12% of 72 is:
=12×72/100
=8.64
So the 12% of 72 is 8.64 is your answer.
We have 8 dozen bagels, or 8*12=96 bagels. Each plate can hold 14 bagels, so we have enough bagels to fill 96/14=about 6.86 plates. However, we cannot have a fraction of a plate, so we round up to have a total of seven plates. To fill all seven plates fully, 7*14=98 bagels would be needed, which is two more than we have.
To summarize, Mr. Corsetti has seven plates of bagels, and would need two more bagels to fill the last one up.
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<u><em>Note: As you may have unintentionally missed to add the value choices. But, I would make sure to explain the concept so that you may improve your understanding in terms of solving these type of questions.</em></u>
Answer:
Any value other than the values
will not be a solution of
.
Step-by-step explanation:
Considering the equation

Steps to solve the equation









As
![\mathrm{For\:}x^3=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt[3]{f\left(a\right)},\:\sqrt[3]{f\left(a\right)}\frac{-1-\sqrt{3}i}{2},\:\sqrt[3]{f\left(a\right)}\frac{-1+\sqrt{3}i}{2}](https://tex.z-dn.net/?f=%5Cmathrm%7BFor%5C%3A%7Dx%5E3%3Df%5Cleft%28a%5Cright%29%5Cmathrm%7B%5C%3Athe%5C%3Asolutions%5C%3Aare%5C%3A%7Dx%3D%5Csqrt%5B3%5D%7Bf%5Cleft%28a%5Cright%29%7D%2C%5C%3A%5Csqrt%5B3%5D%7Bf%5Cleft%28a%5Cright%29%7D%5Cfrac%7B-1-%5Csqrt%7B3%7Di%7D%7B2%7D%2C%5C%3A%5Csqrt%5B3%5D%7Bf%5Cleft%28a%5Cright%29%7D%5Cfrac%7B-1%2B%5Csqrt%7B3%7Di%7D%7B2%7D)
![x=\sqrt[3]{\frac{1}{8}},\:x=\sqrt[3]{\frac{1}{8}}\frac{-1+\sqrt{3}i}{2},\:x=\sqrt[3]{\frac{1}{8}}\frac{-1-\sqrt{3}i}{2}](https://tex.z-dn.net/?f=x%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B1%7D%7B8%7D%7D%2C%5C%3Ax%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B1%7D%7B8%7D%7D%5Cfrac%7B-1%2B%5Csqrt%7B3%7Di%7D%7B2%7D%2C%5C%3Ax%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B1%7D%7B8%7D%7D%5Cfrac%7B-1-%5Csqrt%7B3%7Di%7D%7B2%7D)
So,

Therefore,
Any value other than the values
will not be a solution of
.
Keywords: solution, value
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Answer:
2
Step-by-step explanation:
So I'm going to use vieta's formula.
Let u and v the zeros of the given quadratic in ax^2+bx+c form.
By vieta's formula:
1) u+v=-b/a
2) uv=c/a
We are also given not by the formula but by this problem:
3) u+v=uv
If we plug 1) and 2) into 3) we get:
-b/a=c/a
Multiply both sides by a:
-b=c
Here we have:
a=3
b=-(3k-2)
c=-(k-6)
So we are solving
-b=c for k:
3k-2=-(k-6)
Distribute:
3k-2=-k+6
Add k on both sides:
4k-2=6
Add 2 on both side:
4k=8
Divide both sides by 4:
k=2
Let's check:
:


I'm going to solve
for x using the quadratic formula:







Let's see if uv=u+v holds.

Keep in mind you are multiplying conjugates:



Let's see what u+v is now:


We have confirmed uv=u+v for k=2.