How many solutions does the system of equations x − y = 7 and y equals the square root of the quantity 3 times x plus 3 end quan
1 answer:
9514 1404 393
Answer:
one solution (11, 4)
Step-by-step explanation:
Both equations describe curves with positive slope. The y-intercept of the line (-7) is less than that of the root function (-2), so the line must intersect the root function in exactly one place. There is one solution.
__
Solved in the conventional way, the equation would become a quadratic, with two solutions. One of them is extraneous. (That is why I prefer a graphical solution.)
Given ...
x -y = 7
y = √(3x +3) -2
We can substitute for y to get ...
x -7 = √(3x +3) -2
x -5 = √(3x +3)
x^2 -10x +25 = 3x +3 . . . . . . square both sides
x^2 -13x +22 = 0 = (x -11)(x -2) . . . . . gives solutions x=11, x=2
The value x=2 does not satisfy the equation ...
x -7 = √(3x +3) -2 ⇒ 2 -7 = √(3·2 +3) -2 ⇒ -5 = 1 (false)
You might be interested in
Answer:
A. Your battery is likely defective since such poor performance is extremely unlikely.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
If X is more than two standard deviations from the mean, it is considered an unlikely outcome.
In this question, we have that:
Which of the following conclusions is the most appropriate given this information?
Lasted 400 hours, so X = 400.
4 standard deviations from the mean, so unlikely.
So the correct answer is:
A. Your battery is likely defective since such poor performance is extremely unlikely.
Dimension of rectangular parking lot is width = 112.882 feet and length = 132.882 feet
<h3><u>Solution:</u></h3>Given that
Area of rectangular parking lot = 15000 square feet
Length is 20 feet more than the width.
Need to find the dimensions of rectangular parking lot.
Let assume width of the rectangular parking lot in feet be represented by variable "x"
As Length is 20 feet more than the width,
so length of rectangular parking plot = 20 + width of the rectangular parking plot
=> length of rectangular parking plot = 20 + x = x + 20
<em><u>The area of rectangle is given as:</u></em>
Area of rectangular parking lot = length of rectangular parking plot width of the rectangular parking
But it is given that Area of rectangular parking lot = 15000 square feet
Solving the above quadratic equation using quadratic formula
<em><u>General form of quadratic equation is </u></em>
And quadratic formula for getting roots of quadratic equation is
In our case b = 20, a = 1 and c = -15000
Calculating roots of the equation we get
As variable x represents width of the rectangular parking lot, it cannot be negative.
=> Width of the rectangular parking lot "x" = 112.882 feet
=> Length of the rectangular parking lot = x + 20 = 112.882 + 20 = 132.882
Hence can conclude that dimension of rectangular parking lot is width = 112.882 feet and length = 132.882 feet.