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zmey [24]
3 years ago
9

Find the angles y and x​

Mathematics
1 answer:
Katen [24]3 years ago
3 0

Answer:

x = 67

y = 23.5

Step-by-step explanation:

Sum of angles in a triangle is supplementary,

x + 90 + 23 = 180

x + 113 = 180

x = 180 - 113

x = 67

y = ?

180 - 67 / 2

= 133 / 2

= 66.5

y + 66.5 = 90

y = 90 - 66.5

y = 23.5

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Select the function that represents a parabola with zeros at x = –2 and x = 4, and y-intercept (0,–16). A ƒ(x) = x2 + 2x – 8 B ƒ
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Answer:

D. f(x) = 2\cdot x^{2}-4\cdot x -16

Step-by-step explanation:

Any parabola is modelled by a second-order polynomial, whose standard form is:

y = a\cdot x^{2}+b\cdot x + c

Where:

x - Independent variable, dimensionless.

y - Dependent variable, dimensionless.

a, b, c - Coefficients, dimensionless.

In addition, a system of three linear equations is constructed by using all known inputs:

(-2, 0)

4\cdot a -2\cdot b + c = 0 (Eq. 1)

(4, 0)

16\cdot a + 4\cdot b +c = 0 (Eq. 2)

(0,-16)

c = -16 (Eq. 3)

Then,

4\cdot a - 2\cdot b = 16 (Eq. 4)

16\cdot a + 4\cdot b = 16 (Eq. 5)

(Eq. 3 in Eqs. 1 - 2)

a - 0.5\cdot b = 4 By Eq. 4 (Eq. 4b)

a = 4 + 0.5\cdot b

Then,

16\cdot (4+0.5\cdot b) + 4\cdot b = 16 (Eq. 4b in Eq. 5)

64 + 12\cdot b = 16

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The remaining coeffcient is:

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a = 2

The function that represents a parabola with zeroes at x = -2 and x = 4 and y-intercept (0,16) is f(x) = 2\cdot x^{2}-4\cdot x -16. Thus, the right answer is D.

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4 years ago
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