The system of equations to represent each student comment is:
2x - y = 5
x - y = -9
Solution:
Let "x" be the score point of Elena
Let "y" be the score point of Koran
Elena says, “You earned so many more points than I did
If you earned 5 more points, your score would me twice mine
Which means,
Koran score + 5 = twice of Elena
y + 5 = 2x
Rearranging it we get,
2x - y = 5 ------- eqn 1
Kiran says, “Oh, I don’t think I did that much better
I only scored 9 points higher than you did
Elena score + 9 = Koran score
x + 9 = y
Rearranging it we get,
x - y = -9 --------- eqn 2
Thus eqn 1 and eqn 2 represents eacch student comment
The system of equations which represents the scenario described based on the statements made by kiran and Elena are :
2x - y = 5 - - - - - - (1) x - y = - 9 - - - - - (2)Representing their scores using variables :
Elena's score = x Kiran's score = yUsing Elena's statement :
Kiran's score + 5 = Elena's score × 2
y + 5 = 2x
2x - y = 5 - - - - - - (1)
Using Kiran's statement :
y = x + 9
x - y = - 9 - - - - - (2)
Hence, the system of equation is (1) and (2)
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Cristina is painting the playhouse she made for her sister. She intends to paint only the outside of the house that does not include the floor. The paint she chose must be purchased in full gallons. Each gallon covers 200ft² and costs $15.95 a gallon. How much will it cost cristina to paint the playhouse?
It takes 313131 employees and \$7500$7500dollar sign, 7500 to build a car, and it takes 191919 employees and \$4300$4300dollar sign, 4300 to build a motorcycle.
Genghis Motors wants to spend more than \$84000$84000dollar sign, 84000 to build cars and motorbikes using at most 706706706 employees.
Let CCC denote the number of cars they build and MMM the number of motorbikes they build.
Answer:
a) 31c + 19m ≤ 706
b) 7500c + 4300m > 84000
Step-by-step explanation:
hope it helps :p
Answer:
make sure variables are capital!
Step-by-step explanation:
Find each measure for the given set of data: 11, 13, 17, 20, 22, 25, 27, 31, 31, 33, Mean= Median= Range= interquartile range= I need help please
Answer:
Mean=23
Median =23.5
Range=22
Interquartile range = 14
Step-by-step explanation:
Given set of data
11,13,17,20,22,25,27,31,31,33
Mean [tex]=\frac{11+13+17+20+22+25+27+31+31+33}{10}[/tex]
[tex]=\frac{230}{10}[/tex]
=23
The[tex](\frac{n}{2})[/tex] th term= the 5th term
=22
The [tex](\frac{n}{2}+1)^{th}[/tex] term = The [tex]6^{th[/tex] term
= 25
The median = [tex]\frac{22+25}{2}[/tex]
=23.5
Range = Highest term - lowest term
=33- 11
=22
Here lower half {11,13,17,20,22}
The middle number of lower half is first quartile.
Q₁ = 17
And lower half is{25,27,31,31,33}
The middle number of upper half is third quartile.
Q₃=31
Interquartile Range =Q₃-Q₁
=31-17
=14
Answer:
Mean = 23
Median = 23.5
Range = 22
Interquartile range = 14
is this right. if it's not can you tell me what I did wrong
answer the question Please ASAP
The independent variable is
A: Number of friends (f)
B: Number of cost (c)
The dependent variable is
A: c = 20f
B: f = 20c
C: c = 10f
D: f = 10c
Use similar triangles ABC and XYZ to find the missing height h. around to the nearest tenth if necessary.
Answer:
Therefore,
The height is 23.3 ft.
Step-by-step explanation:
Given:
ΔABC ~ ΔXYZ
AC = 108.5 ft
BC = h
XZ = 14 ft
YZ = 3ft
To Find:
h = ?
Solution:
Δ ABC ~ Δ XYZ….Given
If two triangles are similar then their sides are in proportion.
[tex]\dfrac{AB}{XY} =\dfrac{BC}{YZ}=\dfrac{AC}{XZ} \textrm{corresponding sides of similar triangles are in proportion}\\[/tex]
Substituting the values we get
[tex]\dfrac{BC}{YZ}=\dfrac{AC}{XZ}[/tex]
[tex]\dfrac{h}{3}=\dfrac{108.5}{14}\\\\h=\dfrac{325.5}{14}=23.25=23.3[/tex](nearest tenth)
Therefore,
The height is 23.3 ft.
A fence is to be built to enclose a rectangular area of 450 square feet. The fence along three sides is to be made of a material that costs $3 per foot. The material for the fourth side costs $9 per foot. Find the dimensions of the rectangle that will allow for the most economical fence to be built.
Answer: 25 by 50 ft
Hope this helps
The dimensions of the rectangle will allow for the most economical fence to be built are 30 feet by 15 feet
Given that, rectangular area=450 square feet.
What is the formula to find the area of a rectangle?The formula to find the area of a rectangle is Area=Length×Breadth.
Let the length of the rectangle be x and the breadth of the rectangle be y.
Now, 450=xy.
x=450/y
The cost of three sides is $3 per foot.
That is, 3x+3x+3y
The cost on the fourth side is $9 per foot.
That is, 9y
Total cost=6x+12y
Now, Total cost=6×450/y+18y
Let the minimum cost be 0.
2700/y+12y=0
⇒2700/y²-12=0
⇒12y²=2700
⇒y=15 feet
So, 450/15=x=30 feet.
Therefore, the dimensions of the rectangle are 30 feet by 15 feet.
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order of operation 36divided4+11x8
The answer for 36/4 + 11 [tex]\times[/tex] 8 = 97.
Step-by-step explanation:
The order of operation is done by using BODMAS rule.
B - bracket
O - of
D - division
M - multiplication
A - addition
S - subtraction
step 1 :
36 divided 4 + 11 [tex]\times[/tex] 8
The division operation must be done first.36/4 = 9step 2 :
9 + 11 [tex]\times[/tex] 8
After division, multiplication should be done next.11 [tex]\times[/tex] 8 = 88step 3 :
9 + 88
Finally addition is performed to get the answer.9 + 88 = 97∴ The answer for 36divided4+11x8 is 97.
Billy pays $46 for a meal at restaurant the ratio of the cost of the meal to the amount of tip given is 20 : 3. Find the amount of the tip he gives.
please help asap! ty
The amount of tip is $6
Step-by-step explanation:
Step 1: Given total bill amount = $46. Ratio of cost of meal to tip = 20:3So let cost of meal be 20 x and the tip be 3 x.
⇒ 3x + 20x = 46
⇒ 23x = 46
⇒ x = 2
Step 2: Calculate the tip.⇒ 3x = 3 × 2 = $6
Write two equations that would have the solution of (3,6)
Answer:
Step-by-step explanation:
3x1=3
2x3=6
2+1=3
3+3=6
Two equations that have the solution (3,6) include y = 2x and x + y = 9, satisfying the point when their values are substituted.
To write two equations that would have the solution of (3,6), we need to construct linear equations where the point (3,6) satisfies both equations. Here are two examples that fit the criteria:
The first equation could be y = 2x, because when x=3, then y=2(3)=6.
The second equation could be x + y = 9, because when x=3 and y=6, then 3 + 6 = 9.
These two examples clearly have the solution (3,6) when the respective values for x and y are substituted.
Solve for x in each problem 4x +2=42
Answer:
x = 10
Step-by-step explanation:
Given
4x + 2 = 42 ( subtract 2 from both sides )
4x = 40 ( divide both sides by 4 )
x = 10
Answer:
Step-by-step explanation:
4x+2=42
4x=42-2
4x=40
x=40/4
X=10
A rectangle has side lenghs X +2 and 3X -1 write an expression that represents the perimeter of the rectangle then simplify the expression
Answer: Perimeter = 2(L + W) and
as a simplified expression is, 8x + 2
Step-by-step explanation: The length is represented by L and the width is represented by W in the expression above.
However, since we have been given the sides of the rectangle as x + 2 and 3x - 1, we shall substitute for the values of these in the expression representing the perimeter.
2(L + W) can now be written as
2( {x + 2} + {3x - 1} )
2(x + 2 + 3x - 1)
By collecting like terms, we now have
2(4x + 1)
8x + 2.
The expression can now be simplified as 8x + 2
A straight slide in a playground design makes an isosceles triangle with the
ground and its platform, with area 32 square feet. What is the length of the slide?
A 412 feet 32 © 8/2 feet 126
B 8 feet 6
0 16 feet 256
Answer:
Option D.
Step-by-step explanation:
First, the you need ti understand that the triangle is an isosceles right angled triangle. In other words, the base and height are equal in length. The third side is the slide. This is the longest side. Next, we know that the formula for calculating the area of a right angled triangle is given by:A = 1/2 (base × perpendicular height)
The perpendicular height is equal to the base. Let's say the base is x. It means that the height is also x, since height = base. Therefore, the formula will be:A = 1/2 (x.x)
=1/2 (x²)
32 = 1/2 (x²)
Multiplying both sides by 2 gives:
32×2 = x²
64 = x²
8 = x
To find the third side, we use the Pythagoras theorem:
C² = A² + B²
= 8² + 8²
= 128
C = √128
= 8√2
However, the answer will not be exact, so we multiply the length of the base and height by 2. This gives x = 16 (Length of base = length of height)
Repeating the steps above gives C = √ (16)² + (16)²
= √256
This corresponds to option D.
Which group of three side lengths will form a triangle?
A. 11, 5, 4
B. 22, 17, 14
C. 28, 15, 10(maybe this)
D. 30, 15, 14
Answer:
D.30,15,14
Step-by-step explanation:
Sophia pays a
$19.99 membership fee for an online music store. If Sophia purchases
il songs for
S0.99 each, write an expression for the total cost.
A0.991 - 19.99
B0.997 + 19.99
C0.991 x 19.99
D0.99
Part B
If she buys two songs from a new album, what is the total cost?
Answer:
Answer:
19.99 + 0.99x ; 21.97
Step-by-step explanation:
19.99 + 0.99x
19.99 + 0.99(2)
19.99 + 1.98
21.97
A square orange rug has a yellow square in the center. The side length of the yellow square is x inches. The width of the orange band that surrounds the yellow square is 11 in. What is the area of the orange band?
To find the area of the orange band, subtract the area of the yellow square from the area of the larger square.
Explanation:To find the area of the orange band, we need to subtract the area of the yellow square from the area of the larger square. The side length of the larger square is 8 inches because it is twice the side length of the yellow square, which is x inches. So, the area of the larger square is 8 * 8 = 64 square inches. The area of the yellow square is x * x = x^2 square inches. Therefore, the area of the orange band is 64 - x^2 square inches.
Final answer:
To calculate the area of the orange band, find the area of the larger square using the side length of x + 22 inches and subtract the area of the smaller yellow square with side length x. The expression for the area of the orange band is [tex](x + 22)^2 - x^2[/tex], which simplifies to 44x + 484 square inches.
Explanation:
To calculate the area of the orange band, you need to determine the area of the outer (larger) square and subtract the area of the inner (smaller) yellow square. First, find the side length of the larger square, which is the side length of the yellow square plus twice the width of the orange band, so it's x + 2(11) inches. Thus, the side length of the larger square is x + 22 inches.
Now, calculate the area of both squares. The area of the larger square is [tex](x + 22)^2[/tex] square inches, and the area of the yellow square is [tex]x^2[/tex] square inches. The area of the orange band is the difference between these two areas:
Area of the larger square:[tex](x + 22)^2[/tex]
Area of the yellow square: [tex]x^2[/tex]
Area of the orange band: [tex](x + 22)^2 - x^2[/tex]
To find the area of the orange band, you expand the expression [tex](x + 22)^2[/tex], which gives you [tex]x^2 + 44x + 484[/tex], then subtract the area of the yellow square [tex]x^2[/tex], resulting in 44x + 484 square inches, which is the area of the orange band.
The farmers holdings are in two separate parcels she has planted corn on 30% of the first parcel and 60% on the other supposed the first person I was twice as big as the second what percentage of the farmers turtle land is planted explain your answer with a math drawing
3/5x
= 60%
Step-by-step explanation:
Assume that Parcel 2 is assigned x acres; Parcel 1 will be 2x (because its twice as large as parcel 2).
Therefore if the farmer has planted on 30% on parcel 2;
30/100 * 2x area
60/100x
=3/5x
Parcel 1 ;
60/100 * x area
60/100x
3/5x
The total area planted =
(3/5x + 3/5x ) /2
= 3/5x
3/5 * 100
= 60%
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Devaugh is 12 years younger than Sydney. The sum of their ages is 86. What is Sydney's age
Answer:74
Step-by-step explanation:
You go to a basketball game and buy 3 waters that cost x dollars each. Your brother buys a bottle of water and a bag of peanuts that costs $4.5O. Write an expression in simplest form that represents the total amount of money spent altogether.
Answer: y=3x+4.50
Step-by-step explanation:
Answer:
4.50- 10.50/ 3x
6/3x= 2
Boden conjectures that in a right triangle, the sine of one acute angle is always equal
to the cosine of the other acute angle. Is Boden's conjecture correct? Choose the best
answer.
Answer:
Boden's conjecture is correct
Step-by-step explanation:
we know that
If two angles are complementary, the cofunction identities state that the sine of one equals the cosine of the other and vice versa.
A right triangle, has two acute angles.
The two acute angles are complementary
so
In any right triangle, the sine of one acute angle is equal to the cosine of the other acute angle
therefore
Boden's conjecture is correct
Answer:
Yes, because the leg opposite one of the acute angles is adjacent to the other acute angle
Step-by-step explanation:
It takes 2 1/5 kilometers of thread to make 2 5/6 boxes of shirts. How many kilometers of thread will it take to make 9 boxes of shirts.
It would take 6.99 kilometers of thread to make 9 boxes of shirts.
Step-by-step explanation:
Step 1; First we convert the mixed fractions into improper fractions. So
2[tex]\frac{1}{5}[/tex] becomes [tex]\frac{11}{5}[/tex] after multiplying 2 with 5 and adding 1 while 5 remains.
2[tex]\frac{5}{6}[/tex] becomes [tex]\frac{17}{6}[/tex] after multiplying the 2 with 6 and adding 5 while 6 remains.
Step 2; Next we equate the given data; [tex]\frac{11}{5}[/tex] kilometers of thread = [tex]\frac{17}{6}[/tex] boxes of thread. We must make the RHS equal to 1 to find out the kilometers of thread needed to make 1 box of shirts. So we multiply [tex]\frac{6}{17}[/tex] on both sides to make the RHS equal to 1.
[tex]\frac{11}{5}[/tex] × [tex]\frac{6}{17}[/tex] = [tex]\frac{17}{6}[/tex]× [tex]\frac{6}{17}[/tex]= 1, So [tex]\frac{11}{5}[/tex] × [tex]\frac{6}{17}[/tex] = [tex]\frac{66}{85}[/tex] km of thread. So [tex]\frac{66}{85}[/tex] kilometers of the thread is required to make 1 box of shirts so we multiply this with 9 to see thread required to make 9 boxes of shirts.
Thread required for 9 boxes of shirts = [tex]\frac{66}{85}[/tex] × 9= [tex]\frac{594}{85}[/tex] = 6.9882 kilometers of thread. This is rounded off to 6.99 kilometers of thread.
A card is drawn at random from a pack of 52 playing cards. Given that the card is a diamond, find the probability that the card is a King. Give your answer as a fraction in its simplest form.
================================================
Explanation:
Focus only on the diamond cards. There are 13 of them total. Out of the 13 diamond cards, there is one king of diamonds. So the probability of getting a king, if we know 100% the card is a diamond, is 1/13.
---------------
You can use a slightly longer method through a conditional probability
A = card is a king
B = card is a diamond
P(A and B) = probability of king and diamonds = 1/52
P(A \ B) = probability of event A happens given we know B happens
P(A \ B) = P(A and B)/P(B)
P(A \ B) = (1/52)/(13/52)
P(A \ B) = (1/52) ÷ (13/52)
P(A \ B) = (1/52) * (52/13)
P(A \ B) = 1/13
The probability that the card is a King is 1/13
Probability is the likelihood or chance that an event will occur.
Probability = Expected outcome/Total outcome
Given that a card is drawn at random from a pack of 52 playing cards, the total outcome is 52
If the card is a king, the expected outcome is 4
Pr(selecting a king) = 4/52 = 1/13
Hence the probability that the card is a King is 1/13
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Is the 161 rounded to the nearest 10 or to the nearest 100
Answer:
161 to the nearest 10 = 160
161 to the nearest 100 = 200
Step-by-step explanation:
161 to the nearest 10:
Since you know that 60 is the tenth unit in this number, and 1 is the one unit, the one unit will indicate if it should be rounded up or down. If the one unit it 4 and below, the number will be rounded down. If the one unit is 5 and above, the number will be rounded up.
With this information, we know that he one unit in this number is "1", which will make the 61, be rounded down to 60, resulting in 160.
Using the same information with rounding to the nearest 100, since the tenth unit is above 5, the number will be rounded to the nearest 100, which is 200.
You use the number before the number you are trying to round, to find the nearest "_th".
Answer:
if its rounded to the nearest 10 it would be = 160
if its rounded to the nearest 100 it would be = 200
Step-by-step explanation:
Is there a triangle that has a greater area than its perimeter?
Answer:
no
...
...
...
....
shajajs
Answer:
NO
A= 1/2 x B x H
P= A+B+C
Step-by-step explanation:
ex: triangle side 13, 6,8.5
high: 8
A= 52
P= 27.5
What is the greatest common factor of 10x and 22x“?
Answer:
2x
Step-by-step explanation:
x and 2 are common to both 10x and 22x, so 10x + 22x = 2x(5 + 11)
The GCF is 2x.
Multiply. Write as a mixed number in simplest form 2 1/5 X 2 2/9
Answer:
4 4/9
Step-by-step explanation:
2 1/5 X 2 2/9
= 11/5 * 20/9
= 11/1 * 4/9
= 44/9
= 4 4/9
Harper went into a movie theater and bought 10 bags of popcorn and 6 drinks,
costing a total of $79. Damian went into the same movie theater and bought 3 bags of
popcorn and 5 drinks, costing a total of $36.50. Write a system of equations that
could be used to determine the price of each bag of popcorn and the price of each
drink. Define the variables that you use to write the system.
Answer:
The price of a drink = $4
The price of a bag of popcorn = $5.5
Step-by-step explanation:
Let p represent popcorn and d represent drink
Harper bought 10 bags of popcorn and 6 drinks and paid $79 ➡ 10p + 6d = $79
Damian bought 3 bags of popcorn and 5 drinks and paid $36.50 ➡ 3p + 5d = $36.50
Now multiply first equation by -3 and second equation by 10
-3 × (10p + 6d) = $79 ➡ -30p - 18d = -$237
10 × (3p + 5d) = $36.50 ➡ 30p + 50d = $365
Now add the new equationd
30p + 50d -30p - 18d = $365 - $237 (-30p will eliminate 30p)
32d = $128 divide both sides of the equation by 32
32 ÷ 32d = 32 ÷ $128 ➡ d = 4
If d = 4 that means a drink costs $4 we can use this information to find the price of a bag of popcorn
3p + 5d = $36.50 (replace d with 4)
3p + 4×5 = $36.50
3p + 20 = $36.50
3p = $36.50 - 20
3p = 16.50 divide both sides by 3
p = $5.5
The question asked to set up a system of equations to determine the price of each bag of popcorn and each drink. Using the variables x and y to represent the price of popcorn and drinks respectively, the system of equations based on the information given is 10x + 6y = $79 and 3x + 5y = $36.50.
Explanation:To solve this problem, we need to setup a series of equations based on the information given. Let's say:
x is the price of each bag of popcorny is the price of each drinkAccording to the first scenario with Harper, we get:
10x + 6y = $79
From Damian's shopping, we have:
3x + 5y = $36.50
This gives us the system of equations which can be used to find individual prices of a bag of popcorn and a drink.
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solve the equation
k + 22 = 29
Answer:
K=7
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
k + 22 = 29
collect like terms
k = 29 - 22
k = 7
The number −6 is 2 more than an unknown number. Find the unknown number.
The unknown number is -8.
To find the unknown number, we can set up an equation based on the given information.
We are told that -6 is 2 more than the unknown number, so we can represent this as:
Unknown number + 2 = -6
To isolate the unknown number, we need to subtract 2 from both sides of the equation:
Unknown number = -6 - 2
Unknown number = -8
So, the unknown number is -8. This means that when you add 2 to -8, you get -6, which satisfies the condition given in the problem.
In summary, by setting up and solving the equation Unknown number + 2 = -6, we determined that the unknown number is -8.
This equation represents the relationship between the unknown number and the given value of -6, where -6 is 2 more than the unknown number, as specified in the problem statement.
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What is 85 divided by 4?
Answer:
Decimal form: 21.25
Mixed number: 21 1/4
Exact form: 85/4