Solve: 2x - 3 = x^2 - 5 (at least, this is my interpretation of your 2 x -3).
x^2 - 5 - 2x + 3 + 0, or x^2 - 2x - 2 = 0
I will solve this by "completing the square:"
x^2 - 2x +(1)^2 - (1)^2 - 2 = 0, or x^2 - 2x + 1 - 1 - 2 = 0
This is (x-1)^2 = 3. Taking the sqrt of both sides, we get:
x-1 = plus or minus sqrt(3). Then x=1+sqrt(3) or x=1-sqrt(3). These are the two values of x for which 2x - 3 = x^2 - 5 is true.
Answer:
Right 2, up 3
Step-by-step explanation:
In the vertex form transformations....
f(x) = a(x-h)²+k
- a - indicates <em>vertical stretches</em>, <em>compression</em>, and/or a <em>reflection across the x-axis</em>.
- h - indicates only on the <u><em>x-axis</em></u>. Negative = Goes right, Positive - goes left
- k - indicates only on the y-axis. Positive = up, negative = down
90.476 ..........................................
Answer:
Step-by-step explanation:
Hello!
You have two variables of interest.
X₁: Weight of a popcorn bag.
It's mean is μ= 3.05 ounces and it's standard deviation δ= 0.02 ounces.
X₂: Weight of a potato chips bag.
With mean μ= 5.07 ounces and standard deviation δ= 0.04 ounces.
A bag of popcorn is randomly selected and its weight is X₁= 3.02 and a bag of potato chips is randomly selected with weight X₂= 5.03.
Since these two values are from completely different distributions, you cannot compare them, but if you convert these values to their equivalent Z value. For this, you will subtract the mean of their distribution and dive them by their standard deviation.
Z= (X-μ)/δ ~N(0;1)
Bag of popcorn: Z=(3.02-3.05)/0.02= -1.5
The selected bag of popcorn is 1.5δ away from the mean.
I hope it helps!
Answer:
The volume of the square pyramid is
Step-by-step explanation:
The volume of the pyramid is equal to
where
B is the area of the base of the pyramid
H is the height of the pyramid
In this problem we have
<em>Find the area of the base B</em>
----> is the area of a square
substitute the values and find the volume