Answers
(1, 3) as T and (5, 4) as the midpoint
Alright - we know that the equation for the midpoint of a line segment is
[tex]( \frac{ x_{1} + x_{2} }{2} , \frac{ y_{1} + y_{2} }{2} )[/tex]
Next, we plug the x values in - since the midpoint's x value is 5 and one endpoint's x value is 1, we have
[tex] \frac{1+x_2}{2} =5[/tex] .
Next, we multiply both sides by 2, resulting in 1+x₂=10. Lastly, we subtract 1 from both sides, meaning that x₂, or the x value of the other endpoint, is 9. For the y values, we use a similar process -
[tex] \frac{3+y_2}{2} =4[/tex] .
since 3 is the y value of one endpoint and 4 is the y value of the midpoint. Multiplying both sides by 2, we get 3+y₂=8. Subtracting 3 from both sides, we get y₂=5 and our coordinates for the other endpoint to be (9, 5).
Good luck, and feel free to ask any questions as necessary!
Related Questions
The volume of a box with a square base can be written as V = s² x h where V is the volume, s is one side of the square base, and h is the height. Find the volume of a rectangular prism where s = 6 cm and h = 9 cm.
A.108 cm³
B.54 cm³
C.486 cm³
D.324 cm³
Answers
In the game Kazoo, teams lose one point each time they skip a turn. They earn one point each time their team guesses correctly. Maria's team skipped 888 turns. They guessed correctly 666 times.
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that would be -222 I'd guess... (+666 - 888 = - 222).
If m∠TRK equal 32.5°, what is m∠TSK?
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The measure of angle TSK is 130°, because it is an inscribed angle that intercepts the same arc as angle TRK, and angle TRK is half the measure of the central angle that intercepts the same arc.
The correct answer is option C.
The center of the circle is S, and the measure of angle TRK is 32.5°. We want to find the measure of angle TSK.
We can use the following theorem to solve this problem:
Inscribed Angle Theorem: An inscribed angle is half the measure of the central angle that intercepts the same arc.
In other words, if an angle is inscribed in a circle and intercepts a certain arc, then the measure of that angle is half the measure of the central angle that intercepts the same arc.
In this problem, angle TRK is an inscribed angle that intercepts arc KT. Therefore, the measure of angle TRK is half the measure of the central angle that intercepts arc KT.
Let's call the central angle that intercepts arc KT θ. Since angle TRK measures 32.5°, we know that θ measures 32.5° * 2 = 65°.
Now, we can use the Inscribed Angle Theorem again to find the measure of angle TSK.
Angle TSK is an inscribed angle that intercepts arc KT, and the measure of the central angle that intercepts arc KT is 65°. Therefore, the measure of angle TSK is half the measure of the central angle that intercepts the same arc, which is 65° * 2 = 130°.
The measure of angle TSK is 130° making option C the correct option.
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The question probable may be:
The center of the circle is S. Note: Figure not drawn to scale. If mangle TRK equal 32.5 ° , what is mangle TSK ? A. 32.5 ° B. 65 ° C. 130 ° D. 16.25 °
Which values of x will make the absolute value equation true?
|x – 4| = 7
A.
{–3, 3}
B.
{–3, 11}
C.
{–11, 11}
D.
no solution
Answers
x - 4 = 7 (add 4 to both sides to get x by itself)
x = 11 (one of the answers)
x - 4 = -7
x = -3 (other answer)
So the answer is { -3, 11 }
-----------------------------------------
Checking choice A
Plug in x = -3
|x-4| = 7
|-3-4| = 7 ... replace x with -3
|-7| = 7
7 = 7
We have a true equation so x = -3 works
--------------
Plug in x = 3
|x-4| = 7
|3-4| = 7 ... replace x with 3
|-1| = 7
1 = 7
The last equation is false so x = 3 is not a solution. We can cross choice A off the list.
-----------------------------------------
Checking choice B
We already checked x = -3 (see above in choice A). All we need to do is check x = 11
|x-4| = 7
|11-4| = 7 .... replace x with 11
|7| = 7
7 = 7
We have a true equation so x = 11 works
Since x = -3 and x = 11 work, this means we have the proper solution set {-3, 11}. So this means choice B is the final answer
-----------------------------------------
For the sake of completeness, let's check choice C.
Plug in x = -11
|x-4| = 7
|-11-4| = 7 ... replace x with -11
|-15| = 7
15 = 7
The last equation is false so choice C can be ruled out as well.
-----------------------------------------
We can cross choice D off the list since we found there is a solution set and it is {-3, 11} back in choice B.
-----------------------------------------
Let's say that we didn't have these answer choices and it was a fill in the blank type of problem. Here's how to find the two solutions
|x-4|=7
x-4=7 or x-4=-7 ...... break up the absolute value
x-4+4=7+4 or x-4+4=-7+4 .... add 4 to each side (for each equation)
x = 11 or x = -3
x = -3 or x = 11
So the solution set is {-3, 11}
-----------------------------------------
-----------------------------------------
Final Answer: Choice B) {-3, 11}
8 cakes cost £4.00 how much do three cakes cost
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We can solve this by creating an algebraic equation.
[tex]8/4=3/x[/tex]
Cross Multiply.
[tex]8*x=4*3[/tex]
[tex]8x=12[/tex]
Divide both sides by 8.
[tex](8x)/8=(12)/8[/tex]
The Answer Is:
[tex]x=1.5[/tex]
Three cakes would cost $1.50.
Hope this helps.
-Benjamin
The product of 3 and a number subtracted from 16 is 7. Find the number.
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Which Greek mathematician wrote the most definitive text on geometry, one that is still referred to today?
a.Thales
b.Pythagoras
c.Euclid
d.Archimedes
e.Hippocrates
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Extra information:
Pythagoras has even constructed a famous theorem: Pythagoras' theorem; which is still used every day all over the world!
Answer:
The correct answer is Euclid.
Step-by-step explanation:
Euclid was a Greek mathematician, who is referred as the father of geometry and founder of geometry.
One of Euclid's most notable work, in the form of 'The Elements' has the strongest fundamental texts on geometry.
Apart from geometry, Euclid also developed many mathematical theories.
Right triangle ABC is shown.
a to c is 3m
c to b is a
b to a is c and ab is 50 degrees
Which equation can be used to solve for c?
sin(50o) =
sin(50o) =
cos(50o) =
cos(50o) =
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Answer:
The required equation which can be used to solve for the value of c is given by :
[tex]\bf\sin 50=\frac{3}{c}[/tex]
Step-by-step explanation:
For better understanding of the solution, see the attached figure :
AC = 3 meter
CB = a meter
BA = c meter
m∠ABC = 50°
Now, to find the value of c.
In right angle triangle right angled at C, we need to find the length of hypotenuse, so using the sine rule in the ΔABC
[tex]\implies \sin\theta=\frac{Perpendicular}{Hypotenuse}\\\\\implies \sin 50=\frac{3}{c}[/tex]
Hence, the required equation which can be used to solve for the value of c is given by :
[tex]\bf\sin 50=\frac{3}{c}[/tex]
please help with math
Answers
Here's why, because the first segment extends from 0 to 1. So, x has to be 0 or larger, but less than 1 or 1.
Why does dividing by a fraction make a number bigger?
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What does it mean to divide 2 by 1/2? What we're asking is, in essence, the inverse of a multiplication problem: 1/2 times what number gets us 2? Or, if we split 2 up into pieces 1/2 in size, how many pieces would make up the whole? Well, 1/2 + 1/2 + 1/2 + 1/2 = 2, which means we need four halves to make the whole (2). Similarly, if you divided 3 by 1/3, it would take 9 thirds to make three, so 3/(1/3) = 9.
It also helps to consider the fact that any number divided by 1 simply gives you back that number, and any number divided by a number greater than one produces a number less than the one you started with (i.e. 6/2 = 3, which is less than 6), so it would make sense if dividing by a number between 1 and 0 gave you back a number greater than the one you started with.
A number dividing by a proper fraction always make the number bigger.
What is Fraction?Fractions are a kind of real numbers where we express a number as a part of a whole.
Fractions are of the form p/q, where p is called the numerator and q is called the denominator.
Algebraically speaking when a number is divided by a fraction, then actually the number is getting multiplied by it's reciprocal.
For example [tex]\frac{5}{1/2}[/tex] = 5 × [tex]\frac{2}{1}[/tex] = 10
That is a number when get divided by a proper fraction, operation is changed into the multiplication of the reciprocal.
In other words, we have to find that 5 is divided into how many equal 1/2
parts or 0.5 equal parts. Now, 1/2 part is actually the half part of 1.
Since 1/2 is half part of 1, 1 can be divided into 2 equal 1/2 parts.
We know that 5 when divided into equal 1 parts, we will get 5 parts.
So 5 can be divided into 5 × 2 = 10 equal 1/2 parts.
Hence, dividing by a fraction make a number bigger.
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HELP PLEASE THANKS!!!!!
Answers
Since your going to a power of negative, you go down as a fraction.
Since you know that 2^4 is equal to 16, you just do the reciprocal of it which is 1/16
y=9x+4 is translated 4 units , what would be the equation on a graph?
Answers
If the line is translated (fancy, fancy, talk for MOVED) up. The Y-intercept would change positive (because it is moved up) by four.
4 + 4 equals...well, 8.
Hope I could help you out! If my answer is incorrect, or I provided an answer you were not looking for, please let me know.
However, if my answer is explained well and correct, please consider marking my answer as Brainliest! :)
Have a good one.
God bless!
Evi what to make to pottery she needs 3/5 pounds of clay for one piece and 7/10 Pound of clay for the other piece she has three bags of clay that wiegh 4/5 pound each.how many bags of clay will Eva need to make both pieces of pottery?How many pounds of clay will she have left over ?
Answers
how do you do this system using the equal values method?
Answers
[tex]x+2y=14[/tex]
[tex]x=14-2y[/tex]
For the second equation:
[tex]-x+3y=26[/tex]
[tex]-x=26-3y[/tex]
[tex]x=3y-26[/tex]
Then if we set these two equal to each other:
[tex]3y-26=14-2y[/tex]
[tex]5y-26=14[/tex]
[tex]5y=40[/tex]
[tex]y=8[/tex]
Then we take this y value and plug it back into either of our starting equations. I'll use the first one as an example:
[tex]x+2(8)=14[/tex]
Now just solve for x and you'll have your solution.
ou are cycling around Europe with friends.
A famous cycling race is taking part in the north of Spain. You want to travel there from France, but it will take too long by bike. You decide to catch the train.
You need to take 2 trains to get to Spain. On one website the first train will cost £64.98 and the second train will cost £32.88. There is also a £6.99 charge for cycle storage for the whole trip.
How much would the journey cost you?
Answers
frank averages one strike for every 4 frames that he bowls. if he bowled 48 strikes in one season how many frames did frank bowl
Answers
You just divide 48 divided by 4 = 12
It also says "every" so you know to divide
He sells packets of sweet-pepper seeds for $2.48 each and packets of hot-pepper seeds for $4.56 each. he also offers a 16-packet mixed pepper assortment combining packets of both types of seeds at $3.65 per paket. how many packets of each type of seed are in the assortment
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Solve the following inequality.
-2/3x>8
A) x < - 4
B) x > - 4
C) x > -12
D) x < -12
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[tex]-\frac{2}{3}x \ \textgreater \ \mathrm{Multiply\:fractions}:\ \:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c} \ \textgreater \ -\frac{2x}{3} [/tex]
[tex]\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)} \ \textgreater \ \ \textgreater \ \frac{2x}{3}\ \textless \ -8[/tex]
[tex]\mathrm{Multiply\:both\:sides\:by\:}3 \ \textgreater \ \frac{3\cdot \:2x}{3}\ \textless \ 3\left(-8\right) \ \textgreater \ Simplify \ \textgreater \ 2x\ \textless \ -24 [/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}2 \ \textgreater \ \frac{2x}{2}\ \textless \ \frac{-24}{2} \ \textgreater \ Simplify \ \textgreater \ x\ \textless \ -12[/tex]
[tex]Therefore\; x\ \textless \ -12 \;is\;our\;answer![/tex]
Hope this helps!
Consider the equation 2y−5x=30 . Determine the x-intercept
2 ⋅
−5x=30
−5x=30
=30
x=
Answers
The x-intercept for the equation 2y - 5x = 30 is found when y is set to zero and the equation is solved, resulting in the x-intercept being -6.
Explanation:To find the x-intercept of a given equation, you need to set y equal to zero and solve for x. So, for the equation 2y - 5x = 30, you set y = 0 which leads to the adjusted equation of -5x = 30
To isolate x, you should divide both sides of the equation by -5, which gives x = -6. Therefore, the x-intercept of the equation 2y - 5x = 30 is -6.
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Which line has a slope of 2?
Answers
if y+1 is an even integer, what is the next consecutive even integer?
Answers
If you add an even integer by 2, you get the next consecutive even integer.
Add y+1 with 2
y + 1 + 2
= y + 3
The next consecutive even integer is y+3.
Have an awesome day! :)
The next consecutive even integer will be y + 3
What is Arithmetic Progression?
An arithmetic progression or arithmetic sequence ( AP ) is a sequence of numbers such that the difference between the consecutive terms is constant.
The nth term of an AP is given be aₙ = a₁ + ( n - 1 ) d
where a₁ = first term
d = common difference between terms
Given data ,
y + 1 = even integer
The next consecutive even integer can be calculated by adding 2 because the difference between two consecutive even or odd integers is always two.
Therefore , y + 1 + 2 = y + 3
Hence , the next consecutive even integer will be y + 3
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Dimitri is paid 8 percent commission on his total sales every pay period. Last pay period, he sold $6,300 worth of items. After a state tax of 6 percent is deducted from his commission, how much is left to the nearest dollar?
Answers
Answer:
$ 474 is left.
Step-by-step explanation:
Given,
The amount at which the items are sold = $ 6,300,
Also, commission percentage = 8 %,
Thus, commission = 8% of 6300
[tex]=\frac{8\times 6300}{100}[/tex]
[tex]=\frac{50400}{100}[/tex]
[tex]=\$ 504[/tex]
Now, deducted tax percentage on commission = 6%,
Hence, the left amount of commission = commission - 6% of the commission
[tex]=504-\frac{6\times 504}{100}[/tex]
[tex]=504-\frac{3024}{100}[/tex]
[tex]=504-30.24[/tex]
[tex]=\$ 473.76[/tex]
[tex]\approx \$ 474[/tex]
What is the inverse of the following statement? If at first you don’t succeed, try, try again. Select the best answer from the choices provided. If you try, try again, then you did not succeed at first. If at first you succeed, then do not try, try again. If you don’t try, try again, then you succeeded at first. Try, try again if at first you don’t succeed. NextReset
Answers
Answer:
Try, Try again if at first you dont
exceed
Step-by-step explanation:
Consider the function y = x^2 − 18x. Enter the values for the variables to complete the inverse
Answers
Given the equation:
y = x^2 – 18x
Rewrite in vertex form:
y = x^2 – 18x + (18/2)^2 – (18/2)^2
y = (x – 9)^2 – 81
Swap x and y:
x = (y – 9)^2 – 81
Solve for y:
x + 81 = (y – 9)^2
y – 9 = sqrt (x + 81)
y = sqrt (x + 81) + 9
or
y = (x + 81)^(1/2) + 9
steve saved $2000. he saved $100 in june. what percent of the total amount did her save in june?
Answers
A pilot flies 640 miles with a tail wind of 35 miles per hour. Against the wind, he flies only 455 miles in the same amount of time. Find the rate of the plain in still air
Answers
so, we know the wind rate is 35mph.
when the pilot goes with it, it runs for say "t" hours and covers 640 miles.
when he goes against it, it runs for say also "t" hours, covering 455 miles only.
now, let's say the still air speed of the plane is "r", so when it goes with the wind, is not really going "r" mph, is really going "r + 35", because the wind is adding speed.
likewise, when it goes against it, the speed is not "r" but "r - 35", the wind is slowing it down.
[tex]\bf \begin{array}{lcccll} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{t}\\ &------&------&------\\ \textit{with wind}&640&r+35&t\\ \textit{against the wind}&455&r-35&t \end{array} \\\\\\ \begin{cases} 640=t(r+35)\implies \cfrac{640}{r+35}=\boxed{t}\\\\ 455=t(r-35)\\ ----------\\ 455=\left( \boxed{\frac{640}{r+35}} \right)(r-35) \end{cases}[/tex]
[tex]\bf 455(r+35)=640(r-35)\implies 455r+15925=640r-22400 \\\\\\ 38325=185r\implies \cfrac{38325}{185}=r\implies \cfrac{7665}{37}=r\implies 207\frac{6}{37}=r[/tex]
A large adult elephant weighs 24,000 pounds. A baby elephant, on the other hand, weighs only 260 pounds. How much more does the adult elephant weigh?
Answers
24,000 - 260 = 23,740
23,740 + 260 = 24,000
The adult elephant weighs 23,740 more pounds than the baby elephant.
A color printer prints 9 pages in 3 minutes. how many minutes does it take per page
Answers
3 pages per min
3/60 seconds = .05 seconds
.05 s/ 60 = 0.00083333 min per pg.
Final answer:
To calculate time per page, divide the total printing time by the number of pages. A printer that prints 9 pages in 3 minutes takes approximately 0.333 minutes (or 20 seconds) to print one page.
Explanation:
The question is asking us to calculate the time it takes for a color printer to print one single page. To find this, we need to divide the total time taken to print multiple pages by the number of pages printed. So, if a printer prints 9 pages in 3 minutes, we can calculate the time per page as follows:
First, identify the total time taken for printing multiple pages, which is 3 minutes for 9 pages.
Divide the total minutes by the number of pages to get the time per page. In this instance, it would be 3 minutes ÷ 9 pages.
Perform the division to find the time it takes to print one page. 3 minutes ÷ 9 pages = 0.333... minutes per page.
Therefore, it takes approximately 0.333 minutes (or 20 seconds) for the color printer to print one page.
Question 2
Find the next term in this arithmetic sequence: 2/3, 2, 3 1/3, ____
4 2/3
3 2/3
4
4 1/3
Answers
Can you find the missing angle measurements
Answers
if you notice the tickmarks on those sides, that means they're equal, that means is an isosceles triangle, or with two equal sides, so the 70° angle is the vertex angle, and the other two angles are just two twins, 180 - 70 = 110, split that equally to the twins, and you get that, check the picture.
what's is "x"? well, "x" is just a supplementary angle of the one inside the triangle, thus 180 - 55.