X - y = 5 and x + y = -10
The value of x and y by using the given expressions is x = -5/2 and y = -15/2.
What is an expression?
An expression can be defined as the combination of variables and constants with two or more operations applied to it. The operation can be addition, subtraction, multiplication and division.
Simplifying the expressions for x and y
The given expressions are:
x - y = 5 —--- 1
x + y = -10 —---- 2
Adding the expression 1 and 2, we get,
2x = -5
x = -5/2
Subtracting the expression 1 and 2, we get,
-2y = 15
y = -15/2
Hence, the value of x and y by using the given expressions is x = -5/2 and y = -15/2.
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Question 1 (5 points)
Saved
Which description is best for this set of ordered pairs: (1,4) (2,5) (3,6) ?
A) only a relation
B) only a function
C) relation and function
D) a relation but not a function
Since the pairs of y values have singular and unique x values, the following set of points are a function.
Since an increase in one unit in the x value, yields an increase in one unit in the the y value, there exists a relation between these set of points.
[tex]y (x)= x + 3 \\ D_{f} ∈ [1,3][/tex]
Option: C
Question
Consider the following two loans for Po = $15,000.
• Loan A: 5 year loan, annual interest rate of 8%, monthly repayments of $304.15.
Loan B: 3 year loan, annual interest rate of 11%, monthly repayments of $491.08.
Calculate the absolute difference between the total interest paid on both loans. Give your answer to the nearest ten dollars.
Do not include the dollar sign in your answer
Answer:
570
Step-by-step explanation:
570
The absolute difference that is between the loans paid as 570
How to solve for the absolute differenceWe have the following details:
Po = $15000
loan a 5 year loan, interest = 8 percent and repayments = 304.15 dollars
Loan b
3 year loan, interest = 11 percent repayments = $491.08
Total number of repayments = 5 x 12 = 60
Total repayments = 304.15 dollars x 60
= $18249
The total interest that is paid for A would be
$18249 - $15000
= $3249
For the second loan
Total number of repayments = 3 x 12 months = 36
Total repayment = 36 x 491.08 = $17678.88
The total interest for the loan B would be: $17678.88 - $15,000
= $2678.88
Then the absolute difference between the paid loan would be
$3249 - $2678.88 = 570.12
Hence we would have the absolute difference that is between the loans paid as 570.
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Michael grabs a marble from a bag. There are 5 green marbles and 1 red marble. If he grabs the red marble he loses everything he bet on. The marbles are not put back into the bag. The max amount of times Michael can bet on the same game is 4. If he bets 300 and wins 578 (having 278 as winnings), he has the choice to bet again with everything he earned for 682. Then he has the choice to do so again for 945, then 1312 at max. At what point in the game should Michael stop playing to gain the most given the percent of risk of losing the game? What point in the game is the least beneficial for Michael's gains?
First bet (300 -> 578)
Second bet (578 -> 682)
Third bet (682 -> 945)
Fourth bet (945 -> 1312)
If Michael wins every round he would go from 300 to 1312. If he loses, he doesn't gain any of the rewards and is 300 in debt.
Using the expected value of a discrete distribution, it is found that:
Michael should stop playing the game after the first round.The fourth round is the least beneficial round for Michael.What is the mean of a discrete distribution?The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.
For the probabilities, we consider that it is given by the number of desired outcomes divided by the number of total outcomes.
For one bet, the distribution is given as follows:
P(X = 578) = 5/6 (5 green marbles out of 6).P(X = -300) = 1/6.Hence the expected value is given by:
E(X) = 578 x 5/6 - 300 x 1/6 = $431.67.
For two bets, the distribution is given as follows:
P(X = 682) = 5/6 x 4/5 = 2/3.P(X = -300) = 1/3.Hence the expected value is given by:
E(X) = 682 x 2/3 - 300 x 1/3 = $354.67.
For three bets, the distribution is given as follows:
P(X = 945) = 5/6 x 4/5 x 3/4 = 1/2.P(X = -300) = 1/2.Hence the expected value is given by:
E(X) = 945 x 1/2 - 300 x 1/2 = $322.5.
For four bets, the distribution is given as follows:
P(X = 1312) = 5/6 x 4/5 x 3/4 x 2/3 = 1/3.P(X = -300) = 2/3.Hence the expected value is given by:
E(X) = 1312 x 1/3 - 300 x 2/3 = $237.33.
Hence, considering the greatest and the smallest expected values, we have that:
Michael should stop playing the game after the first round.The fourth round is the least beneficial round for Michael.More can be learned about the expected value of a discrete distribution at https://brainly.com/question/27899440
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How to solve this problem? -2x + 4 < 16
Answer:
the answer is 7+1-7+0/xx{12
Step-by-step explanation:
the answer above stated is correctly corrected correct
-1.12345...
rational, irrational and or real number?
Answer: Irrational Number
Step-by-step explanation: It's Irrational because it cant be represented as a simple fraction.
What are the solutions to –24x – 24 = x3 + 8x2?
Answer:
–24x – 24 = x3 + 8x2
Step-by-step explanation:
-24x-24=x^3+8x^2
x^3+8x^2+24=-24x-24+24
x^3+8x^2+24=-24x
x^3+8x^2+24+24x=-24x+24x
x^3+8x^2+24x+24=0
Answer: x=-2
Step-by-step explanation:
[tex]-24x-24=x^3+8x^2\\-24x-24+24=x^3+8x^2+24\\-24x=x^3+8x^2+24\\-24x+24x=x^3+8x^2+24+24x\\0=x^3+8x^2+24x+24\\x^3+8x^2+24x+24=0\\x^3+8x^2+12x+12x+24=0\\(x)(x^2+8x+12)+(12)(x+2)=0\\(x)(x^2+2x+6x+12)+(12)(x+2)=0\\(x)((x)(x+2)+6(x+2))+(12)(x+2)=0\\(x+2)((x)(x+6)+12)=0\\ (x+2)(x^2+6x+12)=0\\x+2=0\\x+2-2=0+(-2)\\x=-2\\x^2+6x+12=0\\D=(-6)^2-(4)(1)(12)\\D=36-48\\D=-12\\Hence,\\The\ equation\ has\ no\ valid \ roots\\Thus,\\x=-2[/tex]
This week Andrei got a promotion at work that came with a 2 % pay increase. If now his monthly salary is $ 1683 , how much was he making before the raise?
Enter your answer as a decimal. If needed, round to the nearest penny. Do not use commas.
1683 доллара - 102% . Найдем 1 процент и умножим его на 100%, тем самым получив ответ:
1) 1683 / 102 = 16.5 доллара - 1 % от всей зарплаты
2) 16.5 * 100 = 1650 - изначальная сумма, которую получал Андрей до повышения.
Ответ : 1650 $
What are the slope and the y-intercept of the linear function that is represented by the graph?
Answer:
Step-by-step explanation:
it would be great if u had the image, but at least I can give some advice: use the method of rise over run to find the slope. use 2 points and count the number of squares "rising" and turn right and count the number of squares "running". left and down if it's going downward.
for the y intercept, find the x that equals 0. your coodinate should look like this: (0, *insert y*)
The arcade charges 24 tokens to play 6 games.
How many tokens will 10 games cost?
Answer: 40
Step-by-step explanation:
if 6 games = 24 tokens
then 1 game = 24/6=4
so 10 games = 4*10=40
Answer:
40
Step-by-step explanation:
24/6 = 4 tokens per game
4*10 games = 40
3=
X/
3
One step equations with positive whole number
On the weekdays a grocery store has 14301 customers and on the weekends the grocery store has 11856 customers . How many more customers does the grocery store have on weekdays than on weekends?
Answer:
2445
Step-by-step explanation:
it would have 2445 more costumers
Answer:
2445
Step-by-step explanation:
Subtract.
14301 - 11856 = 2445 more people on weekdays
Jack has 80 marbles.
He gives 1/5
of the marbles to his friends.
(c) Work out how many marbles Jack now has.
inq
Answer:
He now has 64 marbles.
Step-by-step explanation:
This is because 1/5 of 80 is 16.
What is: -28/-4 + -48/6
Answer: The answer is -1
Step-by-step explanation:
-28/-4+-48/6
7-8
-1
Answer: -1
Step-by-step explanation:
-28 divided by -4 is 7
-48 divided by 6 is -8
7 - 8 would be a total of -1
A spring with a spring constant of 1N/cm is stretched and has elastic potential energy of 30 j. Calculate the extension experienced by
the spring.
Give your answer to 2 decimal places.
Th elastic potential energy of two decimal places is k=60×1^2 N/M
Given that,
Spring has a potential energy of =30 J
we know that,
Energy of a spring=1/2 kx^2
here, x=1cm
x^2=0.01m
30=1/2 kx^2
30=1/2 k(0.01)^2
60=k(0.01)^2
k=60/(0.01)^2
k=60×1^2N/M
Hence the potential energy of two decimal places is k= 60×1^2 N/M
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40 Members of arwick youth club go on a trip to a leisure centre they go in minibuses that can each seat up to 15 people. It costs £30 for each minibus and £150 for the group to have use of the leisure centre. How much will the trip cost per person
The trip cost per person is 6 pounds.
What is a unit rate?Unit rate is the ratio of two different units, with the denominator as 1.
It means a rate for one of something.
We have,
Total members = 40
Each minibus cost = 30 pounds
Leisure centre cost = 150 pounds
Each minibus can carry = 15 people
The number of minibusses needed to carry 40 members:
= 40 / 15
= 2.67
= 3 minibusses.
This means we need 3 minibusses to carry 40 members.
Now,
The total cost for the trip:
= 150 pounds + 3 x 30 pounds
= 150 + 90
= 240 pounds
The cost per person:
= 240 / 40
= 6 pounds
Thus the trip cost per person is 6 pounds.
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What is the domain of f(x) = 7/(x-10) - 7
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
For the given function :
[tex]\qquad \sf \dashrightarrow \: f(x) = \dfrac{7}{x - 10} - 7[/tex]
f(x) is defined for all real values of x, except the value of x for which the denominator becomes 0, because if denominator is 0, the function at that instant will be undefined.
that is : f(x) is not defined when :
[tex]\qquad \sf \dashrightarrow \: x - 10 = 0[/tex]
[tex]\qquad \sf \dashrightarrow \: x = 10[/tex]
Hence, f (x) is defined for all real values of x except 10
It can be represented as :
[tex]\qquad \sf \dashrightarrow \: f(x) : x \in R \sim \{10 \}[/tex]
Dots sells T-shirts ($7) and shorts ($9). In April, total sales were $572. People bought 5 times as many T-shirts as shorts. How many T-shirts and shorts did Dots sell?
Dots sold 65 T-shirts and 13 shorts
How to calculate the number T-shirts and shorts ?let the x represent the number of T-shirts and y and shorts
7x + 9y= 572.......equation 1
x= 5y........equation 2
substitute 4y for x in the equation
7(5y) + 9y = 572
35y + 9y= 572
44y= 572
y= 572/44
y= 13
substitute 13 for y in equation 2
x= 5(13)
x= 65
Hence there 65 T-shirts and 13 shorts
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translation: (x,y) →(x - 5, y + 1)
Z(−3, –4), K(−2, −1), (0, -1)
The translation of the points as Z' ( - 8 , - 3 ), K' ( - 7 , 0 ) and K' ( - 5 , 0 ).
We are given the translation as:
(x , y) → (x - 5 , y + 1)
Now we have some points:
Z (−3, –4)
K (−2, −1)
M (0, -1)
We need to translate these points.
For Z (−3, –4), we get the translation as:
Z (−3, –4) = Z' ( - 3 - 5 , - 4 + 1)
Z (−3, –4) = Z' ( - 8 , - 3 )
For K (−2, −1), we get the translation as:
K (−2, −1) = K' ( - 2 - 5 , - 1 + 1)
K (−2, −1) = K' ( - 7 , 0 )
For M (0, -1), we get the translation as:
M (0, -1) = K' ( 0 - 5 , - 1 + 1)
M (0, -1) = K' ( - 5 , 0 )
Therefore, we get the translation of the points as Z' ( - 8 , - 3 ), K' ( - 7 , 0 ) and K' ( - 5 , 0 ).
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Determine the point(s), if any, at which the graph of the function has a horizontal tangent line. Y= 1/2x^2 +7x (Give the answer as x,y coordinates)
Answer:
i don't know how to attach the file
Solve the inequality and express your answer in interval notation. x² + 8x + 3 < 0
Solution:
A.) [tex](-4-\sqrt{13},-4+\sqrt{13})[/tex]
Hope this helps!
(3x 3 +4x 2 )+(3x 3 −4x 2 −9x)
Answer:
9x
Step-by-step explanation:
=9x+8x+9x-8x-9x
=9x
find the value of x in 5/9 = x/54
Answer:
[tex] \large \sf \: x=30[/tex]
Step-by-step explanation:
Let's solve your equation step-by-step.
5/9 = x/54
Step 1: Cross-multiply.
5/9 = x/54
(5)*(54)=x*(9)
270=9x
Step 2: Flip the equation.
9x=270
Step 3: Divide both sides by 9.
9x/9 = 270/9
x=30
The formula below relates distance, rate, and time. Solve this formula for t.
The equation when solved for t gives d/r
What is subject of formula?Subject of formula can be defined as a variable or element expressed in terms of other variables in an equation.
Iris also known as the variable that is being worked out in equation.
From the information given, we have the equation as;
d = rt
Where;
d is the distancer is the ratet is the timeNow, let's make 't' the subject
Divide both sides by the coefficient of t
d/r = rt/r
t = d/r
Thus, the equation when solved for t gives d/r
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The complete question:
The formula below relates distance, rate, and time. Solve this formula for t.
d = rt
lisa's plant was 7 3/4 inches tall when she bought it. Three weeks later, it was 4 2/5 times as tall. How tall is lisa's plant after three weeks?
Answer:
[tex]\frac{341}{10} =34\frac{1}{10}[/tex]
Step-by-step explanation:
[tex]7\frac{3}{4} *4\frac{2}{5}[/tex]
→ Convert both fractions into improper
[tex]\frac{31}{4} *\frac{22}{5}[/tex]
→ Simplify
[tex]\frac{31}{2} *\frac{11}{5}[/tex]
→ Calculate
[tex]\frac{341}{10} =34\frac{1}{10}[/tex]
How much colder was Tuesday then Saturday? if
+5 degree.
Formula for Length Change due to Thermal Expansion: The formula for calculating the change in length of a substance due to thermal expansion is ΔL=αLΔT Δ L = α L Δ T where L is the original length of the substance and ΔT is the change in temperature of the substance either in degrees Celsius or in Kelvin.
For comparision of temperature -
Subtract the final temperature from the starting temperature to find the difference. So if something starts at 50 degrees Celsius and finishes at 75 degrees C, then the change in temperature is 75 degrees C – 50 degrees C = 25 degrees C.
Given data
temperature of tuesday = 55 degree
temperature of saturday = 60 degree
Difference between temperature = 60 -55 = 5 degree.
Hence, 5 degree more colder was Tuesday then Saturday.
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Write the equation of the line that passes through the point P (0, 0) and is perpendicular to the line y = – 2x + 10.
The equation of the line that passes through the point (0,0) and is perpendicular to the line y=-2x+10 is .
We will be using the concept of slope and equation of straight line for this question. Here it has been said that the line passes through (0,0) which is the origin, so we know the point ([tex]x_{1},y_{1}[/tex]) is (0,0).This point will be required while solving the equation for the straight line. The line is said to be perpendicular to another line given by y=-2x+10. When two lines are parallel their slopes are equal and when two lines are perpendicular the product of their slopes is equal to -1. The slope of a line can be found from the equation of the line by dividing the coeeficient of x by the coefficient of y.
Slope of y=-2x+10 is -2
mx-2=-1⇒m=1/2
equation of a straight line,
[tex](y-y_{1} )=m(x-x_{1} )\\[/tex]
⇒y-0=[tex]\frac{1}{2}[/tex](x-0)
⇒y=[tex]\frac{x}{2}[/tex]
⇒2y=x
⇒2y-x=0
Thus the equation of the line that passes through (0,0) and is perpendicular to y=-2x+10 is 2y-x=0.
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4+ -1 -5= -2
Please help me know how did I Got this answer the working thank you
Answer:
4 + -1 = 3, 3 - 5 = -2.
Step-by-step explanation:
Hope this helps!!
A 13 foot ladder is leaning on a wall. the bottom of the ladder has a diatance of 5 feet from the base of the wall.
What is the distance, in feet, between the ground and the top of the lafder?
Answer:
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One pizza will feed 5 people. How many pizzas are needed for 40 people?
Answer:
8 pizzas
Step-by-step explanation: