A side of the triangle below has been to from an exterior angle of 141. Find the value of X

Put the quadratic into vertex form and state the coordinates of the vertex. y= y= \,\,x^2-6x-3 x 2 −6x−3

enot [183]

Answer:

$y = (x - 3)^2 - 12$

$(3,-12)$

Step-by-step explanation:

Given

$y = x^2 - 6x - 3$

Solving (a): In vertex form

The vertex form of an equation is:

$y = a(x - h)^2 + k$

To do this, we make use of completing the square method.

We have:

$y = x^2 - 6x - 3$

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Take the coefficient of x (i.e. -6)

Divide by 2; -6/2 = -3

Square it: (-3)^2 = 9

Add and subtract the result to the equation

------------------------------------------------------------------

$y = x^2 - 6x - 3$

$y = x^2 - 6x + 9 - 9 - 3$

$y = x^2 - 6x + 9 - 12$

Factorize $x^2 - 6x + 9$

$y = x^2 - 3x-3x + 9 - 12$

$y = x(x - 3)-3(x - 3) - 12$

Factor out x - 3

$y = (x - 3)(x - 3) - 12$

Express as squares

$y = (x - 3)^2 - 12$

Hence, the vertex form of $y = x^2 - 6x - 3$ is: $y = (x - 3)^2 - 12$

Solving (b): State the coordinates of the vertex.

In $y = a(x - h)^2 + k$ ; the vertex is: (h,k)

The vertex of $y = (x - 3)^2 - 12$ will be $(3,-12)$

3 0

3 years ago

For the vectors Bold uequalsleft angle negative 8 comma 0 comma 1 right angleand Bold vequalsleft angle 1 comma 3 comma negative

trapecia [35]

Answer:

Step-by-step explanation:

Given that there are two vectors U = (-8,0,1)

V = (1,3,-3)

To find projection of u on V and also projection of V on U

First let us find the dot product U and V

U.V = $-8(1)+0(3)+1(-3)\\= -11$

Projection of U on V = $\frac{U.V}{|V|} \\=\frac{-11}{\sqrt{1+9+9} } \\=\frac{-11}{\sqrt{19} }$

Similarly projection of V on U

= $\frac{U.V}{|U|} \\=\frac{-11}{\sqrt{64+0+1} } \\=\frac{-11}{\sqrt{65} }$

4 0

3 years ago

An environmentalist wants to find out the fraction of oil tankers that have spills each month.Step 1 of 2:Suppose a sample of 47

torisob [31]

Answer: The proportion of oil tankers that had spills is $\dfrac{156}{474}$ or 0.329.

Step-by-step explanation:

Since we have given that

Number of tankers is drawn = 474

Number of tankers did not have spills = 318

Number of tankers have spills = 474 - 318 = 156

Proportion of oil tankers that had spills is given by

$\dfrac{Containing\ spill}{Total}=\dfrac{156}{474}=0.329$

Hence, the proportion of oil tankers that had spills is $\dfrac{156}{474}$ or 0.329.

3 0

3 years ago

If sally drives to work 25% faster than she did yesterday, what would be her

dedylja [7]

Answer:

50 percent

Step-by-step explanation:

because sally was tried yesterday and went 25 percent faster today.

6 0

2 years ago

I’m so bad at this ughhhhhhhhhhhhhhhhhhh

Alexus [3.1K]

Answer:

a)6

b)v^2-u^2/2a

Step-by-step explanation:

a)Given that,

u=12

a= -6

s=9

We know that,

v^2=u^2+2as

or, v^2=(12)^2+2×(-6)×9

or,v^2=144-108

or,v^2=36

or, v=√36

∴v=6

(Ans)

b)If ,v^2=u^2+2as

then, u^2+2as=v^2

or,2as=v^2-u^2

or, s=v^2-u^2/2a

∴s=v^2-u^2/2a

Hope ya find it helpful.. Thanks a lot...

6 0

3 years ago