The two inequalities that represents the constraints for the art studio classes per week are:
x + 1.5y = 40
35(x + y) > 1,000
<h3>What two inequalities represent the constraints?</h3>
Here are inequalities signs and what they mean:
> means greater than
< means less than
≥ means greater than or equal to
≤ less than or equal to
= means equal to
The inequality that represents the total hoursthe art studio is open would be an equal to sign. This is because the store is open for a maximum of 40 hours.
The inequality that represents the total earnings would be represented with a greater than sign because the studio earns more than $1000 weekly.
To learn more about inequality, please check: brainly.com/question/5031619
Answer: x only can have complex values, not real values.
x = -1/4 - 1/4i and x = -1/4 + 1/4 i
Explanation:
Finding the possible values of x in the expression given is solving the quadratic equation.
8x² + 4x = - 1
Rearrange the terms:
8 (x² + x/2) = - 1 ← common factor 8 in the left side
x² + x/2 = - 1/8 ← division property
x² + x/2 + 1/16 = - 1/8 + 1/16 ← addition property
(x + 1/4)² = -1/8 + 1/16 ← -factor the perfect square trinomial in the left side
(x + 1/4)² = - 1/16 ← add the fractions in the right side
x + 1/4 = (+/-) √ (-1/16) ← square roots on both sides
x + 1/4 = (+/-) (1/4)i ← complex solution
x = - 1/4 +/- 1/4i
x = - 1/4 - 1/4i and x = - 1/4 + 1/4 i ← answer
Answer:
What
Step-by-step explanation:
What language
Is that
Answer:
Step-by-step explanation:
b.
(0,2)
2y - x > 1
2(2) - 0 > 1
4 - 0 > 1
true, (0,2) is a solution to the inequality
(8,1/2)
2y - x > 1
2(1/2) - 8 > 1
1 - 8 > 1
-7 > 1
false, (8,1/2) is not a solution to the inequality
(-6,3)
2y - x > 1
2(3) - (-6) > 1
6 + 6 > 1
12 > 1
true, (0,2) is a solution to the inequality
(-7,-3)
2y - x > 1
2(-3) - (-7) > 1
-6 + 7 > 1
1 > 1
false, (8,1/2) is not a solution to the inequality
(1 is not greater than one, but equal. since the inequality is not "greater than or equal to", this equation is false)
c. the top half should be shaded
d. no, because the inequality is >, not >=. therefore, the points on the line are not included in the solution set.
