Step-by-step explanation:
- Since m∠ACM = 90°, then by angle addition, m∠ACP + m∠PCM = 90°.
- Since CP⊥ AM, then by definition of perpendicular, m∠APC = 90°. Since angles of a triangle add up to 180°, that means m∠PAC + m∠ACP = 90°.
- By substitution, m∠PCM = m∠PAC.
- Since m∠PCM + m∠CMP = 90°, then by substitution, m∠CMP = m∠PAC.
- Therefore, by AAA, △ACP and △CMP are similar.
Having proven that the triangles are similar, we can write the proportion:
AP / CP = CP / MP
9 / CP = CP / 16
CP² = 144
CP = 12
Now, we can simply use Pythagorean theorem to find the other sides.
AC² = AP² + CP²
AC² = 9² + 12²
AC = 15
CM² = CP² + PM²
CM² = 12² + 16²
CM = 20
The error made by zacharias in solving the quadratic equation 0 = -2x² + 5x - 3 using quadratic formula is; the 2 in the numerator should be –2.
<h3>Quadratic equation</h3>
There are four methods of solving quadratic equation. Namely;
- Factorization method
- Completing the square method
- Graphical method
- Formula method
0 = -2x² + 5x - 3
x = -b ± √b² - 4ac / 2a
where,
x = -b ± √b² - 4ac / 2a
x = -5 ± √5² - 4(-2)(-3) / 2(-2)
= -5 ± √25 - (24) / -2
= -5 ± √1 / -2
= -5/2 ± 1/2
= -5/2 - 1/2 or x = -5/2 + 1/2
= -5-1 / 2 or -5+1/ 2
x = -6/2 or -4/2
x = -3 or -2
Therefore, the solution to the quadratic equation is x = -3 or -2
Learn more about quadratic equation:
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Answer: y= x-2
Step-by-step explanation:
Perpendicularity entails the slope of line a is -1 divided by the slope of line b
m1= (-1/m2)
From y=Mx +c
We compare with x-4y=7
y=(1/4)x-7/4
Meaning m2= 1/4
m1= -1/(1/4)= -1*4= -4
((y-y1)/(x-x1))= ((y2-y1)/(x2-x1))=m1
x1= 2, y1= -4
((y-(-4))/(x-2))= -4
((y+4)/(x-2))= -4
Cross multiply
y+4= -4(x-2)
y= x-2
Answer:
The solution is (0, 3/4)
Step-by-step explanation:
Please copy and share the instructions. Here they are: Solve the following system of linear equations.
Both of the equations can be reduced (simplified):
2x+8y = 6 => x + 4y = 3
15x + 20y = 15 => 3x + 4y = 3
Let's use the elimination by addition and subtraction method. Multiply the first equation by -1, obtaining
-x - 4y = -3
Add the second 3x + 4y = 3
equation to the
first.
We get: 2x = 0.
Thus, x = 0. Substituting 0 for x in the 1st original equation yields:
2(0) + 8y = 6. Then y = 6/8, or y = 3/4.
The solution is (0, 3/4).
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