By solving the given equation, we can plot these two points on a coordinate plane, and then connect the points with a line. The formed line is the graph of the linear equation 3y=2x-7.
What is a coordinate plane?The coordinate plane is made up of two perpendicular lines called the x-axis and the y-axis. The x-axis, which is horizontal, is used to measure the distance of a point from the left and right side of the plane. The y-axis, which is vertical, is used to measure the distance of a point from the top and bottom of the plane.
To graph the equation 3y=2x-7, we first need to identify two points that satisfy the equation. We can do this by plugging in different values for x and solving for y. For example, when x=0, the equation becomes 3y=-7. Thus, one point that satisfies the equation is (0,-7). We can find a second point by plugging in a different value for x. For example, when x=2, the equation becomes 3y=-3. Thus, the second point that satisfies the equation is (2,-3).
Now, we can plot these two points on a coordinate plane, and then connect the points with a line. The formed line is the graph of the linear equation 3y=2x-7.
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What are the coordinates of point D (3/4,3)
after it is reflected across the x-axis?
When a point is reflected across the x-axis, its y-coordinate changes sign while its x-coordinate remains the same.
Therefore, to find the coordinates of the reflected point D, we simply change the sign of the y-coordinate of point D.
Given that the coordinates of point D are (3/4,3), its reflected point D' across the x-axis will have the coordinates (3/4, -3).
Therefore, the reflected point D' is located at the point (3/4, -3).
Coordinates are pairs of numbers used to identify the position of a point in a two-dimensional plane. In a Cartesian coordinate system, the two numbers represent the x-coordinate (the horizontal position) and the y-coordinate (the vertical position) of the point.
For example, the point (3, 5) has an x-coordinate of 3 and a y-coordinate of 5. This means that the point is located 3 units to the right of the origin (the point where the x- and y-axes intersect) and 5 units above the x-axis. Similarly, the point (-2, -1) has an x-coordinate of -2 and a y-coordinate of -1, which means that it is located 2 units to the left of the origin and 1 unit below the x-axis.
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What is 2625/21 please iv been stuck on this for 3 hours bro
Find the cube root of each number or expression. 7. 40 8. 162
10. x^(8)
11. -16a^(5)b
a)2
b)4
c)6
d)x2
e)-2a2b
For questions 7, 8, and 10:
The cube root of 7 is 2, the cube root of 40 is 4, and the cube root of 162 is 6. The cube root of an expression with an exponent can be found by dividing the exponent by 3; for example, the cube root of x8 is x2.
For question 11:
The cube root of -16a5b is -2a2b.
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Please somebody help me it’s due today
The value of the segments DB = 23.32 in, RK = 18.22 in and YK = 6.83 in.
What is Pythagoras Theorem?The Pythagorean Theorem states that the square on the hypotenuse of a right triangle is equal to the sum of the squares on the triangle's legs.
The connection between the four edges of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem.
For the given figure we see the right triangle DHB.
Here, DH = 20 in and HB = 12 in.
Using the Pythagoras theorem we have:
DB² = DH² + HB²
DB² = 20² + 12²
DB² = 400 + 144
DB = 23.32
For the right triangle RHK we have:
HR = 16 and HK = 8.72
Using the Pythagoras theorem:
RK² = 16² + 8.72²
RK= 18.22
Also, KY = YK = 6.83 in.
Hence, the value of the segments DB = 23.32 in, RK = 18.22 in and YK = 6.83 in.
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A cereal company fills boxes with 16 ounces of cereal. The acceptable percent error in filling a box is 2.5%. Find the least and the greatest acceptable weights.
The least acceptable weight is
ounces.
The greatest acceptable weight is
ounces.
Answer:
Least acceptable weight= 15.6 ounces
and Greatest acceptable weight=16.4 ounces
Step-by-step explanation:
A cereal company fills boxes with 16 ounces of cereal.
The acceptable percent error in filling a box is 2.5%.
i.e. the error in decimal is: 2.5/100 x 16 = 25/1000 x 16 = 0.4
Hence,
the least acceptable weight is obtained by subtracting the actual amount with the error.
16-0.4=15.6 ounces.
and the greatest acceptable weight is obtained by adding the error to the actual weight.
16+0.4=16.4 ounces
Hence,
Least acceptable weight= 15.6 ounces
and Greatest acceptable weight=16.4 ounces.
Use the function h(x)=−2x+8 to answer the
following questions
Evaluate h(−9):
h(−9)= ____
For what values(s) of x does h(x)=−10?
x= ___
The value of h(-9)= 26 using the function h(x)=−2x+8
And, the value of x for which h(x) = -10 is x = 9.
To evaluate h(-9), we simply plug in -9 for x in the function h(x) = -2x + 8:
h(-9) = -2(-9) + 8
h(-9) = 18 + 8
h(-9) = 26
So the value of h(-9) is 26.
To find the value(s) of x for which h(x) = -10, we can set the function equal to -10 and solve for x:
-2x + 8 = -10
-2x = -18
x = 9
So the value of x for which h(x) = -10 is x = 9.
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sider the given function n(x)=x^(2)+10x+24 Write the function in vertex form. Identify the vertex. Determine the x-intercept (s). Determine the y-intercept (s).
The given function, n(x)=x^(2)+10x+24, can be written in vertex form by completing the square. Vertex form is given by y=a(x-h)^2+k.
The vertex is at (h,k). To find h and k, first find the average of the x-values of the two roots:
h = ( -b +- sqrt(b^2 - 4ac) ) / 2a
= ( -10 +- sqrt( 10^2 - 4(1)(24) ) ) / 2(1)
= ( -10 +- sqrt(100 - 96) ) / 2
= ( -10 +- sqrt(4) ) / 2
= ( -10 +- 2 ) / 2
= -6
Substituting h into the equation y=a(x-h)^2+k, we have:
k = y - a(x-h)^2
= n(x) - a(x+6)^2
= x^2 + 10x + 24 - a(x+6)^2
= 24 - a(x+6)^2
We know that when x=-6, k=24, so
24 = a( -6+6 )^2
24 = 36a
a = 2/3
Therefore, the equation in vertex form is y = 2/3(x+6)^2 + 24.
The vertex is (h,k) = (-6, 24).
The x-intercepts (s) are the roots of the equation, so they can be found by setting the equation equal to 0 and solving for x.
0 = x^2 + 10x + 24
0 = (x+6)(x+4)
Therefore, the x-intercepts are x=-6 and x=-4.
The y-intercept is when x=0, so it is y = 24.
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HELP ASAP
Find the value of y
Answer:
y = 129°
Step-by-step explanation:
the figure has opposite sides congruent and is therefore a parallelogram.
• consecutive angles are supplementary , that is
y + 51° = 180° ( subtract 51° from both sides )
y = 129°
Watch help video If using the method of completing the square to solve the quadratic equation x^(2)-19x+35=0, which number would have to be added to "complete the square"?
The number that would have to be added to "complete the square" is 90.25.
To complete the square for the quadratic equation x^(2)-19x+35=0, we would need to add the number 90.25 to both sides of the equation.
Step-by-step explanation:
1. Start with the given equation: x^(2)-19x+35=0
2. Move the constant term to the right side of the equation: x^(2)-19x=-35
3. Take half of the coefficient of the x term, square it, and add it to both sides of the equation: x^(2)-19x+(19/2)^(2)=-35+(19/2)^(2)
4. Simplify the right side of the equation: x^(2)-19x+90.25=-35+90.25
5. Combine like terms on the right side of the equation: x^(2)-19x+90.25=55.25
6. Write the left side of the equation as a perfect square: (x-9.5)^(2)=55.25
7. Take the square root of both sides of the equation: x-9.5=±√55.25
8. Solve for x: x=9.5±√55.25
Therefore, the number that would have to be added to "complete the square" is 90.25.
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Martina can run 3 miles without stopping. Last year she could run 3,640 yards witho stopping. How many more feet can Martina
Martina can run 4,920 more feet this year compared to last year.
Martina can run 3 miles without stopping. Last year she could run 3,640 yards without stopping. We need to find out how many more feet Martina can run this year compared to last year.
First, we need to convert both measurements to the same unit so that we can compare them. We will convert both measurements to feet.
1 mile = 5,280 feet
1 yard = 3 feet
So, 3 miles = 3 x 5,280 feet = 15,840 feet
And, 3,640 yards = 3,640 x 3 feet = 10,920 feet
Now, we can subtract the number of feet Martina could run last year from the number of feet she can run this year to find out how many more feet she can run this year.
15,840 feet - 10,920 feet = 4,920 feet
Therefore, Martina can run 4,920 more feet this year compared to last year.
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a. (12 points) Given the following matrix \( A \), compute \( A^{-1} \) using the row reduction method covered in class and discussion. (You may have already seen other methods for computing inverses
So, the inverse of \(A\) is:
\[A^{-1} = \left[\begin{array}{ccc}
a^{-1}_{11} & a^{-1}_{12} & a^{-1}_{13} \\
a^{-1}_{21} & a^{-1}_{22} & a^{-1}_{23} \\
a^{-1}_{31} & a^{-1}_{32} & a^{-1}_{33} \\
\end{array}\right]\]
This is how we can compute the inverse of a matrix using the row reduction method.
To compute \(A^{-1}\) using the row reduction method, we need to first set up an augmented matrix with \(A\) on the left and the identity matrix on the right. Then, we will use elementary row operations to reduce the left side of the matrix to the identity matrix, which will result in the inverse of \(A\) on the right side. Here are the steps:
1. Set up the augmented matrix:
\[\left[\begin{array}{ccc|ccc}
a_{11} & a_{12} & a_{13} & 1 & 0 & 0 \\
a_{21} & a_{22} & a_{23} & 0 & 1 & 0 \\
a_{31} & a_{32} & a_{33} & 0 & 0 & 1 \\
\end{array}\right]\]
2. Use elementary row operations to reduce the left side of the matrix to the identity matrix. For example, we can use the following operations:
- Multiply the first row by a constant to make the first element 1
- Subtract a multiple of the first row from the second and third rows to make the first element of those rows 0
- Repeat these steps for the second and third columns until the left side of the matrix is the identity matrix
3. Once the left side of the matrix is the identity matrix, the right side of the matrix will be the inverse of \(A\):
\[\left[\begin{array}{ccc|ccc}
1 & 0 & 0 & a^{-1}_{11} & a^{-1}_{12} & a^{-1}_{13} \\
0 & 1 & 0 & a^{-1}_{21} & a^{-1}_{22} & a^{-1}_{23} \\
0 & 0 & 1 & a^{-1}_{31} & a^{-1}_{32} & a^{-1}_{33} \\
\end{array}\right]\]
So, the inverse of \(A\) is:
\[A^{-1} = \left[\begin{array}{ccc}
a^{-1}_{11} & a^{-1}_{12} & a^{-1}_{13} \\
a^{-1}_{21} & a^{-1}_{22} & a^{-1}_{23} \\
a^{-1}_{31} & a^{-1}_{32} & a^{-1}_{33} \\
\end{array}\right]\]
This is how we can compute the inverse of a matrix using the row reduction method.
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number pattern
please help!!!
Answer:
it appears to be going up by adding odd numbers
Step-by-step explanation:
2+3=5+5=10+7=17+9=26 ect....
9. Bonnie says that the name of pyramid with 6 vertices is a hexagonal pyramid. How do you respond?
I would respond that Bonnie is correct. A pyramid with 6 vertices, or corners, would have a hexagonal base, which means it would be a pyramid with a base that is a hexagon. Therefore, the correct name for this type of pyramid is a hexagonal pyramid.
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Half Challenge! Taxpayer Name: Bob Tax Bracket Information: Money earned between $0 and $200, 10% tax Money earned between $200 and $500, 20% tax Money earned after $500, 40% tax Finances:
Income: $750 Adjusted Income:
Expenses: $100 Adjusted Expenses: Deductible: $150
Return:
Bob Returned $120 Did Bob commit Tax Fraud? YES NO Bob's Net Income:
Bob did not commit tax fraud based on the given information.
To calculate Bob's net income, we need to start with his adjusted income, which is his income minus his expenses and deductible:
Adjusted Income = Income - Expenses - Deductible
Adjusted Income = $750 - $100 - $150
Adjusted Income = $500
Next, we need to determine the amount of tax that Bob owes based on his tax bracket information:
Tax Owed on first $200 = $200 * 0.10 = $20
Tax Owed on next $300 ($200 to $500) = $300 * 0.20 = $60
Tax Owed on remaining $0 ($500 and above) = $0 * 0.40 = $0
Total Tax Owed = $20 + $60 + $0 = $80
Now, we can calculate Bob's net income by subtracting his tax owed from his adjusted income:
Net Income = Adjusted Income - Tax Owed
Net Income = $500 - $80
Net Income = $420
Finally, we can compare Bob's returned amount to his tax owed to see if he committed tax fraud:
Returned Amount - Tax Owed = $120 - $80 = $40
Since Bob's returned amount is less than his tax owed, he did not commit tax fraud. His net income after taxes is $420.
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Please help me! I’ve been sick and out of school so I don’t understand.. thanks! :)
Answer:
Step-by-step explanation: So first, you're gonna distribute the 4/5 to the b and the -5, by doing that u will get 3.2=4/5b - 4. Then you're gonna cancel out the -4 by adding it on both sides - 3.2+4=4/5b, you get 7.2=4/5b. Multiply by the reciprocal of 4/5 which is 5/4 on both sides. 7.2 x 5/4 = b. you get 9 = b
oey's friend asked him what his math test score was. Joey said, "I did better than 5 points more than the class average." The class average was 88.
Which of the following number sentences represents J, Joey's math test score?
A. 88 + 5 < J
B. 88 + J < 5
C. 88 - 5 > J
D. 88 + 5 > J
Answer: The class average is 88, and Joey did better than 5 points more than the class average. Therefore, Joey's math test score is greater than 88 + 5 = 93.
So, the number sentence that represents Joey's math test score is:
D. 88 + 5 > J
Step-by-step explanation:
i need y'all help on dis
Answer:
Customer A - 5 / 22.45 = $0.22 or 22 cents per quart
Customer B - 7 / 25.45 = $0.27 or 27 cents per quart
The function f(x) will model the roller coaster’s height from the ground in feet over time, measured in seconds since the ride started.
Answer:
50
Step-by-step explanation:
good
Can you solve the inequality 2 ( x − 3 ) ≤ 10 2(x−3)≤10 without using the Distributive Property? Explain.
Answer:
X is Greater than or equal to 31/10
Simplify and find the undefined numbers
The undefined numbers are p = 0, p = 2, q = 0, and q = -2 for the given expression.
What is simplification?In arithmetic, the operation and interpretation of a function to make it simpler or easier to grasp is known as simplifying, and the process itself is known as simplification.
First, let's simplify the expression:
(4p - 8)/(p³ - 2p²) - (q + 2)/(q³ + 2q²) × (p/2q - p)
= 4(p - 2)/(p²(p - 2)) - (q + 2)/(q²(q + 2)) × p(1/2 - q)
= 4/p - 4/p² - p/2q² + p²/2q
= (8q² - 8pq - p³ + 2p²q)/(2pq²(p - 2))
Now, let's find the undefined numbers, which are the values of p and q that make the denominators equal to zero.
For the first fraction, p³ - 2p² = p²(p - 2) = 0 when p = 0 or p = 2.
For the second fraction, q³ + 2q² = q²(q + 2) = 0 when q = 0 or q = -2.
Therefore, the undefined numbers are p = 0, p = 2, q = 0, and q = -2.
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A company makes wax candles in the shape of a rectangular prism. Each candle is 5 inches long, 4 inches wide, and 7 inches tall. How much wax will they need to make 420 candles?
The company will need 58,800 cubic inches of wax to make 420 candles.
How much wax will they need to make 420 candles?To calculate the amount of wax required to make 420 candles,
We need to first calculate the volume of wax required to make one candle,Then multiply that by the total number of candles to find the total amount of wax required.The volume of a rectangular prism is given by the formula V = l x w x h, where l is the length, w is the width, and h is the height.
So, we have
V = 5 in x 4 in x 7 in = 140 cubic inches
To find the total amount of wax required to make 420 candles,
We have
Total amount of wax = 140 cubic inches/candle x 420 candles
= 58,800 cubic inches
Hence, the company needs 58,800 cubic inches
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If triangles QRS and LMN are congruent, then which two segments MUST be congruent?
All congruent segments are QR ≅ LM, RS ≅ MN and QS ≅ LN
What are congruent triangles?The triangles are said to be congruent if their corresponding sides and angles are congruent to each other.
Given are two congruent triangles QRS and LMN, we need to deduce the corresponding congruent parts,
So, according to the definition of congruent triangles :-
Sides :-
QR ≅ LM, RS ≅ MN and QS ≅ LN
Angles :-
∠ Q ≅ ∠ L, ∠ R ≅ ∠ M and ∠ S ≅ ∠ N
Hence, the congruent segments are QR ≅ LM, RS ≅ MN and QS ≅ LN
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A valid inference is one that is true about the ____ based on a ____
A valid inference is a conclusion that is true about the subject based on the evidence or premises provided.
Mathematically, we can represent a valid inference using logical notation. In the example above, we can use the following notation:
Premise 1: All humans are mortal.
Premise 2: Samantha is a human.
Conclusion: Samantha is mortal.
We can use the logical connective "if-then" to represent a valid inference. In this case, we can say, "If all humans are mortal, and Samantha is a human, then Samantha is mortal." This statement is true based on the premises provided.
To determine the validity of an inference mathematically, we can use rules of logic such as the law of detachment or the law of syllogism. The law of detachment states that if we have a conditional statement, "If p, then q," and we know that p is true, then we can validly infer that q is also true.
The law of syllogism is another rule of logic that helps us determine the validity of an inference. This rule states that if we have two conditional statements, "If p, then q," and "If q, then r," we can infer that "If p, then r" is true.
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x^{4}-\frac{1}{3} x^{3}+ 2\sqrt{x} -5
Answer: X^4 - (1/3)X^3 + 2\sqrt{X} - 5 = 0
Step-by-step explanation:
The answer is:
X^4 - (1/3)X^3 + 2\sqrt{X} - 5 = 0
This is a quartic equation, meaning it has four terms with the highest degree of X being 4. It cannot be solved in terms of radicals, so an approximate solution must be used. This can be done through numerical methods, such as the Newton-Raphson method, which uses an iterative process to approximate a solution.
Convert 0.2 to a percent
Answer:
20%
Step-by-step explanation:
Formula - multiply decimal by 100
0.2- Word form= two tenths
Fraction * 2/10 *
0.2 (multiply by 100)
0.2 x 100 = 20
20% is 0.2 as a percent
( hope this helps I’m online so ask any questions you need)
Unit 2: Chapter 7b HW Score: 719 3/4 answered Save Question 3 Based on historical data, your manager believes that 37% of the company's orders come from first-time customers. A random sample of 245 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is between 0.26 and 0.44? (Enter your answer as a number accurate to 4 decimal places.) Question Help: Message instructor
The probability that the sample proportion is between 0.26 and 0.44 is 0.9998, or 99.98%.
The probability that the sample proportion is between 0.26 and 0.44 can be found using the normal distribution formula.
First, we need to find the mean and standard deviation of the sample proportion. The mean of the sample proportion is equal to the population proportion, which is 0.37. The standard deviation of the sample proportion can be found using the formula:
σ = √(p(1-p)/n)
Where p is the population proportion, and n is the sample size. Plugging in the given values, we get:
σ = √(0.37(1-0.37)/245) = 0.0196
Next, we need to find the z-scores for the given sample proportions. The z-score can be found using the formula:
z = (x - μ)/σ
Where x is the sample proportion, μ is the mean of the sample proportion, and σ is the standard deviation of the sample proportion. Plugging in the values for the lower bound of the sample proportion (0.26), we get:
z = (0.26 - 0.37)/0.0196 = -5.61
Similarly, for the upper bound of the sample proportion (0.44), we get:
z = (0.44 - 0.37)/0.0196 = 3.57
Now, we can use the standard normal table to find the probabilities corresponding to these z-scores. The probability for z = -5.61 is 0, and the probability for z = 3.57 is 0.9998.
Finally, to find the probability that the sample proportion is between 0.26 and 0.44, we subtract the lower probability from the upper probability:
P(0.26 < p < 0.44) = 0.9998 - 0 = 0.9998
Therefore, the probability that the sample proportion is between 0.26 and 0.44 is 0.9998, or 99.98%.
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A survey asked 1,200 students which movie genre was their favorite. The results of the survey are shown in the circle graph.
Favorite Movie Genre
Science Fiction
10%
Comedy
20%
Drama
15%
Action
45%
Romance
10%
How many total students chose romance and science fiction movies?
Total students=1,200
Total number of students whose favorite movie genre is Romance= 10%
So,
10% of total students= 10% of 1,200
Therefore, the Total students who chose romance= 10/100*1200=120
Similarly, 10% of students chose Science fiction, and the total number of students who chose science fiction=10/100*1200=120
Therefore,
Total students who chose romance=120
Total students who chose science fiction=120
Do segments with lengths 11, 12, and 20 form a triangle? If so, classify the triangle as acute, right, or obtuse?
Answer:
Yes, the segments with lengths 11, 12, and 20 can form a triangle.
To check this, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, we can check that:
11 + 12 > 20
11 + 20 > 12
12 + 20 > 11
Since all three inequalities are satisfied, the segments can form a triangle.
To classify the triangle, we can use the law of cosines, which relates the lengths of the sides of a triangle to the cosine of one of its angles. Specifically, for a triangle with sides a, b, and c and angle A opposite side a, we have:
c^2 = a^2 + b^2 - 2ab cos(A)
Using this formula, we can find the cosine of each angle and determine if the triangle is acute, right, or obtuse based on the values obtained.
For the given triangle, we have:
a = 11, b = 12, c = 20
cos(A) = (b^2 + c^2 - a^2) / (2bc) = (12^2 + 20^2 - 11^2) / (2 * 12 * 20) ≈ 0.714
Since cos(A) is positive and less than 1, the angle A is acute. Similarly, we can find the cosines of the other angles:
cos(B) = (c^2 + a^2 - b^2) / (2ca) ≈ 0.943
cos(C) = (a^2 + b^2 - c^2) / (2ab) ≈ -0.519
Since cos(B) and cos(C) are both positive and less than 1, angles B and C are also acute.
Therefore, the given triangle is acute.
Suppose you have a job that pays $13.50 per hour and you work anywhere from 10 to 40 hours per week. a. Write an equation, with a restriction on the variable I, that gives the amount of money, y, you will earn for working 2 hours in one week. y = _____ , Preview with ____ <= x <= ____ b. Use the function rule you have written in part a. to find the y values for the given z values: x = 10, y = ___ x = 20, y= ___
x = 30, y = ____. x = 40, y = ____ c. Construct a line graph from the information found in b. 520+ -480+ 440+ 400- 360 320- 280- 240 200 160+ 120+ 80- 40+ 10 20 30 40 Clear All Draw: Line Dot Open Dot d. State the domain and range of this function. Domain: ____ <= x <= ______
Range: <= y <= _____
e. What is the minimum amount you can earn in a week with this job? You'll earn at least $ ______.
What is the maximum amount? You can earn up to $ ____.
The maximum amount you can earn is $540
a. y = 13.50x , 10 <= x <= 40
b. x = 10, y = 135; x = 20, y= 270; x = 30, y = 405; x = 40, y = 540
c. Domain: 10 <= x <= 40; Range: 0 <= y <= 540
d. The minimum amount you can earn in a week with this job is $135. The maximum amount you can earn is $540.
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HELLOOOO PLEASE HELP ME 15 POINTS!!!!!
Answer: C
Step-by-step explanation: Just replace x=1,2,3,4 to see which answers satisfy the given conditions
