Step-by-step explanation:
Explanation:
Given:
−3x2+12x+1=0
This is in the form:
ax2+bx+c=0
with a=−3, b=12 and c=1
In order to decide which method to use, we can first examine the discriminant:
Δ=b2−4ac=122−4(−3)(1)=144+12=156
Since Δ>0 we can tell that the quadratic has 2 distinct real solutions, but because it is not a perfect square we can also tell that those solutions are irrational.
So there is no rational factorisation and we can discount the use of an AC method or similar.
We can use the quadratic formula or we can complete the square.
If we choose to use the quadratic formula, then we find:
x=−b±√b2−4ac2a
x=−b±√Δ2a
x=−(12)±√1562(−3)
x=−12±2√39−6
x=2±√393
When completing the square, note that b=12 is already divisible by a=−3 and by
<span>2n^3-n^2-136 :Equation:
Substitute 0 for n
</span> Simplify {20}^{3}<span> to </span><span>8000
</span>
<span>8000−<span>0<span><span>^2</span><span></span></span></span>−136
</span> Simplify <span>{0}^{2}<span></span></span><span> to </span><span>0
</span><span><span>8000−0−136
= 7864</span></span><span>
</span>
Answer:
Theresa needs 14.3 pounds of Brand A mixed nuts and 13.2 pounds of Brand B mixed nuts.
Step-by-step explanation:
Let A represent the brand A mixed nuts and B represent Brand B mixed nuts.
We have been given that farmer Theresa's Produce Stand sells 27.5 lbs. bags. We can represent this information in an equation as:
We are also told that to make her product she combines Brand A mixed nuts which contain 20% peanuts and Brand B mixed nuts which contain 70% peanuts.
We can represent this information in an expression as:
Since the stand sells 27.5 lbs. bags of mixed nuts that contain 44% peanuts. We can represent this information in an equation as:
Upon substituting equation (1) in equation (2), we will get:
Therefore, Theresa needs 13.2 pounds of Brand A mixed nuts.
To find amount of Brand B mixed nuts, we will substitute in equation (1) as:
Therefore, Theresa needs 14.3 pounds of Brand B mixed nuts.
Answer:
Let's call the first studio, yoga studio A.
Let's call the second studio, yoga studio B.
The equations:
Yoga Studio A: y=10x+55
Yoga Studio B: y=12.5x+25
So, for 12 classes:
Yoga Studio A: y=10(12)+55, y=175
Yoga Studio B: y=12.5(12)+25, y=175
These two numbers are equal, so Griffin is right.
For 10 classes:
Yoga Studio A: y=10(10)+55, y=155
Yoga Studio B: y=12.5(10)+25, y=150.
These two numbers are not equal, so Gigi is wrong.
Let me know if this helps!
