Answer:
The equation has two solutions for x:
<u>x₁ = (8 + 10i)/2</u>
<u>x₂ = (8 - 10i)/2</u>
Step-by-step explanation:
Let's use the quadratic formula for solving for x in the equation:
X^2 - 8X + 41= 0
x² - 8x + 41 = 0
Let's recall that the quadratic formula is:
x = -b +/- (√b² - 4ac)/2a
Replacing with the real values, we have:
x = 8 +/- (√-8² - 4 * 1 * 41)/2 * 1
x = 8 +/- (√64 - 164)/2
x = 8 +/- (√-100)/2
x = 8 +/- (√-1 *100)/2
Let's recall that √-1 = i
x = 8 +/- 10i/2
<u>x₁ = (8 + 10i)/2</u>
<u>x₂ = (8 - 10i)/2</u>
Based on the calculations, the measures of angles 1 and 2 are 50° and 135° respectively.
<h3>What is the theorem of intersecting chord?</h3>
The theorem of intersecting chord states that when two (2) chords intersect inside a circle, the measure of the angle formed by these chords is equal to one-half (½) of the sum of the two (2) arcs it intercepts.
By applying the theorem of intersecting chord to circle U shown in the image attached below, we can infer and logically deduce that angle 1 will be given by this formula:
m∠1 = ½(53 + 47)
m∠1 = ½(100)
m∠1 = 50°.
Since angles 1 and 2 are linear pair, they are supplementary angles. Thus, we have:
m∠1 + m∠2 = 180°
m∠2 = 180 - m∠1
m∠2 = 180 - 50
m∠2 = 130°.
Read more on intersecting chords here: brainly.com/question/27251228
#SPJ1
6*7
=6(1+1+1+1+1+1+1)
=6*1+6*1+6*1+6*1+6*1+6*1+6*1
=6+6+6+6+6+6+6
=42
Answer:
JM = 7
Step-by-step explanation:
Triangles LMN and LJK are similar, so corresponding sides have teh same ratio:
LM/MN = LJ/JK
14/(JM+3) = (14 +JM)/15
210 = (JM +3)(JM +14) . . . . . multiply by 15(JM +3)
JM² +17JM -168 = 0 . . . . . . . subtract 210; put in standard form
(JM +24)(JM -7) = 0 . . . . . . factor
The values for JM that make this true are 7 and -24. The length must be positive, so ...
JM = 7