Answer:
<em><u>let </u></em><em><u>the </u></em><em><u>ratio</u></em><em><u> be</u></em><em><u> in</u></em><em><u> </u></em><em><u>x </u></em>
<em><u>a/</u></em><em><u>q</u></em><em><u>. </u></em><em><u>3</u></em><em><u>x</u></em><em><u> </u></em><em><u>+</u></em><em><u> </u></em><em><u>2</u></em><em><u>x</u></em><em><u> </u></em><em><u>=</u></em><em><u> </u></em><em><u>3</u></em><em><u>0</u></em><em><u>0</u></em><em><u>0</u></em><em><u>0</u></em><em><u>0</u></em>
<em><u> </u></em><em><u> </u></em><em><u>5</u></em><em><u>x</u></em><em><u> </u></em><em><u>=</u></em><em><u> </u></em><em><u>3</u></em><em><u>0</u></em><em><u>0</u></em><em><u>0</u></em><em><u>0</u></em><em><u>0</u></em>
<em><u>x </u></em><em><u>=</u></em><em><u> </u></em><em><u>3</u></em><em><u>0</u></em><em><u>0</u></em><em><u>0</u></em><em><u>0</u></em><em><u>0</u></em><em><u>/</u></em><em><u>5</u></em>
<em><u>x=</u></em><em><u> </u></em><em><u>6</u></em><em><u>0</u></em><em><u>0</u></em><em><u>0</u></em><em><u>0</u></em>
<em><u>Leona </u></em><em><u>=</u></em><em><u> </u></em><em><u>6</u></em><em><u>0</u></em><em><u>0</u></em><em><u>0</u></em><em><u>0</u></em><em><u>*</u></em><em><u>3</u></em><em><u> </u></em><em><u>=</u></em><em><u> </u></em><em><u>1</u></em><em><u>8</u></em><em><u>0</u></em><em><u>0</u></em><em><u>0</u></em><em><u>0</u></em>
<em><u>Janet </u></em><em><u>=</u></em><em><u> </u></em><em><u>6</u></em><em><u>0</u></em><em><u>0</u></em><em><u>0</u></em><em><u>0</u></em><em><u>*</u></em><em><u>2</u></em><em><u> </u></em><em><u>=</u></em><em><u> </u></em><em><u>1</u></em><em><u>2</u></em><em><u>0</u></em><em><u>0</u></em><em><u>0</u></em><em><u>0</u></em>
<em><u>hope</u></em><em><u> it</u></em><em><u> helps</u></em>
Answer:
Step-by-step explanation:
a. Since the parabola is compressed by a factor of 1/3 we can state:
- a parabola is written this way : y=(x-h)²+k
- h stands for the translation to the left ⇒ 2*3=6
- k for the units down ⇒4*3=12
So the equation is : y=(x-6)²+12
b.Here the parabola is stretched by a factor of 2 so we must multiply by 1/2
- We khow that a parabola is written this way : y=(x-h)²+k
- (h,k) are the coordinates of the vertex
- the maximum value is 7*0.5=3.5
- we khow tha the derivative of a quadratic function is null in the maximum value
- so let's derivate (x-h)²+k= x²+h²-2xh+k
- f'(x)= 2x-2h h is 1 since the axe of simmetry is x=1
- f'(x)=2x-2 ⇒2x-2=0⇒ x= 1
- Now we khow that 1 is the point where the derivative is null
- f(1)=3.5
- 3.5=(x-1)²+k
- 3.5= (1-1)²+k⇒ k=3.5
So the equation is : y=(x-1)²+3.5
7.
the maximum height is where the derivative equals 0
- h= -5.25(t-4)²+86
- h= -5.25(t²-8t+16)+86
- h=-5.25t²+42t-84+86
- h=-5.25t²+42t+2
Let's derivate it :
- f(x)= -10.5t+42
- -10.5t+42=0
- 42=10.5t
- t= 42/10.5=4
When the height was at max t=4s
- h(max)= -5.25(4-4)²+86 = 86 m
h was 86m
Answer:
Total crackers on the plate are 12
Step-by-step explanation:
Manuel ate crackers = 
His brother ate crackers = 
Crackers left on the plate = 5
We need to find how many crackers were there on the plate.
Let x be the total crackers on the plate
So, we can write the equation

Because 1/3 and 1/4 crackers are eaten and 5 are left so, we subtract 1/3x and 1/4x from x and equal it to 5

So, we get x = 12
Therefore, total crackers on the plate are 12
Answer:
{-12,0}
Step-by-step explanation:
first to solve this can collect like terms and add
X² +12x=0
and solve it by factorization method
X² +12x=0
x(x+12)=0
it means x multiplied by x = X² then x multiplied by 12 = 12x
so this means x or (x+12) equals to zero
x=0 and (x+12)=0
x+12=0
x=-12
so the solution set is {-12,0}
but can also be done by formula method