Answer: B
Step-by-step explanation: well by graphing the inequality we know it’s a solid line. There’s shading on the right but if you look closely at (0,0), the shading doesn’t go past or near the origin making it B “Does not include the origin”.
Answers: ∠a = 30° ; ∠b = 60° ; ∠c = 105<span>°.
</span>_____________________________________________
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>°
</span>___________________________
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°.
Answer:
4.48 years
Step-by-step explanation:
The formula for simple interest is
A = P(1+r*t), with A being the final amount, P being the initial amount, r being the interest rate, and t being the time. Plugging our values in, we get
1750 = 1500(1+0.0372 * t)
Note that 3.72 was translated into 0.0372 as changing percents to decimals requires dividing by 100
Expanding our equation, we get
1750 = 1500 + 55.8 * t
subtract 1500 from both sides to isolate the t and its coefficient
250 = 55.8 * t
divide both sides by 55.8 to get t
t = 4.48
Answer:
120
Step-by-step explanation:
40*30
Answer:
x2ˣ + 2ˣ
Step-by-step explanation:
<u>Points to remember</u>
(f * g)(x) = f(x) * g(x)
It is given that, f(x)= 2ˣ and g(x)=x+1
<u>To find the value of (f * g)(x) </u>
Let f(x)= 2ˣ and g(x) = x + 1
(f * g)(x) = f(x) * g(x)
= (2ˣ )* (x + 1)
= (2ˣ * x) + ( 2ˣ * 1)
= x2ˣ + 2ˣ
