A student receives test scores of 62, 83, and 91. The student's final exam score is 88 and homework score is 76. Each test is wo
1 answer:
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Answer:
area of the shape below is
53cm^2
.......
Answer:
B. (6, 1)
Step-by-step explanation:
A graph of the solution space shows that the point (6, 1) is the only one that satisfies both inequalities.
___
<em>Verification</em>
3(6) +4(1) = 18 +4 = 22 < 24
3(6) -4(1) = 18 -4 = 14 > 12
_____
<em>Notes on the Solution</em>
The graphing calculator used here only recognizes variables x and y. Since g is the first variable in the ordered pair (g, z) we use x to represent g in the equations that are graphed. Similarly, y is used to represent z in the graphed equations.
You graph an inequality by graphing it as though it were an equation, then choosing the appropriate half-plane (one side of the line or the other) to shade as the solution space. Where the shadings from the two inequalities overlap, both are satisfied by points in that area.
In the first inequality, x and y values that are less than those on the line will satisfy the inequality, so the shading is below the line.
In the second inequality, x values greater than those on the line will satisfy the inequality, so the shading is to the right of the line.
In both cases, the line is graphed as a dashed line. This is because the points on the line do not satisfy the < or > conditions, so are not part of the solution set. (If one or both conditions were ≤ or ≥, then the corresponding line would be solid, and the points on the line would be part of the solution.)
Answer:
The measure of angle B is 41.5°
The length of side a is 30.6 feet ⇒ to the nearest tenth
The length of side b is 32.9 feet ⇒ to the nearest tenth
Step-by-step explanation:
- <em>The sum of the measures of the interior angles in a triangle is 180°</em>
In the given Δ ABC
∵ m∠A = 38.1°
∵ m∠C = 100.4°
→ By using the fact above
∵ m∠A + m∠B + m∠C = 180°
∴ 38.1 + m∠B + 100.4 = 180
→ Add the like terms in the left side
∴ 138.5 + m∠B = 180
→ Subtract 138.5 from both sides
∴ m∠B = 41.5°
∴ The measure of angle B is 41.5°
∵ a is the opposite side of ∠A
∵ b is the opposite side of ∠B
∵ c is the opposite side of ∠C
→ By using the sine rule
∴ =
=
∵ c = 48.4 ft, m∠A = 38.1°, m∠B = 41.5°, and m∠C = 100.4
→ Substitute them in the sine rule above
∴ =
=
→ By using cross multiplication between the 1st and the 3rd fractions
∴ a × sin 100.4 = 48.8 × sin 38.1
→ Divide both sides by sin 100.4
∴ a = 30.61429861
∴ The length of side a is 30.6 feet ⇒ to the nearest tenth
→ By using cross multiplication between the 2nd and the 3rd fractions
∴ b × sin 100.4 = 48.8 × sin 41.5
→ Divide both sides by sin 100.4
∴ b = 32.87596206
∴ The length of side b is 32.9 feet ⇒ to the nearest tenth