The diagrams for parts A and C are included here. For part B, we have circle O. We begin by drawing two radii OA and OC, connecting points A and C to create chord AC. The radius intersects chord AC at point B, bisecting AC into equal segments AB and BC. This gives us two triangles, ΔOBA and ΔOBC, where OA equals OC (since they're radii), OB equals OB (by the reflexive property), and AB is equal to BC (as stated in the question). By applying the SSS triangle congruence criterion, we conclude that ΔOBA is congruent to ΔOBC, allowing us to deduce that ∡OBA equals ∡OBC, both measuring 90°. Thus, OB is perpendicular to AC. Moving on to part D, we again work with circle O and draw the two radii OA and OC, joining points A and C to create chord AC. The radius intersects AC at point B, where AB is perpendicular to AC, meaning ∡B equals 90°. We then consider the right triangles ΔOBA and ΔOBC, and given OA equals OC (the radii), and OB equals OB (reflexive property), we conclude through the HL triangle congruence that ΔOBA is congruent to ΔOBC. Consequently, we find BA equal to BC, thus OB bisects AC.
Regardless of the value of M, it will correspond to 18m squared.
ANSWER:
(-5, 0.5) serves as a solution for the equations x – 4y = –7, 0.2x + 2y = 0.
SOLUTION:
We start with the two equations: x – 4y = -7 → (1)
And 0.2x + 2y = 0 → (2)
We will verify if (-5, 0.5) is a solution.
To do this, we will resolve both equations.
Let’s multiply equation (2) by 2 to facilitate the cancellation of y terms.
This transforms equation (2) into:
0.4x + 4y = 0 → (3)
Now, combine equations (1) and (3), leading to:
1.4x + 0 = -7
Next, input the x value into (2)
0.2(-5) + 2y = 0
-1 + 2y = 0
2y = 1
y = 0.5
Thus, the result for the equations is (-5, 0.5).
Therefore, (-5, 0.5) is the solution to the equations.
