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podryga [215]
3 years ago
14

A salad recipe calls for 1 3/4 cups of chopped tomatoes. The recipe calls for 4 1/7 times as many cups of lettuce as tomatoes. H

ow many cups of lettuce do you need for this recipe?
4 1/7 cups
4 3/28 cups
7 1/4 cups
7 1/7 cups
Mathematics
1 answer:
Alekssandra [29.7K]3 years ago
8 0
Hello! To find the amount of lettuce needed for the recipe, all you have to do is multiply 1 3/4 by 4 1/7. It would be best to change the numbers into improper fractions. 1 3/4 is 7/4 and 4 1/7 is 29/7. 7/4 * 29/7 is 203/28 or 7 1/4 in simplest form. You need 7 1/4 cups of lettuce for the salad recipe. The answer is C.
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=3.201x109

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3 years ago
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)

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