The ladder is approximately 40 meters long to the nearest tenth.
The information will form a right angle triangle.
The base of the ladder 25 meters due west of the burning building is the base(adjacent side) of the triangle formed.
How long is the ladder describe the hypotenuse of the triangle formed.
Therefore, using trigonometric ratio we can find the length of the ladder as follows:
cos 51 = adjacent / hypotenuse
cos 51 = 25 / hypotenuse
hypotenuse = 25 / cos 51°
hypotenuse = 25 / 0.62932039105
hypotenuse = 39.7253932266 meters
hypotenuse ≈ 40 meters
Therefore, the ladder is approximately 40 meters long to the nearest tenth
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Factor the trinomial below.
5x2 + 29x - 6
Which of the following binomials is a factor of the trinomial?
A. x - 6
B. x + 3
C. x - 3
D. x + 6
The trinomial 5x^2 + 29x - 6 factors into (5x - 1)(x + 6)
To factor the trinomial 5x2 + 29x - 6, we need to find two numbers that multiply to (5)(-6) = -30 and add to 29. These two numbers are 30 and -1, as 30 - 1 = 29. Thus, we can rewrite the trinomial as 5x2 + 30x - x - 6 and factor by grouping:
(5x2 + 30x) - (x + 6)
5x(x + 6) - 1(x + 6)
The trinomial factors into (5x - 1)(x + 6), which means the correct binomial factor is option D: x + 6.
The graph shows the quadratic function f(x) . What is the average rate of change for the quadratic function from x = 6 to x = 8? Enter your answer in the box.
Answer:
The average rate of change for the quadratic function from x = 6 to x = 8 is -1.
Step-by-step explanation:
The average rate of change for the quadratic function from x₁ to x₂ is defined as
[tex]m=\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]
From the given graph it is clear that the value of function is 6 at x=6 and the value of function is 4 at x=8.
The average rate of change for the quadratic function from x = 6 to x = 8.
[tex]m=\frac{f(8)-f(6)}{8-6}[/tex]
[tex]m=\frac{4-6}{2}[/tex]
[tex]m=\frac{-2}{2}[/tex]
[tex]m=-1[/tex]
Therefore the average rate of change for the quadratic function from x = 6 to x = 8 is -1.
Dan invests £2200 into a savings account. The bank gives 5% compound interest for the first 3 years and 4% thereafter. How much will Dan have after 7 years to the nearest pound?
The correct answer, to the nearest pound, is:
2979
Explanation:
Compound interest can be written as an equation of the form
[tex]y=a(1+r)^t[/tex],
where a is the initial deposit, r is the interest rate as a decimal number, and t is the number of years.
For the first 3 years, we have a = 2200, r = 5% = 5/100 = 0.05; and t = 3:
[tex]y=2200(1+0.05)^3
\\
\\=2200(1.05)^3=2546.775[/tex]
This will be the "initial deposit" in the account with 4% interest. This gives us that
a = 2546.775; r = 4% = 4/100 = 0.04; and t = 7-3 = 4:
[tex]y=2546.775(1+0.04)^4
\\
\\=2546.775(1.04)^4=2979.367 \approx 2979[/tex]