Answer:
42
Step-by-step explanation:
Yes, you are right.
6 weeks * 7 days in a week.
so 7 days in all 6 weeks is 42 days.
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).
___________________________________________
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°.
4x² + 3x + 5 = 0
x = <u>-3 +/- √(3² - 4(4)(5))</u>
2(4)
x = <u>-3 +/- √(9 - 80)</u>
8
x = <u>-3 +/- √(-71)
</u> 8<u>
</u>x = <u>-3 +/- √(71 × (-1))</u>
8
x = <u>-3 +/- √(71) × √(-1)
</u> 8<u>
</u>x = <u>-3 +/- 8.43i
</u> 8
x = -0.375 +/- 1.05375i
x = -0.375 + 1.05375i x = -0.375 - 1.05375i
<u />
You have to complete the square on this to get it into standard form of a circle. Move the 8 over to the other side because that's part of the radius. Group together the x terms, take half the linear term which is 8, square it and add it in to both sides. Half of 8 is 4, 4 squared is 16, so add in 16 to both sides. I'll show you in a sec. You don't need to do anything to the y squared term. This just means that the center of the circle does not move up or down, only side to side, right or left. Here's your completing the square before we simplify it down to its perfect square binomial.
. Now break down the parenthesis into the perfect square binomial and do the addition of the right:
. This is the standard form of a circle that has a center of (4, 0) and a radius of
X = 4/15 or 0.26
First add the numbers on the left side of the equation.
0.72 = 0.8 - 0.3x
Then move the variable to the left as well.
0.3x + 0.72 = 0.8
Move the constant to the right by subtracting.
0.3x = 0.8 - 0.72
Subtract the numbers
0.3x = 0.08
Divide both sides by 0.3.
And that should yield your answer.
Hope this helps. ^^
