what are possible solutions to a system of linear equations and what do they represent graphically?
Final answer:
Solutions to a system of linear equations are represented graphically as the intersections of lines on a graph and can be unique, infinitely many, or none. Graphical representations are essential in various applications, like economic models, and software like R facilitates solving these systems.
Explanation:
Possible solutions to a system of linear equations can be one of three types: a unique solution, infinitely many solutions, or no solution. Graphically, these solutions are represented by the intersections of lines on a graph. In the case of a unique solution, the lines intersect at exactly one point.
For example, consider two linear equations of the form y = mx + b. Graphically, each equation is represented by a straight line. Where these lines cross is the solution to the system. If both equations produce the same line, they have infinitely many solutions since every point on the line satisfies both equations.
A line with a slope of 2 passes through (3,9) Which choice is an equation of this line?
The equation of the line with a slope of 2 passing through the point (3, 9) is y = 2x + 3.
The equation of a line with slope (m) passing through a point (x₁, y₁) is given by the point-slope form:
y - y₁ = m(x - x₁)
The slope (m) is 2, and the point (x₁, y₁) is (3, 9). Plug these values into the equation:
y - 9 = 2(x - 3)
Now, you can simplify this equation:
y - 9 = 2x - 6
To isolate y, add 9 to both sides:
y = 2x - 6 + 9
y = 2x + 3
Therefore, the equation of the line with a slope of 2 passing through the point (3, 9) is y = 2x + 3.
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does anyone know how to answer this question? it's number four on limits.
The current population of a city can be represented by p. the population is expected to increase by 6.5% next year. Write a expression in simplest form that represents the expected population next year
The expression in the simplest form that represents the expected population next year will be 1.065p.
What is an exponent?Let a be the initial value and x be the power of the exponent function and b be the increasing factor.
The exponent is given as
y = a(b)ˣ
The ongoing populace of a city can be addressed by p. the populace is supposed to increment by 6.5% one year from now.
The expression in the simplest form that represents the expected population next year will be given as,
⇒ p(1 + 0.065)
⇒ 1.065p
The expression in the simplest form that represents the expected population next year will be 1.065p.
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Minnie and Tori combined ate nine pieces of the wedding cake Mindy ate 3 pieces of the wedding cake Tori have one fourth of the total kick write an expression to determine how many pieces of cake C there was in total
24 red marbles is 40% of how many marbles
Answer:
60 marbles
Step-by-step explanation:
Given: 24 red marbles is 40% of how many marbles
Let number of marbles be x
"24 red marbles is 40% of how many marbles"
24 = 40% of x
solve for x
First change % to decimal
24 = 0.40x
Division property of equality, divide by 0.04 both sides
x = 24÷0.40
x = 60
Hence, 40% of 60 is 24
The circumference of a circle is 60π cm. What is the length of an arc of 140°? 11.7π cm 16.1π cm 23.3π cm 29.5π cm
Answer:
c = 23.3
Step-by-step explanation:
Answer:
[tex]23.3 \pi[/tex] cm
Step-by-step explanation:
Circumference of circle = [tex]2 \pi r[/tex]
The circumference of a circle is 60π cm.
So, [tex]2 \pi r=60 \pi[/tex]
[tex]2r=60[/tex]
[tex]r=30[/tex]
Formula of length of arc = [tex]2 \pi r \times \frac{\theta}{360}[/tex]
Length of arc = [tex]2 \pi \times 30 \times \frac{140}{360}[/tex]
Length of arc = [tex]23.3 \pi[/tex]
So, Option C is true
Hence Length of arc is [tex]23.3 \pi[/tex] cm
You are planning to take a group of friends to the movies for your birthday. The local movie theater charges $12.99 per person. When you check the company's website, you find that they also offer a special group rate. The group rate is only $8.99 per person but also includes a $20 reservation fee in addition to the cost per person
Answer: Hello mate!
lets suppose you have (x -1) friends (then when you count yourself, there are x persons in the group) where x is a natural number.
you have two possible prices at the movie theater:
1) the $12.99 per person, then if you have x persons in the group, the total charge is $12.99*x
2) with the promotion they pay $8.99 per person and includes a $20 reservation, then the total charge is $8.99*x + $20
now, let's find the number x is where the second option is cheaper than the first.
in order to do this, we can regulate both equations in order to determine in which x₀ the costs are the same, then if x< x₀, the first option is cheaper and if x>x₀ the second option is cheaper.
$12.99*x₀ = $20 + $8.99x₀
$12.99x₀ - $8.99x₀ = $20
$4x₀ = $20
x₀ = 20/4 = 5
Then if in your group are less than 5 persons, took option 1.
if there are more than 5 persons, took the option 2
if there are exactly 5 persons, both options cost the same.
Find constants a and b such that the function y = a sin(x) + b cos(x) satisfies the differential equation y'' + y' − 8y = sin(x).
Sales of tablet computers at ted glickman's electronics store in washington,
d.c., over the past 10 weeks are shown in the table below: week 1 2 3 4 5 6 7 8 9 10 demand 19 23 28 38 25 29 37 20 26 30 a) the forecast for weeks 2 through 10 using exponential smoothing with alpha = 0.60 and a week 1 initial forecast of 19.0 are (round your responses to two decimal places):
In a study of 100 new cars, 29 are white. find and , where is the proportion of new cars that are white
A researcher measured the heights of forty high-school students. The measurements are recorded here.
Heights (in inches)
58 59 60 60 60 61 61 61 61 62
62 62 62 62 62 63 63 63 64 65
67 67 68 68 68 68 69 69 70 70
70 71 71 71 71 71 72 73 74 76
If Alyssa's height is in the 45th percentile within the group, what is her height in inches?
Answer:
64
Step-by-step explanation:
i just know
A deck of cards has 3 blue, 4 black, and 6 purple cards. Draw 2 cards without replacing any cards. What is the probability of both cards being blue?
what is the slope of the line through point (2/3, 4/7) and (2/3, 11/7)
a. 0
b. 1
c. 2/3
d. undefined
plzz help me out, what is -4a +9>9
Akule borrowed $1500 at an annual simple interest rate of 12%. He paid $270 in interest. For what period of time did Akule borrow money
Using the simple interest formula I = PRT, it is calculated that Akule borrowed $1500 at an annual interest rate of 12% for 1.5 years to pay $270 in interest.
Explanation:The subject of this question is Mathematics, specifically focusing on simple interest calculation. To find out the period of time Akule borrowed money for, we can use the simple interest formula I = PRT, where I is the interest paid, P is the principal amount borrowed, R is the annual interest rate, and T is the time in years. Akule paid $270 in interest on a $1500 loan at 12% annual simple interest. Using the formula, we solve for T as follows:
T = I / (P × R)
T = $270 / ($1500 × 0.12)
T = $270 / $180
T = 1.5 years
Therefore, Akule borrowed the money for 1.5 years.
Akule borrowed the money for 0.18 years.
Explanation:To find the period of time Akule borrowed the money, we can use the formula:
Interest = Principal × Rate × Time
Given that Akule paid $270 in interest and borrowed $1500 at an annual simple interest rate of 12%, we can plug in these values into the formula:
270 = 1500 × 0.12 × Time
Simplifying the equation, we get:
0.12 × Time = 270 / 1500
Time = (270 / 1500) / 0.12
Time = 0.18 years
Hence, Akule borrowed the money for 0.18 years.
Two spherical balloons are filled with water. The first balloon has a radius of 3cm, and the second has a radius of 6cm.
How much greater is the volume of water in the larger balloon than in the smaller balloon?
Use 3.14 to approximate pi. Round to the nearest hundredth if necessary.
Zhi bought 18 tickets for games at a fair. Each game requires 3 tickets. Zhi wrote the expression 18 – 3g to find the number of tickets she has left after playing g games. Diego correctly wrote another expression, 3(6 – g), that will also find the number of tickets Zhi has left after playing g games. Use the drop-down menus to explain what each part of Zhi's and Diego's expressions mean.
Answer: In the picture below.
Step-by-step explanation:
The provided mathematical expressions represent the process of calculating Zhi's remaining tickets after playing 'g' games at a fair. '18 - 3g' symbolizes subtracting three times the number of games played from the initial total (18) tickets. '3(6 – g)', on the other hand, corresponds to multiplying the number of tickets per game (3) by the subtraction of already played games from total possible games (6).
Explanation:The subject of this question is based on mathematical expressions and variables. In the case of Zhi's expression, 18 represents the total number of tickets she bought. 'g' corresponds to the number of games played, and 3 is the number of tickets required for each game. Therefore, '18 – 3g' means subtracting three times the number of games played (3g) from the total quantity of tickets (18), which would give us the number of tickets left.
Diego's expression, however, expresses the same idea differently. '6 – g' symbolises the number of games Zhi could play before she runs out of tickets (since 18 tickets divided by 3 tickets per game equals 6 games). The '3' outside the bracket is again the number of tickets each game requires. As such, '3(6 – g)' expresses the multiplication of the tickets needed per game (3) by the difference between the total games possible and the games already played (6-g). This, therefore, provides the same result—Zhi's remaining tickets after g games.
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Assume that the probability of error-free transmission of a message over a communication channel is . if a message is not transmitted correctly, a retransmission is initiated. this procedure is repeated until a correct transmission occurs. such a channel is often called a feedback channel. assume that successive transmissions are independent.
a. what is the probability that no retransmissions are required? (note that the number of retransmissions is the number of transmissions minus one.)
Answer:
Let the probability of error-free transmission of a message over a communication channel is P.
Then the Probability of Retransmission is =1-P
Now the question is Probability when no retransmission is required
= Probability of error free transmission in first attempt
=P
Now , suppose after first failure error free transmission takes place.
Since events are independent.
∵P[error free transmission after a failure ]= P[1-P]
If after two attempts error free transmission takes place
then P[ error free transmission after two failures]= P [1-P]²
So, For after n failures
P[error free transmission after n failure]=P[tex][1-p]^n[/tex]
the answer to this math question
The drawing shows the friends ended up with 1/2 the pie.
On a fraction line 6 friends want to equally share 3 yards of yarn how much yarn does each friend get
You have a bag of 42 candies you want to give to your 6 friends. the company that makes the candies guarantees that exactly 6 of the candies in the bag are red, the most delicious color. anyone who doesn't get a red candy will be so upset that they will stop being your friend! but the candies are in identical wrappings, so you are forced to give each friend 7 candies and hope for the best. what's the probability you lose one or more friends?
Final answer:
To calculate the probability of losing one or more friends, we need to calculate the probability that a friend does not get a red candy and multiply it by the number of friends. The probability is 0.458.
Explanation:
To answer this question, we need to calculate the probability that at least one friend will not get a red candy.
First, let's calculate the probability that a friend does not get a red candy. There are 42 candies in the bag and 6 of them are red. So, the probability that a friend does not get a red candy is (42-6)/42 = 36/42 = 6/7.
Since each friend gets 7 candies, the probability that one friend does not get a red candy is (6/7)^7, because each candy is independent. Finally, since there are 6 friends, we multiply the probability by 6 to get the probability that at least one friend does not get a red candy: 6 * (6/7)^7 = 0.458 (rounded to 3 decimal places).
A winter sport passed at Wood Middle school costs $15. A stydent without a pass must pay $1.75 for each event. How many events would a student have to attend to pass a better deal?
Answer:
9
Step-by-step explanation:
15 divided by 1.75 equals 9.
And in order to double check, we multiply 9 and 1.75 together which equals 15.75.
Given the area of a triangle is 14x^2 +15x+4 and the base is 4x+2,write the algebraic expression for the height
Solve.
[tex]2\pi \sqrt{ \frac{ \frac{9}{2} }{32} } [/tex]
Evaluate bh for for b = 5 and h = 10. Type a numerical answer in the space provided. If necessary, use the / key to represent a fraction bar. Do not type spaces in your answer.
Answer:
[tex]bh=50[/tex] for b=5 and h=10.
Step-by-step explanation:
Given : The value of b=5 and h=10.
To find : Evaluate bh ?
Solution :
As we have given bh i.e. b and h are multiplied together,
So, [tex]bh=b\times h[/tex]
Substitute, b=5 and h=10
[tex]bh=5\times 10[/tex]
[tex]bh=50[/tex]
Therefore, [tex]bh=50[/tex] for b=5 and h=10.
Find the area of a trapezoid if the altitude is 6 inches and the median is 8 inches. (Hint: Recall that the median of a trapezoid is equal to half the sum of the bases.)
Answer:
48 sq. in.
Step-by-step explanation:
Formula for finding trapezoid area: A = 1/2(h)(b1 + b2)
They said the median of a trapezoid is equal to half the sum of the bases, so multiply the median by 2 to get the sum of the bases.
Sum of the bases = 8(2) = 16
Now plug what you have into the equation to find the area: A = 1/2(6)(16)
Simplify to get: 48
Hope this helps!
What is the value of x in the diagram below?
A 30
B 60
C 90
D 120
could you please explain how you get the answer thank you so much.
What is 235◦, expressed in radian measure?
HURRY!!! PLEASE HELP WITH QUESTIONS!!!! WILL MAKE BRAINIEST ANSWER!!!!
THESE ARE ALL THE ONES I GOT WRONG/W WRONG ANSWER!!!
1.Lauren has gross pay of $765 and federal tax withholdings of $68. Determine Lauren's net pay if she has the additional items withheld: Social Security tax that is 6.2% of her gross pay Medicare tax that is 1.45% of her gross pay State tax that is 22% of her federal tax
A.$691.52
B.$666.21
C.636.98-NOT THE ANSWER
D.$623.52
2.Trevor’s total employment compensation is $33,500. If Trevor has no job expenses and his gross pay is $28,600, then his total employee benefits are _____% of his gross pay.
A.4.9
B.8.5
C.14.6-NOT THE ANSWER
D.17.1
3.Which of the following items may be a good consideration in selecting a bank?
I. The bank sends a representative to the local mall to promote new applications.
II. Number of ATMs or bank branches near where you live, shop, work, or travel.
III. Knowledge of personal usage habits and needs.
A.I and II
B.II and III
C.I and III
D.I, II and III- NOT THE ANSWER
4.When choosing a bank, why might ATM availability be valuable to someone who values convenience over cost?
A.ATM's allow you to conduct bank transactions without going to the bank, so a bank without ATM's will require you to come in to the main office for everything.-NOT THE ANSWER
B.Checks are deposited in ATM's, so some retailers will not accept checks from a bank without ATM service.
C.A greater availability of ATM's may make it easier to do bank transactions. Someone may choose this availability over a higher savings interest rate.
D.ATM cards double as debit cards, so a bank without ATM service cannot issue debit cards.
5.Assume that you are going to open a checking account. You are examining different banks and banking accounts to choose a bank account for your needs. Which of the following statements should not be one of your reasons for examining different banks?
A.Being more informed leads to being better prepared to make financial decisions.-NOT THE ANSWER
B.Bank E offers you a chocolate bar for filling out an application for checking and credit at the same time.
C.Banks could have charges that you do not know about until reading carefully.
D.You will become more aware of how well the banks meet your particular needs.
6. Which of the following is not something that you could do with a normal checking account?
A.Deposit cash into your account.
B.Demand in writing that money be paid to another person from your account.-NOT THE ANSWER
C.Give permission to a merchant to demand money from your account.
D.Make purchases or get cash now, and pay back the bank in monthly payments.
7.A point of sale transaction occurs when an ATM withdrawal is made.
Please select the best answer from the choices provided
T-THIS IS THE CORRECT ANSWER ON E2020
F
8.Elizabeth has $252.00 in her account on Sunday. Over the next week, she makes the following changes to her balance via deposits and purchases:
Day
Debit ($)
Credit ($)
Monday
114.60
150.00
Tuesday
79.68
Wednesday
161.39
Thursday
57.40
Friday
22.85
75.00
Saturday
140.55
On what day does Elizabeth first get charged an overdraft fee?
A.Wednesday
B.Thursday
C.Friday-NOT THE ANSWER
D.Saturday
9.Consider the following incomplete deposit ticket:
What was Art’s total deposit? 1st deposit picture
A.$1,701.23
B.$1,545.83
C.$1,856.63- NOT THE ANSWER
D.$1516.35
10.
1. Given gross salary is = $768
Federal tax withholding = $68
Social security = 6.2% or 0.062*765 = $47.43
Medicare tax = 1.45% or 0.0145*765 = $11.09
State tax = 22% or 0.22*68 = $14.96
Now net salary = gross salary - tax deductions
[tex]765-(68+47.43+11.09+14.96)[/tex] = $623.52 (option D)
2. [tex]\frac{33500-28600}{28600}*100[/tex] = 17.13% (option D)
3. Option B.II and III
4. B.Checks are deposited in ATM's, so some retailers will not accept checks from a bank without ATM service.
5. B.Bank E offers you a chocolate bar for filling out an application for checking and credit at the same time.
6. D.Make purchases or get cash now, and pay back the bank in monthly payments.
7. A point of sale transaction occurs when an ATM withdrawal is made- yes this is right.
8. The answer is Thursday.
9. No picture given.