_
4
Of my number is 12
Work out 5 times my number. You must show your working "
The range of the function is all real numbers.
The vertex of the function is .
The function has two x-intercepts.
The function is increasing over the interval (, ∞).
Answer: -1/4, infinity
Step-by-step explanation:
Answer:
60 yrs old
Step-by-step explanation:
equations and get the letters to decode the hidden message . You
may use the extracting the square root method
P:±6
M: ±7
C:5,6
A : 0
J:4,-1
Q:±√5
L:±11
H:±4
D:-4,1 I:±3
S:16,-6
Y: ±8
B:±4√2
E:±2
A:0,-4
U:6,0
U:±√10
N:6,-16
G:1,-1
T:±2√2
O:±6√2
V:±√3
I:±5
J:-7,-1
K:5,-2
W:±12
F:±2√3
X:±6
R:0,-6
•:9±√6
/4
Message : __________________________________
________________________________________
1. x2 = 49
2. x2 -27 =0
3. 3x2-36= 0
4. 9x2 = 0
5. 5x2- 15=0
6. 2x2- 144=0
7. ( x + 3)2 = 9
8. 4x2 -100 =0
9. 5x2 = 40
10. 3x2 -12 = 0
11. (x-5)2
The corresponding roots of the quadratic equations are given.
Quadratic expressions are polynomial equations of second degree.
The general form of a quadratic equation is ax² + b x + c = 0.
1. x² = 49
Find the square root.
x = ±√49 = ±7
2. x² - 27 = 0
x² = 27 = 9 × 3
x = √27 = √(9×3) = √9 × √3 = ±3√3
3. 3x² - 36 = 0
3x² = 36
Divide 3 on both sides.
x² = 12
x = √12 = √(4 × 3) = ±2√3
4. 9x² = 0
x = 0
5. 5x² - 15 = 0
5x² = 15
x² = 3
x = ±√3
6. 2x² - 144 = 0
2x² = 144
x² = 72
x = √72 = √(36 × 2) = ±6√2
7. (x + 3)² = 9
x + 3 = √9
x + 3 = ±3
x = 3 - 3 = 0 and x = -3 - 3 = -6
8. 4x² - 100 = 0
4x² = 100
x² = 25
x = ±√5
9. 5x² = 40
x² = 8
x = √8 = √(4 × 2) = ±2√2
10. 3x² - 12 = 0
3x² = 12
x² = 4
x = ±2
11. (x - 5)² = 121
x - 5 = √121
x - 5 = ±11
x = 11 + 5 = 16 or x = -11 + 5 = -6
Hence the solutions are found.
Learn more about Quadratic Equations here :
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Answer:
Hot dogs sold: 44
Sodas sold: 132
Step-by-step explanation:
This is is a problem of a system of two equations with two unknowns. This can be solved in multiple ways (the substitution method, the elimination method, the equalization method, the graphic method...) . I will resolve it using the equalization method that is a little bit more practical from my point of view.
First, we have to determine the system by the data we are given:
Where:
Secondly, we are going to isolate any variable from both equations. I chose to isolate Y.
Thirdly, we equalizate both equations.
So we get:
Then we isolate X.
So now we know that the number of hot dogs sold was 44! If the sodas sold were three times the number of hot dogs sold, then we know that there were 132 sodas sold at the hockey game!