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3 years ago

What is an expression for the calculation 2/3 times the sum of 2/8 and 4/8?

1 answer:

8 0

2/3((2/8)+(4/8))
For the 2/8 + 4/8 you wouldn't need the extra set of parentheses, but for I typed it to not confuse you.

So 2/3 times the sum of 2/8 and 4/8. Get the sum of 2/8 and 4/8 (which is
((2/8)+(4/8)) and then add 2/3 outside to parentheses to indicate that you are multiplying them.

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Could someone help me rnnn?

GuDViN [60]

Answer:

vertex = (0, -4)

equation of the parabola: $y=3x^2-4$

Step-by-step explanation:

Given:

y-intercept of parabola: -4
parabola passes through points: (-2, 8) and (1, -1)

Vertex form of a parabola: $y=a(x-h)^2+k$

(where (h, k) is the vertex and $a$ is some constant)

Substitute point (0, -4) into the equation:

$\begin{aligned}\textsf{At}\:(0,-4) \implies a(0-h)^2+k &=-4\\ah^2+k &=-4\end{aligned}$

Substitute point (-2, 8) and $ah^2+k=-4$ into the equation:

$\begin{aligned}\textsf{At}\:(-2,8) \implies a(-2-h)^2+k &=8\\a(4+4h+h^2)+k &=8\\4a+4ah+ah^2+k &=8\\\implies 4a+4ah-4&=8\\4a(1+h)&=12\\a(1+h)&=3\end{aligned}$

Substitute point (1, -1) and $ah^2+k=-4$ into the equation:

$\begin{aligned}\textsf{At}\:(1.-1) \implies a(1-h)^2+k &=-1\\a(1-2h+h^2)+k &=-1\\a-2ah+ah^2+k &=-1\\\implies a-2ah-4&=-1\\a(1-2h)&=3\end{aligned}$

Equate to find h:

$\begin{aligned}\implies a(1+h) &=a(1-2h)\\1+h &=1-2h\\3h &=0\\h &=0\end{aligned}$

Substitute found value of h into one of the equations to find a:

$\begin{aligned}\implies a(1+0) &=3\\a &=3\end{aligned}$

Substitute found values of h and a to find k:

$\begin{aligned}\implies ah^2+k&=-4\\(3)(0)^2+k &=-4\\k &=-4\end{aligned}$

Therefore, the equation of the parabola in vertex form is:

$\implies y=3(x-0)^2-4=3x^2-4$

So the vertex of the parabola is (0, -4)

5 0

2 years ago

Read 2 more answers

A rectangle Has an area of 252 yd.². The length of the rectangle is 10 yards longer than twice it’s worth. Find the width and le

Rama09 [41]

Answer:

Width = 9 yds

Length = 28 yds

Step-by-step explanation:

Width = x

Length = 2x + 10

Area is 252 yd²

x(2x + 10) = 252

2x² + 10x - 252 = 0

2 (x + 14) (x - 9) = 0

(x + 14) (x - 9) = 0

x = - 14 or x = 9

Width = 9 yds

Length = 2x9 + 10 = 28 yds

7 0

2 years ago

Read 2 more answers

13. How many drinks are in a 2 oz martini made with 100 proof alcohol

pentagon [3]

Answer:

4 drinks.

Step-by-step explanation:

-One drink is defined as having one-half ounce of pure ethyl alcohol; each of the following is considered "one drink." *1 oz of 100 proof distilled spirits at 50% alcohol.

$Drinks=\frac{2oz}{0.5oz}\\\\=4$