The solution for the first inequality is a ≥ 2 or a ∈ [2, ∞), and for the second inequality the solutions are b < -5 or b ∈ (-∞, -5)
<h3>What is inequality?</h3>
It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
We have two inequalities:
a.) -12a +7 ≤31
b.) -9 > 3b +6
a) -12a +7 ≤ 31
-12a ≤ 31 - 7
-12a ≤ 24
-a ≤ 2
a ≥ 2 (sign changed because multiplied by a negative number)
a ∈ [2, ∞)
b.) -9 > 3b +6
-15 > 3b
-5 > b
or
b < -5
b ∈ (-∞, -5)
Thus, the solution for the first inequality is a ≥ 2 or a ∈ [2, ∞), and for the second inequality the solutions are b < -5 or b ∈ (-∞, -5)
Learn more about the inequality here:
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Answer:
Number of each ticket is;
$10 tickets = 1115
$20 tickets = 1251
$30 tickets = 934
Step-by-step explanation:
Let x,y and z represent the number of $10,$20 and $30 tickets sold.
Given;
Total number of tickets n = 3300
x+y+z = 3300 .....1
Total sales = $64,190
10x + 20y + 30z = 64,190 .....2
It has sold 136 more $20 tickets than $10 tickets
y = x +136 ........3
Substituting equation 3 into equation 1 and 2;
For 1;
x+y+z = 3300
x+(x+136)+z = 3300
2x + z = 330-136
2x + z = 3164 ........4
For 2;
10x + 20y + 30z = 64,190
10x + 20(x+136) + 30z = 64,190
10x + 20x + 2720 + 30z = 64190
30x + 30z = 64190-2720
30x+30z = 61470
divide through by 30
x+z = 2049 ......5
Subtract equation 5 from 4
2x-x +z-z = 3164-2049
x = 1115
From equation 3
y = x + 136 = 1115+136
y = 1251
From equation 1;
z = 3300 - (x+y)
z = 3300- (1115 + 1251)
z = 934
Number of each ticket is;
$10 tickets = 1115
$20 tickets = 1251
$30 tickets = 934
Answer:
$560
Step-by-step explanation:
10% of $400 is $40. 40% of $400 is 10%x4. 40% of $400 is $160. Since her allowance increased by $160, it is now $560 per week.
Hello,
So Y variable is what you would start with.
20 <= he'll start off with for a
40 <= what he'll start off with for b
And X variables would be the # of hours you're working.
10 <= meaning every hour worked is worth 10 dollars
5 <= meaning every hour worked will be paid 5 dollars
So let's just say for option a he works two hours
(Option A)
10 (2) + 20
20 + 20
= 40
(Option B)
5 (2) + 40
10 + 40
50
As for your equations
Y = 10x + 40
Y= 5x + 40
