Hello,
Let denote
h the number of men in the concert hall (before leaving)
f the number of women in the concert hall (before leaving)
1/5 h quit =60/2
15/100 f =60/2
h=30*5=150
f=30*100/15=200
Tey were 150+200 = 350 humans in the hall.
(why h : homme, f:femme you may call m and w)
9514 1404 393
Answer:
(c) CPCTC
Step-by-step explanation:
The proof might go something like this:
- EH ≅ KH, FH ≅ JH . . . . . given
- ∠EHF ≅ ∠KHJ . . . . . vertical angles are congruent
- ∆EHF ≅ ∆KHJ . . . . . SAS congruence theorem
- EF ≅ KJ . . . . . CPCTC
Note that JK is an alternate name for segment KJ. We used KJ in the proof because vertices K and J correspond directly to vertices E and F in the congruent triangles.
Answer:
The equation of the line passing through the given points is:
![y=-\frac{8}{3}x-11](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B8%7D%7B3%7Dx-11)
Step-by-step explanation:
Given:
The two points are: ![(x_1,y_1)=(-6,5)\textrm{ and }(x_2,y_2)=(-3,-3)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%3D%28-6%2C5%29%5Ctextrm%7B%20and%20%7D%28x_2%2Cy_2%29%3D%28-3%2C-3%29)
The equation of a line when two points are given is:
![y-y_1=\left (\frac{y_2-y_1}{x_2-x_1} \right )(x-x_1)](https://tex.z-dn.net/?f=y-y_1%3D%5Cleft%20%28%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%20%5Cright%20%29%28x-x_1%29)
Plug in all the values and simplify.
![y-5=\left (\frac{-3-5}{-3-(-6)} \right )(x-(-6))\\y-5=\left (\frac{-8}{-3+6} \right )(x+6)\\y-5=\left (\frac{-8}{3} \right )(x+6)\\y-5=\frac{-8}{3}x-16\\y=\frac{-8}{3}x-16+5\\\\y=-\frac{8}{3}x-11](https://tex.z-dn.net/?f=y-5%3D%5Cleft%20%28%5Cfrac%7B-3-5%7D%7B-3-%28-6%29%7D%20%5Cright%20%29%28x-%28-6%29%29%5C%5Cy-5%3D%5Cleft%20%28%5Cfrac%7B-8%7D%7B-3%2B6%7D%20%5Cright%20%29%28x%2B6%29%5C%5Cy-5%3D%5Cleft%20%28%5Cfrac%7B-8%7D%7B3%7D%20%5Cright%20%29%28x%2B6%29%5C%5Cy-5%3D%5Cfrac%7B-8%7D%7B3%7Dx-16%5C%5Cy%3D%5Cfrac%7B-8%7D%7B3%7Dx-16%2B5%5C%5C%5C%5Cy%3D-%5Cfrac%7B8%7D%7B3%7Dx-11)
Therefore, the equation of the line passing through the above points is
![y=-\frac{8}{3}x-11](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B8%7D%7B3%7Dx-11)
Find y by maybe Pulling out like terms :
<span> 1.1 </span> Pull out like factors :
-y - 3 = -1 • (y + 3)
<span>Equation at the end of step 1 :</span><span>Step 2 :</span>Solving a Single Variable Equation :
<span> 2.1 </span> Solve : -y-3 = 0<span>
</span>Add 3 to both sides of the equation :<span>
</span> -y = 3
Multiply both sides of the equation by (-1) : y = -3
One solution was found : y = -3
<span>
Processing ends successfully</span>
Answer:
number 12 is the 5th one E
Step-by-step explanation:
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