A line segment AB has the coordinates A (2,3) AND B ( 8,11) answer the following questions (1) What is the slope of AB? (2) What is the length of AB? (3) What are the coordinates of the mid point of AB?(4) What is the slope of a line perpendicular to AB ?
Answer:
1) The slope of the line segment AB is [tex]\frac{4}{3}[/tex].
2) The length of the line segment AB is 10.
3) The coordinates of the midpoint of the line segment AB is [tex]M(x,y) = (5,7)[/tex].
4) The slope of a line perpendicular to line segment AB is [tex]-\frac{3}{4}[/tex].
Step-by-step explanation:
1) Let [tex]A(x,y) = (2,3)[/tex] and [tex]B(x,y) = (8,11)[/tex]. From Analytical Geometry, we get that slope of AB ([tex]m_{AB}[/tex]), dimensionless, is determined by the following formula:
[tex]m_{AB} = \frac{y_{B}-y_{A}}{x_{B}-x_{A}}[/tex] (1)
If we know that [tex]x_{A} = 2[/tex], [tex]x_{B} = 8[/tex], [tex]y_{A} = 3[/tex] and [tex]y_{B} = 11[/tex], the slope of the line segment is:
[tex]m_{AB} = \frac{11-3}{8-2}[/tex]
[tex]m_{AB} = \frac{4}{3}[/tex]
The slope of the line segment AB is [tex]\frac{4}{3}[/tex].
2) The length of the line segment AB ([tex]l_{AB}[/tex]), dimensionless, can be calculated by the Pythagorean Theorem:
[tex]l_{AB} =\sqrt{(x_{B}-x_{A})^{2}+(y_{B}-y_{A})^{2}}[/tex] (2)
If we know that [tex]x_{A} = 2[/tex], [tex]x_{B} = 8[/tex], [tex]y_{A} = 3[/tex] and [tex]y_{B} = 11[/tex], the length of the line segment AB is:
[tex]l_{AB} = \sqrt{(8-2)^{2}+(11-3)^{2}}[/tex]
[tex]l_{AB} = 10[/tex]
The length of the line segment AB is 10.
3) The coordinates of the midpoint of the line segment AB are, respectively:
[tex]x_{M} = \frac{x_{A}+x_{B}}{2}[/tex] (3)
[tex]y_{M} = \frac{y_{A}+y_{B}}{2}[/tex] (4)
If we know that [tex]x_{A} = 2[/tex], [tex]x_{B} = 8[/tex], [tex]y_{A} = 3[/tex] and [tex]y_{B} = 11[/tex], the coordinates of the midpoint of the line segment AB are, respectively:
[tex]x_{M} = \frac{2+8}{2}[/tex]
[tex]x_{M} = 5[/tex]
[tex]y_{M} = \frac{3+11}{2}[/tex]
[tex]y_{M} = 7[/tex]
The coordinates of the midpoint of the line segment AB is [tex]M(x,y) = (5,7)[/tex].
4) From Analytical Geometry we can determine the slope of a line perpendicular to line segment AB as a function of the slope of the line segment:
[tex]m_{\perp} = -\frac{1}{m_{AB}}[/tex] (5)
If we know that [tex]m_{AB} = \frac{4}{3}[/tex], then the slope of a line perpendicular to AB is:
[tex]m_{\perp} = - \frac{1}{\frac{4}{3} }[/tex]
[tex]m_{\perp} = -\frac{3}{4}[/tex]
The slope of a line perpendicular to line segment AB is [tex]-\frac{3}{4}[/tex].
Scores on a recent ACT test yielded mean 20.9 and standard deviation 4.7. find the probability that a random sample of 32 test scores had a mean below 20.
a) .1914
b) .5753
c) .8599
d) .4247
e) .1401
Answer:
E. 0.1401
Step-by-step explanation:
The mean here has been given as 20.9
The standard deviation sd = 4.7
Random sample n = 32
Sd/√n
= 4.7/√32
= 0.8309
Probability of x less than 20
= 20-20.9/0.8309
= -0.9/0.8309
= -1.083
P(z<-1.083)
When we go to the z table
= 0.1401
Therefore the probability is 0.1401 and the answer to this question is E.
HELP ASAP PLS I DONT UNDERSTAND IM GIVING 15 POINTS AND ILL GIVE BRAINLIEST TO WHOS RIGHT
Answer:
(1.5, -2.5)
Step-by-step explanation:
Mate, I think you best get to studying, plotting coordinates are the fundamentals of algebra and euclidean geometry.
Anyways, (x, y). When you replace the variables, you determine the coordinates are (1.5, -2.5).
Answer:
C, 1.5, -2.5
Step-by-step explanation:
Count the lines between each axis to figure out the coordinates. If the point is in between a line, it is a half.
What is 2 1/2 written as an improper fraction?
2 1/2 as an improper fraction is 5/2
First, split the mixed fraction into the sum of a whole number and a fraction:
2 1/2 =>2+ 1/2
Then, rewrite the whole number as an equivalent fraction: 2 => 4/2
Lastly, add together the two fractions to get the answer:
4/2 + 1/2 = 5/2
Steven needs to unload a truck containing boxes filled with video consoles. He wants to determine the time required to unload the truck. Which quantity will help Steven to determine the time required?
Answer:
the last one
Step-by-step explanation:
A national consumer agency selected independent random samples of 45 owners of newer cars (less than five years old) and 40 owners of older cars (more than five years old) to estimate the difference in mean dollar cost of yearly routine maintenance, such as oil changes, tire rotations, filters, and wiper blades. The agency found the mean dollar cost per year for newer cars was $195 with a standard deviation of $46. For older cars, the mean was $286 with a standard deviation of $58. Which of the following represents the 95 percent confidence interval to estimate the difference (newer minus older) in the mean dollar cost of routine maintenance between newer and older cars?
A. (195 - 286) + 1.992 underroot46/45 + 58/40
B. (286 - 195) + 1.992 underroot46^2/45+ 58^2/40
C. (195 - 286)+ 1.992 underrot 140² 158²/45+40
D. (286 - 195) + 1.992 46 1582 45 +40
E. (195-286) +1.992 462 + 58 45 40
Answer:
(195 - 286) ± 1.992 * sqrt((46^2/45) + (58^2/40))
Step-by-step explanation:
Given that:
NEWER CARS:
Sample size = n1 = 45
Standard deviation s1 = 46
Mean = m1 = 195
OLDER CARS:
Sample size = n2 = 40
Standard DEVIATION s2 = 58
Mean = m2 = 286
Confidence interval at 95% ; α = 1 - 0.95 = 0.05 ; 0.05 / 2 = 0.025
Confidence interval is calculated thus : (newer--older)
(m1 - m2) ± Tcritical * standard error
Mean difference = m1 - m2; (195 - 286)
Tcritical = Tn1+n2-2, α/2 = T(45+40)-2 = T83, 0.025 = 1.99 (T value calculator)
Standard error (E) = sqrt((s1²/n1) + (s2²/n2))
E = sqrt((46^2/45) + (58^2/40))
Hence, confidence interval:
(195 - 286) ± 1.992 * sqrt((46^2/45) + (58^2/40))
The 95% confidence interval for estimating the difference in the mean dollar cost of the routine maintenance between newer and older cars is given by:
[tex]CI=(\overline{x_1} - \overline{x_2}) \pm t_{critical} \sqrt{\dfrac{s_1^2}{n_1} + \dfrac{s_2^2}{n_2}}[/tex]
Given that:The first sample consists of owners of newer cars
First sample's size = [tex]n_1 =45[/tex]First sample's mean = [tex]\overline{x_1}=\$195[/tex]First sample's standard deviation = [tex]s_1 = \$46[/tex]The second sample consists of owner of older cars.
Second sample's size = [tex]n_2 = 40[/tex]Second sample's mean = [tex]\overline{x_2}=\$286[/tex]Second sample's standard deviation = [tex]s_2 = \$58[/tex]To find:95% confidence interval for difference between both samples' means.
Calculations and Explanations:Since the sample sizes are > 30, thus we can use the z table for finding the Confidence interval.
The CI is given as:
[tex]CI=(\overline{x_1} - \overline{x_2}) \pm t_{critical} \sqrt{\dfrac{s_1^2}{n_1} + \dfrac{s_2^2}{n_2}}[/tex]
For 0.95 probability confidence, we have t at 40+45-3= t at 83 at 0.05/2 is 1.992 (from T tables)
Thus,
[tex]CI=(195-268) \pm 1.992 \sqrt{\dfrac{46^2}{45} + \dfrac{58^2}{40}}[/tex]
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mean median mode range
Answer:
I think your question is the differences between these terms in mathematical explanation? Well, the median is the middle. You add and divide for the mean. The mode is the one that appears the most. And the range is the difference in between.
Other:
Brainliest? Thanks!
[tex]mean = \frac{sum \: \: of \: \:all \: \: obsevations}{no. \: \: of \: \: observations} [/tex]
[tex]median = middle \: \: most \: \: value[/tex]
[tex]mode = most \: \: occuring \: term[/tex]
[tex]range = highest \: \: observation \: - lowest \: \: observation[/tex]
PLS HELP Which number has a product of -6/5 when multiplied by -12/5
A. -18/5
B -1/2
C 1/2
D 2/1
select the pair of perpendicular segments from the figure below
Felipe sold t-shirts and hats at a festival. He made a $5 profit for each t-shirt he sold. He also made a profit of $40 from selling hats. If he made a total profit
$125, how many t-shirts did he sell?
Answer:
He sold 17 shirts at the festival.
The total number of t-shirts Felipe sold is 17 t-shirts.
Consider that the number of t-shirts Felipe sold be "x".
Since He made a profit of $5 for each t-shirt sold. Therefore, his profit from selling t-shirts is 5x. also made a profit of $40 from selling hats.
His total profit is given as $125.
So we can write the following equation:
5x + 40 = 125
Subtracting 40 from both sides;
5x = 85
Dividing both sides by 5, we get:
x = 17
Therefore, Felipe sold 17 t-shirts.
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HELP IM IN CLASS DOING IT RIGHT NOW The absolute value of any number is always positive. True False
Answer:
True
Step-by-step explanation:
Answer:
[tex] \huge\purple{TRUE}[/tex]
Step-by-step explanation:
The absolute value of any number is always positive.
The graph represents the height y, in feet, above the ground of a water balloon x seconds after it is dropped from a window.
Which statement is true?
Select each correct answer.
The maximum height of the water balloon occurs at x = 0.
The water balloon is in the air for 2 s.
The water balloon hits the ground in 64 s.
The water balloon rises above 64 ft before falling toward the ground.
The maximum height of the water balloon is 64 ft.
Answer:
O The maximum height of the water balloon occurs at x = 0.
O The water balloon is in the air for 2 s.
O The maximum height of the water balloon is 64 ft.
Step-by-step explanation:
Firstly, by simply looking at the x axis on the graph (time), you will see that it starts at 0 and the 64 ft maximum height is aligned with the starting point of 0 seconds.
The graph also shows (x axis) the 'time' represented, and as the height rapidly decreases the graph eventually reaches the 2 second mark, going no further and no lower.
Finally, the graph shows (y axis) the peak of the water balloon's height is 64 ft, as it is the highest number reached while the water balloon was airborne.
The correct options are (A) The maximum height of the water balloon occurs at x = 0, (B) The water balloon is in the air for 2 s, and (5) The maximum height of the water balloon is 64 ft are correct.
What is a parabola?It is defined as the graph of a quadratic function that has something bowl-shaped.
We have:
The graph represents the height y, in feet, above the ground of a water balloon x seconds after it is dropped from a window.
The water balloon follows a path such that it makes half parabola.
From the graph:
At x = 0
Height(h) = 64 feet
Which is the maximum height of the water balloon.
After t = 2 seconds
The water balloon hits the ground
The correct options are:
The maximum height of the water balloon occurs at x = 0. The water balloon is in the air for 2 s. The maximum height of the water balloon is 64 ft.Thus, the correct options are (A) The maximum height of the water balloon occurs at x = 0, (B) The water balloon is in the air for 2 s, and (5) The maximum height of the water balloon is 64 ft are correct.
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What is the least common multiple of the two denominators 6/8, 4/32
Answer:
32
Step-by-step explanation:
What is the solution to the following system of equations?
3x - 6y = -12
x - 2y = -8
(1) Use the substitution method to justify that the given system of equations has no solution.
(2) What do you know about the two lines in this system of equations?
Answer:
1.) x=2y-4
2.) x=2y-4 :)
Answer:
[tex]3x - 6y = - 12 ..........i)\\ x - 2y = - 8............ii) \\ x = 2y - 8 \\ Substituting \: the \: value \: of \: x \:in \: equation \: i) \: we \: get \\ 3(2y - 8) - 6y = - 12 \\ 6y - 24 - 6y = - 12 \\ Here \: we \: can \: see \:that\: the \: value \: of \: y \: cannot \: be \: found \\ Equation \: is \: in \: form \: a \frac{}{1} x + b \frac{}{1} y + c \frac{}{1}= 0\:and \\ a \frac{}{2} x + b \frac{}{2} y + c \frac{}{2} = 0 \\ where, \: \: \frac{a \frac{}{1} }{a \frac{}{2} } = \frac{b \frac{}{1} }{b \frac{}{2} } \\ Therefore \: lines \: are \: parallel \: to \: each \: other \\ Lines \: have \: no \: solution.[/tex]
is the anwers to 4,690 × 141 going to be even or odd
Answer:
661290
Step-by-step explanation:
even number ........
i need help dont just answer if you dont know the question only answer if you know the question
Answer:
164 cookies each
Step-by-step explanation:
divide 492 by 3. 3 Because it says Diana and her friends, and 492 because that is the total cookie count.
Thank you! WIll mark brainliest.
Answer:
B.) David should pull his goalie
Step-by-step explanation:
32. Sinead bought 2 shirts for $15.82 each and a pair of shoes for $42.37. If she
paid for the items with a $100 bill, how much change did she receive?
$25.99
$10.17
$74.01
$41.81
15.82x2=31.64
31.64+42.37=74.01
100-74.01=25.99
Sinead received $25.99 for change.
Answer:
Sinead received $25.99 for change.
Step-by-step explanation:
Which represents the equation of the roll line?
Answer:
A) y=3x-4
Step-by-step explanation:
Part A
If she spends 3x + 5 dollars on the first order of light bulbs, which of the following represents how much she spends on the second order?
A. 10x + 18
B. 4x + 8
C. 21x + 65
D. 10x + 8
Part B
If the store owner spent a total of $90 on both orders, how much does a box of light bulbs cost in dollars?
Answer:
B
11 dollars
Step-by-step explanation:
7x+13 is the sum of the two order
you know that one order is 3x+5, so if you subtract it from the total you get the other order
7x+13-(3x+5) =7x+13-3x-5 = 4x+8
if he spent 90 dollars in total then we can say that
7x+13 = 90
7x=77
x=11
11 dollars per box
Step-by-step explanation:
Please Help fast I don’t know
5/13 as a decimal rounded to the nearest hundredth
Answer:
0.40
Step-by-step explanation:
5/13 = 0.38461538461. Hundreths place is the 2nd number after decimal so if you round 8 it'll be .40
Answer:
5/13 as a decimal to the nearest hundredth is 0.39 or 0.40.
Step-by-step explanation:
You simply need to divide 5 by 13, and you get 0.384615, but round to the nearest hundredth gets you 0.40
cark earned grades of 62, 78, 59, and 89 on four tests.
what is the mean of his grades
Answer:
72
Step-by-step explanation:
mean=average. to get average, you add up the numbers and divide by how many numbers. they add upp to 288 and since theres 4 test grades, divide by 4 to get 72.
i think the answer is 579
What is an equation in point-slope form the line that passes through the point (-3,5) and (2,-3)?
Answer
Y-5=-8/5 (x+3)
Answer:
Y-5=-8/5 (x+3)
Step-by-step explanation:
Answer:
Y-5=-8/5 (x+3) good luck
Question 1
Mathematical Relationships
Part A
In general, what can you say about the relationship between health (life
expectancy at birth) and wealth? Mention possible reasons for this
relationship
someone with wealth without health is nobody
Step-by-step explanation:
when someone that is wealthy didn't give birth d Husband would say they should adopt a child or he should marry another wife
15.) whats the approximately measure of one interior angle of the regular polygon shown
16.) the shape in the figure is a square . Use the properties to determine the value of X
Answer:
15) For a regular polygon of N sides, the measure of one interior angle is:
A = (N - 2)*180°/N
In this case, the figure has 11 sides, then we have N = 11, and the measure of each interior angle will be:
A = (11 - 2)*180°/11
A = 9*180°/11 = 147.27°
Rounding to the first decimal after the decimal point, we get:
A = 147.3°
Then the correct option is B.
16) We know that the length of all the sides of a square is the same.
In the image, we can see that the length of the right side is 4, and the length of the top side is 2x + 4
And those lengths must be the same, then we have the equation:
2x + 4 = 4
subtracting 4 in each side of the equation we get:
2x + 4 - 4 = 4 - 4
2x = 0
The only solution for this equation is x = 0.
Then the correct option is C
Dan was at the beach for five days and found 28 seashells. He plans to give all of his seashells equally to his four friends. How many seashells will each friend get?
Which expression is equivalent to -3(4x-0.50)?
PLEASEEEEEEEEEEEEE HELPPP
Final Answer: [tex]-12x + 1.5[/tex]
Steps/Reasons/Explanation:
Question: Which expression is equivalent to [tex]-3(4x - 0.50)?[/tex]
Step 1: Expand by distributing terms.
[tex]-3[/tex] × [tex]4x - 3[/tex] × [tex]-0.50[/tex]
Step 2: Simplify [tex]-3[/tex] × [tex]4x[/tex] to [tex]-12x[/tex].
[tex]-12x - 3[/tex] × [tex]-0.50[/tex]
Step 3: Simplify [tex]3[/tex] × [tex]-0.50[/tex] to [tex]-1.5[/tex].
[tex]-12x - (-1.5)[/tex]
Step 4: Remove parentheses and add.
[tex]-12x + 1.5[/tex]
~I hope I helped you :)~
Write an equation of the line that passes through (7,10) and is perpendicular to the line y=12x−9.
Answer:
y = - [tex]\frac{1}{12}[/tex] x + [tex]\frac{127}{12}[/tex]
Step-by-step explanation:
y = 12x - 9
Slope of line perpendicular to given is m = - [tex]\frac{1}{12}[/tex]
P(7, 10)
y - 10 = - [tex]\frac{1}{12}[/tex] (x - 7)
y = - [tex]\frac{1}{12}[/tex] x + [tex]\frac{127}{12}[/tex]
An equation of the line that passes through (7,10) and is perpendicular to the line y=12x−9 is y - 10 = -1/12(x-7)
The equation of a line in point-slope form is expressed as;
y - y0 = m(x-x0)
m is the slope of the line(x0, y0) is any point on the lineGiven the equation of a line y = 12x - 9
Slope = 12Slope of the line perpendicular is -1/12Substitute m = -1/12 and ()7, 10) into the equation above to have;
y - 10 = -1/12(x-7)
Hence an equation of the line that passes through (7,10) and is perpendicular to the line y=12x−9 is y - 10 = -1/12(x-7)
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Write this number in expanded form 36.91
Answer:
30+6+0.9+0.01 =36.91
Step-by-step explanation: Here ya go ;>