No, it's not possible for the sides of a triangle to have those lengths.
According to the triangle inequality theorem, the sum of any two sides of the triangle has to be bigger than the last side. Let's test this.
This inequality satisfies the triangle inequality theorem.
This also satisfies the theorem.
Uh oh. This does not satisfy the triangle inequality theorem. Thus, it is not possible for a triangle to have these side lengths.
Step-by-step explanation:
A left Riemann sum approximates a definite integral as:
Given ∫₂⁸ cos(x²) dx:
a = 2, b = 8, and f(x) = cos(x²)
Therefore, Δx = 6/n and x = 2 + (6/n) (k − 1).
Plugging into the sum:
∑₁ⁿ cos((2 + (6/n) (k − 1))²) (6/n)
Therefore, the answer is C. Notice that answer D would be a right Riemann sum rather than a left (uses k instead of k−1).
Answer:
log(32/125)
=log32 - log125 [log(x/y)=log(x) - log(y)]
=log(2)^2 - log(5)^3
=2log2-3log5 [log(x)^p=p log x]
=2a-3b
Answer:
21. The slope is 50.
22. 0
23. y=50x
24. $2600
Step-by-step explanation:
21. The slope of the line is 50. Slope is defined as "rise over run". As the line increases, each segment moves up the y-axis by $50, and to the right on the x-axis 1 segment. (Work: 50 divided by 1)
22. The y-intercept is (0, 0), or simply 0. If you look at the graph you can see that the line crosses the y-axis at the origin. This makes the y-intercept equal to 0.
23. The slope tells you that the student makes $50 every week. The y-intercept is 0. Using the formula y=mx+b, an appropriate equation would be y=50x.
24. The equation found in problem 23 can me used to determine how much a student makes (y) after "x" weeks. Substitute 52 for x to solve for y. This becomes y=50(52). This can be simplified to y=2600. This means that after 52 weeks, the student will have made $2,600.
Answer:
Step-by-step explanation:
Angle 1 = 1, 3, 5, 7
Angle 3 = 1, 3, 5, 7
Angle 4 = 2, 4, 6, 8
Pretty much just look at the congruent symbols and you can figure it out.
