3. a circle is given by the equation x^2+y^2=100. which of the following points are on the circle?
a. (0,10)
b. (−8,6)
c. (−10,−10)
d. (45,55)
e. (−10,0)

Options A, B and E

Step-by-step explanation:

To the breakdown:

For a point to be on the circle it must satisfy the equation of a circle.

From the question we are given the equation of the circle as:

x^2 + y^2 = 100;

To determine the points that can be present in the circle we check each point against the equation and see if the Left hand (LHS)and Right hand (RHS)side of the equation are equal. So lets start:

a) (0,10) => x = 0, y = 10;

(0)^2 + (10)^2 = 100; so the LHS and RHS of the equation are the same.

b) (-8, 6) => x= -8, y = 6;

(-8)^2 + (6)^2 = 64 + 36 = 100; so the LHS and RHS are equal.

c) (-10, -10) => x=-10, y=-10;

(-10)^2 + (-10)^2 = 100+100= 200; the LHS is greater than the RHS.

d) (45, 55) => x=45, y=55;

(45)^2 + (55)^2 = 2025 + 3025 = 5050; the LHS is greater than the RHS.

e) (-10, 0) => x=-10, y= 0;

(-10)^2 + (0)^2 = 100; so the LHS and the RHS are equal.        

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.