Answer:
![x=3](https://tex.z-dn.net/?f=x%3D3)
Step-by-step explanation:
![3x+5=14](https://tex.z-dn.net/?f=3x%2B5%3D14)
Subtract 5 from both sides:
![3x+5-5=14-5](https://tex.z-dn.net/?f=3x%2B5-5%3D14-5)
![3x=9](https://tex.z-dn.net/?f=3x%3D9)
Divide both sides by 3:
![\frac{3x}{3}=\frac{9}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B3x%7D%7B3%7D%3D%5Cfrac%7B9%7D%7B3%7D)
![x=3](https://tex.z-dn.net/?f=x%3D3)
Answer:
Number of cm= 40 cm
Step-by-step explanation:
Giving the following information:
3 cm equals 45 kilometers
1 cm= 45 /3 = 15km
<u>We need to determine how many centimeters represents 600 km. We will use the following formula:</u>
<u></u>
Number of cm= total km / km per one cm
Number of cm= 600 / 15
Number of cm= 40 cm
Answer:
distance between (-2,3) and (5,-3) is 9.21 units
Step-by-step explanation:
![\sqrt{(x_{2 - }x _{1}) {}^{2} + (y _{2} - y _{1}) {}^{2} }](https://tex.z-dn.net/?f=%20%5Csqrt%7B%28x_%7B2%20-%20%7Dx%20_%7B1%7D%29%20%7B%7D%5E%7B2%7D%20%20%2B%20%28y%20_%7B2%7D%20-%20y%20_%7B1%7D%29%20%20%7B%7D%5E%7B2%7D%20%20%7D%20)
Answer:
![x=0.25\,,\,y=1.75\,,\,z=0.25](https://tex.z-dn.net/?f=x%3D0.25%5C%2C%2C%5C%2Cy%3D1.75%5C%2C%2C%5C%2Cz%3D0.25)
Step-by-step explanation:
Let
denotes number of pencils, markers, erasers respectively.
For Andrea:
![6x+7y+8z=15.75\,\,\,(i)](https://tex.z-dn.net/?f=6x%2B7y%2B8z%3D15.75%5C%2C%5C%2C%5C%2C%28i%29)
For Justin:
![6x+8y+5z=16.75\,\,\,(ii)](https://tex.z-dn.net/?f=6x%2B8y%2B5z%3D16.75%5C%2C%5C%2C%5C%2C%28ii%29)
For Virginia:
![5x+5y+7z=11.75\,\,\,(iii)](https://tex.z-dn.net/?f=5x%2B5y%2B7z%3D11.75%5C%2C%5C%2C%5C%2C%28iii%29)
On subtracting equations (i) and (ii), we get
![(6x+7y+8z)-(6x+8y+5z)=15.75-16.75\\-y+3z=-1\\y-3z=1\\y=1+3z](https://tex.z-dn.net/?f=%286x%2B7y%2B8z%29-%286x%2B8y%2B5z%29%3D15.75-16.75%5C%5C-y%2B3z%3D-1%5C%5Cy-3z%3D1%5C%5Cy%3D1%2B3z)
Put
in equation (i)
![6x+7(1+3z)+8z=15.75\\6x+29z=8.75\,\,\,(iv)](https://tex.z-dn.net/?f=6x%2B7%281%2B3z%29%2B8z%3D15.75%5C%5C6x%2B29z%3D8.75%5C%2C%5C%2C%5C%2C%28iv%29)
Put
in equation (iii)
![5x+5(1+3z)+7z=11.75\\5x+22z=6.75\,\,\,(v)](https://tex.z-dn.net/?f=5x%2B5%281%2B3z%29%2B7z%3D11.75%5C%5C5x%2B22z%3D6.75%5C%2C%5C%2C%5C%2C%28v%29)
Multiply equation (iv) by 5 and equation (v) by 6 and then subtract both the equations.
![5(6x+29z)-6(5x+22z)=5(8.75)-6(6.75)\\13z=3.25\\z=\frac{3.25}{13}=0.25](https://tex.z-dn.net/?f=5%286x%2B29z%29-6%285x%2B22z%29%3D5%288.75%29-6%286.75%29%5C%5C13z%3D3.25%5C%5Cz%3D%5Cfrac%7B3.25%7D%7B13%7D%3D0.25)
Put
in equation ![y=1+3z](https://tex.z-dn.net/?f=y%3D1%2B3z)
![y=1+3(0.25)=1.75](https://tex.z-dn.net/?f=y%3D1%2B3%280.25%29%3D1.75)
Put
in equation (i)
![6x+7(1.75)+8(0.25)=15.75\\6x+12.25+2=15.75\\6x=1.5\\x=0.25](https://tex.z-dn.net/?f=6x%2B7%281.75%29%2B8%280.25%29%3D15.75%5C%5C6x%2B12.25%2B2%3D15.75%5C%5C6x%3D1.5%5C%5Cx%3D0.25)
Let the second angle = X
The first angle = 2X+42 ( 42 more than 2 times the second angle)
Now you have 2x+42 + x = 90 ( first angle + second angle = 90)
2x + x = 3x
Now you have:
3x +42 = 90
Subtract 42 from both sides:
3x = 48
Divide both sides by 3:
x= 48/3
x = 16
The second angle = 16 degrees.
The first angle = 2(16) + 42 = 32+42 = 74 degrees