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Dominik [7]
3 years ago
6

Solve the equation m²+4m=-2

Mathematics
2 answers:
lozanna [386]3 years ago
7 0

Answer: There's two solutions to this problem:

1. m =(4-√8)/2=2-√ 2 = 0.586

2. m =(4+√8)/2=2+√ 2 = 3.414

UNO [17]3 years ago
4 0
Step 1: Subtract -2 from both sides.<span><span><span><span>
m2</span>+<span>4m</span></span>−<span>(<span>−2</span>)</span></span>=<span><span>−2</span>−<span>(<span>−2</span>)</span></span></span><span><span><span><span>
m2</span>+<span>4m</span></span>+2</span>=0</span>
Step 2: Use quadratic formula with a=1, b=4, c=2.<span>
m=<span><span><span>−b</span>±<span>√<span><span>b2</span>−<span><span>4a</span>c</span></span></span></span><span>2a</span></span></span><span>
m=<span><span><span>−<span>(4)</span></span>±<span>√<span><span><span>(4)</span>2</span>−<span><span>4<span>(1)</span></span><span>(2)</span></span></span></span></span><span>2<span>(1)</span></span></span></span><span>
m=<span><span><span>−4</span>±<span>√8</span></span>2</span></span><span><span>
m=<span><span>−2</span>+<span><span><span>√2</span><span> or </span></span>m</span></span></span>=<span><span>−2</span>−<span>√2</span></span></span><span>
</span>
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Step-by-step explanation:

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but before we do that, we will use the vertex form, since it will make our work easier at the beginning.  

First and foremost, when we plot the vertex and the given point, the vertex is higher up than is the point; that means that this parabola opens upside down, and its vertex form will be

y=-|a|(x - h)² + k

The absolute value is out in front of the a, so we know that the value of a is positive, but the quadratic itself is negative (upside down) and we will find that math takes care of that negative that needs to be out front.  So we need to solve for a by filling in the x, y, h, and k values from the point and the vertex:  x = -7, y = 0, h = -3, k = 4

0 = a(-7 - (-3))² + 4 and

0 = a(-7 + 3)² + 4 and

0 = a(-4)² + 4 and

0 = a(16) + 4 and

0 = 16a + 4 and

-4 = 16a so

a=-\frac{1}{4}

Now that we know a, we can plug it back into the vertex form and then put it into standard form from there.

y=-\frac{1}{4}(x+3)^2+4

Now we will FOIL out what's inside the parenthesis to get

y=-\frac{1}{4}(x^2+6x+9)+4

Simplify by distributing the -1/4 into the parenthesis:

y=-\frac{1}{4}x^2-\frac{3}{2}x-\frac{9}{4}+4

Combine like terms to get

y=-\frac{1}{4}x^2-\frac{3}{2}x+\frac{7}{4}

And there you go!

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2 years ago
The admission fee at a small fair is $1.50 for children and $4.00 for adults. John spent $12.00 for admission. Write an equation
g100num [7]
So what you are trying to find is the certain amount of children tickets and adult tickets. the final amount is a total of $12. This means that a unknown number of children tickets (c) times 1.50 (price of each ticket for children) plus the unknown number of adult tickets (a) times 4.00 (price of each ticket for adults) equals a final cost of $12.00.

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4 0
3 years ago
Any help would be appreciated
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Answer:

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Every horizontal and vertical stair has the same area.

Area of one stair = Length × Width

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Total area to be painted in gold = 8 × Area of one stair

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Total area to be painted in gold = 24000 cm²

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2 years ago
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