The intersection of a line segment's two endpoints is known as the midpoint. From the midpoint to one endpoint and the midpoint to the other endpoint, you will be given two equal distances.
The formula for calculating the midpoint is given below:
[tex] \boxed{ \bold{ \: \: M = \bigg(\dfrac{x_1 + x_2}{2}, \dfrac{y_1 + y_2}{2}\bigg) \: \: }}[/tex]For example, let us try solving this sample problem below using the midpoint formula:
Sample problem: A new transmission tower will be put up midway between two existing towers. On a map drawn on a coordinate plane, the coordinates of first existing tower are (-5, -3) and the coordinates of the second existing tower are (9, 13). What are the coordinates of the point where the new tower will be placed?
From inspection on the given problem:
[tex]\sf (x_1, y_1) = (-5, -3) [/tex][tex]\sf (x_2, y_2) = (9, 13) [/tex]Substitute the given values into the midpoint formula and solve for M:
[tex]\sf M = \bigg(\dfrac{x_1 + x_2}{2}, \dfrac{y_1 + y_2}{2}\bigg)[/tex][tex]\sf M = \bigg(\dfrac{-5 + 9}{2}, \dfrac{-3 + 13}{2}\bigg)[/tex][tex]\sf M = \bigg(\dfrac{4}{2}, \dfrac{10}{2}\bigg)[/tex][tex]\sf M = (2, 5)[/tex]Therefore, the coordinates of the point are (2, 5).
[tex]\\[/tex]
Now, wasn't that easy? Try this other sample problem:
The endpoints of a segment are (-5, 2) and (9, 12), respectively. What are the coordinates of its midpoint?From the sample problem above, you may solve it on your own to enhance your skill on calculating the midpoint.
Cheers!
Nell has a piggy bank full of dimes and nickels. She empties the bank and counts the coins. She counts 30
coins in all, with a total value of $2.90. Nell says she has 14 dimes and 16 nickels.
(a) Write a system of linear equations to represent the number of coins that Nell had in her piggy bank
and the total value of the coins.
(b) Determine whether Nell could have counted the number of dimes and nickels correctly. Show all your
work to prove whether she counted the coins correctly.
[a] A dime is worth 10 cents (0.10 dollars) and a nickel is worth 5 cents (0.05 dollars). If there are 30 coins in all, we can set up a linear equation in standard form to look like this:
30 - n = d
Since the total is 2.9, we can do the following:
{ 30 - n = d
{ .05n + .10d = 2.90
And our system is in bold
(where n is nickels and d is dimes, you could also use x and y if you wish)
[b] She could have counted the number of dimes and nickles correctly, but she did not. The number of nickles is 2 with there being 28 dimes.
Now, we will solve:
.05n + .10(30 - n) = 2.90
.05n + 3 - .1n = 2.9
3 - .05n = 2.9
3 = .05n + 2.90
.05n = 0.1
n = 2
(dimes is 30 - 2 = 28)
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
help me with math!!!!
Answer:
5+4 < 10+2
Step-by-step explanation:
5+4=9
10+2=12
Two architects bid for a small government project, both
charging a flat fee added to an hourly rate. Amazing
Designs bids $250 plus $45 per hour, while Super Structures
bids $100 plus $60 per hour. At what point in time will the
two companies charge exactly the same amount?
Answer:
10 hours
Step-by-step explanation:
let x be the total number of hours
Amazing design total charge = 45x+250
super structures total charge = 60x+100
both companies charge the same amount when both equation equals
45x+250=60x+100
60x-45x=250-100
15x=150
x=10
therefore at 10 hours both companies will charge the same amount
What single decimal multiplier would you use to decrease by 19% followed by
a 10%
Increase
Answer:
1.26 is the single decimal multiplier
Step-by-step explanation:
Answer:
Answer: 1.26 is the single decimal multiplier.
Step-by-step explanation:
1 2 3 4 01 6 7 8 00 9 A laptop has a listed price of $590.99 before tax. If the sales tax rate is 6.25%, find the total cost of the laptop with sales tax included Round your answer to the nearest cent, as necessary.
Answer: $627.93
Step-by-step explanation:
If tax is 6.25%
6.25% of $590.99= $36.94
Price + tax = total cost
Total cost = $590.99 + $36.94 = $627.93
Complete the missing factors
6a^2 + 11b - 35b^2 = ( 3a _______)(2a______)
please help me, thank you.
90,891 rounded to the thousands place
Answer:
Well thousands place is in this case 0 here in the 90,891
Now we look at the digit to the right which is suppose to be 5 or above in order to round up or 4 or below to stay the same.
91,000 is the answer
integer operations
11. -60
12. 10
13. -9
14. 14
15. 37
Answer:
[tex]11. - 60 = - 49 \\ 12.10 = 12.1 \\ 13. - 9 = 4 \\ 14.14 = \frac{707}{50} \\ 15.37 = \frac{1537}{100} [/tex]
6. Three bunches of flowers can be bought for $9.48. Four bunches can be bought for $10.64. Which is the better buy?
An electronics store had a special sale on two different models of calculators. The more high-tech model sold for $33.02 and
the older model sold for $18.55. All together, 28 calculators were sold. Total sales came out to $736.45. Which system of
equations can be used to determine how many high-tech models were sold, x, and how many older models were sold, y?
Answer:
$736.45/$33.02 = 22.30 high tech
x($33.02) = $736.45
$736.45/$18.55 = 39.70 older models
y($18.55) = $736.45
I need help asap look at last question
Answer:what’s the question
Step-by-step explanation:
Answer:
i answer your question correctly, please mark it as brainliest and thank you.
What is the product of (3^5) (2^5) (3^4)
help? plssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss
Answer:
you're right, d measures 180 degrees
Step-by-step explanation:
the protractor is measuring a straight line and straight lines measure 180 degrees
hope this helps
Which of the following is a perfect square trinomial?
A. x²-6x+9
B. 4x²-20x-25
C. 4x²+20xy+9y2
D. 9a²-6a²bc+a²b²c²
(10). An article marked at 1,200 is sold at an 8% discount . Find the S.P of the article?
Answer:
$1,104
Step-by-step explanation:
If the discount is 8%, then you would need to subtract 8% (0.08) from 1, which would be 0.92. Now multiply $1,200 by 0.92 and you'll get $1,104.
=================================================
Solution:[tex] \rightarrow [/tex] 1,200 x (100% - 8%)
[tex] \rightarrow [/tex] = 1,200 x 0.92
[tex] \rightarrow [/tex] = 1,104
Simplify this expression 3(2h + 5)
Functions or Not a Function? Explain?
Answer:
not a function
Step-by-step explanation:
the last box (3-5) does not follow the rule +5
Molly drew a map of her town. She graphed the point L(−1.75, −3) for the library. The ice cream shop is located at L′, a reflection of L across the x-axis. The fire station is located at L′′, a reflection of L′ across the y-axis. Identify the ordered pair that describes the location of the fire station. Express your answer using decimal notation.
(__,__)
Answer:
(1.75, 3)
Step-by-step explanation:
Let's find L' first: We are reflecting L over the x axis, it means it stays on the same vertical (x=-1.75) and it's y changes sign, going to (-1,75,3).
This new point gets reflected again, over the y-axis. The horizontal coordinate (y=3) remains the same, and the x coordinate changes sign, going to it's final destination (1,75, 3)
IM TIMED PLEASE HELP ILL GIVE U BRAINLIEST D:
what is 8.52 divided by 12
show your work in partial quotient
Answer:
look at the photo...............Help me please!! This is timed and I’m stuck
Let's solve
[tex]\\ \sf\longmapsto 2x^2+7x-15=0[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{-7\pm\sqrt{7^2-4(2)(-15)}}{2(2)}[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{-7\pm\sqrt{169}}{4}[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{-7\pm13}{4}[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{-7+13}{4}\:or \:\dfrac{-7-13}{4}[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{6}{4}\:or\:\dfrac{-20}{4}[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{3}{2}\:or -5[/tex]
Subtract
[tex]\\ \sf\longmapsto 3/2-(-5)=3/2+5=13/2[/tex]
Option B
Answer:
Option (B.)
Step-by-step explanation:
Answer in the picture.hu
You can wash a car 1.5 times as fast as your friend. Working together, the two of you can wash 1 car in 6 minutes. How long does it take each of you to wash the car when working alone? Leave your answer as a fraction!
If the two of you can wash 1 car in 6 minutes:
It will take you 10 minutes to wash the car alone
take your friend 15 minutes to wash the car alone
Let the duration you can work be represented by y
Let the duration your friend can work be represented by x
You can wash a car 1.5 times as fast as your friend
That is, y = 1.5x
Working together, the two of you can wash 1 car in 6 minutes
This can be represented by the equation
[tex]\frac{1}{x}+\frac{1}{y} = \frac{1}{6}[/tex]
Substitute x = 1.5y into the equation above
[tex]\frac{1}{1.5y}+\frac{1}{y} = \frac{1}{6}\\\\\frac{1+1.5}{1.5y} = \frac{1}{6}\\\\\frac{2.5}{1.5y} = \frac{1}{6}\\\\1.5y=2.5(6)\\\\1.5y=15\\\\y=\frac{15}{1.5} \\\\y=10[/tex]
It will take you 10 minutes to wash the car alone
Substitute y = 10 into x = 1.5y
x = 1.5(10)
x = 15 minutes
It will take your friend 15 minutes to wash the car alone
Learn more here: https://brainly.com/question/25547756
Quadrilateral PQRS is shown
40+1
Q
R
(6x + 13)
6b
/11b-10
(7x- 500
P
s
2a +9
What must mZQPS be for PORS to be a parallelogram?
A 18
B 59
C 121
OD not enough information
Answer:
m∠QPS = 59
Step-by-step explanation:
59 + (7x-5) = 180
x = 18
If you substitute 59 with the other answer options you will get a decimal.
I hope that this could help!!!!
please help soon i need to get this pre-test. done
Answer:
65.5 in
Step-by-step explanation:
Ok, the two triangles are similar, since they're both right triangles, the angle in C are congruent, and the third has to be by difference. It means that the distance DC is proportional to 44 inches, on the proportion[tex]x:44 = 11.5:23.5 \rightarrow x= 44\frac{11.5}{23.5} = 21,5 in[/tex] To this we need to add the 44 inches traveled in the first part, to get a total of 65.5 in
Answer:
A.
Step-by-step explanation:
The triangles are similar, so we can estimate that the ratio between them is 1:2 (23.5/11.5~~2). Now we have that 44/2 is 22 and 44+22 is 66. The closest answer to 66 is 65.5, which is A.
when 1760 is divided into 14 equal parts, the remainder is 10. what is the correct way to write the quotient?
Answer:
125 R10
Step-by-step explanation:
You have to do (1760-10)/14=125
Slope of a line pls answer
Answer:
[tex]m = - \frac{1}{2}[/tex]
Step-by-step explanation:
hope this helps!
Kent has paid a total of $589 For internet service. Each month of service cost $19. How many months, m, of internet service has Ken't paid for? Use the model.
Giving brainliest
Answer:
589/19=31 dollars a month
Step-by-step explanation:
Hope this helps!
Erin finds 5% sales tax for a shirt that costs $21. She calculates the tax as
0.05 * 21 = 1.05 or $1.05.
Erin notices that she can add 21 + 1.05 = 22.05 to find the total cost, $22.05.
She uses the Distributive Property to write (1 * 21) + (0.05 * 21) = 1.05 * 21.
For each item, write the total cost of
the item as the product of two
numbers.
Tax
1.05 x 21
a.
b.
c.
d.
Item Name Price Tax Rate
shirt
$21.00 5%
bicycle $45.90 7%
shoes
$67.50 6%
laptop $299.99 8%
$39.95 4%
Credit Debit Subtotal
Check Cash
Tax
Order total
Print Receipt Cash
video game
$474.34
Answer:
Step-by-step explanation:
a. Bicycle (1.07 x 45.90)
b. Shoes (1.06 x 67.50)
c. Laptop (1.08 x 299.99)
d. Video Game (1.04 x 39.95)
You and a friend tutor for a total of 12 hours. Use the tape diagram to find how many hours you tutor.
Answer:
You tutor for 4 hours
Step-by-step explanation:
If you count all the boxes, there are 6
12/6 is 2
You have 2 boxes so you do 2*2 which is 4
THE ANSWER IS 4
Answer:
24
Step-by-step explanation:
i added the time frame of you both tutoring ig.
Can I get some help on this I have so many assignments to do and I just want to go to sleep
find the mode of the following set data
3, 10, 36, 26, 19, 2, 2, 40
Answer:
2
Step-by-step explanation:
it is the only number that occurs more than once