Answers
Given:
The vertices of a triangle are D(1,5), O(7,-1) and G(3,-1).
To find:
The perpendicular bisector of line segment DO.
Solution:
Midpoint formula:
[tex]Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]
The midpoint of DO is:
[tex]Midpoint=\left(\dfrac{1+7}{2},\dfrac{5+(-1)}{2}\right)[/tex]
[tex]Midpoint=\left(\dfrac{8}{2},\dfrac{4}{2}\right)[/tex]
[tex]Midpoint=\left(4,2\right)[/tex]
Therefore, the midpoint of DO is (4,2).
Slope formula:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Slope of DO is:
[tex]m=\dfrac{-1-5}{7-1}[/tex]
[tex]m=\dfrac{-6}{6}[/tex]
[tex]m=-1[/tex]
Therefore, the slope of DO is -1.
We know that the product of slopes of two perpendicular line is -1.
[tex]m_1\times m_2=-1[/tex]
[tex]m_1\times (-1)=-1[/tex]
[tex]m_1=1[/tex]
The slope of perpendicular bisector is 1 and it passes through the point (4,2). So, the equation of the perpendicular bisector of DO is:
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-2=1(x-4)[/tex]
[tex]y-2+2=x-4+2[/tex]
[tex]y=x-2[/tex]
Therefore, the equation of the perpendicular bisector of DO is [tex]y=x-2[/tex].
Related Questions
On an English test, John scored 50 points on the essay portion. The test also had short-answer questions worth 2.5 points each. Choose an expression for John’s total points if he answered r short-answer questions correctly.
Answers
Answer:
2.5x+50
Step-by-step explanation:
r = numbers of right answers
Points the essay worth = 50
2.5 = points each right short answer
a drinks company use 76.8 kg of sugar in April .How much sugar the day use each day?
Answers
Answer:
2.56 kgs
Step-by-step explanation:
76.8kg ÷ 30 days = 2.56 kgs
Amount of sugar used - 76.8 kg
No. Of Days in Month of April - 30 days
∴ Sugar used each day is = 76.8 ÷ 30
[tex]76.8 \div 30 \\ \\ = \frac{76.8}{30} \\ \\ = \frac{768}{30 \times 10} \\ \\ = \frac{ \cancel{768}}{ \cancel{30} \times 10} \fbox{cancelling by 3} \\ \\ = \frac{256}{10 \times 10} \\ \\ = \frac{256}{100} \\ \\ = 2.56 \: kg[/tex]
So 2.56 kg is used everyday.Hope This Helps YouThe table below represents a linear function f(x), and the equation represents a function g(x): X) -1, 0, 1 F(x) -5, -1, 3 G(x)=4x+3
Part A. Write a sentence to compare the slope of the two functions and shows the steps you used to determine the slope of f(x) and g(x)
Part B which functions has greater y-intercept. Justify
Answers
Answer:
(a) g(x) has a greater slope
(b) g(x) has a greater y intercept
Step-by-step explanation:
Given
[tex]x \to -1,0,1[/tex]
[tex]f(x) \to -5,-1,3[/tex]
[tex]g(x) = 4x + 3[/tex]
Solving (a): Compare the slopes
Slope (m) is calculated as:
[tex]m =\frac{y_2 - y_1}{x_2 - x_1}[/tex]
So, for f(x), we have:
[tex]m =\frac{-1- 0}{-5- -1}[/tex]
[tex]m =\frac{-1}{-4}[/tex]
[tex]m =\frac{1}{4}[/tex]
For g(x), we have:
Assume [tex]g(x) = mx + c[/tex] then the slope is m
Compare the above to [tex]g(x) = 4x + 3[/tex]
Then the slope of g(x) is 4
g(x) has a greater slope
Solving (b): Function with greater y intercept
Here we set [tex]x= 0[/tex]
From the table of f(x)
[tex]f(x) = -1[/tex] when [tex]x = 0[/tex]
From [tex]g(x) = 4x + 3[/tex]
[tex]g(0) = 4 * 0 + 3[/tex]
[tex]g(0) = 3[/tex]
Hence:
g(x) has a greater y intercept
Which rates are equal? Choose 2.
A. 630 miles per 9 hours
B. 1,320 miles
per 24 hours
C. 1,170 miles per 18 hours
D. 455 miles per 7 hours
E. 840 miles per 14 hours
Answers
Answer:
C. 1170 miles per 18 hours
D. 455 miles per 7 hours
Step-by-step explanation:
1170/18=65
455/7=65
Grayson is 1.25 meters tall. At 12 noon, he measures the length of a tree's shadow to be 22.75 meters. He stands 17.6 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow . Find the height of the tree to the nearest hundredth of a meter.
Answers
Answer:
5.52m
Step-by-step explanation:
First, we can see that two similar triangles are formed. One similar triangle is the big triangle, with the base being 22.75m and the height being the tree's height. Another triangle is formed with Grayson's height as the height and the and the difference between where he is standing and the edge of the tree's shadow (the red outline in the picture) . We know that these are similar triangles because both the bases are parallel, as well as the heights and hypotenuses.
The base length for the triangle with Grayson as the height is 22.75-17.6 = 5.15 .
For similar triangles, we know that the ratios between sides are the same. For example, base₁/base₂ = height₁/height₂ . We can apply this here, making 5.15 base₁ and 1.25 height₁ (note that the same triangle's sides should be on top)
If we make the tree's height t, we thus have
5.15/22.75 = 1.25/t (height 2 is the tree's height
multiply both sides by t to remove one denominator
5.15 * t / 22.75 = 1.25
multiply both sides by 22.75 to remove the other denominator
5.15 * t = 1.25 * 22.75
= 28.4375
divide both sides by 5.15 to isolate the t
t = 5.52m
A claim is reviewed for MOHS surgery on the foot that was performed in 1 stage with 6 tissue blocks. The claim was reported with 17311, 17312-51, 17312-51. Is this correct
Answers
Answer:
17311, 17315
Step-by-step explanation:
Explanation,
Mohs surgery, also known as chemosurgery, created by a general surgeon, Dr. Frederic E. Mohs, is performed to remove complex or ill-defined cutaneous malignancy.List Of CPT Codes For Mohs Surgery
CPT Code 17311 and CPT Code 17313 are the base codes for the range of this surgery. CPT Code 17312, CPT Code 17314, and CPT Code 17315 are the add-on codes for this range.
Description Of CPT Code 17311
Moh’s micrographic technique, including removal of all gross tumor, surgical excision to tissue specimens, mapping, color coding of specimens, microscopic examination of specimens by the surgeon, and histopathologic preparation including routine stain(s) (eg. Hematoxylin and eosin, toluidine blue), head, neck, hands, feet genitalia, or any location with surgery directly involving muscle, cartilage, bone, tendon, major nerves, or vessels; first stage, up to 5 tissue blocksDescription Of CPT Code 17315 (addon)
CPT Code 17315 may be used to report each block after the first 5 blocks for any single-stage.
Moh’s micrographic technique, including removal of all gross tumor, surgical excision of tissue specimens, mapping color coding of specimens, microscopic examination of specimens by the surgeon, and histopathologic preparation including routine stains(s) (eg. Hematoxylin and eosin, toluidine blue), each additional block after the first 5 tissue blocks, any stage (List separately in addition to code for primary procedure)Extras
Description Of CPT Code 17312 (addon)
Each additional stage after the first stage, up to 5 tissue blocks (List separately in addition to code for primary procedure)
Description of CPT Code 17313
Moh’s micrographic technique, including removal of all gross tumor, surgical excision of tissue specimens, mapping, color coding of specimens, microscopic examination of specimens by the surgeon, and histopathologic preparation including routine stains(s) (eg. Hematoxylin and eosin, toluidine blue), of the trunk, arms, or legs; first stage, up to 5 tissue blocks
Description Of CPT Code 17314 (addon)
Each additional stage after the first stage, up to 5 tissue blocks (List separately in addition to code for primary procedure).
help me please!!!!!!!!
Answers
Answer:
1/2
Step-by-step explanation:
8/m - b/n simplified
Answers
Answer:
[see below]
Step-by-step explanation:
[tex]\frac{8}{m}-\frac{b}{n}\\\\\rightarrow \text{Adjust based on LCM}\\\text{LCM: } mn\\\\\frac{8n}{mn}-\frac{bm}{mn}\\\\\boxed{\frac{8n-mb}{mn}}[/tex]
Hope this helps.
Which of the following quadratic regression equations best fits the data
shown below?
Х
-4
-3
-2
-1
0
1
N
3
4
y
35
20
10
5
00
10
15
30
48
O A. y = 0.98x2 +3.06x+ 6.02
O B. y = 2.23x2 + 1.62x+ 5.26
O c. y = 3.72x2 + 2.94x + 3.21
O D. y = 4.63x2 + 0.84x+ 4.14
Answers
Answer:
C
Step-by-step explanation:
The method that is not used on graphs to lead the reader to misinterpret the graph is - Comparing two sets of related data on the same graph for the sake of comparison.
What is graph?A graph is a intersection of {x} and {y} axis. On the graph, the coordinate points can be plotted in the form (x, y). In this, {x} represents the horizontal distance along the {x} axis and {y} is the vertical distance along the {y} axis.
Given is to identify the methods that are not used on graphs to lead the reader to misinterpret the graph.
The method that is not used on graphs to lead the reader to misinterpret the graph is - Comparing two sets of related data on the same graph for the sake of comparison.
Therefore, the method that is not used on graphs to lead the reader to misinterpret the graph is - Comparing two sets of related data on the same graph for the sake of comparison.
To solve more questions on graphs, visit the link below-
https://brainly.com/question/17267403
#SPJ7
For the given triangle find the exact value for sin(A). Assume angle C is a right angle.
Answers
Answer:
53.13 degrees
Step-by-step explanation:
In order to use sin we have to use the opposite side over the hypotenuse.
[tex]\frac{4}{5}[/tex] in this case
sin(A) = [tex]\frac{4}{5}[/tex]
[tex]A = sin^{-1} \frac{4}{5}[/tex]
Plugging this into the calculator you get about 53.13 degrees
What is the value of the constant in the equation that relates the height and
width of this rectangle?
Answers
Answer:
14 or 10.4
Step-by-step explanation:
I don’t really understand the question but here I go I’ll try;
The height is 4 and the width is 10, so I think it’s 14 or 10.4.
The Constant that relates the height and width is 5/2.
What is Constant of Proportionality?The constant of proportionality k is given by k=y/x where y and x are two quantities that are directly proportional to each other.
Once you know the constant of proportionality you can find an equation representing the directly proportional relationship between x and y, namely y=kx, with your specific k.
Given:
we have the coordinates as (10, 4)
The coordinates shows that when the height of the rectangle is 4 unit then the width of the rectangle is 10.
Using Constant of Proportionality
y= k x
10 = k(4)
k = 10/ 4
k = 5/2
Learn more about Constant of Proportionality here:
https://brainly.com/question/29126727
#SPJ2
someone help me please with this algebra problem
Answers
Answer:
x=44-y
Step-by-step explanation:
In this problem, there are 44 glasses in total. Additionally, we want to know how many ice teas she can have; therefore, we must find x. The problem tells us that when x and y are added together they should equal 44. One way to solve this is to write the equation, x+y=44, because we know it is true and then solve for x. To find x subtract y from both sides. This equals x=44-y, the final answer.
explanation: y is the lemonade, and every time a glass of it is poured it is taking away from the 44 glasses. after the lemonade is poured it leaves x iced tea glasses. you can eliminate half of the answers off the bat because you know you’re looking for iced tea glasses, so whatever equation is there must equal x which elimates option 1 and 3.
Can you help with 7-10
Answers
Answer:
7.Mean=Ex/n
= 88+96+92+84+86+92+98/7
=90
(b). Median = {84,86,88},92,{92,96,98}
=92
(C).Mode=92 ; it is the number with the highest frequency
9.Mean=Ex/n
=28+26+32+24+27+32+29/7
=28
(b).Median={24,26,27},28,{29,32,32}
=28
(c).Mode=32;it is the number with the highest frequency.
8.Mean=Ex/n
=3.5+5.7+9.8+7+12.4+10.2/6
=8.1
(b).Median={3.5,5.7},7,9.8,{10.2,12.4}
=7+9.8/2
=8.4
(c).Mode=no mode
10.Mean=Ex/n
=2+6+9+8+8+2+8+7+5+4/10
=5.9
(b).Median={2,2,4,5},6,7,{8,8,8,9}
=6+7/2
=6.5
(c).Mode= 8;it is the number with the highest frequency.
I hope this helps.
what is the missing reason in the proof?
Answers
can you help me do this Question if you can?
Answers
Answer:
A
Step-by-step explanation:
To the nearest square metre, calculate the curved surface area of the half pipe if it is 9m long? (With a radius of 2.5m)
Answers
Answer:
70.686 [tex]m^{2}[/tex]
Step-by-step explanation:
A=2πrh (area of cylinder without top or bottom)
A = 2[tex]\pi[/tex](2.5)(9)
A = 141.372
divide by two for half of pipe.
A = 70.686
Multiply the following rational expressions and simplify the result
Answers
Answer:
Step-by-step explanation:
We have to solve the given expression,
[tex]\frac{9y-33y^2-3y^4}{100-49y^2}.\frac{7y^2+17y+10}{14y^2+28y}[/tex]
[tex]\frac{9y-33y^2-3y^4}{100-49y^2}.\frac{7y^2+17y+10}{14y^2+28y}[/tex] = [tex]\frac{-y(-9+33y+3y^3)}{100-49y^2}.\frac{7y^2+17y+10}{14y(y+2)}[/tex]
= [tex]\frac{-y(-9+33y+3y^3)}{(10-7y)(10+7y)}.\frac{7y^2+10y+7y+10}{14y(y+2)}[/tex]
= [tex]\frac{-y(-9+33y+3y^3)}{(10-7y)(10+7y)}.\frac{y(7y+10)+1(7y+10)}{14y(y+2)}[/tex]
= [tex]\frac{-y(-9+33y+3y^3)}{(10-7y)(10+7y)}.\frac{(y+1)(7y+10)}{14y(y+2)}[/tex]
= [tex]\frac{-3y(-3+11y+y^3)}{(10-7y)}.\frac{(y+1)}{14y(y+2)}[/tex]
= [tex]\frac{-3(-3+11y+y^3)}{(10-7y)}.\frac{(y+1)}{14(y+2)}[/tex]
= [tex]\frac{3(3-11y-y^3)(y+1)}{(10-7y)(14(y+2)}[/tex]
Could somebody explain this to me please
Answers
Answer:
it will be 50°
Step-by-step explanation:
I'll give you some of the other answers to see if you get it:
m <1 : 180-50 =130
m <5: 180
m <4: 180
m<7: 50
Step-by-step explanation:
I'm not good at geometry but I was trying to explain that you need to follow all your rules at geometry so that you canget your answer right
hello what I can say to you is that you need to follow the rules whereby they say the corresponding angles to the exterior angles then make sure that you follow all the rules that straight line add up into 180 degrees say for example a is equal to b
solve for
(6x + 9)/3 =
Answers
Hello!
(6x + 9)/3 =
= 3(2x + 3)/3 =
= 2x + 3
Good luck! :)
In the past year Maya watched 34 movies that she thought were very good. She watched 40 movies over the whole year. Of the movies she watched, what percentage did she rate as very good?
Answers
Answer:
90 percent
Step-by-step explanation:
the fraction is 90/100 so the percentage is 90%
the temperature of a city was 26 degrees celsius on Monday the temperature rise by 2 degrees celsius on everyday upto thrusday and fell by 5 degree Celsius on Friday what was the temperature of the city on Friday
Answers
Answer: 29 degrees Celsius
Step-by-step explanation:
On Monday, Tuesday, Wednesday, and Thursday, the temperature increased by 2 degrees for a total increase of 8 degrees. Then, on Friday, the temperature decreased by 5 degrees. Since 8 - 5 = 3, the total temperature change is +3 degrees, so the answer is 26 + 3 = 29 degrees
HELP ME ASAP NO LINKS
Which student's expression results in a quotient of 12.5?
KWAN
VERA
16.25 : 1.3
- 11.25 = (-9)
Mark only one oval.
0000
a. Kwan's only
b. Vera's only
c. Both Kwan and Vera's
d. Neither Kwan nor Vera's
Answers
Answer:
I wanna say its B. Vera's only
Suzi is 1.7 meters tall. At 2:00 pm, Suzi measures her shadow to be 0.3 meters long. At the same time, a near by tree casts a shadow that is 2.4 meters long. How tall is the tree? (Give your answer in tenths.)
Answers
What is the common difference between successive terms in the sequence 0.36, 0.26,0.16,0.06,-0.04,-0.14
Answers
Answer:
- 0.1
Step-by-step explanation:
please someone help I know the answer but I don't know how to place it on the scales below. (15 Points)
Answers
Given:
a. 35% of 150 g
b. 113% of $55
To find:
The correct values for the given blanks.
Solution:
a. 35% of 150 g
Here, the percent part is 35% and percent whole is 100%.
35% of 150 g is:
[tex]\dfrac{35}{100}\times 150=52.5[/tex]
So, the number part is 52.5 g and the whole number is 150 g.
Therefore, the percent part is 35%, number part is 52.5 g and the whole number is 150 g.
b. 113% of $55 g
Here, the percent part is 113% and percent whole is 100%.
113% of $55 is:
[tex]\dfrac{113}{100}\times 55=62.15[/tex]
So, the number part is $62.15 and the whole number is $55.
Therefore, the percent part is 113%, number part is $62.15 and the whole number is $55.
question in picture, math.
Answers
Answer:
beginning of march 4.1
beginning of jun 6.4
Step-by-step explanation:
A student drops their notes and their papers scatter. The fact that the papers scatter and do not remain neatly stacked is an illustration of :
Answers
Answer:
-- increase in entropy
-- second law of thermodynamics
Step-by-step explanation:
The 1st law of thermodynamic states that there is conservation of energy, i.e. we cannot create energy and we cannot destroy energy also in an isolated system.
The given example is not a representative of the 1st law.
The [tex]\text{2nd law of thermodynamics}[/tex] states that there is a natural tendency of an isolated system to [tex]\text{degenerate}[/tex] into a more [tex]\text{disordered state.}[/tex] Before dropping the notes and papers were in an isolated ordered system.
After dropping the papers scattered and did not remain in a stack position. It moves into a more disordered state.
Begore dropping down the notes and papers, they were in a stable position, i.e. no kinetic energy is there. No randomness when the notes and the papers were dropped. There is an increase in kinetic energy. There is randomness among the molecules by bombardment. So there is an increase in entropy.
Thus, above illustrations represents :
an increase in entropythe second law of thermodynamicsWhich of the following graphs represents the equation y=3x+2? A.Graph B. Graph B C. Graph C D. Graph D
Answers
A discount site decreases the price of cell phones by . Select the two expressions that represent the discounted price of a phone costing dollars.
A
0.40ddd
B
0.60ddd
C
d−d-d−0.60
D
d−d-d−0.60ddd
E
1−-−0.60ddd
Answers
The percentage discount given on the prove is not supplied ; Assume the percentage discount given on the phone is 60%
Answer:
0.4d
d - 0.6d
Step-by-step explanation:
Given that :
Percentage Discount given on phone = 60%
The discounted pice :
Initial percentage = 100%
Discount percentage = 60%
(100% - 60%) of price
(100% - 60%) * d
40%*d
0.4d
Also ;
(100% - 60%) * d
100%*d - 60%d
d - 0.6d
-3 raised to the power 0=
Answers
Given:
The statement is "-3 raised to the power 0".
To find:
The value of the given expression.
Solution:
We know that [tex]a[/tex] raised to the power [tex]b[/tex] can be written as [tex]a^b[/tex].
Any non zero number raised to the power 0 is always 1. It means,
[tex]a^0=1[/tex], where [tex]a\neq 0[/tex].
-3 raised to the power 0 [tex]=(-3)^0[/tex]
[tex]=1[/tex]
Therefore, the value of the given statement is 1.
