M > -2 (I think?)
-3 can’t be right because 3(-3) = -9 and -9 + 14 = 5, which is less than 8 so 5>8 would be false.
For this case we will solve the equations step by step:
a2 - 9a + 14 = 0
(a-7) * (a-2) = 0
a1 = 7
a2 = 2
{7, 2}
a2 + 9a + 14 = 0
(a + 7) * (a + 2) = 0
a1 = -7
a2 = -2
{-2, -7}
a2 + 5a - 14 = 0
(a + 7) * (a-2) = 0
a1 = -7
a2 = 2
{2, -7}
a2 - 5a - 14 = 0
(a-7) * (a + 2) = 0
a1 = 7
a2 = -2
{-2, 7}
Answer:
The system is of equations is:
Where g is the amount of general tickets and r is the amount of reserve tickets.
35 general tickets and 25 reserve tickets were sold.
Step-by-step explanation:
Let general tickets be represented by g and reserved tickets be represented by r.
Each general ticket sells for $10 each and reserved tickets $15 each. Dave collected a total of $725. Thus:
And a total of 60 tickets were sold. Hence:
Our system of equations is:
We can solve by substitution. First, divide both sides of the first equation by 5:
Next, we can subtract a variable (r in this case) from the second equation:
Substitute:
Distribute:
Simplify:
Subtract:
Using the previous equation:
Substitute and evaluate:
So, 35 general tickets and 25 reserve tickets were sold.
Answer:
Dimension => 10 m × 9.6 m
Step-by-step explanation:
From the question given above, the following data were obtained:
Area (A) = 96 m²
Circumference (C) = 39.2 m
Dimension =.?
Next, we shall determine the Lenght and breadth of the rectangle. This can be obtained as follow:
Let L be the Lenght
Let B be the breadth
Area of a rectangle = L × B
96 = L × B ..... (1)
Circumference of rectangle = 2(L + B)
39.2 = 2(L + B) .... (2)
From equation 2, make L the subject
39.2 = 2(L + B)
Divide both side by 2
39.2 /2 = L + B
19.6 = L + B
Rearrange
L = 19.6 – B ....(3)
Substitute the value of L in equation 3 into equation 1
96 = L × B
L = 19.6 – B
96 = (19.6 – B ) × B
Clear bracket
96 = 19.6B – B²
Rearrange
B² – 19.6B + 96 = 0
Solving by factorisation
B² – 10B – 9.6B + 96 = 0
B(B – 10) – 9.6(B – 10) = 0
(B – 9.6)(B – 10) = 0
B – 9.6 = 0 or B – 10 = 0
B = 9.6 or B = 10
Substitute the value of B into equation 3:
L = 19.6 – B
B = 9.6
L = 19.6 – 9.6
L = 10
Or
L = 19.6 – B
B = 10
L = 19.6 – 10
L = 9.6
Since the length is always longer than the breadth,
Length (L) = 10 m
Breadth (B) = 9.6 m
Finally, we shall determine the dimension of the rectangle. This can be obtained as follow:
Length (L) = 10 m
Breadth (B) = 9.6 m
Dimension =?
Dimension = L × B
Dimension = 10 m × 9.6 m
Answer:
50%
Step-by-step explanation:
5 question is what percentage of 10 question
Step 1: Divide 5 by 10
5/10 = 0.5
Step 2: multiply 0.5 by 100
0.5 × 100
= 50%
Therefore, percentage of 5 questions out of 10 questions is 50%
