Answer:
(7 x - 1) (x + 1)
Step-by-step explanation:
Factor the following:
7 x^2 + 6 x - 1
Factor the quadratic 7 x^2 + 6 x - 1. The coefficient of x^2 is 7 and the constant term is -1. The product of 7 and -1 is -7. The factors of -7 which sum to 6 are -1 and 7. So 7 x^2 + 6 x - 1 = 7 x^2 + 7 x - x - 1 = (7 x - 1) + x (7 x - 1):
(7 x - 1) + x (7 x - 1)
Factor 7 x - 1 from (7 x - 1) + x (7 x - 1):
Answer: (7 x - 1) (x + 1)
The graph of the exponential function f(x) = 5(2)ˣ is as shown in the attached file.
<h3>How to draw the graph of an exponential Function?</h3>
We want to draw the graph of the exponential function;
f(x) = 5(2)ˣ
At input of x = 0, we have;
f(x) = 5(2)⁰ = 5
At input of x = 1, we have;
f(x) = 5(2)¹ = 10
At x = -1, we have;
f(x) = 5(2)⁻¹ = 2.5
At x = -2, we have;
f(x) = 5(2)⁻² = 1.25
Read more about Graph of Exponential Function at; brainly.com/question/12940982
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Those points you can see on the graph.
The first one refers to the x value and the second, to y value. If you notice, when you have x = 0, y = 3. When x = -5, y = 0.
When the line intercepts one of the axis, means the other coordinate is = 0.
3 is y intercept, it means the x value of that point is 0. The same happens to the x intercept - 5. It means the y value of that point is 0.
A ( -5 | 0 )
B ( 0 | 3 )
m = Delta y / Delta x.
Delta y is the variation over the x-axis. Delta x, the x axis.
Be safe!
Step-by-step explanation:
5y + 3 > -7y + 13
12y > 10
y > 10/12
y > 5/6
Answer:
A)
62/3 = 20.67 hours
B)
60.00 hours
C)
2074.29 miles
Step-by-step explanation:
If we assume the earth is a perfect circle, then in a complete rotation the earth covers 360 degrees or 2π radians.
A)
In 24 hours the earth rotates through an angle of 360 degrees. We are required to determine the duration it takes to rotate through 310 degrees. Let x be the duration it takes the earth to rotate through 310 degrees, then the following proportions hold;
(24/360) = (x/310)
solving for x;
x = (24/360) * 310 = 62/3 = 20.67 hours
B)
In 24 hours the earth rotates through an angle of 2π radians. We are required to determine the duration it takes to rotate through 5π radians. Let x be the duration it takes the earth to rotate through 5π radians, then the following proportions hold;
(24/2π radians) = (x/5π radians)
Solving for x;
x = (24/2π radians)*5π radians = 60 hours
C)
If the diameter of the earth is 7920 miles, then in 24 hours a point on the equator will rotate through a distance equal to the circumference of the Earth. Using the formula for the circumference of a circle we have;
circumference = 2*π*R = π*D
= 7920π miles
Therefore, the speed of the earth is approximately;
(7920π miles)/(24 hours) = 330π miles/hr
The distance covered by a point in 2 hours will thus be;
330π * 2 = 660π miles = 2074.29 miles