Given mA+ mB=mB + mC prove mC= mA Write a paragraph proof to prove the statement

Mathematics

2 answers:

ra1l [238]4 years ago

8 0

Answer: So, you can subtract m_B from both sides to transform the equality into

m_A+ m_B=m_B + m_C \to m_A+ m_B-m_B=m_B + m_C-m_B \to m_A=m_C

as required.

Step-by-step explanation:

soldi70 [24.7K]4 years ago

4 0

As a property of equations, you can add or subtract the same quantity to/from both sides, and the truth value of the equality will remain the same: if you start with something true, e.g. 7=7 and add the same quantity to both sides, e.g. 7+4=7+4, you will still have something true, i.e. 11=11.

On the other hand, if you start with something false, e.g. 3=7 and add the same quantity to both sides, e.g. 3+6=7+6, you will still have something false, i.e. 9=13.

So, you can subtract $m_B$ from both sides to transform the equality into

$m_A+ m_B=m_B + m_C \to m_A+ m_B-m_B=m_B + m_C-m_B \to m_A=m_C$

as required.

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the vertex of this parabola is at (2,-1). when the y-value is 0, the x-value is 5. what is the coefficient of the squared term i

timama [110]

We know that

case a)
the equation of the vertical parabola write in vertex form is
y=a(x-h)²+k,
where (h, k) is the vertex.

Using our vertex, we have:
y=a(x-2)²-1
We know that the parabola goes through (5, 0),

so
we can use these coordinates to find the value of a:
0=a(5-2)²-1
0=a(3)²-1
0=9a-1

Add 1 to both sides:
0+1=9a-1+1
1=9a
Divide both sides by 9:
1/9 = 9a/9
1/9 = a
y=(1/9)(x-2)²-1

the answer is
a=1/9

case b)
the equation of the horizontal parabola write in vertex form is
x=a(y-k)²+h,
where (h, k) is the vertex.

Using our vertex, we have:
x=a(y+1)²+2,
We know that the parabola goes through (5, 0),

so
we can use these coordinates to find the value of a:
5=a(0+1)²+2
5=a+2
a=5-2
a=3
x=3(y+1)²+2

the answer is
a=3

see the attached figure