The drama club is selling tickets to their play to raise money for the show's expenses.
Each student ticket sells for $7 and each adult ticket sells for $10. The auditorium can
hold no more than 85 people. The drama club must make no less than $690 from
ticket sales to cover the show's costs. Also, they must sell a minimum of 10 student
tickets and at least 55 adult tickets. If a represents the number of student tickets sold
and y represents the number of adult tickets sold, write and solve a system of
inequalities graphically and determine one possible solution.
Answers
On solving the inequalities a ≥ 10, y ≥ 55, 7a + 10y ≥ 690, the solution is obtained as (20,55).
What is an inequality?
In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.
Use the variables a and y to represent the number of student and adult tickets sold, respectively.
Then write the following system of inequalities -
a ≥ 10 (they must sell a minimum of 10 student tickets)
y ≥ 55 (they must sell at least 55 adult tickets)
7a + 10y ≥ 690 (they must make no less than $690 from ticket sales)
The first two inequalities are constraints on the number of tickets sold, and the third inequality represents the revenue constraint.
To find a possible solution, graph these inequalities on a coordinate plane and look for the feasible region that satisfies all three inequalities.
Alternatively, solve the system of inequalities using algebra.
First, simplify the third inequality by subtracting 7a from both sides -
10y ≥ 690 - 7a
Then, divide both sides by 10 -
y ≥ (690 - 7a)/10
This inequality represents the revenue constraint in terms of the number of student tickets sold.
Now combine the revenue constraint with the other two constraints -
a ≥ 10
y ≥ 55
y ≥ (690 - 7a)/10
Use substitution to solve for a in terms of y -
y ≥ (690 - 7a)/10
10y ≥ 690 - 7a
7a ≥ 690 - 10y
a ≥ (690 - 10y)/7
To find a possible solution, substitute a = (690 - 10y)/7 into the other two constraints -
(690 - 10y)/7 ≥ 10
y ≥ 55
These inequalities can be simplified -
690 - 10y ≥ 70
y ≥ 55
The first inequality can be solved for y -
-10y ≥ -620
y ≤ 62
Since it is known y ≥ 55, the feasible values for y are between 55 and 62, inclusive -
55 ≤ y ≤ 62
Now use the expression for a in terms of y to find the corresponding values of a -
a = (690 - 10y)/7
For each value of y between 55 and 62, inclusive, we can calculate a and check whether it satisfies the constraints -
a ≥ 10
y ≥ 55
7a + 10y ≥ 690
For example, when y = 55 -
a = (690 - 10(55))/7 = 20
7a + 10y = 7(20) + 10(55) = 690
Therefore, these values satisfy all three constraints, so one possible solution is a = 20 and y = 55.
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Related Questions
Find the arc measure of DEG
Answers
The solution is, radius: 23 inches.
What is arc length?Arc length formula is used to calculate the measure of the distance along the curved line making up the arc (a segment of a circle). In simple words, the distance that runs through the curved line of the circle making up the arc is known as the arc length.
here, we have,
Formula: ∅r = arc length
Here the ∅ is 2 rads and arc length is 46 inches.
using the formula:
2*r = 46
r = 23 inches
The solution is, radius: 23 inches.
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Rs.2250 is deposited for 2 years in an account, it amounts to Rs.2560 compounded annually. What is the annual interest rate?
Answers
The annual interest rate for the given compound interset is 6%
What is interest rate?The interest rate is the amount a lender charges a borrower and is a percentage of the principal—the amount loaned.
Given that, Rs.2250 is deposited for 2 years in an account, it amounts to Rs.2560 compounded annually.
A = P(1+r)ⁿ
2560 = 2250(1+r)²
2560 / 2250 = (1+r)²
1.13 = (1+r)²
Taking roots,
1+r = √1.13
r = 0.06
r = 6%
Hence, the annual interest rate for the given compound interset is 6%
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ay+3y+9=27 solve for y
Answers
Finally, we can solve for y by dividing both sides by (A + 3):
y = 18 / (A + 3)
Therefore, the solution for y is y = 18 / (A + 3).
How do you define an equation?By connecting two expressions with an equal sign, a mathematical statement known as an equation is produced. An equation is something like 3x - 5 = 16. The answer of this equation, which indicates that the value of the variable x is 7, is 7.
To solve for y in the equation Ay + 3y + 9 = 27, we need to isolate y on one side of the equation. We can do this by first combining the like terms on the left-hand side of the equation, and then subtracting 9 from both sides to get:
Ay + 3y = 18
Next, we can factor out the y term on the left-hand side:
y(A + 3) = 18
Finally, we can solve for y by dividing both sides by (A + 3):
y = 18 / (A + 3)
Therefore, the solution for y is y = 18 / (A + 3).
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Evaluate the expression 1/3x^2 for x=6
Answers
The value for the expression 1/3x² for x = 6 is 1/108. The solution has been obtained by using arithmetic operations.
What are arithmetic operations?
The four fundamental operations, often known as "arithmetic operations," are said to allow every real number to be stated, according to mathematicians. Divide, multiply, add, and subtract are the four mathematical operations that result in quotient, product, sum, and difference, respectively.
We are given an expression as 1/3x².
We need to find its value for x = 6.
Substituting this in the expression, we get
⇒1/3(6)²
⇒1/3(36)
⇒1/108
Hence, the value for the expression 1/3x² for x = 6 is 1/108.
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Daniela brought 1/4 of a pound of choclate chip cookies to school and Emily brought 3/7 of a pound of peanut butter cookies.
How many pounds of cookies do we have in total?
Answers
Answer:
19/28
Step-by-step explanation:
1/4 = 7/28
3/7 = 12/28
Then:
1/4 + 3/7 = 7/28 + 12/28 = (7+12)/28
= 19/28
The rim of the volcanic crater shown below is a circle. The diameter is 620 m. What is the circumference of the rim of the crater in kilometres (km)?
Answers
C = πd
where C is the circumference, d is the diameter, and π is a mathematical constant approximately equal to 3.14159.
In this case, the diameter of the crater is given as 620 m, so we can use the formula to find the circumference:
C = πd
C = π(620 m)
C ≈ 1946.95 m
However, the question asks for the circumference in kilometers, so we need to convert the answer to kilometers by dividing by 1000:
C ≈ 1946.95 m ÷ 1000 m/km
C ≈ 1.947 km
Therefore, the circumference of the rim of the crater is approximately 1.947 km.
Please brainliest I spend so much doing it
and give simple working out :)
Answers
Angles on a straight line add up to 180, and since you’re told that angle y is equal to 143, you can do 180-143, giving you 37.
The drama club is selling tickets to their play to raise money for the show's expenses.
Each student ticket sells for $7 and each adult ticket sells for $10. The auditorium can
hold no more than 85 people. The drama club must make no less than $690 from
ticket sales to cover the show's costs. Also, they must sell a minimum of 10 student
tickets and at least 55 adult tickets. If a represents the number of student tickets sold
and y represents the number of adult tickets sold, write and solve a system of
inequalities graphically and determine one possible solution.
Number of Inequalities: 3
Answers
Answer:
Step-by-step explanation:
Let's start by defining our variables:
a = number of student tickets sold
y = number of adult tickets sold
To write the system of inequalities, we need to take into account the given conditions:
The auditorium can hold no more than 85 people, so the total number of tickets sold cannot exceed 85:
a + y ≤ 85
The drama club must make no less than $690 from ticket sales:
7a + 10y ≥ 690
They must sell a minimum of 10 student tickets and at least 55 adult tickets:
a ≥ 10
y ≥ 55
To solve this system of inequalities graphically, we can plot the lines representing each inequality on the same graph and shade the feasible region. The feasible region is the area that satisfies all the inequalities.
First, let's plot the line a + y = 85. To do this, we can find the intercepts:
a + y = 85
a = 0 ⇒ y = 85
y = 0 ⇒ a = 85
Plotting these points and connecting them with a straight line, we get:
|
85| /
| /
| /
| /
| /
|/______
85
Next, let's plot the line 7a + 10y = 690. To do this, we can find the intercepts:
7a + 10y = 690
a = 0 ⇒ y = 69
y = 0 ⇒ a = 99
Plotting these points and connecting them with a straight line, we get:
|
85| /
| /
| /
| /
|/
|______
99
Finally, we need to shade the feasible region. We know that a ≥ 10 and y ≥ 55, so we can shade the region above the line a = 10 and to the right of the line y = 55.
markdown
Copy code
|
85| /\
| / \
| / \
| / \
| / \
/_________\
99 55
This shaded region represents all the possible solutions that satisfy all three inequalities. We can now find one possible solution by picking any point within this region. For example, the point (20, 65) represents selling 20 student tickets and 65 adult tickets, which meets all the conditions and generates a total revenue of 720 + 1065 = $690.
PLEASE ANSWER QUICKLY! 20 POINTS
Answers
0.1728 is the correct answer. This represents the proportion of suburban park users who bike on the trail,
What does propotion mean?Proportion is a mathematical term that describes the relationship between two values. It is used to compare two parts of a whole, two ratios, or two fractions. It is expressed as a ratio, fraction, or percentage.
For example, if a person has 3 apples and 2 oranges, the proportion is 3:2 or 3/2. This means that for every 3 apples, there are 2 oranges.
Proportion can also be used to compare the size of two objects. For example, if one object is twice as long as the other, the proportion is 2:1. Proportion can also be used to compare two fractions, such as 1/4 and 1/2. In this example, the proportion is 1:2, as 1/4 is half of 1/2.
Proportion is also used to compare two percentages, such as 30% and 60%. In this example, the proportion is 3:6, as 30% is half of 60%.
Step 1: Calculate the total number of users on the suburban park trail by adding the numbers in the 'Suburban' column in the table: 125 + 76 + 42 = 243.
Step 2: Calculate the proportion of suburban park users who bike on the park trail by dividing the number of bike users (42) by the total number of users (243): 42/243 = 0.1728.
Step 3: Round the answer to the nearest thousandth: 0.1728 ≈ 0.1730.
Answer: The proportion of suburban park users who bike on the park trail is 0.1730.
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Find the original price of a fitness watch that is $105 after 30% discount
Answers
To find the original price of the fitness watch, we need to work backwards from the discounted price of $105.
Let X be the original price of the fitness watch.
After a 30% discount, the discounted price is:
X - 0.3X = 0.7X
We know that the discounted price is $105, so we can set up the equation:
0.7X = 105
Solving for X, we divide both sides by 0.7:
X = 105 / 0.7
X = 150
Therefore, the original price of the fitness watch was $150.
Need helping solving this problem
Answers
The cost of the burger and the cost of an order of fries to Lynn would be :
Cost of burgher - $3.00Cost of fries - $ 1. 60How to find the cost ?From the problem, we know that Lynn spent $20.00 and purchased 4 hamburgers and 5 orders of fries. Similarly, we know that Ricardo spent $41.20 and purchased 10 hamburgers and 7 orders of fries, which gives us the equations:
4h + 5f = 20
10h + 7f = 41.20
Using substitution, we can express h in form of f to be :
4h + 5f = 20
4 [ ( 3 f + 1. 20 ) / 2] + 5 f = 20
6 f + 2 . 40 + 5 f = 20
11 f = 17. 60
f = $ 1. 60
We can then find the cost of hamburgers using the first equation :
4h + 5f = 20
4h + 5 ( 1. 60 ) = 20
4h + 8 = 20
4h = 12
h = $ 3
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Solve the quadratic equation numerically (using tables of x- and y- values). x(x + 3) = 0 a. x = -1 or x = 3 c. x = 0 or x = -3 b. x = 0 or x = -5 d. x =1 or x = -1 Please select the best answer from the choices provided A B C D
Answers
Explanation:
If A*B = 0, then either A = 0 or B = 0 or both are zero. This is the zero product property.
For this problem we'll have x(x+3) = 0 lead to x = 0 or x+3 = 0
Solve x+3 = 0 to get x = -3
At the craft store, Rudy bought a bag of green and red marbles. The bag contained 60 marbles, and 60% of them green. How many green marbles did Rudy receive?
Answers
Answer:
36 green marbles
Step-by-step explanation:
If 60% of the 60 marbles in the bag are green, then the number of green marbles can be calculated as:
Green marbles = 60% x 60 marbles
To simplify this calculation, we can convert 60% to a decimal by dividing by 100:
Green marbles = 0.60 x 60 marbles
Green marbles = 36 marbles
Therefore, Rudy received 36 green marbles.
Answer: 36
Step-by-step explanation:
60 is 6/10 of 100 so if you are taking a percent of 60 just multiply the percentage by 6/10. 6/10 of 60 is 36
You have a credit card that has a balance of $3589.90 and a credit limit of $5000. How much is the balance over the acceptable debt ratio percentage?
Answers
The balance over the acceptable debt ratio is $1089.90.
What is debt ratio percentage?A debt ratio calculates a company's leverage by comparing its total debt to its total assets.
Although this ratio varies greatly between industries, capital-intensive enterprises typically have significantly larger debt ratios than other types of businesses.
Divide total debt by total assets to find a company's debt ratio.
A debt ratio of less than 100% signifies a corporation has more assets than debt, and a debt ratio of larger than 1.0 or 100% means the opposite.
According to some sources, the debt ratio is calculated by dividing all obligations by all assets.
Given that, credit card balance = $3,589.90
credit limit = $5,000
Debt Ratio percentage = 50% = 0.50
The balance over is given as
balance = Current Balance - (Credit Limit × 0.50 )
balance = 3589.90 - (5000 × 0.5)
balance = 3589.9 - 2500
balance = 1089.9
Hence, the balance over the acceptable debt ratio is $1089.90.
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Carissa the chessplayer is a very, very slow walker. In fact, she walks at 100 meters per hour when walking uphill, 180 meters per hour when walking across flat ground, and 250 meters per hour when walking downhill. One day, Carissa walks across Boston from a café to a boba shop, and then takes the same route in reverse to return to the café. If there are equal parts of uphill, flat ground, and downhill, then what was Carissa's average speed during the entire round trip?
Answers
According to the statement, the Ship must move at an average pace of 150 meters per hour.
Is Downhill unfavorable?The variable under examination is lessened when the gradient is "downhill" (negative). When used as a gauge of how well things are doing, "downhill" denotes a downward trend. Yet, if this indicates trouble or some other unpleasant quality, the situation is improving.
The chess player Carissa walks very, very slowly. She actually moves at speeds of 100 meters per hr upward, 150 meters per hr on flat terrain, and 200 meters every hour on downhill terrain.
Here,
Carissa traverses Boston on foot from a coffeehouse to a boba store before returning over the same path.
Total distance walked = 2 [200 + 100 + 150] = 900 meter
Total time = 2 [1 + 1 + 1] = 6 hour
Average speed is calculated as distance divided by time (900 / 6 = 150 m/s),
As a result, the needed Carissa average speed is 150 meters per hr.
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the median wait time for angioplasty is greater than the median wait time for bypass surgery but the mean wait time is shorter for angioplasty than for bypass surgery. what does this suggest about the distribution of wait times for these two procedures? both means are ---select--- their respective medians, suggesting that both distributions are ---select--- . the fact that the median is greater for angioplasty and the mean is greater for bypass surgery tells us that the median-to-mean increase is ---select--- in the case of bypass surgery, suggesting that the ---select--- is ---select--- pronounced for bypass surgery than for angioplasty.
Answers
Based on the given information, we can make the following conclusions: Both means are shorter than their respective medians. The median-to-mean increase is greater in the case of bypass surgery
What is median?In statistics, the median is a measure of central tendency that represents the middle value of a dataset when the data is arranged in ascending or descending order. It is the value that separates the lower 50% of the data from the upper 50% of the data. To find the median of a dataset, the data is first arranged in order. If the number of data points is odd, the median is the middle value. If the number of data points is even, the median is the average of the two middle values. The median is a useful measure of central tendency because it is less sensitive to outliers than the mean, which makes it a better indicator of the typical or central value of a dataset when the data is skewed or contains extreme values.
Here,
1. Both means are shorter than their respective medians, suggesting that both distributions are skewed to the right. This means that there are some patients who wait for a very long time, causing the right tail of the distribution to be longer.
2. The fact that the median is greater for angioplasty and the mean is greater for bypass surgery tells us that the median-to-mean increase is greater in the case of bypass surgery, suggesting that the skewness is more pronounced for bypass surgery than for angioplasty. This means that there are relatively more patients who wait for a very long time for bypass surgery compared to angioplasty, which is reflected in the longer right tail of the distribution for bypass surgery.
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PLS HELP! Divide.
(x4 +14) = (x + 2)
x[²] + [ ]x² + [ ]x + [ +
x+2
Answers
please see the picture I but the answer on the top and the explanation in the bottom.
The value of a new car is $30,000. The car will lose 12% of its value each year.
Use an exponential function to find the value of the car after 5 years.
Show all work. Round to the nearest whole number.
Answers
The solution is, if depreciation is involved it will NEVER be greater than the amount the car was. $16464
What is an exponent in math?An exponent refers to the number of times a number is multiplied by itself. For example, 2 to the 3rd (written like this: 23) means: 2 x 2 x 2 = 8. 23 is not the same as 2 x 3 = 6. Remember that a number raised to the power of 1 is itself.
here, we have,
30000(1+ -.012/4) ^4*5
Use the compounded continuously formula
A= intial amount
Pe^rt
A=30000e
the small e means euler
r= rate
t= t
A= 30000e ^(-0.12x5)
=$16464
the answer is 16,464
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-95 times a number -14 is equal to -70 one less thing the number
Answers
The equation for the given statement can be written as:
-95x - 14 = -70 - x
To solve for x, we can rearrange the equation and combine like terms:
-95x + x = -70 + 14
-94x = -56
Next, we can divide both sides by -94 to isolate x:
x = -56/-94
Finally, we can simplify the fraction to get our answer:
x = 28/47
Therefore, the solution to the equation is x = 28/47.
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Haddad purchases a new surround system with a store credit card if haddad pays the minimum monthly payment he will have his balance paid off in 58 months if he pays an additional $30 each month he will have his balance paid off in 24 months what percent of time will haddad save by paying the extra $30 per month?
Answers
Answer:
Let M be the minimum monthly payment and A be the additional monthly payment of $30. Let B be the balance on the store credit card.
From the problem, we have:B = M * 58 (if only minimum payments are made)
B = (M + A) * 24 (if an additional $30 is paid each month)
Simplifying these equations, we get:M = B / 58
M + A = B / 24
Substituting the first equation into the second equation, we get: B / 58 + A = B / 24
Solving for A, we get:A = B / 24 - B / 58
A = B * (58/24 - 1/58)
Simplifying, we get:A = B * 0.08275862
To find the percent of time that Haddad will save by paying the extra $30 per month, we need to find the difference in time between the two scenarios and divide by the longer time (58 months).
The time it takes to pay off the balance with only the minimum payments is 58 months, while the time it takes to pay off the balance with the additional $30 each month is 24 months.
The difference in time is:58 - 24 = 34
So Haddad will save 34 / 58 = 0.5862, or 58.62% of the time by paying the extra $30 per month.
How do you solve this
Answers
Answer:
Step-by-step explanation:
1st you solve the triangle by L x W then round it by x 10, hope this helps!
Eve had to purchase 2 bags of chocolate chips for her cookie recipe. She paid $20 and received $5.86 in change. How much was each bag of chocolate chip
This question has 3 parts.
Part A: What does the variable represent in this situation?
Part B Which of the following equations represents how much each bag of chocolate chips costs?
Part C What is the price of each bag of chocolate chips?
Answers
Part A: The variable in this situation represents the unit cost or the unit rate of each bag of chocolate.
Part B: The equation that represents the cost of each bag of chocolate chips is x = (20 - 5.86)/2.
Part C: The price of each bag of chocolate chips that Eve bought for her cookie recipe is $7.07.
What is an equation?An equation is an algebraic statement of the equality or equivalence of two or more mathematical expressions.
Mathematical expressions combine constants, numbers, variables, and values with algebraic operands but without the equation symbol (=) as an equation.
The number of bags of chocolate chips bought = 2 bags
The total amount given to the cashier for the purchase = $20
The balance in change received = $5.86
The cost of the 2 bags of chocolate chips = $14.14 ($20 - $5.86)
The cost of each bag = $7.07 ($14.14)
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A deposit of $500 earns 5 percent the first year, 6 percent the second year, and 7 percent the third year. What would be the third year value
Answers
Answer:
Step-by-step explanation:
To find the third year value of the deposit, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the amount of money after t years, P is the principal (the initial deposit), r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
For the first year, we have:
P = $500
r = 0.05
n = 1 (compounded annually)
t = 1
So, the amount after the first year is:
A1 = $500(1 + 0.05/1)^(1*1) = $525
For the second year, we have:
P = $525 (the amount after the first year)
r = 0.06
n = 1
t = 1
So, the amount after the second year is:
A2 = $525(1 + 0.06/1)^(1*1) = $556.50
For the third year, we have:
P = $556.50 (the amount after the second year)
r = 0.07
n = 1
t = 1
So, the amount after the third year is:
A3 = $556.50(1 + 0.07/1)^(1*1) = $594.64
Therefore, the third year value of the deposit is $594.64.
Help me!!!!!!!!!!!!!!!!!!
Answers
Answer:
x = 10
Step-by-step explanation:
We know that it's a right triangle and it's two sides, which are 6 and 8
So we can find the third side, the Hypotenuse or x, using the Pythagoras Theorem
6² + 8² = Hypotenuse ²
36 + 64 = Hypotenuse²
100 = Hypotenuse²
Hypotenuse = root100
Hypotenuse = 10
Therefore x = 10
Solve for x
2/5(2)^x = 32/5
Answers
Rearrange = 2^ 1+x /5 =32/5
Multiply = 5 x 2^x+1/5 = 5 x 32/5
Cancel multiplied terms in denominator= 2^ x+1=32
X +1=5
Subtract 1 from both sides
X+1-1= 5-1
New term= x=5-1=4
X=4
Determine the limit using what you know about special limits:
Answers
The limits represented by [tex]\lim _{x\to 0}\left(\frac{\sin\left(x\right)}{13x}\right)[/tex] has its value to be 1/13
How to determine the limitsFrom the question, we have the following parameters that can be used in our computation:
[tex]\lim _{x\to 0}\left(\frac{\sin\left(x\right)}{13x}\right)[/tex]
To determine the limits, we make use of the L'Hôpital's rule
Using the above as a guide, we have the following:
[tex]\lim _{x\to 0}\left(\frac{\sin\left(x\right)}{13x}\right) = \lim _{x\to 0}\left(\frac{\cos\left(x\right)}{13}\right)[/tex]
Substitute the known values in the above equation, so, we have the following representation
[tex]\lim _{x\to 0}\left(\frac{\sin\left(x\right)}{13x}\right) = \frac{\cos\left(0\right)}{13}\right)[/tex]
This gives
[tex]\lim _{x\to 0}\left(\frac{\sin\left(x\right)}{13x}\right) = \frac{1}{13}\right)[/tex]
Hence, the value is 1/13
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Graph the system of inequalities. Then use your graph to identify the point that represents a solution to the system. x – y ≥ 7 x + 2y < 5
Answers
Answer: To graph this system of inequalities, we can first graph each inequality separately and then find the region where they overlap.
Starting with the first inequality, x - y ≥ 7, we can rearrange it to y ≤ x - 7 and graph the line y = x - 7. Since the inequality includes the line, we will use a solid line to represent it, and shade below the line to show the region where y is less than or equal to x - 7.
Next, for the second inequality, x + 2y < 5, we can rearrange it to y < (-1/2)x + 5/2 and graph the line y = (-1/2)x + 5/2. Since the inequality excludes the line, we will use a dashed line to represent it, and shade below the line to show the region where y is less than (-1/2)x + 5/2.
Now we can combine the two shaded regions to find the overlapping region where both inequalities are satisfied. This region is shown in the graph below:
| /
| /
| /
| /
| /
|/
---------------
The point that represents a solution to the system is the point where the two lines intersect. To find this point, we can solve the system of equations:
y = x - 7
y = (-1/2)x + 5/2
Substituting the first equation into the second, we get:
x - 7 = (-1/2)x + 5/2
Simplifying this equation, we get:
(3/2)x = 19/2
x = 19/3
Substituting this value of x into either of the original equations, we get:
y = 19/3 - 7 = 2/3
So the point that represents a solution to the system is (19/3, 2/3).
Step-by-step explanation:
I’m confused what’s the answer
Answers
Answer:
No real solutions
Step-by-step explanation:
If lines are parallel, it means that they will never meet each other indicating that there are no real solutions.
In the walkathon, Jose asks his sponsors to donate $10 for the first 5 kilometers he walks and $1 per kilometer after 5 kilometers
Sketch a graph that represents the relationship between the money collected from each sponsor and the number of kilometers walked.
Answers
The resulting graph should have a vertical intercept at (0, 0), a flat portion from (0, 0) to (5, 10), and a linearly increasing portion from (5, 10) to (10, 15). The slope of the second line should be $1 per kilometer.
Describe Graph?In mathematics, a graph is a visual representation of a set of data or a mathematical function. It consists of a collection of points, called vertices, and the lines or curves, called edges, that connect them. A graph can be used to show relationships between sets of data, to model real-world situations, and to represent mathematical functions.
There are many types of graphs, including bar graphs, line graphs, pie charts, scatter plots, and more. Each type of graph is used to represent different types of data or to show different relationships between the data.
Bar graphs are used to show the frequency or quantity of discrete data items, such as the number of people who prefer a certain type of food. Line graphs are used to show the relationship between two sets of data, such as the relationship between temperature and time. Pie charts are used to show the relative proportions of different parts of a whole, such as the percentage of a budget that is allocated to different expenses. Scatter plots are used to show the relationship between two sets of numerical data, such as the relationship between height and weight.
Graphs are an important tool in mathematics and many other fields, including economics, engineering, physics, and computer science. They allow us to visualize and analyze complex sets of data and to make predictions about future trends or patterns.
We can sketch a piecewise linear graph to represent the relationship between the money collected from each sponsor and the number of kilometers walked:
For the first 5 kilometers, the sponsor donates a flat rate of $10.
After the first 5 kilometers, the sponsor donates $1 per kilometer.
To sketch this graph, we can plot two points:
(0, 0): This represents the starting point of the walkathon, where no money has been collected yet.
(5, 10): This represents the end of the first 5 kilometers, where the sponsor has donated a flat rate of $10.
Then, we can draw a line connecting these two points to represent the flat rate portion of the donation.
Next, we can plot a third point:
(10, 15): This represents the end of the next 5 kilometers (from 5 to 10 kilometers), where the sponsor has donated an additional $5 ($1 per kilometer).
Finally, we can draw a second line connecting (5, 10) to (10, 15) to represent the $1 per kilometer portion of the donation.
The resulting graph should have a vertical intercept at (0, 0), a flat portion from (0, 0) to (5, 10), and a linearly increasing portion from (5, 10) to (10, 15). The slope of the second line should be $1 per kilometer.
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What is the equation of the midline for the function f(x)? f(x)=12sin(x)+6 enter your answer in the box.
Answers
The equation of the midline for the function f(x) = 12sin(x) + 6 is y = 12. The midline of a periodic function is a horizontal line that represents the average value of the function over one period.
For a sinusoidal function, the midline is the line that passes through the center of the graph, or the average of the maximum and minimum values of the function.
To find the midline equation for the function f(x) = 12sin(x) + 6, we first need to find the maximum and minimum values of the function. The amplitude of a sinusoidal function is half the difference between its maximum and minimum values. In this case, the amplitude is 12, so the maximum value is 12+6=18, and the minimum value is 6-12=-6.
The midline of the function is the line halfway between the maximum and minimum values, or at a height of (18 - 6)/2 + 6 = 12. Therefore, the equation of the midline is y = 12. This means that the function oscillates above and below this line by a maximum of 12 units.
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