We know that
The sum of the lengths of any two sides of a triangle is greater than the length of the third side (Triangle Inequality Theorem)
Let
A------> Lincoln, NE
B------> Boulder, CO
C------> third city
we know that
in the triangle ABC
AB=500 miles
BC=200 miles
AC=x
Applying the Triangle Inequality Theorem
1) 500+200 > x------> 700 > x------> x < 700 miles
2) 200+x > 500----> x > 500-200------> x > 300 miles
the solution for x is
300 < x < 700
the interval is------> (300,700)
the possible distances, d, in miles, between Lincoln, NE, and the third city, are in the range between 300 and 700 miles
9514 1404 393
Answer:
top down: ∞, 0, 1, 0, ∞
Step-by-step explanation:
The equation will have infinite solutions when the left side and right side simplify to the same expression. This is the case for the first and last expressions listed.
2(x -5) = 2(x -5) . . . . expressions are already identical
x +2(x -5) = 3(x -2) -4 ⇒ 3x -10 = 3x -10 . . . the same simplified expression
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The equation will have no solutions when the x-coefficients are the same, but there are different added constants.
5(x +4) = 5(x -6) ⇒ x +4 = x -6 . . . not true for any x
4(x -2) = 4(x +2) ⇒ x -2 = x +2 . . . not true for any x
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The equation will have one solution when coefficients of x are different.
5(x +4) = 3(x -6) ⇒ 2x = -38 ⇒ x = -19
This is a neat little question. I don't think I've seen it before.
Step one
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Find c
3^2 + 4^2 = c^2
9 + 16 = c^2
c^2 = 25
c = 5
Step 2
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Set up your first equation for b^2
a^2 + 4^2 = b^2 from triangle XWY
Step 3
=====
Set up your second equation for b^2
25 +b^2 = (a + 3)^2 from triangle XWZ
Step 4
=====
Put the results of Step 2 into step 3 and solve
25 + a^2 + 16 = (a + 3)^2 Collect the like terms on the left.
41 + a^2 = (a + 3)^2 Expand the brackets on the right
41 + a^2 = a^2 + 6a + 9 Transfer the 9 to the left.
32 + a^2 = a^2 + 6a Subtract a^2 from both sides.
6a = 32 Divide by 6
a = 32 / 6
a = 5 2/6
a = 5 1/3
f(x) = 4*2ˣ = 2ˣ⁺²
The answer is B because it is an exponential function since x is an exponent. Also, decay mean decreasing and growth means increasing. The function 2ˣ⁺² is "growing" as x gets bigger because the base is not a fraction.
Step-by-step explanation:
y - 8 = -8(x + 2)
y - 8 = -8x - 16
y = -8x - 8
The slope-intercept form is y = -8x - 8.
