X^2 + y^2 = 8 X-y=0 Select all of the following that are solutions to the system shown

Mathematics

1 answer:

ludmilkaskok [199]3 years ago

5 0

X^2 + y^2 = 8
X-y=0 so x = y

replace x = y into X^2 + y^2 = 8

y^2 + y^2 = 8

2y^2 = 8

y^2 = 8/2

y^2 = 4

y = - 2 and y = 2

because x = y

so x = - 2 and x = 2

solutions:

x= - 2 and x = + 2

y= - 2 and y = + 2

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Find the angle made by the x axis and the terminal side resulting from connecting the origin to (5,7), rounded to the nearest in

prohojiy [21]

<h2>Answer:</h2>

55°

<h2> Step-by-step explanation:</h2>

To solve this, follow these steps:

i. <em>Make a sketch of the problem</em>.

The sketch has been attached to this response.

ii. <em>Label the sketch properly</em>

As shown in the sketch, θ is the angle between the x-axis and the terminal side resulting from connecting the origin to (5,7).

iii. <em>Solve using the tangent trigonometric ratio</em>

With the proper sketch and labelling, a right triangle is formed with the adjacent and opposite sides to the angle being 5 units and 7 units respectively.

Using the tangent formula,

tan θ = opposite / adjacent

tan θ = 7 / 5

θ = tan⁻¹ (7/5)

θ = tan⁻¹ (1.4)

θ = 54.46

θ = 55° to the nearest integer.

Therefore, the angle made by the x axis and the terminal side resulting from connecting the origin to (5,7), rounded to the nearest integer is 55°