Answer:
y = 5x2 + 10x - 15
We want this in format y = a(x-h)2 + k
where the vertex will be at (h,k)
y = 5(x2+2x) - 15
Complete the square on x2+2x
y = 5(x2+2x+1) - 15 - 5
We subtract 5 at the end because we are actually adding 5(1) = 5
so we need to remove it also to keep the total equal
y = 5(x+1)2 - 20
The vertex is at (-1,-20)
Answer:
(3/2, 6)
Step-by-step explanation:
y = 4x
8x + y = 18
this says y is 4x so you can replace y with 4x
8x + 4x = 18
12x = 18
/12 /12
x = 3/2
now sub x into y = 4(3/2)
y = 12/2
y = 6
If you choose 10 swimmers and 4 are Stingrays, you can say that Stingrays make up roughly 40% of the swimmers. If 20 Stingrays make up 40% of all the swimmers, we just have to find what number 20 is 40% of. That’s easy enough by cross multiplication:
20/x = 40/100
20/x = 4/10
20/x = 2/5
x = 50.
Double check by multiplying 50 * 0.4. Since 50 * 0.4 = 20, we know we have the right answer. There are about 50 swimmers on this team.
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<u><em>The correct answer is: </em></u>C) his solution for x is correct, but in order for 6 to be an extraneous solution, one denominator has to result in 0 when 6 is substituted for x.
<u><em>Explanation: </em></u><span><u>To solve this rational equation, we cross multiply: </u>
8*(x-4)=2*(x+2).
<u>Using the distributive property, we have </u>
8*x-8*4=2*x+2*2;
8x-32=2x+4.
<u>Subtract 2x from each side: </u>
8x-32-2x=2x+4-2x;
6x-32=4.
<u>Add 32 to each side: </u>
6x-32+32=4+32;
6x=36.
<u>Divide both sides by 6:</u>
</span></span>

<span><span>=</span></span>

<span><span>;
x=6.
<u>Extraneous solutions</u> are solutions that come about in the problem but are not valid solutions to the problem; the only values of x that would give this sort of answer are -2 and 4, since these are the two values that would make one of the denominators 0 (we cannot divide by 0).</span></span>
When you multiply a number by 5 and then by 2 it is the same as multiplying by 10. multiplying by 10 means you add a zero to the end of the number so the digit in the ones column will be always be zero