Answers:
- x = 11
- angle RQS = 106 degrees
- angle SQT = 74 degrees
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Explanation:
Straight angles are always 180 degrees in measure.
The two smaller angles shown add up to 180
(angle RQS) + (angle SQT) = angle RQT
(9x+7) + (6x+8) = 180
(9x+6x) + (7+8) = 180
15x+15 = 180
15x = 180-15
15x = 165
x = 165/15
x = 11
From here, we then know that,
- angle RQS = 9x+7 = 9*11+7 = 99+7 = 106 degrees
- angle SQT = 6x+8 = 6*11+8 = 66+8 = 74 degrees
Note how the two results add to 106+74 = 180 to help confirm the answers.
Let the number of apples be x and that of pears be y, then:
0.64x + 0.45y = 5.26 . . . (1)
0.32x + 0.39y = 3.62 . . . (2)
(2) x 2 => 0.64x + 0.78y = 7.24 . . . (3)
(1) - (3) => -0.33y = -1.98
y = -1.98 / -0.33 = 6
From (2), 0.32x + 0.39(6) = 3.62
0.32x = 3.62 - 2.34 = 1.28
x = 1.28 / 0.32 = 4
Therefore, he bought 4 apples and 6 pears.
Answer 17/18 , 19,20
Step-by-step explanation:
Answer: a) √50
b) n = 1 + 7i
Step-by-step explanation:
first, the modulus of a complex number z = a + bi is
IzI = √(a^2 + b^2)
The fact that n is complex does not mean that n doesn't has a real part, so we must write our numbers as:
m = 2 + 6i
n = a + bi
Im + nI = 3√10
Im + n I = √(a^2 + b^2 + 2^2 + 6^2)= 3√10
= √(a^2 + b^2 + 40) = 3√10
a^2 + b^2 + 40 = 3^2*10 = 9*10 = 90
a^2 + b^2 = 90 - 40 = 50
√(a^2 + b^2 ) = InI = √50
The modulus of n must be equal to the square root of 50.
now we can find any values a and b such a^2 + b^2 = 50.
for example, a = 1 and b = 7
1^2 + 7^2 = 1 + 49 = 50
Then a possible value for n is:
n = 1 + 7i
