<u>Given</u>:
Let x represents the number of weeks.
Let y represents the amount of money.
Given that you are saving money for a new cell phone.
At week 0 you have saved $20 and at week 10 you have $100.
Writing this as coordinates, we get;
(0,20) and (10,100)
We need to determine the slope of the linear equation.
<u>Slope</u>:
The slope of the equation can be determined using the formula,
![m=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
Substituting the coordinates, we get;
![m=\frac{100-20}{10-0}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B100-20%7D%7B10-0%7D)
![m=\frac{80}{10}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B80%7D%7B10%7D)
![m=8](https://tex.z-dn.net/?f=m%3D8)
Thus, the slope of the linear equation is $8.
Hence, $8 is put away each week.
Answer:
Length of Shorter leg = 27 feet
Length of Longer leg = 36 feet
Length of Hypotenuse = 45 feet
Step-by-step explanation:
Given:
Let,
Length of Shorter leg = x,
According to the given condition we have
∴ Length of Longer leg = x + 9 feet
∴ Length of Hypotenuse = 2x - 9 feet
To Find:
Length of Shorter leg = ?
Solution:
Now In Right Angle Triangle, By Pythagoras theorem we have
![(\textrm{Hypotenuse})^{2} = (\textrm{Shorter leg})^{2}+(\textrm{Longer leg})^{2}](https://tex.z-dn.net/?f=%28%5Ctextrm%7BHypotenuse%7D%29%5E%7B2%7D%20%3D%20%28%5Ctextrm%7BShorter%20leg%7D%29%5E%7B2%7D%2B%28%5Ctextrm%7BLonger%20leg%7D%29%5E%7B2%7D)
substituting the given values we get
![(2x-9)^{2} = (x)^{2}+(x+9)^{2}\\](https://tex.z-dn.net/?f=%282x-9%29%5E%7B2%7D%20%3D%20%28x%29%5E%7B2%7D%2B%28x%2B9%29%5E%7B2%7D%5C%5C)
By using Identity (A ± B)² = A² ± 2AB +B² we get
![4x^{2} -36x+81=x^{2} +(x^{2} +18x+81)\\\\4x^{2} -2x^{2} -36x-18x=81-81\\\\2x^{2} -54x=0\\2x(x-27)=0\\2x=0 or x-27=0\\\therefore x\ cannot\ be \ zero\\\therefore x = 27 \feet](https://tex.z-dn.net/?f=4x%5E%7B2%7D%20-36x%2B81%3Dx%5E%7B2%7D%20%2B%28x%5E%7B2%7D%20%2B18x%2B81%29%5C%5C%5C%5C4x%5E%7B2%7D%20-2x%5E%7B2%7D%20-36x-18x%3D81-81%5C%5C%5C%5C2x%5E%7B2%7D%20-54x%3D0%5C%5C2x%28x-27%29%3D0%5C%5C2x%3D0%20or%20x-27%3D0%5C%5C%5Ctherefore%20x%5C%20cannot%5C%20be%20%5C%20zero%5C%5C%5Ctherefore%20x%20%3D%2027%20%5Cfeet)
Substituting x=27 we get
∴ Length of Longer leg = x + 9 =27 +9 = 36 feet
∴ Length of Hypotenuse = 2x - 9 = 2×27 -9 = 45 feet
If yellow is 15, then we set 2/5 = x/15, letting x = green. 5x = 30, so x = 6. Again, with yellow being 15, then we set 3/4 = 15/x, letting x = orange. 3x = 60, so x = 20. Then, the ratio of green to orange is 6:20 = 3:10. Hope this helps!
If you have any questions let me know
I hope this helps you again!
Answer:
y = -1x - 8
Step-by-step explanation:
y = -1x + b
-3 = -1(-5) + b
-3 = 5 + b
-8 = b
Answer:
30
Step-by-step explanation:
Consecutive even numbers can be written as X,X+2,X+4,X+6, and so forth. You only have three consecutive even numbers that equal 96, so write the following equation:
X+X+2+X+4=96
1) Combine alike terms:
3X+6=96
2) Subtract 6 from both sides:
3X=90
3) Divide both sides by 3:
X=30
Now plug in 30 for each of the consecutive even numbers' equations:
X=30
X+2=32
X+4=34
The smallest of these three numbers is 30, therefore the answer is 30!