Domain of 
are the values of x for which 2x + 1 < 0
2x < -1
x < -1/2
Therefore, domain is all real numbers less than -1/2
2x < -1
x < -1/2
Therefore, domain is all real numbers less than -1/2
A basketball is thrown, and its height above ground is represented by the function f(x)=-3x^2+10x+4. At the same time, a drone t
akes off from the ground, and its height above ground is represented by the function f(x)=3^x-1. The heights above the ground of the ball and the drone are shown in the graph below.
If x represents time in seconds, approximately how many seconds does it take for the drone to be higher than the basketball?
If x represents time in seconds, approximately how many seconds does it take for the drone to be higher than the basketball?
1 answer:
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Answer:
○ 3
○ y + ½ = 3(x - 2)
○ Multiply both sides of the equation by 3. The Standard Form of the equation is 12x - 2y = 24.
○ 5x - 3y = 15
○ y = ½x + 5⁄2
Step-by-step explanation:
Find the <em>rate</em><em> </em><em>of</em><em> </em><em>change</em><em> </em>[<em>slope</em>]:
-y₁ + y₂\-x₁ + x₂ = m → (-1, 1) and (-2, -2)
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According to the Point-Slope Formula, <em>y - y₁ = m(x - x₁)</em>, all the negative symbols give the OPPOSITE terms of what they really are, so be EXTREMELY CAREFUL inserting this coordinate into the formula with their CORRECT SIGNS:
(2, -½) → y + ½ = 3(x - 2)
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We do not want fractions in our Standard Equation, so multiply by the denominator to get rid of it:
-3[4x - ⅔y = 8] → -12x + 2y = -24
** They should have multiplied by -3 instead of 3 because that negative is hooked up to everything in the fraction, but since the exercise gave you 12x - 2y = 24, go with 12x - 2y = 24.
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If you would take a look at this graph real closely, you will see that this graph intersects the y-axis and x-axis at ENDPOINTS, so to find the x-intercept, you simply plug in <em>zero</em> for <em>y</em>: 5x = 15, and you will know right away that <em>x</em><em> </em>is set to equal 3, which is what you see in the graph, (3, 0). Now, to find the y-intercept, you simply plug in <em>zero</em><em> </em>for <em>x</em>: -3y = 15, and you will know right away that <em>y</em><em> </em>is set to equal -5, which is what you see on the graph as well, (0, -5). With that being said, you have your answer.
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y - 3 = ½(x - 1)
y - 3 = ½x - ½
+ 3 + 3
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y = ½x + 2½
* 2½ = 5⁄2
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