Answers: ∠a = 30° ; ∠b = 60° ; ∠c = 105<span>°.
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1) The measure of Angle a is 30°. (m∠a = 30°).
Proof: All vertical angles are congruent, and we are shown in the diagram that angle A — AND the angle labeled with the measurement of 30°— are vertical angles.
2) The measure of Angle b is 60°. (m∠b = 60<span>°).
Proof: All three angles of a triangle add up to 90 degrees. In the diagram, we can examine the triangle formed by Angle A, Angle B, and a 90</span>° angle. This is a right triangle, and the angle with 90∠ degrees is indicated as such (with the "square" symbol). So we know that one angle is 90°. We also know that m∠a = 30°. If there are three angles in a triangle, and all three angles must add up to 180°, and we know the measurements of two of the three angles, we can solve for the unknown measurement of the remaining angle, which in this case is: m∠b.
90° + 30° + m∠b = 180<span>° ;
</span>180° - (<span>90° + 30°) = m∠b ;
</span>180° - (120°) = m∠b = 60<span>°
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Now we need to solve for the measure of Angle c (<span>m∠c).
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All angles on a straight line (or straight "line segment") are called "supplementary angles" and must add up to 180</span>°. As shown, Angle c is on a "straight line". The measurement of the remaining angle represented ("supplementary angle" to Angle c is 75° (shown on diagram). As such, the measure of "Angle C" (m∠c) = m∠c = 180° - 75° = 105°.
Complete Question
Veronikas four test scores are 59, 80, 95, 88 and 93 if the outlier of 59 is removed what is the mean absolute deviation of the remaining four test scores?
Answer:
5
Step-by-step explanation:
We have the four test scores
80, 95, 88 and 93
Step 1
We find the mean of the 4 test scores
= 80 + 95 + 88 + 93/4
= 356 / 4
89
Step 2
The formula for Mean Absolute Deviation =
Summation( x - Mean)/n
Hence,
|(80 - 89 )+( 95 - 89) + (88 - 89) + (93 - 89)|/5
= 9 + 6 +1 + 4/4
= 20/4
= 5
To find the inverse of a function, you swap the x and y values. So instead of y=4x+8, it becomes x=4y+8. Now you re-solve for y, and that’s your answer:
x=4y+8
x-8=4y
1/4x-2=y
So h(x)=1/4x-2, or the first option
