Answers
Answer:
see attached
Step-by-step explanation:
Given a partially-filled circle pattern, you want to place the remaining numbers so the sum in each circle is 21.
ApproachThere are seven (7) circles, and nine (9) unknown values. This means there are a couple of "free choice" values that cannot be found directly. Our approach is to limit the number of possibilities we must examine.
EquationsWe note that if we multiply the sum (21) by the number of circles, that product includes the "single cover" circle shapes once, and each of the overlapping "double cover" areas twice. There are three unknown "single cover" values, and six unknown "double cover" values. If we represent the sums of these by "s" and "d" respectively then we have ...
(10 +11 +6 +4 +s) +2(d +5) = 7×21
41 +d +2s = 147 . . . simplify
d +2s = 106 . . . . . . subtract 41
The total of all of the unplaced numbers is ...
(2 +12 +7 +14 +1 +8 +9 +3 +13) = s +d
69 = s +d
Now, we have two equations in s and d:
d +2s = 106d +s = 69Subtracting the second from the first gives ...
(d +2s) -(d +s) = (106) -(69)
s = 32
The sum s is the sum of 'a', 'b', and 'c' as marked in the attachment. There is only one set of unplaced numbers that has a total of 32: {7, 12, 13}.
Using these numbers means that the set of allowed values for the "double cover" areas is {1, 2, 3, 8, 9, 14}.
Trial and errorWorking clockwise from the space marked 'c' in the attachment, the "double cover" oblong spaces must have the values ...
16 -cc -515 -c6 -(a -c)9 +(a -c)8 -(a -c)As we noted above, {a, b, c} is some permutation of {7, 12, 13}. This means the value (a-c) will be one of ±1, ±5, ±6.
If (a-c) = ±6, then 6 -(a-c) = {0, 12}. Neither value is allowed: 0 is not on the list, and 12 is already used.
If (a-c) = ±5, then we would have ...
for (a-c) = -5, 6 -(a-c) = 11, not an allowed value (already used).
for (a-c) = 5, all of the values 6-5=1, 9+5=14, and 8-5=3 are allowed. This case corresponds to {a, b, c} = {12, 13, 7}.
If (a-c) = ±1, then we would have 6 -(±1) = {5, 7}. Neither value is allowed.
ConclusionThe only allowed choice for {a, b. c} is {12, 13, 7}. Using c=7 and (a-c)=5, the "double cover" values clockwise from 'c' are ...
16-7 = 97 -5 = 215 -7 = 86 -5 = 19 +5 = 148 -5 = 3When all of the values are filled in the diagram it looks like the attachment.
__
Additional comment
As you might imagine, there was a bit of thrashing around before this method of solution presented itself. The system of 7 equations in 9 unknowns cannot be solved directly, and we know of no way to include the requirement that the solution set must include each number of the given set, used only once.
Fortunately, the method we tried here proved to find a solution in fairly straightforward fashion.
Related Questions
Write the number for 160,060 in expanded form and using number names
Answers
We know that the number written as sum of the place-values of its digits is called the expanded form of a number.
160,060 in expanded form:
100,000
+ 60,000
+ 0
+ 0
+ 60
+ 0
Number name form:
Number name form can be written for all the natural numbers, based on the place value of digits, such as ones, tens, hundreds, thousands, and so on.
160,060 is written as
One hundred sixty thousand sixty.
A department store advertises a sale where the customer chooses the discount. A customer may choose a flat discount of $20 off any purchase or 20% off the total purchase price. The final purchase price of an item was $175.
a. What are the possible prices of the item before each discount?
b. Which discount represents a bigger savings in cost for the customer?
Answers
The answers will be :
A. The possible prices at flat discount of $ 20 will be $195 and at flat discount of 20% will be $218.75
B. The discount of flat 20 % gives a bigger savings in cost for the customer.
What do you mean by discount ?
The discount is the difference between the purchase price and the item's par value or simply deduction from the cost price of a good.
It is given that the final purchase price of the item is $175.
A.
Let's try to find out the possible price of item before each discount.
So , price before discount can be calculated by using formula which is :
Price before discount = Discount + Final purchase price
As in first case the flat discount is of $20 , so :
Price before discount = $20 + $ 175
Price before discount = $195
Now as per the question , there is a flat discount of 20% off the total purchase price .
So , let's assume if price before discount is P then :
[ P - ( 20P / 100) ] = 175
P - 0.2 P = 175
0.8 P = 175
or
P = $ 218.75
B.
From the above calculations which we have done , we can conclude that the discount of 20 % represents a bigger savings in cost for the customer because customer is saving an amount of $218.75 which is greater than $195.
Therefore , the answers will be :
A. The possible prices at flat discount of $ 20 will be $195 and at flat discount of 20% will be $218.75
B. The discount of flat 20 % gives a bigger savings in cost for the customer.
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if two angles are not adjacent, then they are not a linear pair
Answers
False, if two angles are not adjacent, then they are not a linear pair.
Given that,
To justify that if two angles are not adjacent, then they are not a linear pair.
The angle can be defined as the one line inclined over another line. The measure of angle is in degrees and radians.
Here,
When two angles are not adjacent can be linear pairs,
But pair can be linear pair whether the angle is not adjacent.
Thus, the statement is false False, if two angles are not adjacent, then they are not a linear pair.
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Evaluate. Write your answer as a fraction in simplest form. 3/8 - 1/6 + 5/12
Answers
Answer:
5/8
Step-by-step explanation:
Get LCD of 24 and do the math
9/24 - 4/24 - 10/24
15/24
Divide top and bottom by 3
5/8
The florist makes the greatest number of identical arrangements with the carnations and asters. She has 72 carnations and 42 asters. How can she decide how many carnations to place in each arrangement?
Answers
The carnations to place in each arrangement is 6.
How to calculate the value?It should be noted that from the information, the florist makes the greatest number of identical arrangements with the carnations and asters and she has 72 carnations and 42 asters.
In order to know the carnations to place in each arrangement, this can be done by finding the common factor. This will be illustrated that the numbers have a highest common factor of 6.
Therefore, the number of carnation is 6.
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Solve each system by substitution
Answers
-x - y = 9
x = -y - 9
-3(-y - 9) + y = 3
4y + 27 = 3
y = -6
x = -(-6) - 9
x = 6 - 9
x = -3
Name all segments on the line that contain point c
Answers
The name of all segments on the line that contain point c are AD, BD, AE, BE
How to name all segments on the line that contain point c?The points on the number line are given as:
A, B, C, D and E
On this number line, the point either sides of point C are
A and B & D and E
This means that the point C is on the lines AD, BD, AE, BE
Hence. the name of all segments on the line that contain point c are AD, BD, AE, BE
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represent the expression please help
Answers
Answer:
10,350.98
Step-by-step explanation:
The decimal number is the sum of the terms of the expression.
Sum(1×10,000) +(3×100) +(5×10) +(9×1/10) +(8×1/100)
= 10,000 +300 +50 +0.9 +0.08
= 10,350.98
__
Additional comment
If you can't do this in your head, you can input the expression to your calculator, and it will give this same result.
PLEASE ANSWER! WILL GIVE BRAINLIEST
Owen draws the cube shown. Pat draws a cube with a side length that is 3 units greater than the side length of Owen's cube, show an equation and answer to represent the volume of Pat's cube.
Answers
Volume = side³.
Cube drawn by Owen From the drawing:Side = 7 in.
Cube drawn by PatSide length is 3 units greater than the side length of Owen’s cube:Side = 7in + 3in = 10 in
So the 3 sides= 10 you multiply 10 x 10 x 10 and would give you 1000
Lucie works out 25 x 12.2 without a calculator.
Here is her working.
10 × 12.2 = 12.20
20 × 12.2 = 24.40
5 x 12.2 = 61
25 x 12.2 = 24.40 +61 = 85.40
Lucie's working is incorrect.
Identify and (only) correct the lines containing a mistake
to work out the correct answer.
122
244
Answers
Answer:
[tex]25 \times 12.2 = 305.00[/tex]
Which is a true statement? Question 3 options:
–4 > 0
–12 < –3
–15 > –5
2 < –5
Answers
Answer:
-12<-3
Step-by-step explanation:
-3 is bigger than -12 and is closer to 0
A taxi company charges an initial fee
of $2.80 plus $3.50 per mile traveled.
a. Does the situation represent a function? If so, identify
the independent and dependent variables.
b. You have enough money to travel at most 20 miles
in the taxi. Find the domain and range.
Answers
The situation is a function, & the independent and dependent variables are the number of miles and total fee, respectively
a. Does the situation represent a function? If so, identify the independent and dependent variables.The given parameters are
Initial Fee = $2.80
Rate = $3.50 per mile
Let the number of miles be x and the total fee be y
So, we have
Total fee = Initial Fee + Rate * Number of miles
This gives
y = 2.8 + 3.5x
This means that the situation is a function, & the independent and dependent variables are the number of miles and total fee, respectively
b. You have enough money to travel at most 20 miles in the taxi. Find the domain and range.Here, we have
Maximum number of miles = 20
This means that the domain is 0 <= x <= 20
Substitute 20 for x in y = 2.8 + 3.5x
y = 2.8 + 3.5 x 20
Evaluate
y = 72.8
This means that the range is 0 <= x <= 72.8
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ALGEBRA 1 HW!! I WILL GIVE BRAINLYEST please explain how u got ur answer too..
Answers
Answer: yes the graph and the table represents the same relationship between x and y.
Step-by-step explanation: the table "x" is going up by X1 and y is going by x2 for each number meaning it does have a relationship, and the graph also has a relationship because is going (1,2) then (2,4) then (3,8) then (4,16) just like the table so yes it does have a relationship.
need to find the value of x
Answers
Answer:
(6x+10)+(10x+10)=180
16x+20=180
16x=160
x=10
Step-by-step explanation: Due it being a supplementary angle which means 180 degrees in total.
Which number set is the most reasonable to describe a baby’s weight at birth?
Whole numbers
Rational numbers
Irrational numbers
Integers
Answers
Answer this!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Based on the distance between the park bench and the basketball court, the distance between the park bench and the pond is 57¹/₈ feet
What is the distance between the park bench and pond?The distance between the park bench and the basketball is the sum of the distance between the park bench and the pond and the pond and the basketball court.
The distance between the park bench and the pond is therefore:
= Distance between park bench and basketball court - Distance between pond and basketball court
Solving gives:
= 75³/₄ - 18⁵/₈
= 75.75 - 18.625
= 57.125
= 57¹/₈ feet
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Answer:h
el]lo you commented on a post that helped me alot
Step-by-step explanation:
Step up an inequality for this situation below. Define your variable, but do not solve.
Mr. Bass charges his music students $25 per lesson plus a recital fee of $50. How many lessons can a student take if they pay no more than $175?
Answers
The student can take 5 number of lessons if they pay no more than $175
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the number of music lessons. The student can pay no more than $175, hence:
25x + 50 ≤ 175
x ≤ 5
The student can take 5 number of lessons if they pay no more than $175
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example of a vertical line test
Answers
Answer:
The vertical line test is a method that is used to determine whether a given relation is a function or not. The approach is rather simple. Draw a vertical line cutting through the graph of a relation, and then observe the points of intersections.
Step-by-step explanation: hope this helps
515,060 to the nearest hundred thousand
Answers
Answer:
500,000
hope this helps
All you have two unmarked cups 6 ounces and 10 ounces respectively how can you use the two cups to obtain exactly 8 ounces of liquid in the 10 ounce cup
Answers
I don’t know the rules but here it goes.
I would fill up the 10-oz glass with liquid and use it to fill the 6-oz glass.
Now I have 4-oz left in the 10-oz glass.
Empty the liquid from the 6-oz glass and pour the 4-oz remaining from the 10-oz glass to the 6-oz glass.
Now I have 4-oz.
Then, I would fill up the 10-oz glass again and use it to fill up the 6-oz glass that has 4-oz in it.
There are 4 oz in the glass already, so I can only add 2-oz more.
10 oz minus 2 oz = 8 oz left in the 10-oz glass.
Problem solved!!
According to a recent survey, 62 % of the population owns a cat. 37 Percent of cat owners are married, while 44 % of non-cat owners are married. If you randomly select a person, what is the probability that she/he is married?
Answers
Answer:
There are two possibilities that you need to take into account:
1) having a cat and being married
2) not having a cat and being married
P(having a cat) = 0.19
P(no cat) = 1 - P(having a cat) = 1 - (0.19) = 0.81
Since 9% of cat owners are married: (0.19)(0.09) = 0.0171
Since 11% of non-cat owners are married: (0.81)(0.11) = 0.0891
Probability of randomly selected person being married = 0.0171 + 0.0891 = 0.1062
the circle below centred at O has a radius of 12cm
Answers
Answer:
x = 9.7 cmStep-by-step explanation:
OB is perpendicular bisector of AC (since AB = BC) so triangle OBC is right triangle.
We have:
OB = x,OC = 12 cm,BC = 7 cmUse Pythagorean to find the missing value:
x² + BC² = OC²x² = OC² - BC²x² = 12² - 7²x² = 144 - 49x² = 95x = √95x = 9.7 cm (rounded)if a ball is thrown into the air with a velocity of 20 ft/second it's height in feet and seconds is given by f(t) = 20t - 10t^2. find average velocity for the time period t0 = 1 to t=2
Answers
The average velocity is -10 ft/s.
What is Average velocity?Average velocity is just the average speed with a direction. If a trip starts and ends at the same point, the total displacement is zero, so the average velocity is zero.
For example, someone who takes 40 minutes to drive 20 miles north and then 20 miles south (to end up at the same place), has an average speed of 40 miles divided by 40 minutes, or 1 mile per minute (60 mph).
Given:
f(t) = 20t - 10t²
Now, from t=1 to t=2
f(1)= 20*1 - 10 * 1*1
f(1)= 10
and, f(2)=20*2-10*2*2
f(2)= 40-40
f(2)=0
Now,
Average velocity:
v = ( 0-10 ) / ( 2- 1 )
= -10 ft/s
hence, the average velocity is -10 ft/s.
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What is the slope of a line graphed below?
Answers
Answer:
Undefined
Step-by-step explanation:
The slope of a horizontal line is zero. The slope of a vertical line is undefined.
An accounting machine operator wanted to divide a 65 minute job between two identical machines so that one machine would take one and a half times as long as the other. How much time was taken by the machine doing the longer job?
Answers
The slow machine did the job is 39 minutes as calculated with the help of a linear equation in one variable.
A linear equation in one variable is given by the combination of the variable with constants and coefficients such that a unique relationship is established between the terms.
Let us consider the faster machine takes x minutes the finish the job.
Hence the slower machine will take one and a half times .
∴ slower machine takes 1.5 x minutes.
Total time taken by the two machines = x + 1.5x = 2.5 x
But together the two machines will take 65 minutes to complete the job .
So now we form a linear equation with the variable x to solve for the value of x
∴ 2.5 x = 65
or, x = 65 ÷ 2.5
or, x = 26 minutes
Therefore the faster machine takes 26 minutes.
Hence the slower machine will take 1.5 x = 1.5 × 26 = 39 minutes.
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Members of a softball team raised $1353 to go to a tournament. They rented a bus for $943.50 and budgeted $31.50 per player for meals. Write and solve an equation which can be used to determine x, the number of players the team can bring to the tournament.
equation:
x=
Answers
Answer:
13 players
Step-by-step explanation:
1353 - 943.50 = 409.50
$31.50 per player for meals
31.50*x = 409.50
x = 13
13 players
Shreya is training for a marathon. The graph shows the miles she ran each day of her training. Shreya did not plot the distance she ran on day 5 of her training, but you can calculate the distance she ran that day using the trend in the data she did record. How far did Shreya run on day 5 of her training? Shreya ran 8 miles on day 5. Shreya ran 6 miles on day 5. Shreya ran 3 miles on day 5. Shreya ran 7 miles on day 5.
Answers
She ran the distance on the day of 5 is 2miles.
Shreya did not plot the distance she ran on day 5 of her training, but you can calculate the distance she ran that day using the trend in the data she did record. Shreya ran 8 miles on day 5. Shreya ran 6 miles on day 5. Shreya ran 3 miles on day 5. Shreya ran 7 miles on day 5.
⇒ (8-6-3-7)/5
⇒ (-8)/5
⇒ 1.8
⇒ 2 miles
The fraction whose numerator is 8 minus 6 minus 3 minus 7, whose denominator is 5 which is equal to the fraction of 2 miles.
Hence, Shreya ran on the day of 5 in her training is 2 miles.
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1 .If m∠SUT = 3x + 6 and m∠RUS = 5x – 4, find x
2.If m∠SUT = 3x + 6 and m∠RUS = 5x – 4, find m∠SUT.
same pic for both
*
Answers
Answer:
1.If you are to check the figure you will find that it is a rectangles. You should know the properties of a rectangle.
we are goin to use the property: Each vertex of a rectangle has angle equal to 90 degreesmeaning since m∠SUT and m∠ RUS form the vertex when added they give 90°3x+6+(5x-4)=90°
3x+5x+6°-4°=90°
8x+2°=90°
8x=90°-2°
8x=8°
[tex]\frac{8x}{8} =\frac{88}{8} \\x=11[/tex]
2.m ∠SUT is donated by 3x+6
and now we know the value of x=11°
m∠SUT=3(11°)+6
m∠SUT=33°+6°
m∠SUT=39°
please help
maths geometry
Answers
Step-by-step explanation:
ABCD is a rectangle.
so, it has 2 pairs of equal and parallel sides.
all 4 angles are 90°.
both diagonals are equally long and intersect each other at their midpoint. so, all 4 half-diagonal segments are equally long.
(1)
2x + 4y = 4x - y = 36/2 = 18 cm
we can split this into 2 equations
2x + 4y = 4x - y
5y = 2x
x = 5y/2
and e.g.
4x - y = 18
now we use the first equation in the second
4(5y/2) - y = 18
20y/2 - y = 18
10y - y = 18
9y = 18
y = 2
x = 5y/2 = 5×2/2 = 5
(2)
I cannot draw here, but the shortest distance between a point and a line is always a height (a line segment from the point meeting it intersecting the line at a right angle, 90°).
(3)
e.g.
AE, AD/2 and the drawn height from E to AD create a right-angled triangle.
we know AD/2 = 15 cm
from (1) we know AE = 4x - y = 4×5 - 2 = 20 - 2 = 18 cm.
the height E to AD we get via Pythagoras
AE² = (AD/2)² + height²
height² = AE² - (AD/2)² = 18² - 15² = 324 - 225 = 99
height = sqrt(99) = sqrt(9×11) = 3×sqrt(11)
remember trigonometry ?
this height = sin(theta) × AE
sin(theta) = height / AE = 3×sqrt(11) / 18 = sqrt(11)/6 =
= 0.552770798...
theta = 33.55730976...° ≈ 34°
(4)
the diagonals of a square bisect the angles of the square, so that theta would become 90/2 = 45°.
A box is launched upward from the ground at a speed of 69 feet per second. Calculate the height, in feet, of the box at 2 seconds if the height is given by h(t)=−16t2+69t where t is seconds.
Answers
According to the solving the Hight in feet at 2 second is 74.
What is the link between height and time, as well as height and velocity?This asserts that the height (h) of a projectile is equal to the combination of two products: its initial velocity and time in the air, and indeed the acceleration constant as well as half of the time squared.
What is the Max height formula?max = h plus V02 / (4 * g) When launching from the ground, the range is maximized (h = 0). If = 0°, therefore vertical velocity becomes equal to zero (Vy = 0), indicating horizontal projectile motion.
According to the given data:Given h(t)=−16t²+69t
t = 2 sec
substituting the value of t = 2.
h(2)=−16(2)²+69(2).
= -64 + 138
= 74
According to the solving the height and time in feet at 2 second is 74.
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