6