Solve the following equation 5x-3(x-2)=10+x
1 answer:
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The measure of angle RQS is 50°.
Solution:
Given data:
m(ar QTS) = 260°
<u>Tangent-chord theorem:</u>
<em>If a tangent and chord intersect at a point, then the measure of each angle formed is half of the measure of its intercepted arc.</em>
m∠PQS = 130°
<em>Sum of the adjacent angles in a straight line is 180°.</em>
m∠PQS + m∠RQS = 180°
130° + m∠RQS = 180°
Subtract 130° from both sides.
130° + m∠RQS - 130° = 180° - 130°
m∠RQS = 50°
The measure of angle RQS is 50°.
Problem 1
Answer: C) No solution
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Explanation:
We have z = -4 and 4z = -4 at the same time. Solving 4z = -4 leads to z = -1
So in effect we have z = -4 and z = -1 at the same time, but this is a contradiction. A variable can only hold one number at a time.
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Problem 2
Answer: C) Infinitely many solutions
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Explanation:
The two equations are equivalent. You can prove as such by isolating 2y in the first equation.
5x = 8-2y
5x+2y = 8
2y = 8-5x
2y = -5x+8
-5x+8 = 2y
This shows the first equation is equivalent to the second, and vice versa. They both graph the same line. Any point along the line is a solution. So that's why there are infinitely many of them.
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Problem 3
Answer: Choice A)
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Explanation:
The range is the set of the possible y values. We're concerned with every y coordinate of each (x,y) solution. So we only focus on the shaded region.
The dashed line means we exclude the boundary. It's an electric fence we cannot touch. So y > -6 or -6 < y describes part of the range
The other part is since y = 3 is the when the highest point occurs.
So writing describes all possible y values of each (x,y) solution in the shaded region.