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].
makayla is painting her house.each room needs 1/2 gallon of paint if she has three gallons of paint,how many rooms can she paint?
Answer:
6 rooms.
Step-by-step explanation:
3 x 2 = 6
it takes 2 halves to make a whole so 3 x 2 = 6
What is 3×7×7×7×7 using index notation
Answer: 3 x 7^4
Because there's one 3 & four 7's .
Step-by-step explanation:
Which function is represented by this graph
y=-1/2x +3 it's last one
which of the following is a characteristic of the circumcenter of a triangle? multi-choice. A. it is the center of the only circle that can be inscribed in the triangle. , B. it is the center of the circle that can be inscribed in given a given triangle. C. it is the center of the only circle that can be circumscribed about the triangle. D. it is equidistant from all three sides of the triangle.
Answer:
C
Step-by-step explanation:
The circumcenter is called ”the circumcenter” because it is the center of the circle that ”circumscribes” the triangle.
I hope this helps!
Further explanation:
For a circle to circumscribe something, it circles it so that each of the vertices are on the circle, so each of the vertices are equidistant from the circumcenter. The circumcenter of a triangle is formed by the perpendicular bisectors of its sides.
Side note:
The rest of the choices describe an incenter.
HELP!!!! 2 dot plots. Both number lines go from 0 to 10. Plot 1 is titled fifth grade. There are 2 dots above 1, 3 above 2, 1 above 3, 4 above 4, 5 above 5, 5 above 6, 2 above 7, 2 above 8, 0 above 9, 0 above 10. Plot 2 is titled seventh grade. There are 2 dots above 0, 2 above 1, 3 above 2, 5 above 3, 5 above 4, 3 above 5, 3 above 6, 1 above 7, and 0 above 8, 9, and 10.
The dot plot shows the number of hours, to the nearest hour, that a sample of 5th graders and 7th graders spend watching television each week. What are the mean and median?
The 5th-grade mean is
.
The 7th-grade mean is
.
The 5th-grade median is
.
The 7th-grade median is
.
Answer:
5th grade mean - 4.67
7th grade mean - 3.46
5th-grade median - 5
7th-grade median - 3.5
Least to greatest 0.4, 5/8, 74%, 3/5
Answer:
0.4,3/5,5/8,74%
Step-by-step explanation:
Change them all into decimals.
Get 0.4,0.625,0.74,0.6
Then reorder and see what their original values were
What is the quotient of 4/5 divided by 17/9
Answer:
0.42352941176
Step-by-step explanation:
hope this helps
The value of quotient will be 0.42.
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The expression is,
''4/5 divided by 17/9''
Now,
Since, The expression is,
''4/5 divided by 17/9''
Hence, After solving we get;
⇒ 4/5 ÷ 17/9
⇒ 4/5 × 9/17
⇒ 36/85
⇒ 0.42
Thus, The value of quotient = 0.42
Learn more about the divide visit:
brainly.com/question/844312
#SPJ2
sophia used 1/10 of a liter of water to fill 1/4 of a fish aquarium. How much water, in liter is required to fill the aquarium?
Answer:
4/10 of a liter
Step-by-step explanation:
if 1/10 of a liter fills 1/4 of the aqauium then your ratio is .1:.25 out of 100 so
100/25=4
Which line is parallel to y = -5/2x - 7?*
O 2x + 5 y = -5
O 2x - 5 y = 30
O 5x + 2y = 4
O 5x-2y = 8
Answer:
the answer is
5x + 2y = 4
please help meee!!!!!!!
Answer:
A
Step-by-step explanation:
8+(-15)=-7
I-7 I=7
HELP!!! STATS!!!
A random sample of 100 felony trials showed a sample mean waiting time between arrest and trial = 173 days with a population standard deviation of waiting times = 28 days. Find a 99% confidence interval for the population mean waiting time.
Stats question, I'm really stck please help me!
Answer:
The 99% confidence interval is [tex] 165.776 < \mu < 180.224 [/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 100
The sample mean is [tex]\= x = 173 \ days[/tex]
The population standard deviation is [tex]\sigma = 28 \ days[/tex]
From the question we are told the confidence level is 99% , hence the level of significance is
[tex]\alpha = (100 - 99 ) \%[/tex]
=> [tex]\alpha = 0.01[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 2.58 [/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
[tex]E = 2.58 * \frac{28 }{\sqrt{100} }[/tex]
=> [tex]E = 7.224 [/tex]
Generally 95% confidence interval is mathematically represented as
[tex]\= x -E < \mu < \=x +E[/tex]
=> [tex] 173 -7.224 < \mu < 173 + 7.224 [/tex]
=> [tex] 165.776 < \mu < 180.224 [/tex]
Y=^2+5x-7 find the vertex
Answer:
-5/2-39/2
Step-by-step explanation:
What is 2-1x(57\7) ?
Answer:
2 - [tex]\frac{57}{7}[/tex]x
Step-by-step explanation:
2-1x(57/7)
2 - [tex]\frac{57}{7}[/tex]x
what is the relationship of the angles
Answer:
Alternate Interior Angles
Answer:
a
Step-by-step explanation:
PLS ITS A TEST ILL GIVE BRAINLIEST the equation is y = -3x + 2
y=x-6
Identify proportional relationships
Does the following table show a proportional relationship between the variables g and h?
g
3
6
9
9
36
81
Answer:
sure easy man the carrot is blue and green and orange there naswer soled
What is MR? Explain.
Answer:
MR is 20 because if the side lengths that are shown are congruent, then the bottoms are too. so each part of the bottom that has a number, that number repeats on the part that's part of that triangle. so the bottom lengths go " 4 6 6 4" and you add those together and get 20
Help anyone
8th grade math need it asap
Answer:
[tex] \frac{7}{10} [/tex]
Answer:
7/10
Step-by-step explanation:
If you move the decimal point to over to the right, also known as multiplying by a hundred, then you get 70. Right now we have 70/100
Simplify even further you would get 7 / 10
Hewo plz help can u answer
PUT A REAL ANSWER!!!!!!!!!!
5 pts.
175+8w≥425
Answer:
w≥31.25
Step-by-step explanation:
175+8w≥425
-175 -175
8w≥250
/8 /8
w≥31.25
Answer:
X is greater than or equal to 125/4
Step-by-step explanation:
Subtract 175 from both sides which will turn 425 into 250
Divide 8 from 8x to the other side to turn 250 into 125/4
In the end, you get X is greater or equal to 125/4
Evaluate -5-15+4+15−5−15+4+15minus, 5, minus, 15, plus, 4, plus, 15.
Answer:
-2
Step-by-step explanation:
ur welcome
-1
Step-By step Explanation:
god please help me i’ve been stuck on this problem for hours and i’m so hungry:(
Answer:
B
Step-by-step explanation:
u should go eat
Answer:
A)
because it passes the line twice instead of once
(fuctions only cross once)
hope that helped you:)
please make my answer brainiest as im trying get 3 brainiest answers
Which expression is equivalent to one over three p + 15?
one over three(p + 45)
one over three(p + 5)
3(p + 45)
3(p + 5)
Answer:
1/3p + 5
Step-by-step explanation:
1/3 of 15 is 5
If you think in terms of multiplication: 3 groups of 5 is 15 so 1 group of 15 would be 5
Answer:
a) 1/3 (p+45)
Step-by-step explanation:
that's the answer
Hello there ^^ I'd love it if you would help me :D
Answer:
Great question
Step-by-step explanation:
Where is it :p
What basic fact can you use to divide 2,800 by 7
Step-by-step explanation:
2800/7 = 400, ,
please you can see the upper paper which
can to solve this division math
if 7/12 is multiplied by a fraction less than 1 what would be the product
Answer:
Examples below
Step-by-step explanation:
We have the fraction
[tex]\frac{7}{12}[/tex]
It's required to multiply it by any fraction less than 1. Let's select the following fractions. All of them are less than 1 because the numerator is less than the denominator:
[tex]\frac{1}{7}[/tex]
[tex]\frac{4}{5}[/tex]
[tex]\frac{6}{35}[/tex]
The required products are:
[tex]\frac{7}{12}\cdot \frac{1}{7}=\frac{7}{7*12}=\frac{1}{12}[/tex]
[tex]\frac{7}{12}\cdot \frac{4}{5}=\frac{4*7}{12*5}=\frac{7}{15}[/tex]
[tex]\frac{7}{12}\cdot \frac{6}{35}=\frac{6*7}{12*35}=\frac{1}{10}[/tex]
Suppose that an individual has a body fat percentage of 12.7% and weighs 132 pounds. How many pounds of his weight is made up of fat? Round your answer to the nearest tenth.
Answer:
just go with your heart
Colin invests £14100 into his bank account. He receives 9.0% per year simple interest. How much will Colin have after 5 years? Give your answer to the nearest penny where appropriate.
Answer:
6350
Step-by-step explanation:
Brooke measures the height of her bean plant for a science project. The bean plant is 12.5 inches tall.
How many centimeters tall is Brooke’s bean plant?
Answer:31.75 centimeters
Step-by-step explanation:
Kellen got an e-mail from his bank on June 7th, June 21st, July 5th, and July 19th. Use inductive reasoning to predict the next time Kellen will receive an e-mail from his bank. A. July 21st B. July 26th C. August 2nd D. August 3rd
Answer:
August 2nd
Step-by-step explanation:
31 days in july, last email on the 19th
19-5=14
31-19=12
12+2=14
August 2nd, please mark brainliest
Help me out please don’t pass this question help me !
Answer:
20L + 45 = 225
Step-by-step explanation:
20 is the slope making it constant
45 is a one time fee making it a y intercept
equaling 225
Answer:
20L+45=225
Step-by-step explanation:
20 represents how much she paid for each lesson, we don't know how many lessons she paid for so we use the variable L and multiply it by 20. She only had to pay the registration fee once so 45. Unknown lessons taken by 20 + the one-time fee of 45 equals 225
Hope this helps!