Answers
Answer:
x=102
Step-by-step explanation:
Related Questions
which is the graph of x-y=1
Answers
an island has three towns located at points with the coordinates a (15,3) b (25,10) and c (0,20) where the coordinates have units of Km the government wants to locate a toxic waste dump at a position as far as possible away from each town you may assume that this location is not on the edge of the island find the coordinates at the point where the toxic waste dump should be located
Answers
9514 1404 393
Answer:
(13.06, 16.41)
Step-by-step explanation:
Any point not on a perpendicular bisector of the line between towns will be closer to one town than the other. So, the intersection of perpendicular bisectors will be the equidistant from all towns. That point is the circumcenter of the circle circumscribing the triangle with the towns as its vertices. This can be found as the intersection of two perpendicular bisectors of the segments between the towns.
The midpoint of AB is ...
(A +B)/2 = ((15, 3) +(25, 10))/2 = (40, 13)/2 = (20, 6.5)
The midpoint of AC is ...
(A +C)/2 = ((15, 3) +(0, 20))/2 = (15, 23)/2 = (7.5, 11.5)
__
The differences between points are ...
B -A = (25, 10) -(15, 3) = (10, 7)
C -A = (0, 20) -(15, 3) = (-15, 17)
Then the perpendicular bisector equations can be written as ...
bisector of AB ⇒ 10(x -20) +7(y -6.5) = 0
10x +7x -245.5 = 0
bisector of AC ⇒ -15(x -7.5) +17(y -11.5) = 0
-15x +17y -83 = 0
These have coefficients that aren't particularly nice, so a method similar to Cramer's Rule is suitable for solving this pair of equations. Using the "cross multiplication method", we have ...
x = (7(-83) -17(-245.5))/(10(17) -(-15)(7)) = 3592.5/275 = 13 7/110 ≈ 13.06
y = (-245.5(-15) -(-83)(10))/275 = 4512.5/275 = 16 9/22 ≈ 16.41
The point as far as possible from each town within the boundary of the island has coordinates (13.06, 16.41).
_____
Further detail regarding the solution
Here, we have written the equation for the perpendicular bisector this way. The difference in coordinates between points R and S can be called ...
R -S = (∆x, ∆y)
The midpoint of segment RS can be called ...
(R +S)/2 = (h, k)
Then the line that is a perpendicular bisector of RS can be written as ...
∆x(x -h) +∆y(y -k) = 0
This is the form that is used above.
__
The "cross multiplication method" for solving a pair of general-form linear equations ...
ax +by +c = 0
dx +ey +g = 0
will give the solution as ...
1/(ae -db) = x/(bg -ec) = y/(cd -ga)
If you write the coefficients in two rows of four, the pattern of products and differences is easy to see.
[tex]\left[\begin{array}{cccc}a&b&c&a\\d&e&g&d\end{array}\right][/tex]
Answer this question quickly plz
Answers
Answer:
a.
1 quarter=0.25
240*0.25=60
again,
b.349/60=5.81 weak
Answer:
Step-by-step explanation:
a) he saves £60 per week
b) 60 x 6= 360
he needs to save £60 for 6 weeks to have enough money to buy a bike
Find the equation of the line that passes through the given points. Write the equation in slope-intercept form.
(-2,-4) and (-4,-3)
Answers
Step-by-step explanation:
m=(y1-y)/(x1-x2)
m=(3-(-4))/(-4-(-2))
m=7/-2=-7/2
y=mx+c
y=-7/2x+c
Gabriel was given a gift card for a coffee shop. Each morning, Gabriel uses the card to
buy one cup of coffee. Each cup of coffee costs $4 and the original amount of money
on the gift card was $20. Make a table of values and then write an equation for A, in
terms of x, representing the amount money remaining on the card after buying x
cups of coffee.
Number of Cups of Coffee Amount of Money Remaining on Card
Answer: A =
Answers
Is the equation proportional?
y = 2x + 6
Answers
Answer:
yep
Step-by-step explanation:
Answer:
yes
Step-by-step explanation:
2x + 6 is equal
Karen performs a transformation on parallelogram ABCD that is plotted on a coordinate grid to form parallelogram A'B'C'D'. The image of
each point is shown in the table below.
Image
Original
Point
| A(-4,-1)
B (-7,-6)
C (-14, -6)
D(-11, -1)
(1.-4)
(6.-7)
(6.-14)
(1.-11)
Which best describes the transformation Karen performed?
A.reflection over the y-axis
B.dilation of scale factor
-1/4
C.counterclockwise rotation of 90 degrees about origin
D.translation of 5 units to the right and 3 units down
Answers
Answer:
its c
Step-by-step explanation:
took the test
Karen performed a transformation of (C) counterclockwise rotation of 90 degrees about origin
Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.
If a point A(x, y) is rotated 90° counterclockwise about the origin, the new point is at A'(-y, x).
Parallelogram ABCD has vertices at A(-4,-1) , B (-7,-6) , C (-14, -6) , D(-11, -1), if it is rotated 90° counterclockwise about the origin, the new point would be at A'(1.-4) , B'(6.-7), C'(6.-14) , D'(1.-11)
Find out more at: https://brainly.com/question/11707700
A machine produces 264 bolts in 42 minutes. At the same rate, how many minutes would it take to produce 308 bolts?
minutes
Answers
Answer:
49.6 minutes to create 308 bolts
Step-by-step explanation:
hope this helps :)
Write the Slope-Intercept and Point-Slope forms of the line passing through the point (-3, 2) and having a slope of -4/5
Answers
Answer:
slope-intercept: [tex]y=\frac{-4}{5} x-\frac{2}{5}[/tex]
point-slope: [tex]y-2=\frac{-4}{5} (x+3)[/tex]
Step-by-step explanation:
The slope-intercept form of a line is written as y = mx + b, where m is the slope and b is the y-intercept.
The point-slope form of a line is written as y - y1 = m(x - x1), where (x1, y1) is a given point and m is the slope.
Here, we see that the slope is -4/5, which means that m = -4/5. Since we're given a point (-3, 2), let's go ahead and just write the point-slope form already. (x1, y1) = (-3, 2) so x1 = -3 and y1 = 2. Then:
y - y1 = m(x - x1)
y - 2 = (-4/5) * (x + 3)
[tex]y-2=\frac{-4}{5} (x+3)[/tex]
Now, we want to find the slope-intercept form, so we need to figure out the y-intercept. Well, first, let's plug in what we know:
y = mx + b
y = (-4/5)x + b
Any point on this line will satisfy the above equation. Since (-3, 2) is on this line, if we plug -3 in for x and 2 in for y, the equation should hold true, so we can solve for b:
y = (-4/5)x + b
2 = (-4/5) * (-3) + b
2 = 12/5 + b
b = -2/5
So, the y-intercept is -2/5. Then the slope-intercept form is:
[tex]y=\frac{-4}{5} x-\frac{2}{5}[/tex]
Thus, our two equations are:
slope-intercept: [tex]y=\frac{-4}{5} x-\frac{2}{5}[/tex]
point-slope: [tex]y-2=\frac{-4}{5} (x+3)[/tex]
Mr. Gonzalez invested $4,200 into an account that earns a simple interest rate of 3% per year.
What is the amount of interest Mr. Gonzalez will earn at the end of one year?
Answers
Answer:
4326
Step-by-step explanation:
4200/100x3=126
4200 + 126=4326
Answer:
b
Step-by-step explanation:
4326
Reuben bought 5CDS that were each the same priceIncluding sales tax, he paid a total of \$81.50. Each CD had a tax of $0.60. what was the price of each cs before tax ?
Answers
Answer:
The price of each CD before tax is $15.70
Step-by-step explanation:
Given that:
Number of CDs bought by Reuben = 5
Cost of five CDs = $81.50
Sales tax on each CD = $0.60
Sales tax on 5 CDs = 0.60*5 = $3.00
Price of CDs without tax = 81.50 - 3.00 = $78.50
Price of each CD = [tex]\frac{Cost\ of\ CDs}{No.\ of\ CDs}[/tex]
Price of each CD = [tex]\frac{78.50}{5}[/tex]
Price of each CD = $15.70
Hence,
The price of each CD before sales tax is $15.70
Can someone help me with this problem?
Answers
Explanation:
The 2 polygons are similar
So 25/30 = 25.5/30.6 = 5/6 or 5:6
If DF=61 and EF=18, find DE.
Answers
what is x in 4x²-12x+ 9 = 0
Answers
Answer: x = √9/8
answer is x = square root of 9/8
Step-by-step explanation:
Given the conditional statement: "If it is Wednesday, then Kayden doesn't
have baseball practice." What is the hypothesis of this statement? *
Answers
Answer:
if it's wednesday
Step-by-step explanation:
You and your friend join a new gym that requires a one-time joining fee and monthly payments. Your friend chooses the 1 year plan and pays $687, while you elect the 18 month contract which costs $981. Use this information to determine the linear model used to calculate cost from months of membership.
Answers
Answer:
C = 99 + 49m
x = $99
y = $49
Step-by-step explanation:
Let
x = one time joining fee
y = monthly payment
Your friend:
1 year = 12 months
x + 12y = $687
You:
x + 18y = $981
x + 12y = 687 (1)
x + 18y = 981 (2)
Subtract (1) from (2)
18y - 12y = 981 - 687
6y = 294
Divide both sides by 6
y = 294 /6
= 49
x = $49
Substitute y = 49 into
x + 12y = 687
x + 12(49) = 687
x + 588 = 687
x = 687 - 588
= 99
x = $99
C = 99 + 49m
Where,
C = total charges
m = number of months
99 = a one time joining fee
49 = charges per month
A baseball bat factory produces 24,000 bats per day and uses 50 boxes for packing the bats. If the number of boxes needed for packing is proportional to the number of bats produced, how many boxes would be needed on a day when 36,000 bats are produced?
Answers
Answer:
Total boxes= 75
Step-by-step explanation:
Giving the following information:
A baseball bat factory produces 24,000 bats per day and uses 50 boxes for packing the bats.
First, we need to determine the number of bats that fits into a box:
Bats per box= 24,000 / 50
Barts per box= 480
Now, the number of boxes for 36,000 bats:
Total boxes= total bats / bats per box
Total boxes= 36,000/480
Total boxes= 75
Answer:75
Step-by-step explanation:
Bats 24000/50
Box 480
The volume of a cylinder is 401.92 cubic inches.
If the height of the cylinder is 2 inches, what is
its radius?
Answers
Radius = sqr 401.92/(3.14 * 2)
Radius = sqr 401.92/6.28
Radius = sqr 64
Square root of 64 = 8
Solution: the radius is 8
Norma made 16 braided bracelets. She split them evenly among g gift boxes. Write an expression that shows how many bracelets were in each box.
Answers
Answer:
16/g
Step-by-step explanation:
Answer:
the correct answer is 16÷g
Step-by-step explanation:
why 16÷g because the explanation said 16 braided bracelets. and the gift boxes was g so i think its 16÷g
Any help here please I don’t understand these math problems.
Answers
m= 5/1
3. b= 2
m= 2/3
4. B= 5
m= -3/1
for the second one you can make the -5 a +-5
Simplify.
9/3x + 4+ 2x
Answers
Answer:
5x+4
Step-by-step explanation:
WILL GIVE A BRAINLIEST
1 fourth as a decimal?
1 fourth as a fraction?
1 fourth as a percent?
3 fourths as a decimal?
3 fourths as a fraction?
3 fourths as a percent?
Answers
Answer:
1/4=0.25
1/4
1/4=25℅
3/4=0.75
3/4
3/4=75℅
Max has a drawer full of green and red socks. He has three times times as many red socks subtracted from four times as many green socks which he believes is 50 socks. Half the number of green socks plus one-third of the number of red socks is 36. How many of each colour does he have?
Answers
Answer:
There are 42 red colour socks and 44 green color socks
Step-by-step explanation:
Let there are r red socks and g green socks.
ATQ,
He has three times times as many red socks subtracted from four times as many green socks which he believes is 50 socks.
4g-3r=50 ....(1)
Half the number of green socks plus one-third of the number of red socks is 36.
[tex]\dfrac{g}{2}+\dfrac{r}{3}=36\\\\3g+2r=216\ .....(2)[/tex]
Multiply equation (1) by 2 and equation (2) by 3.
8g-6r = 100 ....(3)
9g +6r = 648 ....(4)
Add equation (3) and (4)
8g-6r + 9g +6r = 100+648
17g = 748
g = 44
Put the value of g in equation (1).
4(44)-3r=50
176-3r = 50
176-50 = 3r
r = 42
Hence, there are 42 red colour socks and 44 green color socks.
Write the ratio
2/3 /5
in simplest form
Answers
Answer:
A) 2/15
Step-by-step explanation:
So just divide it normally, do keep change flip
2/3*1/5
2/3 keep
divison change
Denomeinator, flip it, 5 to 1/5
now multiply
2/15
which is an equation for the line passing through the points (-3,3) and (6,9)
Answers
Answer:
y=2/3x +5
hope this helps
Answer:
[tex] \red{ \boxed{ \bold{2x - 3y + 15=0}}}[/tex]
Explanation
[tex] slope \:of \:the\: required\:\: line \implies\\\frac{9-6}{6-(-3)}=\frac{6}{9} [/tex]
[tex] equation \:of \:the\: required\:\: line\implies\:\\y - 3 = \frac{6}{9} (x + 3)[/tex]
[tex] \implies \: 9y - 27 = 6x + 18[/tex]
[tex] \implies \: 6x - 9y + 45=0[/tex]
[tex] \implies\:2x-3y+15=0[/tex]
Hence the equation of the line is
[tex] \green{ \boxed{ \bold{2x - 3y + 15=0}}}[/tex]
toni can carry up to 15 lbs in her backpack. her lunch weights 1 lb, her gym clothes weight 2 lb, and her books (b) weight 3 lb each. How many books can she carry in her backpack?
Answers
Answer:
4 books
Step-by-step explanation:
15-3=12
12/3=4
I need help and D. Is x>-25
Answers
Answer:
x>50
Step-by-step explanation:
Answer:
x < 25
Step-by-step explanation:
Given
- 2x > - 50
Divide both sides by - 2, reversing the symbol as a result of dividing by a negative quantity
x < 25
Perry currently has $238 dollars and is spending $6 per day. Nick has no money but is earning $8 each day. After how many days will they have the same amount of money?
Answers
Answer:
are you sure it is not 180? if it is it is 12.87
but if it is 238 it is 21 days or something close
Order from least to greatest, (15 points) and brainy award.
Answers
Answer:
pi/2 ... 2pi -square root 9..... and then pi +3
Step-by-step explanation:
pretty much the opposite of what it is now
Someone help!
Three customers have accounts owing money. The table shows the account balances.
Which customer owes the least amount of money?
Customer Balance
M. Palmer –$56.72
B. Leftwich –$74.19
R. Jordan –$54.31
M. Palmer
B. Leftwich
R. Jordan
Answers
jordan owes the least amount of money