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]
Learn more here:
https://brainly.com/question/17117378
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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
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Answer:
3/4
Step-by-step explanation:
24-6=18--> role playing games
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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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If the sum of the greatest and smallest of 4 consecutive even integers equals 30, what is the sum of all four integers?
Answers
Answer:
The sum of all four integers is 60.
Step-by-step explanation:
Let the integers be x, x + 2, x + 4, and x + 6.
x + x + 6 = 30
2x = 24
x = 12
So x + x + 2 + x + 4 + x + 6 = 4x + 12 = 60
Answer:
________________________
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.
Answers
Answer
I know how to solve it just don't know how to explain how you came up with the equation
Step-by-step explanation:
To solve 9y+7=2y+98 you add 9y+2y and you get 11y and then you add 7+98 and get 105 then you put 11y=105 divide both ides by 11 y= 9.54
10.) A fitness center
charges a $100 initiation
fee plus $40 per month.
f(m) =
Answers
The Fitness center charges $40 per month(your x) and it is a $100 initiation(your y)
Answer:
f(m)=40x+100
Step-by-step explanation:
40 is your rate which is x and 100 is the initial fee which is y.
It there sufficient evidence to conclude that more than 75% of US businesses monitor employees web site visits? Test the appropriate hypotheses using a significance level of 0.01
Answers
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.
Is there sufficient evidence to conclude that more than 75% of U.S. businesses monitor employees' web site visits? Test the appropriate hypotheses using a significance level of 0.01. (Round your test statistic to two decimal places and your P-value to four decimal places.)
Answer:
There's not sufficient evidence to suggest that more than 75% of U.S. businesses monitor employees website visits.
Step-by-step explanation:
Population proportion; p^ = 430/565 = 0.761
Sample proportion; p = 75% = 0.75
Significance level; α = 0.01
Sample size; n = 560
Let's define the hypotheses;
Null hypothesis; H0: p = 0.75
Alternative hypothesis: p > 0.75
Formula for the test statistic is;
z = (p^ - p)/√[p^(1 - p^)/n]
z = (0.75 - 0.761)/√(0.75(1 - 0.75)/560)
z = -0.011/√0.00033482143
z = -0.011/0.0183
z = -0.60
From online p-value from z-score calculator attached, using; z = -0.60, significance level = 0.01, one tailed hypothesis, we have;
P-value ≈ 0.2743
The p-value is greater than the significance level and so we will fail to reject the null hypothesis and conclude that there's not sufficient evidence to suggest that more than 75% of U.S. businesses monitor employees website visits.
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Answers
Answer:
the vertex of a quadratic equation:
a*x^2 + b*x + c = y
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x = -b/2a.
In this case, x = -2
Then:
-b/2a = -2.
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a*(-2)^2 + b*-2 + c = 3
Then we have two equations:
-b/2a = -2
a*(-2)^2 + b*-2 + c = 3
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Let's begin with c = 0, our equations are:
-b/2a = -2
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b = 4*a
Now we can replace this in the other equation and solve this for a.
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then:
b = 4*a = 4*-3/4 = -3
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(-3/4)*x^2 - 3*x = y.
Now, to find the second let's use a different value of c.
c = 1
b = 4*a
a*(-2)^2 + b*-2 + 1 = 3
Let's solve in the same way as before:
a*4 + (4*a)*-2 + 1 = 3
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Then our equation is:
(-1/2)*x^2 - 2*x + 1 = y
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then our equations are:
b = 4*a
a*(-2)^2 + b*-2 + 2 = 3
Same as before, replace the first equation in the second.
a*4 + (4*a)*-2 + 2 = 3
-4*a + 2 = 3
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a = -1/4
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(-1/4)*x^2 - 1*x + 2 = y
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Answers
Answer:
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Step-by-step explanation:
Answer:
Step-by-step explanation:
1:2
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Step-by-step explanation:
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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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Answers
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1
Step-by-step explanation:
it is right ok stop now
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Answer:
With something like this you have to start out with 3 givens. what I do for these specific kinds of questions is just put something random in the first half, then put something random twice in the second slot, click clear, then it'l give you a button that says "clear" then a little after it'll say "hint" or "demo" the click those buttons and just put the second half in something random until it pops off, this works every time and will allow you to go to the next task.
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Answer:
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Step-by-step explanation:
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Answers
Answer:
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Answers
Answer:
y = -2x - 9
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Answers
Answer:
You can buy 10 mangoes for $4.
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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
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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.
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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]
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Answers
Answer:
Maybe c
Step-by-step explanation:
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Answer:
0
Step-by-step explanation:
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Answers
A is the correct answer
10. At a certain company, the average starting salary s for a new worker is $25,000. The actual
salary has an absolute deviation of at most $1800. Write and solve an inequality to find the
range of the starting salaries.
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
25,000 - 1,800 <= x <= 25,000 + 1,800
23,200 <= x <= 26,800
The range of the salary is the closed interval [23,200, 26,800].
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Answers
Answer:
Rational
Step-by-step explanation:
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
divide both sides by 10
x=520/10
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L=208-5
L=203 yards
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Answer:
y<4
Step-by-step explanation:
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Answers
Answer:Complex numbers in the coordinate plane. Each complex number x + yi corresponds to a number pair (x, y) in the plane, so we may say that the complex numbers form a two-dimensional collection. The two coordinates of the pair (x, y) are called the real part and the imaginary part of the complex number.
Step-by-step explanation:
1. A watch with a regular price of $85.00 is now on sale with a discount of 20%. Calculate
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Answers
Answer:
$68
Step-by-step explanation: All you do is divided 85 by 20 boom
Answer:
$68
Step-by-step explanation:
20% of $85
= 20/100 * 85
= $17
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write the equation of a line that has a slope of 3 and passes through the point (1,2) in slope intercept form
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
A scatter plot containing the point (12, 12) has the regression equation yˆ=14x+1.
What is the residual e when x = 12?
Enter your answer in the box.
e =
Answers
Answer:
Im pretty sure it is E=8
Step-by-step explanation:
Answer:
E=8
Step-by-step explanation:
took the test :)