Answer:
<h3>A. </h3>
- log
= log 3 - x³ log x = log 3
- 3x³ log x = 3 log 3
- x³ log x³ = log 3³
= 3³- x³ = 3
- x =
<h3>B.</h3>
- 4ˣ + 6ˣ = 9ˣ
- 2²ˣ + 2ˣ3ˣ = 3²ˣ
<u>Divide both sides by 2²ˣ</u>
<u>Substitute (3/2)ˣ = t</u>
<u>Solve for t:</u>
<u>Positive root is considered as (3/2)ˣ can't be negative.</u>
- (3/2)ˣ = (1 + √5)/2
- x = log [(1 + √5)/2] / log (3/2)
- x = 1.18681439028
So your goal is to set it equal to Y, so you have to start by subtracting k and you get t-k, then you have to get rid of the fraction by multiplying both sides by the denominator (n), so then you get n(t-k) and the only thing left is to divide by the e, and you get 4
We know that the perimeter of a rectangle = 2(l + w)
l = length
w = width
In our problem,
l = 5x
w = 5x - 4
Let's create an inequality to help us solve this problem.
2(5x + (5x - 4)) ≥ 96
Let's start off by simplifying the terms inside the parentheses.
2(10x - 4) ≥ 96
Distribute the 2
20x - 8 ≥ 96
Add 8 to both sides.
20x ≥ 104
Divide both sides by 20
x ≥ 5.2
Let's plug 5.2 into x for our length and width.
Length = 5x = 5(5.2) = 26 cm
Width = 5x - 4 = 5(5.2) - 4 = 26 - 4 = 22 cm
The smallest possible dimensions for the rectangle are, length = 26 cm and width = 22 cm
Using proportions, it is found that the correct statement is:
D. The number of visitors who prefer camping will be 2 times the number of visitors who prefer water sports.
<h3>What is a proportion?</h3>
A proportion is a fraction of a total amount.
In this problem, the table is from a sample of 80 visitors.
Since the <u>proportions stay the same</u>, just the number of visitors change, the correct statement is given by:
D. The number of visitors who prefer camping will be 2 times the number of visitors who prefer water sports.
As from the 80 students, 28 prefer camping and 14 prefer water sports, hence from 200, these numbers will be of 70 and 35 respectively.
More can be learned about proportions at brainly.com/question/24372153
A) (6,0)
Since the points of R are found after x = 0 and x = 2, and found before x = 8, the value for x cannot start with those numbers so it would have to be either 4 or 6.
The rhombus is a square but more like a diamond shape with all equal sides. So if the difference between Q & T is (2,4), then you would have to go backwards by the same amount from (8,4)
So mathematically speaking...
(8,4) - (2,4) = (6,0)
