What is the range of the function f(x) = -2(64) + 3?<br> 0 (-♾-2]<br> 0 (-0,3)<br> (-2,♾)<br> (3.♾)

Olga flips 2 fair coins. What is the probability of obtaining a different result on each coin?

BaLLatris [955]

Answer:

2/4

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

Sandra wants 1/6 of the fruit in her fruit baskets to be bananas. If the greatest number of fruit that will fit in each basket i

irina [24]

If the total capacity of the basket is 24 to find 1/6 you divide 24 by 6 and get 4. 4 is equal to 1/6 of 24 which means Sandra can only bring 4 bananas.

7 0

3 years ago

Y=-1/3x^2-4x-5 in vertex form

grigory [225]

Answer:

$Y=-\frac{1}{3}(x+6)^2+7$ [Vertex form]

Step-by-step explanation:

Given function:

$Y=-\frac{1}{3}x^2-4x-5$

We need to find the vertex form which is.,

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

where $(h,k)$ represents the co-ordinates of vertex.

We apply completing square method to do so.

We have

$Y=-\frac{1}{3}x^2-4x-5$

First of all we make sure that the leading co-efficient is =1.

In order to make the leading co-efficient is =1, we multiply each term with -3.

$-3\times Y=-3\times\frac{1}{3}x^2-(-3)\times4x-(-3)\times 5$

$-3Y=x^2+12x+15$

Isolating $x^2$ and $x$ terms on one side.

Subtracting both sides by 15.

$-3Y-15=x^2+12x-15-15$

$-3Y-15=x^2+12x$

In order to make the right side a perfect square trinomial, we will take half of the co-efficient of $x$ term, square it and add it both sides side.

square of half of the co-efficient of $x$ term = $(\frac{1}{2}\times 12)^2=(6)^2=36$

Adding 36 to both sides.

$-3Y-15+36=x^2+12x+36$

$-3Y+21=x^2+12x+36$

Since $x^2+12x+36$ is a perfect square of $(x+6)$ , so, we can write as:

$-3Y+21=(x+6)^2$

Subtracting 21 to both sides:

$-3Y+21-21=(x+6)^2-21$

$-3Y=(x+6)^2-21$

Dividing both sides by -3.

$\frac{-3Y}{-3}=\frac{(x+6)^2}{-3}-\frac{21}{-3}$

$Y=-\frac{1}{3}(x+6)^2+7$ [Vertex form]

8 0

3 years ago

the formula y-y1 =m(x-x1) is the pot slope form of the equation of a line where m is the slope of the line and(x,y) and (x1,y1)

oksano4ka [1.4K]

$\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&&(~{{ 4}} &,&{{ -2}}~) 
% (c,d)
&&(~{{ 5}} &,&{{ 0}}~)
\end{array}
\\\\\\
% slope = m
slope = {{ m}}\implies 
\cfrac{\stackrel{rise}{{{ y_2}}-{{ y_1}}}}{\stackrel{run}{{{ x_2}}-{{ x_1}}}}\implies \cfrac{5-(-2)}{0-4}\implies \cfrac{5+2}{0-4}\implies -\cfrac{7}{4}$

$\bf \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-(-2)=-\cfrac{7}{4}(x-4)
\\\\\\
y+2=-\cfrac{7}{4}(x-4)\implies y+2=-\cfrac{7}{4}x+7\implies y=-\cfrac{7}{4}x+9$

6 0

3 years ago

What two number multiplies to get 15 and adds to get 6

OverLord2011 [107]

Asking the Math Gods...

The factors of 15 Answer : 1,3,5,15

so 3 and 5 are the only that would get 15

therefore this problem isnt correctly written.. You can't get 6 by adding any of the factored numbers

5 0

2 years ago

What is the range of the function f(x) = -2(64) + 3? 0 (-♾-2] 0 (-0,3) (-2,♾) (3.♾)