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torisob [31]
3 years ago
9

Which ordered pair is a solution of the equation? 3r - y = 13

Mathematics
1 answer:
Svetach [21]3 years ago
6 0

Answer:

(0,-13)(1,-10)(2,-7)

Step-by-step explanation:

It has three values for x

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The minimum/maximum value of the function y = a(x − 2)(x − 1) occurs at x = d, what is the value of d?
daser333 [38]

Answer:

d=\frac{3}{2}=1.5

Step-by-step explanation:

We have the function:

y=a(x-2)(x-1)

And we want to find x=d for which the minimum/maximum value will occur.

Notice that our function is a quadratic in factored form.

Remember that the minimum/maximum value always occurs at the vertex point.

And remember that the x-coordinate of the vertex is the axis of symmetry.

Since a quadratic is always symmetrical on both sides of its axis of symmetry, a quadratic’s axis of symmetry is the average of the two roots/zeros of the quadratic.

Therefore, the value x=d such that it produces the minimum/maximum value is the average of the two roots.

Our factors are <em>(x-2) </em>and <em>(x-1)</em>.

Therefore, our roots/zeros are <em>x=1, 2</em>.

So, the average of them are:

d=\frac{1+2}{2}=3/2=1.5

Therefore, regardless of the value of <em>a</em>, the minimum/maximum value will occur at <em>x=d=1.5</em>.

Alternative Method:

Of course, we can also expand to confirm our answer. So:

y=a(x^2-2x-x+2)\\y=a(x^2-3x+2)\\y=ax^2-3ax+2a

The x-coordinate of the vertex is still going to be the place where the minimum/maximum is going to occur.

And the formula for the vertex is:

x=-\frac{b}{2a}

So, we will substitute <em>-3a</em> for <em>b</em> and <em>a</em> for <em>a</em>. This yields:

x=-\frac{-3a}{2a}=\frac{3}{2}=1.5

Confirming our answer.

4 0
3 years ago
Rewrite the function y= x^2 + 14x + 4 in vertex form
Step2247 [10]
Vertex form is basically commplete the square
y=a(x-h)^2+k


y=x^2+14x+4
take 1/2 of 14 and square it, (7^2=49)
add that and its negative to right side
y=x^2+14x+49-49+4
factor perfect squaer
y=(x+7)^2-49+4
y=(x+7)^2-45

answer is A
4 0
3 years ago
A professional baseball diamond is a square. The distance from base to base is 90 ft. To the nearest foot, how far does a catche
mamaluj [8]

BSE is square.

Let side be s

  • s=90ft

Diagonal be d

\\ \tt\longmapsto s=\dfrac{d}{\sqrt{2}}

\\ \tt\longmapsto d=s\sqrt{2}

\\ \tt\longmapsto d=90\sqrt{2}

\\ \tt\longmapsto d=127ft

3 0
2 years ago
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How many gallons of water does a hose supply in 10 minutes
lina2011 [118]

Answer: 170 Gallons

Step-by-step explanation: A water hose can let out 17 gallons of water in a minute. In 10 Minutes, if you multiply 17 by 10, you get 170.

7 0
3 years ago
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What is the area of 4x3x+1
Leya [2.2K]

Answer:

12, I think.

Step-by-step explanation:

3 0
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