Find point
on the x-axis so that AC + BC is a minimum.
A(4,-5), B(12,3)
Answers
Answer:-3
Step-by-step explanation:
The minimum value of a function can be obtained from its derivative
The point on the x-axis that makes [tex]\overline{AC}[/tex] + [tex]\overline{BC}[/tex] minimum is the point [tex]\underline{(9, \, 0)}[/tex]
Reason:
Let (d, 0) represent the coordinate of the point, on the x-axis, we have;
[tex]\overline{AC}[/tex]² = (4 - d)² + (-5)²
[tex]\overline{AC}[/tex] = √((4 - d)² + (-5)²)
[tex]\overline{BC}[/tex]² = (12 - d)² + 3²
[tex]\overline{BC}[/tex] = √((12 - d)² + 3²)
[tex]\overline{AC}[/tex]² + [tex]\overline{BC}[/tex]² = L = 4² + (-5 - d)² + 12² + (3 - d)²
When [tex]\overline{AC}[/tex] + [tex]\overline{BC}[/tex] is minimum, we have;
[tex]\lim_{n \to \infty} a_n \dfrac{d}{dd} (\overline{AC} + \overline{BC}) = \dfrac{d}{dd} \left(\sqrt{ (4 - d)^2 + (-5)^2)} + \sqrt{ (12 - d)^2 + 3 ^2)} \right) = 0[/tex]
Which gives;
[tex]\dfrac{d}{dd} \left(\sqrt{ (4 - d)^2 + (-5)^2)} + \sqrt{ (12 - d)^2 + 3 ^2)} \right) = \dfrac{2 \cdot d - 24}{2 \cdot \sqrt{d^2-24 \cdot d + 153} } + \dfrac{2 \cdot d - 8}{2 \cdot \sqrt{d^2 - 8\cdot d + 41} }[/tex]
Therefore;
[tex]\dfrac{2 \cdot d - 24}{2 \cdot \sqrt{d^2-24 \cdot d + 153} } + \dfrac{2 \cdot d - 8}{2 \cdot \sqrt{d^2 - 8 \cdot d + 41} } = 0[/tex]
[tex]\dfrac{2 \cdot d - 24}{2 \cdot \sqrt{d^2-24 \cdot d + 153} } =- \dfrac{2 \cdot d - 8}{2 \cdot \sqrt{d^2 - 8 \cdot d + 41} }[/tex]
Squaring both sides and cross multiplying gives;
16·d² - 528·d + 3456 = 0
Which gives;
16·(d - 24)·(d - 9) = 0
Therefore, d = 24, and d = 9
The point (9, 0), is closer to the given points than the point (24, 0), therefore;
The point on the x-axis that makes [tex]\overline{AC}[/tex] + [tex]\overline{BC}[/tex] minimum is the point [tex]\underline{(9, \, 0)}[/tex]
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Complete question is;
In a survey of 565 U.S. businesses, 430 of these companies indicated that they monitor employees' web site visits. For purposes of this exercise, assume that it is reasonable to regard this sample as representative of businesses in the United States.
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Sample size; n = 560
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Alternative hypothesis: p > 0.75
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
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Answers
Answer:
the vertex of a quadratic equation:
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Answers
Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Your comment will be deleted along with your account BlueDragon123r5 You are working on finding x in the diagram above. You come up with the equation: 9y + 7 = 2y + 98. Your friend who has just started Algebra is blown away and doesn't understand how you came up with the equation. Explain to your friend how you found the equation and how to solve it.
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Answer
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Step-by-step explanation:
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Copyright © Big Ideas Learning, LLC
Integrated Mathematics 1
57
Answers
Answer:
Step-by-step explanation:
Let 'x' represent the actual salary.
|x - 25,000| <= 1800
- 1,800 <= x - 25,000 <= 1,800
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Answers
Answer:
The equation is y = 3x - 1
Step by Step Explanation:
Ok, so your first step in solving this would be substituting m in the equation with the slope, since m represents the slope. So then you would have y = 3x + b. Now, to find b, you would have to substitue the point (1,2) into the equation. You would replace 2 with y since that's the y coordinate, and 1 with x since that's the x coordinate. Then you have 2 = (3*1) + b. Now, you solve for this. You get 2 = 3 + b. Isolating the variable b, you have b = -1. So, the result is y = 3x - 1. That's your answer
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WRITE THE ANSWER AS A SIMPLIFIED FRACTION PLEASE
Answers
Answer:
-2/3
Step-by-step explanation:
The formula for slope is [ y2-y1/x2-x1 ]. Use the given points to substitute and solve.
12-8/4-10
4/-6
-2/3
Best of Luck!
Answer:
[tex]-\frac{2}{3}[/tex]
Step-by-step explanation:
Slope formula is:
[tex]\frac{y_{2} - y_{1} }{x_{2}-x_{1}}[/tex]
Let's plug-in our numbers.
[tex]\frac{12 - 8}{4 - 10} = \frac{4}{-6} = -\frac{4}{6}[/tex]
Now, we must simplify the fraction. We can do this by by finding the GCF (Greatest Common Factor). Let's list out what 6 and 4 have in common.
What can 6 be divided into?
2 * 3 = 6
1 * 6 = 6
What can 4 be divided into?
2 * 2 = 4
1 * 4 = 4
The GCF of these two numbers is 2!
[tex]-\frac{4\div2}{6\div2} = -\frac{2}{3}[/tex]
So, our slope is [tex]-\frac{2}{3}[/tex]
Another way to solve this is [tex]\frac{rise}{run}[/tex]I have shown how to do this in the picture below. We get the same answer solving this way as well.
~ [tex]InLoveWithPugs[/tex]
[tex]Math \ Enthusiast\\Moderator[/tex]
Albert wants to buy two pomegranates and some peaches • The price of one pomegranate is $1.59. • The price of peaches is $1.19 per pound. Albert wants to spend no more than $10.00. How many whole pounds of peaches can Albert buy if he wants to spend less than $10.00? 4 5 6 7
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Answer: 5
Step-by-step explanation:
Answer: 5
Step-by-step explanation: hope this helps
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Answer:
0
Step-by-step explanation:
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A new youth sports center is being built in a safe harbor. The perimeter of the rectangular playing field is 510 yards. The length is the field is 5 yards less than quadruple the width. What are the dimensions of the plying field?
Answers
Answer:
L=203 yardsW=52 yardsStep-by-step explanation:
Step one:
given data
perimeter= 510 yards
let the width be x, width=x
length= (4x-5)-----quadruple mean 4 times
Step two:
the expression for perimeter is
P=2L+2W
510=2(4x-5)+2x
510=8x-10+2x
510+10=8x+2x
520=10x
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x=520/10
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Answer:
the answer is -120
Step-by-step explanation:
trust :)
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Answer:
x = 8mi
Step-by-step explanation:
Use Pythagorean theorem! It states that you can find any side of the triangle using the equation + = . The sides a and b are the sides that are shortest, and c is the longest/slanted side (hypotenuse). So plug in what they give you to get + = ( a and b can be used for either number that is not the hypotenuse). A little bit of basic algebra will lead you to get x=8 mi.
Hai has 24 video games. Six of his games are sports related and the rest are role-playing games. Which ratio represents the number of his role-playing games to the total number of games? One-fourth One-third Two-thirds Three-fourths
Answers
Answer:
3/4
Step-by-step explanation:
24-6=18--> role playing games
18/24=3/4
Answer: 3/4
Step-by-step explanation: