The area of a rectangle is 77 yd2, and the length of the rectangle is 3 yd more than twice the width find the dimensions of the rectangle
Answers
Length is 3 more than twice the width = 2x + 3
Area = x*(2x + 3)
x*(2x + 3) = 77
2x² + 3x = 77
2x² + 3x - 77 = 0 This is a quadratic equation. Solve by factorization.
Multiply first and last coefficients: 2*-77 = -154
We look for two numbers that multiply to give -154, and add to give the middle coefficient +3
Those two numbers are 14 and -11.
Check: 14*-11 = -154 14 + -11 = 14 - 11 = +3
We replace the middle term of +3x in the quadratic expression with 14x -11x
2x² + 3x - 77 = 0
2x² + 14x -11x - 77 = 0
2x(x + 7) - 11(x + 7) = 0
(2x - 11)(x + 7) = 0
2x - 11 = 0 or x + 7 = 0
2x = 0 + 11 x = 0 - 7
2x = 11 x = -7
x = 11/2 = 5.5
The solutions are x = -7 or 5.5.
Since we are solving for length of rectangle, x can't be negative. So we do away with x = -7.
x = 5.5 is the only valid solution.
Recall width = x = 5.5,
Length = 2x + 3 = 2*5.5 + 3 = 11 + 3 = 14
Therefore length = 14 yards, and width = 5.5 yards.
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Answers
So:
the line drops one unit.
Its slope is -1.
What can you tell about the means for these two months?
The mean for December is higher than January's mean.
It is almost certain that January's mean is higher.
There is no way of telling what the means are.
The narrow IQR for January causes its mean to be lower.
Answers
There is no way of telling what the means are.
What is a box plot?
A box plot is a measure of dispersion and a method of displaying the spread and measure of centers.
- The measure of spread usually includes a range class of numbers from which the first quartile, interquartile range, and third quartile can be determined.
- The measure of centers include the mean, median, and mode.
Since the bar in the diagram is not aligned with the data values below them, we can conclude that there is no sufficient information in determining the mean of these two months.
Therefore, there is no way of telling what the means are.
Learn more about the box plot here:
Answers
10 times the denominator 12=120
plus the numerator 5=125
=125 over the original denominator 12
125/12
Hope this helped
Answers
Answer:
j
Step-by-step explanation:
Answers
Answer: the account earns interest of $40.16
Step-by-step explanation:
We would apply the formula for determining compound interest which is expressed as
A = P(1+r/n)^nt
Where
A = total amount in the account at the end of t years
r represents the interest rate.
n represents the periodic interval at which it was compounded.
P represents the principal or initial amount deposited
From the information given,
P = 875.83
r = 9% = 9/100 = 0.09
n = 12 because it was compounded 12 times in a year.
t = 6 months = 6/12 = 0.5 year
Therefore,.
A = 875.83(1+0.09/12)^0.5 × 12
A = 875.83(1+0.0075)^6
A = 875.83(1.0075)^6
A = 915.99
The interest that she earns is
915.99 - 875.83 = $40.16
Answers
y = x² + 6x + 3
y - 3 = x² + 6x
6x ⇒ 6x / 2x = 3 ⇒ 3² = 9
y - 3 + 9 = x² + 6x + 9
y + 6 = (x+3)²
y = (x+3)² - 6
vertex of the parabola is (x+3)²
y = (x+3)(x+3) - 6
y = x(x+3)+3(x+3) - 6
y = x² + 3x + 3x + 9 - 6
y = x² + 6x + 3