ANSWER
1. No solution
2. 4 and 6
3. 81
EXPLANATION
1. The given quadratic equation is
![{x}^{2} + 1 = 0](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20%20%2B%201%20%3D%200)
This implies that:
![{x}^{2} = - 1](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20%20%3D%20%20-%201)
There is no real number whose square is negative one.
This quadratic equation has no solution.
2. The given quadratic equation is
![{x}^{2} - 10x + 24 = 0](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20%20-%2010x%20%2B%2024%20%3D%200)
We split the middle term with -6,-4 because their product is 24 and their sum is -10
![{x}^{2} - 6x - 4x+ 24 = 0](https://tex.z-dn.net/?f=%7Bx%7D%5E%7B2%7D%20%20-%206x%20%20-%204x%2B%2024%20%3D%200)
We factor by grouping
![{x}(x - 6)- 4(x - 6)= 0](https://tex.z-dn.net/?f=%7Bx%7D%28x%20%20-%206%29-%204%28x%20-%206%29%3D%200)
![(x - 6)(x - 4)= 0](https://tex.z-dn.net/?f=%28x%20%20-%206%29%28x%20-%204%29%3D%200)
We have x=4 and x=6.
3. The given quadratic equation is
![{x}^{2} - 18x = 7](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20-%2018x%20%3D%207)
We the square of half the coefficient of x to both sides of the equation.
![( - \frac{18}{2} )^{2} = ( { - 9)}^{2} = 81](https://tex.z-dn.net/?f=%28%20%20-%20%20%5Cfrac%7B18%7D%7B2%7D%20%29%5E%7B2%7D%20%20%3D%20%28%20%7B%20-%209%29%7D%5E%7B2%7D%20%20%3D%2081)
The correct choice is C.
17. First expand the left side:-
(2x + 1)(ax + b)
= 2ax^2 + ax + 2bx + b
= 2a x^2 + x(a + 2b) + b = 6x^2 - 5x + c.
Comparing coefficients:-
2a = 6 so a = 3
a + 2b = -5
3 + 2b = -5
2b = -5 - 3 = -8
b = -4
Also b = c, so c = - 4
Answer: a = 3, b = -4 and c = -4
Answer:
Step-by-step explanation:
HUNYA~~~~~ YES DADDY~~ OH YEAH~~~ (spills the milk)
Answer:
27.2 of a tank
Step-by-step explanation:
= ![\frac{x}{4}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B4%7D)
136 = 5x
x = 27.2
<u>Answer</u>:
189 tickets were sold in amusement park on Saturday.
<u>Step-by-step explanation:</u>
Given:
The ratio of child and adult tickets = 8:1
sold 147 more child tickets than adult tickets
To Find:
Number of tickets sold on Saturday in the amusement park = ?
Solution:
Let
The number of child ticket be x
The number of adult ticket be y
Then from the ratio we know that there are 8 child ticket than adult ticket
=> x =8y------------------------------(1)
Also, they sold 147 more child tickets than adult tickets
=> x = 147 +y--------------------------(2)
Equating (1) and (2)
8y = 147 +y
8y-y = 147
7y=147
y =![\frac{147}{7}](https://tex.z-dn.net/?f=%5Cfrac%7B147%7D%7B7%7D)
y =21
So The number of adult tickets were 21
Now the child ticket
x = 147 +y
x = 147+21
x= 168
Total tickets = adult ticket + child ticket
=>21 +168
=> 189 tickets