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2 years ago

6

Can someone please please help me with this question !!!

1 answer:

Alex_Xolod [135]2 years ago

5 0

Answer: b and d

Step-by-step explanation:

Since the roots are x=2 and x=6, we can write the equation as

$f(x)=a(x-2)(x-6)$

Substituting in the coordinates of the vertex,

$-4=a(4-2)(4-6)\\\\-4=a(2)(-2)\\\\-4=-4a\\\\a=1$

So, the equation is $f(x)=(x-2)(x-6)$ .

On expanding, we get $f(x)=x^2 - 8x+12$

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A square piece of confetti has an area of 25 square millimeters. How long is each side?

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s^2=25

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3 years ago

Read 2 more answers

For ΔABC with A(–5, –4), B(3, –2), and C(–1, 6), M is the midpoint of

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Answer:

The proposition is true, as $\overrightarrow{MN} = (2,5)$ and $\overrightarrow {AC} = (4, 10)$ satisfies the given expression ( $\overrightarrow{MN} = \frac{1}{2}\cdot \overrightarrow{AC}$ ).

Step-by-step explanation:

Vertices of the triangle ABC are located in $A(x,y) = (-5,-4)$ , $B(x,y) = (3,-2)$ and $C(x,y) = (-1, 6)$ , respectively. By definition of midpoint, we get that M and N are located in the following coordinates:

$M(x,y) = \frac{1}{2}\cdot A(x,y) +\frac{1}{2}\cdot B(x,y)$ (Eq. 1)

$M(x,y) = \frac{1}{2}\cdot (-5,-4)+\frac{1}{2}\cdot (3,-2)$

$M(x,y) = \left(-\frac{5}{2},-2 \right)+\left(\frac{3}{2},-1\right)$

$M(x,y) = (-1,-3)$

$N(x,y) = \frac{1}{2}\cdot B(x,y) + \frac{1}{2}\cdot C(x,y)$ (Eq. 2)

$N(x,y) = \frac{1}{2}\cdot (3,-2)+\frac{1}{2}\cdot (-1,6)$

$N(x,y) = \left(\frac{3}{2},-1\right)+\left(-\frac{1}{2},3 \right)$

$N(x,y) = (1, 2)$

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$\overrightarrow{AC} = C(x,y)-A(x,y)$ (Eq. 3)

$\overrightarrow{AC} = (-1, 6) -(-5,-4)$

$\overrightarrow {AC} = (4, 10)$

$\overrightarrow {MN} = N(x,y)-M(x,y)$ (Eq. 4)

$\overrightarrow {MN} = (1,2)-(-1,-3)$

$\overrightarrow{MN} = (2,5)$

By getting back into (Eq. 3), we find the following the result after some algebraic handling:

$\overrightarrow {AC} = (4, 10)$

$\overrightarrow{AC} = 2\cdot (2,5)$

$\overrightarrow {AC} = 2\cdot \overrightarrow {MN}$

$\overrightarrow{MN} = \frac{1}{2}\cdot \overrightarrow{AC}$

Which proofs the given affirmation.

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