Answer:
[tex]r=4\\ \\s=3\\ \\t=-1[/tex]
Step-by-step explanation:
Given the system of three linear equations:
[tex]\left\{\begin{array}{l}-6r+5s+2t=-11\\ \\-2r+s+4t=-9\\ \\4r-5s+5t=-4\end{array}\right.[/tex]
Cheange the positions of the first and the second equations:
[tex]\left\{\begin{array}{l}-2r+s+4t=-9\\ \\-6r+5s+2t=-11\\ \\4r-5s+5t=-4\end{array}\right.[/tex]
Multiply the first equation by -3 and add it to the second equation and then multiply the first equation by 2 and add it to the third equation:
[tex]\left\{\begin{array}{r}-2r+s+4t=-9\\ \\2s-10t=16\\ \\-3s+13t=-22\end{array}\right.[/tex]
Multiply the second equation by 3, the third equation by 2 and add them:
[tex]\left\{\begin{array}{r}-2r+s+4t=-9\\ \\2s-10t=16\\ \\-4t=4\end{array}\right.[/tex]
From the third equation,
[tex]t=-1[/tex]
Substitute it into the second equation:
[tex]2s-10\cdot (-1)=16\\ \\2s+10=16\\ \\2s=6\\ \\s=3[/tex]
Substitute [tex]t=-1[/tex] and [tex]s=3[/tex] into the first equation:
[tex]-2r+3+4\cdot (-1)=-9\\ \\-2r+3-4=-9\\ \\-2r-1=-9\\ \\-2r=-9+1\\ \\-2r=-8\\ \\2r=8\\ \\r=4[/tex]
Hence,
[tex]r=4\\ \\s=3\\ \\t=-1[/tex]
Use the row of numbers shown below to generate 12 random numbers between 01 and 99.
25060 12315 86244 97348 36173 32710 80033 16160
Answer:
Below is the complete answer.
Step-by-step explanation:
Given the row of numbers
25060 12315 86244 97348 36173 32710 80033 16160
As we have to generate 12 random numbers between 01 and 99 from the above row of numbers.
Minimum Value = 01
Maximum Value = 99
25060
Lets take 25060 as seed in the calculator as
25060 ➡️ rand
[tex]randInt(1,99,12)[/tex]
Which will generate the following 12 random numbers between 01 and 99.
85 90 62 45 26 97 40 55 67 17 10 32
12315
Lets take 12315 as seed in the calculator as
12315 ➡️ rand
[tex]randInt(1,99,12)[/tex]
Which will generate the following 12 random numbers between 01 and 99.
33 20 26 68 73 09 46 14 82 74 17 04
86244
Lets take 86244 as seed in the calculator as
86244 ➡️ rand
[tex]randInt(1,99,12)[/tex]
Which will generate the following 12 random numbers between 01 and 99.
54 93 02 50 37 01 86 51 38 28 23 36
97348
Lets take 97348 as seed in the calculator as
97348 ➡️ rand
[tex]randInt(1,99,12)[/tex]
Which will generate the following 12 random numbers between 01 and 99.
04 79 01 86 51 02 50 37 38 28 23 36
36173
Lets take 36173 as seed in the calculator as
36173 ➡️ rand
[tex]randInt(1,99,12)[/tex]
Which will generate the following 12 random numbers between 01 and 99.
13 03 28 17 14 31 98 47 40 48 68 19
32710
Lets take 32710 as seed in the calculator as
32710 ➡️ rand
[tex]randInt(1,99,12)[/tex]
Which will generate the following 12 random numbers between 01 and 99.
22 80 42 03 27 89 98 46 14 31 72 56
80033
Lets take 80033 as seed in the calculator as
80033 ➡️ rand
[tex]randInt(1,99,12)[/tex]
Which will generate the following 12 random numbers between 01 and 99.
29 86 51 01 23 64 37 36 35 72 14 59
16160
Lets take 16160 as seed in the calculator as
16160 ➡️ rand
[tex]randInt(1,99,12)[/tex]
Which will generate the following 12 random numbers between 01 and 99.
93 54 72 58 30 14 48 87 99 95 83 29
Keywords: number, random number generator
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50
decreased by
twice vidya's
height
Answer
Step-by-step explanation:
Let Vidya's height be x
2x - 50
A truck enters a highway driving 60 miles per hour a car enters the highway at the same place 9 minutes later and drive 68 miles per hour in the same direction from the time the car enters the highway how long will it take the car to pass the truck
The time taken by car to pass the truck is 1.125 hours
Solution:
A truck enters a highway driving 60 miles per hour a car
The car enters the highway at the same place 9 minutes later and drive 68 miles per hour in the same direction from the time the car enters the highway
Let us first convert 9 minutes to hours
[tex]1 \text{ minute } = \frac{1}{60} \text{ hour }[/tex]
[tex]9 \text{ minute } = \frac{9}{60} = \frac{3}{20} \text{ hours }[/tex]
Let the truck covers 'x' m distance in time 't' hour the car will take [t -(3/20)] hour to cover the same distance 'x'
We know that,
[tex]Distance = Speed \times Time[/tex]
For truck : [tex]x = 60t[/tex] ----------- eqn 1
For car: [tex]x = 68 \times (t - \frac{3}{20})[/tex] ------------ eqn 2
From equations (i) and (ii)
[tex]60t = 68 \times(t-\frac{3}{20})\\\\60t = 68t-10.2\\\\68t - 60t = 10.2\\\\8t = 10.2\\\\t = 1.275[/tex]
Thus the time taken by car to pass the truck is:[tex]t - \frac{3}{20} = 1.275 - \frac{3}{20} = 1.275 - 0.15 = 1.125[/tex]
Thus the time taken by car to pass the truck is 1.125 hours
A dog pen is 18
feet wide. Its length
is twice the width.
What is the total
perimeter of the
pen?
Answer:
108 ft
Step-by-step explanation:
18x2=36
36+36+18+18=108
Perimeter is the total added amount that surrounds the shape.
The length of the dog pen is twice the width, hence 36 feet. Using the formula for perimeter of a rectangle, the total perimeter of the pen is 108 feet.
Explanation:To calculate the perimeter of a rectangle, we use the formula 2(length + width). Given the width of the dog pen is 18 feet, and the length is twice the width, we first calculate the length: 2 * 18 feet = 36 feet. With that, we can now calculate the perimeter: 2(18 feet + 36 feet) = 2 * 54 feet = 108 feet. Therefore, the total perimeter of the dog pen is 108 feet.
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The table shows the number of bathrooms in some selected houses and apartments.
1 Bathroom 2 Bathrooms
Apartment 44 18
House 24 70
Drag and drop the correct percentage to complete each statement.
Of the apartments, about __ have 1 bathroom and about __ have 2 bathrooms.
Answer: 1 bathroom 44/62=71% 2 bathrooms 18/62=29%
Step-by-step explanation:
Answer:
Of the apartments, about 71% have 1 bathroom and about 29% have 2 bathrooms.
Step-by-step explanation: i took the test it was right :)
A certain paint is sold in both 1-gal cans and 1-qt cans. The gallon can cost $13 and the quart can cost $5. How much more do you save per gallon by buying the larger cans?
Answer:
8% or 80%
Step-by-step explanation:
$13.00 - $5.00 = $8.00
Which of the following would likely weigh about 8 pounds?
A. newborn baby
B. mother whale
C. large dog
D. professional football player
Which would you most likely measure using inches?
A. width of a road
B. length of a hallway
C. length of your nose
D. distance in the moon
Complete the statement. 8 c = _ pt
A. 1
B. 2
C. 4
D. 16
7 3/5 ft = _ yd
A. 15 1/5
B.3 4/5
C.2 8/15
D. 22 4/5
Answer:
Around 8 pounds: A,NewBorn Baby (I was 7.8 pounds)
Most likely used in inches: C,length of your nose
Complete the statement. 8 c = C,4pt
7 3/5 ft = C
Little Explanation:
Around 8 pounds is a newborn because I was about 8 pounds, a large dog would weigh WAYYY more than that!
We might measure nose length with inches. Centimeter might be used occasionally, but inches is more common. (proccess of elimination)
2 Cups = 1 pint. 8 divided by 2 is 4.
1 yard is 3 feet, therefore you can only think it's 2 8/15
Contact for questions!!!
Final answer:
A newborn baby typically weighs 8 pounds. Inches are ideal for measuring the length of your nose. 8 cups convert to 4 pints and 7 3/5 feet is equivalent to 2 8/15 yards.
Explanation:
Understanding Weights and Measurements
Out of the given options, a newborn baby is likely to weigh about 8 pounds. This rules out the mother whale, large dog, and professional football player, as they all typically weigh significantly more than 8 pounds.
When it comes to measuring in inches, the length of your nose is the most appropriate of the given options. Width of a road, the length of a hallway, and the distance to the moon are all too large and would be better measured in feet, meters, or miles respectively.
For the conversion of cups to pints, we know that there are 2 cups in a pint. Therefore, 8 cups is equal to 4 pints because 8 divided by 2 equals 4.
Lastly, converting feet to yards for 7 3/5 feet to yards, we use the fact that 1 yard is equal to 3 feet. So, we divide 7 3/5 by 3, which gives us 2 8/15 yards.
one dozen golf balls have a mass of 551.16g.calculate the mass of one golf ball
Answer: Each golf ball weights 45.93g
Step-by-step explanation:
divide 551.16 by 12
Answer:
Step-by-step explanation:
What are the roots of the equation x²= 5x+6
Answer: -1 and +6
Step-by-step explanation:
Given :
[tex]x^{2}[/tex] = 5x + 6
re - writing the equation , we have
[tex]x^{2}[/tex] - 5x - 6 = 0
We will look for two factors that when multiplied will give -6[tex]x^{2}[/tex] and when added will give -5. The factors are +x and -6x
Then the equation becomes :
[tex]x^{2}[/tex] -6x + x - 6 = 0
factorizing , we have
x (x-6)+1(x-6) = 0
(x-6)(x+1) = 0
Therefore :
x - 6 = 0 or x + 1 = 0
Therefore :
x = 6 or x = -1
Therefore : the rots of the equation are -1 and +6
PLEASE I HAVE SO MUCH WORK TN
Which of the following figures can also be classified as a parallelogram?
Select all that apply.
square
trapezoid
rhombus
right triangle
rectangle
pentagon
Figures that can also be classified as a parallelogram include a square, rhombus, and rectangle due to their properties of having parallel opposite sides and specific angle characteristics.
Explanation:Among the given figures, the ones that can also be classified as a parallelogram are square, rhombus, and rectangle. A parallelogram is defined as a quadrilateral with both pairs of opposite sides parallel. A square is a parallelogram with all sides equal in length and all angles equal to 90 degrees.
A rhombus is a parallelogram with all four sides of equal length; moreover, the diagonals of a rhombus are always perpendicular to each other due to the properties of the scalar product of vectors.
A rectangle is a parallelogram with opposite sides equal and all angles equal to 90 degrees. A trapezoid, right triangle, and pentagon do not fit the definition of a parallelogram because they do not have both pairs of opposite sides that are parallel.
Please help!!!!!! just 7 and 8
Doris wants to hang a mirror that is 14 3/4 inches wide in the center of a wall that is 25 inches wide what width
which should be on each side of the mirror
To center a 14 3/4-inch-wide mirror on a 25-inch-wide wall, subtract the mirror's width from the wall's width and divide by two. There should be 5.125 inches of space on each side of the mirror.
Explanation:Doris wants to make sure the mirror that is 14 3/4 inches wide is centered on a wall that is 25 inches wide. To find the width that should be on each side of the mirror, we need to subtract the width of the mirror from the width of the wall and divide the result by two. The calculation looks like this:
Width of the wall: 25 inchesWidth of the mirror: 14 3/4 inches (which is 14.75 inches in decimal)Space on each side: (25 inches - 14.75 inches) / 2 = 5.125 inchesTherefore, there should be 5.125 inches of space on each side of the mirror.
Many times does 5 go into 125
Answer:
25 times
Step-by-step explanation:
125÷5 = 25
5 goes into 125 exactly 25 times. This result is obtained by dividing 125 by 5. The answer is 25.
To determine how many times the number 5 goes into 125, we need to perform division:
Set up the division problem: 125 divided by 5.Divide 125 by 5.This means if you divide 125 by 5, the result is 25, showing that 5 fits into 125 exactly 25 times.
Rewrite y = -x + 6 in standard form. Identify the x-intercept of the line.
Answer:
x+y=6
Step-by-step explanation:
The standard form equation is ax+by=c.
9) In one year, Angie's height went from 58 to 60 inches. What was the percentage increase in Angie's height? (Round to the nearest percentage)
The percentage increase in Angie's height is 3 %
Solution:
Given that, In one year, Angie's height went from 58 to 60 inches
To find: percentage increase
The percent increase between two values is the difference between a final value and an initial value, expressed as a percentage of the initial value.
The percent increase is given as:
[tex]\text { percent increase }=\frac{\text { final value - initial value}}{\text { initial value }} \times 100[/tex]
Here in this problem,
Initial value = 58 inches
Final value = 60 inches
Substituting the values we get,
[tex]percent\ Increase = \frac{60-58}{58} \times 100\\\\percent\ Increase = \frac{2}{58} \times 100\\\\percent\ Increase = 0.0344 \times 100\\\\percent\ Increase = 3.45 \approx 3[/tex]
Thus percentage increase in Angie's height is 3 %
Please help me. My math teacher said that there is some sort of pattern that will help us understand how to win the game. Here is what the question is:
You will be competing with other contestants for a grand prize of 1 million dollars. All of the contestants will form a circle around the host. Starting at seat #1, The person to the left of that contestant seat #1 is out of the game. The next remaining contestant is in seat #3. The person left of that remaining contestant is out of the game. This pattern continues until there is one contestant remaining. The object is simple. Determine what seat # you must sit on the circle in order to be the last contestant remaining. Since you do not know how many contestants are on the show, you must come up with an explanation of how to win at this game.
Thank you friends!
Let n = number of players
The chart showing the values of n and the final winners is shown below in the attached image.Drawing out each scenario is optional, but it helps visualize what is going on.
Let's play out scenarios for n = 2 through n = 12 to see what the pattern might be.
------------------
n = 2 players
Seat #1 eliminates seat #2
Winner = seat #1
This is fairly trivial and boring as there is only one round and one elimination.
------------------
n = 3 players
Seat #1 eliminates seat #2
Seat #3 eliminates seat #1
Winner = seat #3
Like with n = 2, this game is over in one round. For n = 4 and greater, we'll start to see multiple rounds.
------------------
n = 4 players
Start of Round 1
Seat #1 eliminates seat #2
Seat #3 eliminates seat #4
End of Round 1
Seats remaining = {seat #1, seat #3}
Start of Round 2
Seat #1 eliminates seat #3
End of Round 2
Winner = seat #1
------------------
n = 5 players
Start of Round 1.
Seat #1 eliminates seat #2
Seat #3 eliminates seat #4
Seat #5 eliminates seat #1
End of Round 1.
Seats remaining = {seat #3, seat #5}
Start of Round 2.
Seat #3 eliminates seat #5
End of Round 2
Winner = seat #3
------------------
n = 6
Start of round 1.
Seat #1 eliminates seat #2
Seat #3 eliminates seat #4
Seat #5 eliminates seat #6
End of Round 1
Seats remaining = {seat #1, seat #3, seat #5}
Start of round 2
Seat #1 eliminates seat #3
Seat #5 eliminates seat #1
End of Round 2
Winner = seat #5
------------------
Up next is n = 7 players
Start of round 1.
Seat #1 eliminates seat #2
Seat #3 eliminates seat #4
Seat #5 eliminates seat #6
Seat #7 eliminates seat #1
End of Round 1
Seats remaining = {seat #3, seat #5, seat #7}
Start of round 2
Seat #3 eliminates seat #5
Seat #7 eliminates seat #3
End of Round 2
Winner = seat #7
------------------
n = 8 players
Start of Round 1
Seat #1 eliminates seat #2
Seat #3 eliminates seat #4
Seat #5 eliminates seat #6
Seat #7 eliminates seat #8
End of Round 1
Seats remaining = {seat #1, seat #3, seat #5, seat #7}
Start of round 2
Seat #1 eliminates seat #3
Seat #5 eliminates seat #7
End of Round 2
Seats remaining = {seat #1, seat #5}
Start of Round 3
Seat #1 eliminates seat #5
End of Round 3
Winner = seat #1
------------------
n = 9 players
Start of Round 1
Seat #1 eliminates seat #2
Seat #3 eliminates seat #4
Seat #5 eliminates seat #6
Seat #7 eliminates seat #8
Seat #9 eliminates seat #1
End of Round 1
Seats remaining = {seat #3, seat #5, seat #7, seat #9}
Start of round 2
Seat #3 eliminates seat #5
Seat #7 eliminates seat #9
End of Round 2
Seats remaining = {seat #3, seat #7}
Start of Round 3
Seat #3 eliminates seat #7
End of Round 3
Winner = seat #3
------------------
n = 10 players
Start of Round 1
Seat #1 eliminates seat #2
Seat #3 eliminates seat #4
Seat #5 eliminates seat #6
Seat #7 eliminates seat #8
Seat #9 eliminates seat #10
End of Round 1
Seats remaining = {seat #1, seat #3, seat #5, seat #7, seat #9}
Start of Round 2
Seat #1 eliminates seat #3
Seat #5 eliminates seat #7
Seat #9 eliminates seat #1
End of Round 2
Seats remaining = {seat #5, seat #9}
Start of Round 3
seat #5 eliminates seat #9
End of Round 3
Winner = seat #5
------------------
n = 11 players
Start of Round 1
Seat #1 eliminates seat #2
Seat #3 eliminates seat #4
Seat #5 eliminates seat #6
Seat #7 eliminates seat #8
Seat #9 eliminates seat #10
Seat #11 eliminates seat #1
End of Round 1
Seats remaining = {seat #3, seat #5, seat #7, seat #9, seat #11}
Start of Round 2
Seat #3 eliminates seat #5
Seat #7 eliminates seat #9
Seat #11 eliminates seat #3
End of Round 2
Seats remaining = {seat #7, seat #11}
Start of Round 3
Seat #7 eliminates seat #11
End of Round 3
Winner = seat #7
------------------
n = 12 players
Start of Round 1
Seat #1 eliminates seat #2
Seat #3 eliminates seat #4
Seat #5 eliminates seat #6
Seat #7 eliminates seat #8
Seat #9 eliminates seat #10
Seat #11 eliminates seat #12
End of Round 1
Seats remaining = {seat #1, seat #3, seat #5, seat #7, seat #9, seat #11}
Start of Round 2
Seat #1 eliminates seat #3
Seat #5 eliminates seat #7
Seat #9 eliminates seat #11
End of Round 2
Seats remaining = {seat #1, seat #5, seat #9}
Start of Round 3
Seat #1 eliminates seat #5
Seat #9 eliminates seat #1
End of Round 3
Winner = seat #9
------------------
Admittedly this is a lot of things to keep track of and it's easy to get lost. Hopefully the process is fairly straight forward even if it requires a lot of drawings.
The chart showing the values of n and the final winners is shown below in the attached image.Each pattern block is color coded to separate the start and stop of each sequence. Note the pattern of {1,3} then {1,3,5} then {1,3,5,7} then {1,3,5,7,9} and so on. The next pattern block would likely be {1,3,5,7,9,11}. This table will help you determine what seat you will want to sit in if you know how many players there are at the start. Of course you won't know ahead of time how many players there are, but when it comes to you picking your seat you can quickly look at the table (either on the paper or just something you memorize) and you can select the ideal seat based on what n is.
solve the inequality.
x\6 <1
Answer:
x < 6
Step-by-step explanation:
treat it as a normal equation
Can someone help me out here?
You work at an appliance store. A customer purchases a refrigerator and a dishwasher. Installation charges are $50 for the refrigerator and $100 for the dishwasher. The company is offering a rebate of $20 for each appliance installation. What is the total amount the customer pays for installation after the rebates? $40 $110 $130 $170 $190
The total would be 170 for it all.
Answer:
Step-by-step explanation:
50 + 100 - 2(20) =
150 - 40 =
$ 110 <===
Find the x and y intercepts of the line 8y=2x-4
Answer:
Step-by-step explanation:
Hdheidncnfjxhxjd
Answer: Just do 2x4 to get the answer.
Step-by-step explanation:
On a coordinate plane, a straight line with a negative slope, labeled f of x, crosses the y-axis at (0, 4), and the x-axis at (4, 0). Which is true regarding the graphed function f(x)?
The graph of function f(x) that crosses the y-axis at (0, 4) and the x-axis at (4, 0) is a straight line with a negative slope, making option a correct.
Explanation:Considering the information given, the graph of the function f(x) intersects the y-axis at (0, 4) and the x-axis at (4, 0). By determining the slope of the line, which is the change in y divided by the change in x (rac{ ext{rise}}{ ext{run}}), we can conclude that the slope is negative because the line goes down as it goes right.
The slope is rac{0 - 4}{4 - 0} = -1.
Therefore, option a, stating it is a straight line with a negative slope, correctly describes the graph of function f(x).
Dion shares 1/3 cup of nuts equally with his brother.
How much does each person get?
Enter your answer as a fraction in simplest form by filling in the boxes.
_/_cups
Each person will get [tex]\frac{1}{6}[/tex] cups of nuts.
Step-by-step explanation:
Given,
Quantity of nuts to share = 1/3 cups of nuts
As Dion will share this with his brother, it means,
1 share of Dion, 1 share of his brother = 2 shares
We will divide the quantity of nuts with 2.
Share of each person = [tex]\frac{1}{3}*\frac{1}{2}[/tex]
Share of each person = [tex]\frac{1}{6}[/tex] cups of nuts
Each person will get [tex]\frac{1}{6}[/tex] cups of nuts.
Keywords: fraction, division
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Answer: 6=1/6(9)
Step-by-step explanation:
Name
9. Bayshore Elementary students
collected $3,200 for new library
books. Each of the 8 classes collected
the same amount. How much did each
claşs collect?
Answer: $ 400
Step-by-step explanation:
Amount collected for new library = $ 3,200 and there are 8 classes and they collected the same amount. This means that each class will collect
3200/ 8 = $400
A daycare center has 4 infants and 11 toddlers. What fraction of the children is infants?
StartFraction 4 Over 15 EndFraction
StartFraction 4 Over 11 EndFraction
StartFraction 11 Over 15 EndFraction
StartFraction 11 Over 4 EndFraction
Answer:
Option A [tex]\frac{4}{15\\}[/tex]
Step-by-step explanation:
4 infants + 11 toddlers = 15 children
4 infants / 15 children = [tex]\frac{4}{15}[/tex]
Answer:
The answer is B, or the second option: The sequence is recursive and can be represented by the function f(n + 1) = f(n) + f of n plus 1 equals f of n plus StartFraction 3 Over 8 EndFraction..
Step-by-step explanation:
What is the product of (5x + 1)(5x - 1)?
O
O
O
A. 10x2-1
B. 10x2 + 10x-1
C. 25x2 + 10x-1
O
D. 25x2 - 1
Answer:
D) 25x^2-1
Step-by-step explanation:
(5x+1)(5x-1)
25x^2+5x-5x-1
25x^2-1
One number is 5 times a first number. A third number is 100 more than the first number. If the sum of the three numbers is 730, find the numbers.
Answer:
the number 1.46
Step-by-step explanation:
because 5×100×1.46=730
What is the sum of – 95 and its additive inverse?
Answer:
0
Step-by-step explanation:
In mathematics, the additive inverse of a number a is the number that, when added to a, yields zero. This number is also known as the opposite, sign change, and negation.
Hence, -96 + 96 = 0
Find each value (1.2) 3
Answer: im not sure how you typed this but if its 1.2 x 3 then its 3.6
Step-by-step explanation:
A company is expanding its building area from 19,000 square feet to 24,320 square feet. What is the percentage increase of the area of the building space?
Answer:
28%
Step-by-step explanation:
What value of X make this equation true? Negative 2X -10 equals 5X -3
Answer:
c
Step-by-step explanation:
c
Answer: x=-2+1/3
Step-by-step explanation:
We move all terms to the left:
2x-10-(5x-3)=0
We get rid of parentheses
2x-5x+3-10=0
We add all the numbers together, and all the variables
-3x-7=0
We move all terms containing x to the left, all other terms to the right
-3x=7x=7/-3x=-2+1/3