Now there is a square city of unknown size with a gate at the center of each side. There is a tree 20 b from the north gate. That tree can be seen when one walks 14 bu from the south gate, turns west and walks 1775 bu. Find the length of each side of the city.
Answers
Answer:
The length of each side of the city is 250b
Step-by-step explanation:
Given
[tex]a = 20[/tex] --- tree distance from north gate
[tex]b =14[/tex] --- movement from south gate
[tex]c = 1775[/tex] --- movement in west direction from (b)
See attachment for illustration
Required
Find x
To do this, we have:
[tex]\triangle ADE \sim \triangle ACB[/tex] --- similar triangles
So, we have the following equivalent ratios
[tex]AE:DE = AB:CB[/tex]
Where:
[tex]AE = 20\\ DE = x/2 \\ AB = 20 + x + 14 \\ CB = 1775[/tex]
Substitute these in the above equation
[tex]20:x/2 = 20 + x + 14: 1775[/tex]
[tex]20:x/2 = x + 34: 1775[/tex]
Express as fraction
[tex]\frac{20}{x/2} = \frac{x + 34}{1775}[/tex]
[tex]\frac{40}{x} = \frac{x + 34}{1775}[/tex]
Cross multiply
[tex]x *(x + 34) = 1775 * 40[/tex]
Open bracket
[tex]x^2 + 34x = 71000[/tex]
Rewrite as:
[tex]x^2 + 34x - 71000 = 0[/tex]
Expand
[tex]x^2 + 284x -250x - 71000 = 0[/tex]
Factorize
[tex]x(x + 284) -250(x + 284)= 0[/tex]
Factor out x + 284
[tex](x - 250)(x + 284)= 0[/tex]
Split
[tex]x - 250 = 0 \ or\ x + 284= 0[/tex]
Solve for x
[tex]x = 250 \ or\ x =- 284[/tex]
x can't be negative;
So:
[tex]x = 250[/tex]
Related Questions
A party rental company has chairs and tables for rent. The total cost to rent 2 chairs and 5 tables is $53. The total cost to rent 8 chairs and 3 tables is $42. What is the cost to rent each chair and each table?
Answers
Answer:
c=cost of one chair rental
t=cost of one table rental
8c+3t=42
2c+5t=53
multiply the second equation, each term on both sides, by -4
8c+3t=42
-8c-20t=-212
add the two equations
-17t=-170
divide both sides by -17
t=$10 to rent one table
substitute t=10 into either original equation
2c+5(10)=53
2c+50=53
2c=3
c=$1.50 to rent one chair
The slope of the line below is 2. Which of the following is the point-slope form
of the line?
Answers
Answer:
y+1 = 2(x-1)
Step-by-step explanation:
Point slope form for a line is
y-y1 = m(x-x1) where m is the slope and (x1,y1) is a point on the line
We are given the point(1,-1)
y --1 = 2(x-1)
y+1 = 2(x-1)
help I was never taught how to do this im confused
Answers
Answer:
36
Step-by-step explanation:
Area of a triangle = (bh)/2
Where b = base length and h = height
Given base length: 18ft
Given height: 4ft
This being known let's define the variables
b = 18
h = 4
Now to find the area we simply plug in these values into the formula
Area = (18)(4)/2
Simplify multiplication 18 * 4 = 72
Area = 72/2
Simplify division
Area = 36
A cube has an edge of 8cm. Calculate its Volume.
Answers
Answer:
512cm³
Step-by-step explanation:
to get the volume the formula is Base area x height
BA X H
=8x8x8 because all sides of a cube are equal
=512cm³
Find the equation of a line that passes through the points (2,7) and (4,6). Leave your answer in the form y = m x + c
Answers
Answer:
I think the answer would be
y = 0.5x -8
tough this might be wrong?
Step-by-step explanation:
(2, 7) ( 4,6)
to find the gradient- mx
y2-y1/ x2 - x1
chose which would be 1/ 2
if I chose (2,7) as 1 then (4, 6) as 2
mx = 6- 7/ 4-2
= -0.5x
y = -0.5x + c
substitute
6 = -0.5(4) + c
6= -2+ c
c = -8
Which of the following best describes a type of growth that is exponential at
first but slows as the amount reaches a certain maximum value?
A. Exponential decay
B. Exponential growth
C. Linear growth
D. Logistic growth
Answers
9514 1404 393
Answer:
D. Logistic growth
Step-by-step explanation:
The logistic growth function models a situation where the rate of growth is jointly proportional to the population and to the difference between the population and the carrying capacity.
Attached is an example of such a function.
¿COMO PUTAS SE HACE i¹⁰⁰²?
Answers
Answer:
nose
Step-by-step explanation:
How to do questions 19 and 20
Answers
Answer & Step-by-step explanation:
Using the information given in the question we can form the following 3 equations (in the order of the first 3 sentences)
w = 2h (twice the price)
t = h - 4 ($4 less)
3w + 2h + 5t = 136 (total purchasing and cost)
We can solve all 3 equations for h first, by substituting the first two equations, into the third equations w and t
3(2h) + 2h + 5(h-4) = 136
Simplify
6h + 2h + 5h - 20 = 136
13h = 136 + 20
13h = 156
h = 156/13
h = $12
Using this information, we can solve for w and t
w = 2h
w = 2(12)
w = $24
And finally
t = h - 4
t = 12 - 4
t = $8
If there is a song that is 2 minutes and 58 seconds long and it plays 40 times how long does it play convert answer into seconds.
Answers
Answer: I got 7120 seconds
Step-by-step explanation:
There's 178 seconds in the song (for more context, I just converted the 2 minutes into seconds and added it with 58) then I multiplied it by the total amount of times it played (in this case, 40)
Hope this helps
A golf ball is hit from ground level. Its path is modelled by the relation h(t) = -4.9 t2 + 27.2t , where h is the ball’s height above the ground, in meters, and t is the time, in seconds. Determine the time the ball is in the air.
Answers
If x+y=6 and xy =2find x³+y³(please help me fast with explanation also please) T^T
Answers
Answer: x³+y³=180
Step-by-step explain: let's remember the formula x³+y³=(x+y)(x²-xy+y²) and also x³+y³=(x+y)³-3xy(x+y) then [tex]\displaystyle\boldsymbol{ x^3+y^3=\underbrace{(x+y)^3}_{6}-3\underbrace{xy}_{2}\underbrace{(x+y)}_6}=\\\\6^3-3\cdot 2\cdot 6=216-36=180[/tex]
Determine whether the three points are colinear (0,-4),(-3,-18),(2,6) are the three points colinear?
Answers
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Answer:
they are not collinear
Step-by-step explanation:
A graph shows that a line through points A and C misses point B, so the points are not collinear.
__
If the points are collinear, then the slope of the segment between the first pair would be the same as the slope of the segment between the second pair.
m = (y2 -y1)/(x2 -x1)
m = (-18 -(-4))/(-3 -0) = -14/-3 = 14/3 . . . . slope of AB
__
m = (6 -(-18))/(2 -(-3)) = 24/5 . . . . slope of BC ≠ slope of AB
The points are not collinear.
_____
Additional comment
With about the same amount of computational effort, you can find the area of the triangle bounded by the three points. If it is zero, then the points are collinear. Here, it is 1 square unit, so the points are not collinear.
what is the slope intercept equation of the line below?
Answers
Answer:
[tex]{ \tt{slope, \: m = \frac{1 - ( - 1)}{1 - 0} }} \\m = 2 \\ y - intercept : y = mx + c \\ { \tt{1 = (2 \times 1) + c}} \\ c = - 1 \\ { \boxed{ \bf{y = 2x - 1}}}[/tex]
Question 4 4 pts Lori buys a $1500 certificate of deposit (CD) that earns 6% interest that compounds monthly. How much will the CD be worth in: 5 years? 10 years? 486 months?
Answers
Answer:
Step-by-step explanation:
5 years
[tex]1500(1+\frac{.06}{12})^{12*5}=2023.275229[/tex]
10 years
[tex]1500(1+\frac{.06}{12})^{10*12}=2729.095101[/tex]
486 months:
[tex]1500(1+\frac{.06}{12})^{486}=16935.47074[/tex]
round those as you please
A professor has learned that nine students in her class of 35 will cheat on the exam. She decides to focus her attention on ten randomly chosen students during the exam. a. What is the probability that she finds at least one of the students cheating
Answers
Answer:
[tex]\frac{73,331}{75,516}\approx 97.11\%[/tex]
Step-by-step explanation:
The probability that she will find at least one student cheating is equal to the probability that she finds no students cheating subtracted from 1.
Each time she randomly chooses a student the probability she will catch a cheater is equal to the number of cheaters divided by the number of students.
Therefore, for the first student she chooses, there is a [tex]\frac{9}{35}[/tex] chance that the student chosen is a cheater and therefore a [tex]\frac{26}{35}[/tex] chance she does not catch a cheater. For the second student, there are only 34 students to choose from. If we stipulate that the first student chosen was not a cheater, then there is a [tex]\frac{9}{34}[/tex] chance she will catch a cheater and a [tex]\frac{25}{34}[/tex] chance she does not catch the cheater.
Therefore, the probability she does not catch a single cheater after randomly choosing ten students is equal to:
[tex]\frac{26}{35}\cdot \frac{25}{34}\cdot \frac{24}{33}\cdot \frac{23}{32}\cdot \frac{22}{31}\cdot \frac{21}{30}\cdot \frac{20}{29}\cdot \frac{19}{28}\cdot \frac{18}{27}\cdot \frac{17}{26}[/tex]
Subtract this from one to get the probability she finds at least one of the students cheating after randomly selecting nine students. Let event A occur when the professor finds at least one student cheating after randomly selecting ten students from a group of 35 students.
[tex]P(A)=1-\frac{26}{35}\cdot \frac{25}{34}\cdot \frac{24}{33}\cdot \frac{23}{32}\cdot \frac{22}{31}\cdot \frac{21}{30}\cdot \frac{20}{29}\cdot \frac{19}{28}\cdot \frac{18}{27}\cdot \frac{17}{26},\\\\P(A)=1-\frac{2,185}{75,516},\\\\P(A)=\boxed{\frac{73,331}{75,516}}\approx 0.97106573441\approx \boxed{97.11\%}[/tex]
Someone help so lost I didn’t understand the course and now I’m stuck please help a girl out
Answers
Answer:
the answer is b. you are basically multiplying them
At a store, 2 gallons of milk cost $6.
Which is the value of the ratio of dollars to gallons of milk?
0.33
per gallon
$3 per gallon
Answers
Answer:
B
Step-by-step explanation:
$3 per gallon
that is the procedure above
A group of dental researchers are testing the effects of acidic drinks on dental crowns. They have five containers of crowns labeled V, W, X, Y, and Z. They will randomly select one of the containers to be the control for the experiment by drawing one of five well-mixed slips of paper with the same labels from a hat. Which of the following is the probability model for the control container?
Answers
Answer:
[tex]\begin{array}{cccccc}{x} & {V} & {W} & {X} & {Y} & {Z} & P(x) & {0.20} & {0.20} & {0.20} & {0.20} & {0.20} \ \end{array}[/tex]
Step-by-step explanation:
Given
[tex]S = \{V,W,X,Y,Z\}[/tex]
[tex]n(S) = 5[/tex]
Required
The probability model
To do this, we simply calculate the probability of each container.
So, we have:
[tex]P(V) = \frac{n(V)}{n(S)} = \frac{1}{5} = 0.20[/tex]
[tex]P(W) = \frac{n(W)}{n(S)} = \frac{1}{5} = 0.20[/tex]
[tex]P(X) = \frac{n(X)}{n(S)} = \frac{1}{5} = 0.20[/tex]
[tex]P(Y) = \frac{n(Y)}{n(S)} = \frac{1}{5} = 0.20[/tex]
[tex]P(Z) = \frac{n(Z)}{n(S)} = \frac{1}{5} = 0.20[/tex]
So, the probability model is:
[tex]\begin{array}{cccccc}{x} & {V} & {W} & {X} & {Y} & {Z} & P(x) & {0.20} & {0.20} & {0.20} & {0.20} & {0.20} \ \end{array}[/tex]
Answer:
answer is V=.20, W=.20, X=.20, Y=.20, X=.20
Step-by-step explanation:
How can the distributive property be use to solve this expression?
53x24
Answers
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Answer:
= 53(20 +4) or =24(50 +3) or =(20 +4)(50 +3)
Step-by-step explanation:
Either number can be rewritten as a sum. Typically, the sum will be based on place value: 53 = 50 + 3, for example, as opposed to something like 53 = 26 +27.
The usual method of multiplication taught in grade school makes use of this sort of rewriting.
53 × 24 = 53 × (4 +20) = 53×4 +53×20 = 212 +1060 = 1272
__
Additional comment
We find this easier to multiply as 53(20 +4) than as 24(50 +3) because doubling (multiplying by 2) and doubling again (multiplying by 4) is generally easier than multiplying by 3 or 5.
In grade school, we did this digit by digit, so ...
53×24 = (3 +50)(4 +20) = 3(4 +20) +50(4 +20) = 3×4 +3×20 +50×4 +50×20
= 12 +60 +200 +1000 = 1272
I am need help and an explanation on how to read these graphs.
Answers
Answer:
i think its b
Step-by-step explanation:
in the given figure poq is a line. if x=30 then find qor and ros
Answers
Answer:
[tex]2y + 3y + x = 180 \\ 5y + 30 = 180 \\ 5y = 180 - 30 \\ 5y = 150 \\ y = 30[/tex]
QOR =3Y
=3×30
=90°
ROS = 2Y
=2×30
=60°
Write a linear equation in point slope form that passes through the points (-2,18) and (1,9)
Answers
Answer:
y-18=-3(x+2)
Step-by-step explanation:
The Slope-intercept form is -3x+12
Solve for x in this equation: 3/4+|5-x|=13/4
Answers
Find the lcm of the denominator
And then use the lcm to multiple
Plz help me find zero x on the triangle and show work thanks
Answers
Answer:
x= 30 degrees
Step-by-step explanation:
This is an isosceles triangle as indicates by the lines on the sides.
Since the sides lengths are equal, the base angles are equal
x= 30 degrees
A small manufacturing company recently instituted Six Sigma training for its employees. Two methods of training were offered: online and traditional classroom. Management was interested in whether the division in which employees worked affected their choice of method. Below is a table summarizing the data.
Sales Quality Operations Total
Traditional 16 10 8 34
Online 35 23 44 102
Total 51 33 52 136
Required:
a. What is the probability that an employee chose online training?
b. What is the probability that an employee is in the Quality division and chose online training?
c. What is the probability that an employee chose online training given that he/she is in the Sales division?
Answers
Answer:
(a) [tex]P(Online\ Training) = 0.750[/tex]
(b) [tex]Pr = 0.169[/tex] --- Quality Division and Online Training
(c) [tex]P(A\ |\ B) = 0.686[/tex] --- Online Training given Sales Division
Step-by-step explanation:
Given
The two-way table
Solving (a): P(Online Training)
The total employee is:
[tex]Total = 136[/tex]
The employees for online training is:
[tex]Online\ Training = 102[/tex]
So, the probability is:
[tex]P(Online\ Training) = \frac{102}{136}[/tex]
[tex]P(Online\ Training) = 0.750[/tex]
Solving (b): P(Quality Division and Online Training)
The number of employees that choose quality Division and online training is 23
So, the probability is:
[tex]Pr = \frac{23}{136}[/tex]
[tex]Pr = 0.169[/tex]
Solving (c): P(Online Training | Sales Division)
This is calculated as:
Let:
[tex]A \to[/tex] Online training
[tex]B \to[/tex] Sales division
So, we have:
[tex]P(A\ |\ B) = \frac{n(A\ n\ B)}{n(B)}[/tex]
From the table:
[tex]n(A\ n\ B) =35[/tex]
[tex]n(B) = 16 + 35 = 51[/tex]
So, the probability is:
[tex]P(A\ |\ B) = \frac{35}{51}[/tex]
[tex]P(A\ |\ B) = 0.686[/tex]
Given C(4, 3) and D(-4, -3) are two points on a circle, centered at the origin. Given
that CD is a diameter of the circle?
a) Find the radius of the circle.
b) State the equation of the circle
Answers
that CD is a diameter of the circle?
a) Find the radius of the circle.
Sixty out of every 100 pieces of candy is red. Which Indicates the
proportion of red candies? 60
60/100
60/40
40/100
Answers
Answer:
60/100
Step-by-step explanation:
Hope it helps you in your learning process
HAVE A GREATTTT DAYYY
a baceball team won 11 on its first 18 games at this rate how many games will the team win in a 162 game season
Answers
Answer:
Step-by-step explanation:
Set up the following proportion. x is the number of games you should win.
11/18 = x / 162
11*162 / 18 = x
x = 99 You likely would be out of the playoffs with a number like this.
Owens Orchards sells apples in a large bag by weight. A sample of seven bags contained the following numbers of apples: 23, 19, 26, 17, 21, 24, 22. a. Compute the mean and median number of apples in a bag. (Round your answers to 2 decimal places.)
Answers
Answer:
The mean and median number of apples in a bag are 21.71 and 22 respectively.
Step-by-step explanation:
The mean is the arithmetic mean of a set of numbers. In other words, the mean is the average value of all my data.
The mean is calculated by adding all the values and dividing the sum by the total number of values. In this case:
[tex]Mean=\frac{23+19+26+17+21+24+22}{7}[/tex]
[tex]Mean=\frac{152}{7}[/tex]
Mean= 21.71
The median of a set of numbers is the average number in the set, that is, it is the value that occupies the central place of all the values.
The median can be calculated by putting the numbers in ascending order and then:
if the quantity is numbers it is odd: the median is the number in the center of that distribution. if the number of numbers is even: the median is the mean of the two middle numbers.In this case:
Putting the numbers in ascending order: 17, 19, 21, 22, 23, 24, 26
Since the quantity is odd numbers, the median is the number in the center of that distribution. So Median= 22
The mean and median number of apples in a bag are 21.71 and 22 respectively.
PLEASE HEP ME
PLEASE HELP AND BE CORRECT BEFORE ANSWERING
Answers
9514 1404 393
Answer:
TrueTrueStep-by-step explanation:
The center of dilation (point D) is a point that doesn't move. Any line not through that point will be moved to a parallel location when a dilation factor is applied.
Any line through the center of dilation will still go through the center of dilation. Its slope does not change, so the line will appear to be the same.
AB ║ A'B' — True
AD ≅ A'D' — True
_____
You can see these relationships in the attached figure.
