Answer:
x = 12, z = 86
Step-by-step explanation:
Two angles are called supplementary when their measures add up to 180 degrees.
(12x -58 + 13x - 62 ) = 180°
12 x + 13x -58 - 62 = 180°
25x - 120 = 180
25x = 180 + 120
x = 300/ 25
x = 12
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(z° + 13x - 62) = 180
(z° + 13(12) - 62 )= 180
(z° + 156 - 62 )= 180
(z° + 94 ) = 180
z° = 180 - 94
z = 86
Answer:
In words, Cosine theta equals plus or minus square root of seven over 4,tangent theta equals plus or minus three over root seven
Step-by-step explanation:
Given that sin ∅ =3/4 It means the ratio of the opposite side to the hypotenuse side is 3:4.
Using the Pythagoras theorem we can calculate the hypotenuse adjacent as follows.
a²+b²=c²
a²=c²-b²
a²=4²-3²
a²=16-9
a²=7
a=√7
Then Cos ∅= opposite/ adjacent
=√7/4
Then Tan ∅ = opposite/adjacent
=3/√7
In words, Cosine theta equals plus or minus square root of seven over 4,tangent theta equals plus or minus three over root seven.
<h3>
Answer: x^2-3x+36</h3>
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Explanation:
The larger rectangle has area of (x+1)(x+1) = x^2+2x+1 through the use of the FOIL rule or distribution
If you use distribution, then it might help to let y = x+1 so we'd have y(x+1) lead to xy+1y which becomes x(x+1)+1(x+1). From there it might be easier to see how to get x^2+2x+1 after everything distributes again and simplifies.
The smaller rectangle has area 5x-35 which is found by distributing 5(x-7)
To get the shaded area, we subtract the two rectangle areas found above
shaded area = (larger area) - (smaller area)
shaded area = (x^2+2x+1) - (5x - 35)
shaded area = x^2+2x+1 - 5x + 35
shaded area = x^2-3x+36
The answer would be <QRZ
Since you are looking for an angle congruent to <UQR using the alternate interior angles theorem, interior suggests that the angle must be inside the parallel lines, se we can get rid of options <WRT and <TRZ since they are exterior angles
Furthermore, in the alternate interior angles theorem, the two angles must be alternate or opposite of each other which would show that the only possible answer would be <QRZ
hope this helped!
