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the original price of a comic book was $10, but it is on sale 2/5 off the original price. what is the sale price of the comic book
.4
Answer:
Option D. No solution
Step-by-step explanation:
<u>We have the equation of a line:
</u>
![y = - x - 10](https://tex.z-dn.net/?f=y%20%3D%20-%20x%20-%2010)
We find their cut points.
<em>Cut point with the y axis. (x = 0)
</em>
![y = -(0) -10\\y = -10](https://tex.z-dn.net/?f=y%20%3D%20-%280%29%20-10%5C%5Cy%20%3D%20-10)
<em>Cut point with the x axis. (y = 0)
</em>
.
The line cuts to the x-axis at
and cuts the y-axis at
<u>We have a parabola
</u>
![y = x ^ 2 - 2x - 3](https://tex.z-dn.net/?f=y%20%3D%20x%20%5E%202%20-%202x%20-%203)
We can factor this quadratic equation by looking for 2 numbers that when multiplied give as result -3 and that when adding these numbers as a result -2. These numbers are -3 and 1.
Then the factors are:
![(x-3)(x + 1) = 0](https://tex.z-dn.net/?f=%28x-3%29%28x%20%2B%201%29%20%3D%200)
The zeros are 3 and -1. So <em>the parabola cuts to the x axis at points </em><em>3</em><em> and</em><em> -1</em><em>.
</em>
<em>Now we find the cut points with the y axis. (x = 0)
</em>
![y = (0-3)(0 + 1)\\y = -3.](https://tex.z-dn.net/?f=y%20%3D%20%280-3%29%280%20%2B%201%29%5C%5Cy%20%3D%20-3.)
<em>The parabola cuts to the axis y in y = -3.
</em>
Now we can graph the line and the parabola. Observe the attached image.
<em>The system has no solution because the line and the parabola never intersect or touch each other. The answer is the option D</em>
Answer:
Step-by-step explanation:
x^2 - 9x - 70
we need to find two numbers whose sum is -9 and product id -17
The numbers are -14 and 5
By splitting the middle term,
x^2 - 14x + 5x - 70
= x ( x - 14 ) + 5 ( x - 14 )
( x + 5 ) ( x - 14 )
Hope this helps
Plz mark as brainliest!!!!!
Answer:
Number of hot dogs sold = 56
Number of hamburgers sold = 52
Step-by-step explanation:
Let
Number of hot dogs sold = x
Number of hamburgers sold = y
We can make equation from given equations:
(Hot dogs were sold for $.50 (fifty cents), and hamburgers were sold for $1 (one dollar). The total money raised by your class was $80. )
(Together you sold 108 hot dogs and hamburgers.)
Now we cam solve these system of equations to find value of x and y
![0.50x+y=80--eq(1)\\x+y=108--eq(2)](https://tex.z-dn.net/?f=0.50x%2By%3D80--eq%281%29%5C%5Cx%2By%3D108--eq%282%29)
Subtract both equations to get value of x:
![0.50x+y=80\\x\:\:\:\:\:\:\:\: + y=108\\-\:\:\:\:\:\:\:\: -\:\:\:\:\:\: -\\---------\\-0.5x=-28\\x=\frac{-28}{-0.5}\\x=56](https://tex.z-dn.net/?f=0.50x%2By%3D80%5C%5Cx%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%20%2B%20y%3D108%5C%5C-%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%20-%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%20-%5C%5C---------%5C%5C-0.5x%3D-28%5C%5Cx%3D%5Cfrac%7B-28%7D%7B-0.5%7D%5C%5Cx%3D56)
We get value of x = 56
Now putting value of x in equation 2 to find value of y
![x+y=108\\56+y=108\\y=108-56\\y=52](https://tex.z-dn.net/?f=x%2By%3D108%5C%5C56%2By%3D108%5C%5Cy%3D108-56%5C%5Cy%3D52)
So, we get y = 52
Therefore,
Number of hot dogs sold = x = 56
Number of hamburgers sold = y = 52