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S_A_V [24]
3 years ago
10

One number is seven more than a second number. Twice the first is 2 less than 3 times the second. Find the numbers.

Mathematics
1 answer:
Keith_Richards [23]3 years ago
4 0

Step-by-step explanation:

Linear equations. Make 2 new equations from the question. Name the first number as x and the second as y...

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No-Freeze antifreeze mixture contains 30% alcohol. How much alcohol is there in 15 quarts of No-Freeze
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How much does the original mixture produce? is the original 1 quart? 1 gallon? 1 cup?

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What is the equation of the quadratic graph with a focus of (3, 1) and a directrix of y = 5?
telo118 [61]

Answer:

f(x)=-\frac{1}{8}(x-3)^2+3

Step-by-step explanation:

We want to find the equation of the parabola with a focus of (3,1) and directrix y=5.

Considering the directrix, the quadratic graph must open downwards.


The equation of this parabola is given by the formula,

(x-h)^2=4p(y-k), where (h,k) is the vertex of the parabola.


The axis of this parabola meets the directrix at (3,5).

Since the vertex is the midpoint of the focus and the point of intersection of the axis of the parabola and the directrix,


h=\frac{3+3}{2}=3 and k=\frac{5+1}{2}=3.


The equation of the parabola now becomes,


(x-3)^2=4p(y-3).


Also |p| is the distance between the vertex and the directrix.


|p|=2


This implies that p=-2\:or\:2.


Since the parabola turns downwards,


p=-2.



Our equation now becomes,


(x-3)^2=4(-2)(y-3).


(x-3)^2=-8(y-3).


We make y the subject to get,

y=-\frac{1}{8}(x-3)^2+3).


This is the same as

f(x)=-\frac{1}{8}(x-3)^2+3).









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3 years ago
Fourteen thousand seven hundred ninety three in standard form
NeTakaya

Answer:

14,793

Step-by-step explanation:

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3 years ago
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