Directed line segment PT has endpoints whose
coordinates are P(-2, 1) and 1(4,7). Determine
the coordinates of pointſ that divides the segment
in the ratio 2 to 1.
Answers
Answer:
(2 , 5)
Step-by-step explanation:
point (x,y) that divides the segment PI in the ratio 2 to 1
PD=4 - (-2) = 6 PE/ED=2/1 PE=2ED PE+ED=6 3ED=6 ED=2 PE=4
coordinate of E (2,1) .... 2 is x coordinate of E
DI=7-1=6 DF/FI=2/1 DF=4
coordinate of F (4,5) .... .... 5 is y coordinate of E
CF // PD PC/CI=DF/FI=2/1
C (2,5)
Coordinates of the point intersecting segment PT in the ratio of 2 : 1 will be (2, 5).
Given in the question,
Segment PT with endpoints P(-2, 1) and T(4, 7).Point (h, k) divides the segment in the ratio of 2 : 1.If the endpoints of a segment PQ have been given as[tex]P(x_1,y_1)[/tex] and [tex]Q(x_2,y_2)[/tex] and a point [tex](h,k)[/tex] divides this segment in the ratio of m : n,
[tex]h=\frac{mx_2+nx_1}{m+n}[/tex]
[tex]k=\frac{my_2+ny_1}{m+n}[/tex]
If the extreme ends of a segment PT are [tex]P(-2,1)[/tex] and [tex]T(4,7)[/tex] and a point (h, k) divides this segment in ratio of 2 : 1,
[tex]h=\frac{2(4)+1(-2)}{2+1}[/tex]
[tex]h=2[/tex]
[tex]k=\frac{2(7)+1(1)}{2+1}[/tex]
[tex]k=5[/tex]
Therefore, coordinates of the point intersecting segment PT in the ratio of 2 : 1 will be (2, 5).
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Step-by-step explanation:
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Step-by-step explanation:
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Answer: the Y-axis
Step-by-step explanation:
y is swapped To negative
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Answer:
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Step-by-step explanation:
Subtract r, rearrange, then take the square root.
[tex]\dfrac{m}{u^2}+r=-k-y \qquad\text{given}\\\\ \dfrac{m}{u^2}=-k-y-r\\\\-\dfrac{m}{k+r+y}=u^2\\\\ \boxed{u=\pm\sqrt{-\dfrac{m}{k+r+y}}}[/tex]
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Step-by-step explanation:
The low temperature in City A is -8°F. The low temperature in City B is -12°F Complete the statement below
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Answer:
City B is 4 degrees colder than City A
Step-by-step explanation:
When in degrees negatives a much colder. So if the number is negative the higher the number the colder the tempeture.
Have a great day!
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The perimeter of the triangle is 30 cm.
The perimeter of the rectangle is also 30 cm.
Answers
Answer:
The perimeter of the triangle is 30 cm.
The perimeter of the rectangle is also 30 cm.
Step-by-step explanation:
The perimeter of the triangle is 30 cm.
The perimeter of the rectangle is also 30 cm.
So who knows the right answer?
Answers
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Step-by-step explanation:
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Which of the following are integer solutions to the inequality below?
-3 < x ≤ 4
Answers
-2,-1,0,1,2,3,4
Let me know if you have any questions
rationalize root 3+root 5
Answers
Answer:
- 2
Step-by-step explanation:
To rationalise multiply by its conjugate.
The conjugate of [tex]\sqrt{3}[/tex] + [tex]\sqrt{5}[/tex] is [tex]\sqrt{3}[/tex] - [tex]\sqrt{5}[/tex] then
([tex]\sqrt{3}[/tex] + [tex]\sqrt{5}[/tex] )([tex]\sqrt{3}[/tex] - [tex]\sqrt{5}[/tex] ) ← expand using FOIL
= ([tex]\sqrt{3}[/tex] )² - [tex]\sqrt{15}[/tex] + [tex]\sqrt{15}[/tex] - ([tex]\sqrt{5}[/tex] )²
= 3 - 5
= - 2
Solve the system by substitution. -8.x --- 3y -2x + 1 = y Submit Answer
Answers
Step-by-step explanation:
What integer values satisfy both inequalities? − 2 < x < 3 − 2 ≤ x < 2
Answers
Given:
The inequalities are:
[tex]-2<x<3[/tex]
[tex]-2\leq x<2[/tex]
To find:
The integer values that satisfy both inequalities.
Solution:
We have,
[tex]-2<x<3[/tex]
[tex]-2\leq x<2[/tex]
For [tex]-2<x<3[/tex], the possible integer values are
[tex]x=-1,0,1,2[/tex] ...(i)
For [tex]-2\leq x<2[/tex], the possible integer values are
[tex]x=-2,-1,0,1[/tex] ...(ii)
The common values of x in (i) and (ii) are
[tex]x=-1,0,1[/tex]
Therefore, the integer values -1, 0 and 1 satisfy both inequalities.
Need help due in 10 mins pls
Answers
A semicircle was cut from a square sheet of blue construction paper . What is the area of the remaining blue construction paper as seen in the figure? (Do not include units)
Answers
Answer:
60.73cm
Step-by-step explanation:
10cm=diameter so raduis of circle=5cm
area of full circle=78.5398...
area of semicircle=39.2699...
area of square=100cm
100-39.26990817=60.73 cm
Tom works 12 hours a day at a café. He is paid $8 an hour. How much
money is he paid in 10 days?
Answers
Answer:
Tom will be paid $140 in 10 days
Step-by-step explanation:
Answer:
Tom will be paid 960$ is 10 days
(x + 13y) + 8y=
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Answers
Answer:
x+21 y
Step-by-step explanation:
+
2
1
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Ramona is counting the posts between mile markers on the highway. In 1 mile, she counts 33 posts. If the posts are evenly spaced, how many feet apart are they? (1 mile = 5,280 feet)
Answers
Answer:
160 feet
Step-by-step explanation:
In order to solve this, we need to realize that the mile is being divided into 33 equal parts. Therefore our operation should look like this:
5,280 (the number of feet in 1 mile) / 33
5,280/33=160
The posts are 160 feet apart from each other.
HTH :)
how far does the train go in 100 minutes
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Answer: It definitely depends
Step-by-step explanation:
You have 100 dollars and you give away 25% each week. How many weeks would it take to run out?
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Answer:
1 day
Step-by-step explanation:
day if you're like mee because I will buy chips cards for games
Answer:
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Step-by-step explanation:
Mean, Median, Mode and Range. Easy hard math. Please show work and give answers . Need help appreciate you all
Quiz Scores:
You and your friend are having a friendly competition about the scores on your math quizzes. Both of your scores for the first five quizzes are given below:
Your quiz scores: 18, 16, 19, 15, 17
Friend’s quiz scores: 20, 20, 13, 12, 17
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World Populations:
The populations (in millions) in 2000 on each of the six inhabited continents were:
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b. Find the mean, median, and mode(s) of the populations.
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The heights (in inches) of eight tomato plants are:
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a. What is the range of the tomato plant heights?
b. Find the mean, median, and mode(s) of the tomato plant heights.
Answers
Answer:
:)
Step-by-step explanation:
quiz scores:
a. arrange them all from least to greatest to figure out the median first
your quiz: 15, 16, 17, 18, 19 middle # = 17 median = 17
friend's quiz: 12, 13, 17, 20, 20 middle # = 17 median = 17
now for mean add all of your quiz scores up and divide by how many #s
15 + 16 + 17 + 18 + 19 = 85 / 5 = 17 mean = 17
now your friend's:
12 + 13 + 17 + 20 + 20 = 82 / 5 = 16.4 mean = 16.4
mode is which number is used the most
your mode = you don't have a mode your friend's mode = 20
b. you have a higher mean than your friend
world populations:
a. range is to subtract the smallest number from the largest
803 - 31 = 772
b. mean is adding it all up and dividing by how many numbers there are:
803 + 487 + 348 + 368 + 730 + 31 = 2767 / 6 = 461.17
median is arranging them in order and finding the middle #
31, 348, 368, 487, 730, 803
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mean = 461.17
median = 427.5
mode = no mode
tomato plants:
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52 - 36 = 16
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median is the middle from least to greatest
36, 38, 40, 41, 45, 48, 50, 52
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median = 43
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I need help solving these two questions
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x-5x=-10
Answers
Answer:
x=0 and x=5/2
Step-by-step explanation:
Combine like terms.
-2x=0
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Which equation represents a line which is parallel to the line 7x - y = 4?
Answers
Answer:
Step-by-step explanation: step : Place the given line’s equation in slope- intercept form y = mx + b. A line parallel to this line will have the same slope.
7x - y = 4. Yields y = 7 x - 4. Therefore y = 7x - 5 is the correct answer.
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Answers
Answer:
translation left 5 units
The ratio of white mice to gray mice for sale at the pet store is 5 to 2. There are 24 grey mice. What is the total number of mice for sale at the pet store?
F.62 H.210
G.150 J.84
Answers
Answer:
the ratio of black mice*
Step-by-step explanation:
Pls help me I’m not that smart at fractions
Answers
Answer:
Step-by-step explanation:
5/8
you need to add all numerators, same denominator
5/8 because the denominator is the same, so you can just add 1+1+1+1+1 and put that over 8 (confusing)
﹛(-4,3), (-2,-1), (0,0), (1,4), (2,6)﹜Given this set, what is the domain?
Answers
Domain : {-4 , -2 ,0 ,1 }
Range : { 3 , -1 , 0, 4 }
(6x - 4) - ( 2x + 8) is equivalent to
What is the answer to this ?
Answers
Answer:
4x - 13
Step-by-step explanation:
( 6x - 4 ) - ( 2x + 8 )
The "-" sign outside of the parenthesis is equivalent to "-", hence one can distribute the "-" sign
( 6x - 4 ) - ( 2x + 8 )
6x - 4 - 2x - 8
Combine like terms
6x - 5 - 2x - 8
4x - 13
The drawing below represents a 22-foot ladder with its base placed 10 feet from the bottom of a vertical wall.
which value is the best estimate for x?
a.24.3
b.63.0
c.27.0
d.65.6
Answers
Answer:
63°
Step-by-step explanation:
To get the value of x we will use the Pythagoras theorem
hyp² = opp²+adj²
Given
hyp is the length of the ladder = 22ft
Adjacent is the distance from the base of the ladder to the wall = 10ft
Angle of elevation = x
Using the SOH CAH TOA identity
Cos theta = adjacent/hypotenuse
Cos x = 10/22
Cos x = 5/11
x = arccos(5/11)
x = arccos(0.4545)
x = 62.96°
Hence the best estimate of x is 63°
(-)*(-)*(-)
a. +
b. -
c. 0
pls help
Answers
Answer:
b. -
Step-by-step explanation:
Note the rules of multiply/dividing negative numbers:
1) A positive number multiplied/divided by a positive number = a positive answer.
2) A positive number multiplied/divided by a negative number (and vice versa) = a negative answer.
3) A negative number multiplied/divided by a negative number = a positive answer.
~
Note the question.
The first part is multiplying a negative number with a negative number:
(-) * (-) = (+) , based on the rules given above.
Next, multiply the next number. Note that it is also a negative number:
(+) * (-) = (-) , based on the rules given above.
b. - is your answer.
~
Deja, Ryan, and Jamie walked in the same race on Friday. their race was 1/4 the length of Alex's 20-kilometers race on Sunday. How many more meters did Alex than Deja and Jamie walked together.
1 kilometer=1,000 meters
Answers
Answer:
Their race was 1/4 the length of Alex's 20km = 20 x 1/4 = 5 km
Alex than Deja and Jamie walked together : 20 - 5 = 15 km = 15000 m
Step-by-step explanation:
Solve this system using the substitution method.
2x + 2y = 14
y = 3x - 5
x=
y=
Answers
Answer:
The solution is:
x=3
y=4
Step-by-step explanation:
We need to solve this system using the substitution method.
2x + 2y = 14
y = 3x - 5
Substitution method involves placing value of x or y from one equation to other equation.
We have:
[tex]2x + 2y = 14--eq(1)\\y = 3x-5 --eq(2)[/tex]
We will put value of y from equation 2 into equation 1.
[tex]2x + 2y = 14\\Put\:y = 3x - 5\\2x+2(3x-5)=14\\2x+6x-10=14\\8x=14+10\\8x=24\\x=\frac{24}{8}\\x=3[/tex]
So, we get x =3
Now, put value of x in equation 2 to find value of y
[tex]y = 3x - 5\\Put\:x=3\\y=3(3)-5\\y=9-5\\y=4[/tex]
So, we have y = 4
The solution is:
x=3
y=4
Jason has 34 raspberry scones and 51 blackberry scones. He wants to make as many identical bags of scones as possible. Each bag should have an equal number of raspberry scones and an equal number of blackberry scones. What is the greatest number of bags Jason can fill? Explain how you know.
Answers
Answer: The greatest number of bags Jason can fill = 17
Step-by-step explanation:
Given: Jason has 34 raspberry scones and 51 blackberry scones.
To make identical bags of scones as possible.
Each bag should have an equal number of raspberry scones and an equal number of blackberry scones.
The greatest number of bags Jason can fill = Greatest common divisor of 3
and 51.
= 17 [Since 34 = 2 x 17 , 51 = 3 x 17]
Hence, the greatest number of bags Jason can fill = 17