Answer:
x=6
Step-by-step explanation:
In a square, its angles are all 90 degrees. So, cutting a square in half into two triangles from corner to corner produces 45 degree angles on both sides. Since the triangles are now 45-45-90 triangles, we can use the rule where the hypotenuse of the triangle is equal to the square root of 2 times the length of either side. So, the side length is 6.
Simplifying
8a + 12b = 92
Solving
8a + 12b = 92
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-12b' to each side of the equation.
8a + 12b + -12b = 92 + -12b
Combine like terms: 12b + -12b = 0
8a + 0 = 92 + -12b
8a = 92 + -12b
Divide each side by '8'.
a = 11.5 + -1.5b
Simplifying
a = 11.5 + -1.5b
Answer:
Step-by-step explanation:
<u>The described is the rule:</u>
This is the 180 degrees rotation
Correct option is A.
Answer:
89.008
Step-by-step explanation:
z = (x– mean)/ standard deviation
x = z * standard deviation + mean
Now, z value for the top 4% of the exams (which is the same as getting a score below the 96%) has to be found using a z table.
In this case z = 1.751
x = 1.751 * 8 + 75
x = 89.008
Answer:
a. 235°
b. 146.03 km
c. 105 km
d. 193 km
Step-by-step explanation:
a. The bearing of E from A is given as 55°. The bearing in the opposite direction, from E to A, is this angle with 180° added:
bearing of A from E = 55° +180° = 235°
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b. The internal angle at E is the difference between the external angle at C and the internal angle at A:
∠E = 134° -55° = 79°
The law of sines tells you ...
CE/sin(∠A) = CA/sin(∠E)
CE = CA(sin(∠A)/sin(∠E)) = (175 km)·sin(55°)/sin(79°) ≈ 146.03 km
CE ≈ 146 km
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c. The internal angle at C is the supplement of the external angle, so is ...
∠C = 180° -134° = 46°
The distance PE is opposite that angle, and CE is the hypotenuse of the right triangle CPE. The sine trig relation is helpful here:
Sin = Opposite/Hypotenuse
sin(46°) = PE/CE
PE = CE·sin(46°) = 146.03 km·sin(46°) ≈ 105.05 km
PE ≈ 105 km
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d. DE can be found from the law of cosines:
DE² = DC² +CE² -2·DC·CE·cos(134°)
DE² = 60² +146.03² -2(60)(146.03)cos(134°) ≈ 37099.43
DE = √37099.43 ≈ 192.6 . . . km
DE is about 193 km
