11-3 = 8
8y = 24
8y/8 = 24/8
y = 3
Answer:
x = 8, and y = 12
Step-by-step explanation:
There are 2 variables, so you need 2 equations to form a system of equations in two variables.
The upper left triangle has all angle measures given: 100, 2x + y, 5x + y. We know that the sum of the measures of the angles of a triangle is 180.
First equation:
100 + 2x + y + 5x + y = 180
Simplify:
7x + 2y = 80 (First equation)
Now we see that the upper and lower sides are parallel, so alternate interior angles are congruent. The angles measuring 2x + y and 5x - y are alternate interior angles and are congruent.
Second equation:
2x + y = 5x - y
Simplify:
3x - 2y = 0 (Second equation)
Now we use the first equation and the second equation as a system of simultaneous equations to solve for x and y.
7x + 2y = 80
3x - 2y = 0
Solve the second equation for 2x.
3x = 2y
Now replace 2y in the first equation with 3x.
7x + 3x = 80
10x = 80
x = 8
Replace x with 8 in the second equation.
3(8) - 2x = 0
24 = 2x
x = 12
Answer: x = 8, and y = 12
Let's simplify step-by-step.
<span><span>12<span>x^2</span></span>+<span>9<span>x^2
</span></span></span>Combine Like Terms:
<span>=<span><span>12<span>x^2</span></span>+<span>9<span>x^2
</span></span></span></span><span>=<span>(<span><span>12<span>x^2</span></span>+<span>9<span>x^2</span></span></span>)
</span></span><span>=<span>21<span>x^<span>2</span></span></span></span>
The total cost when Q = 10 is $150
Step-by-step explanation:
Th equation y = mx + b represents any linear function, where
- m is the unit rate
- b is the fixed amount
∵ The fixed costs are $100
∵ The variable costs are $5 per unit
∵ There are Q units
- Represent the total cost by the function c(Q)
∴ c(Q) = 5 Q + 100, where c(Q) is the total cost of Q units
∵ c(Q) = 5 Q + 100
∵ Q = 10
- Substitute Q by 10
∴ c(10) = 5(10) + 100
∴ c(10) = 50 + 100
∴ c(10) = 150
The total cost when Q = 10 is $150
Learn more:
You can learn more about word problems in brainly.com/question/884169
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