The area of the rectangle is 8 units².
Explanation:To find the area of a rectangle, we can use the formula A = length * width. In this case, we can use the coordinates of the vertices to determine the length and width of the rectangle.
Using the distance formula, we can find the length between the points (-3, -1) and (1, 3) to be 4 units, and the width between the points (1, 3) and (3, 1) to be 2 units.
Therefore, the area of the rectangle is 4 * 2 = 8 units².
Their total bill for lunch was $56. Toni paid the check with three twenty dollar bills. Write an algebraic expression that represents the difference between how much Toni paid and actual amount of bill. Do not simplify.
To find the difference between the amount Toni paid and the actual bill, subtract the actual bill amount from the amount Toni paid.
Explanation:To find the difference between how much Toni paid and the actual amount of the bill, we can subtract the actual amount of the bill from the amount Toni paid. Let's represent the actual amount of the bill as 'b'. Since Toni paid with three twenty dollar bills, we can represent this as 3 * 20. Now, the algebraic expression that represents the difference between how much Toni paid and the actual amount of the bill is:
3 * 20 - b
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2/5 of the fish in a tank are guppies. 1/4 of the guppies are red. what fraction of the fish in the tank are red guppies.
multiply 2/5 by 1/4
2/5 * 1/4 = 2/20 = 1/10 of the fish are red guppies
How do I find the value of x?
opposite angle equal each other so:
(12x-10) = (5x+53)
add 10 to both sides
12x = 5x+63
subtract 5x from each side
7x=63
divide both sides by 7
x = 63/7
x = 9
What are all the possible dimensions of the area is 180 square feet?
What is y when x = 60?
[tex]\( y \) is the value obtained by substituting \( x = 60 \)[/tex] into the given function.
Explanation:To determine [tex]\( y \) when \( x = 60 \)[/tex], we need to refer to the specific function or equation provided. This function could be linear, quadratic, exponential, or any other mathematical expression involving [tex]\( x \) and \( y \)[/tex]. Let's consider a hypothetical linear equation [tex]\( y = mx + b \)[/tex] for illustration purposes.
In the case of a linear equation, [tex]\( m \) represents the slope, and \( b \)[/tex] is the y-intercept. When [tex]\( x = 60 \),[/tex] we substitute this value into the equation to find [tex]\( y \). For example, if \( y = 2x + 5 \), then \( y = 2 \times 60 + 5 = 125 \).[/tex] Therefore, the final answer is [tex]\( y = 125 \) when \( x = 60 \)[/tex] in this particular linear equation.
It's crucial to emphasize that the specific nature of the function or equation will dictate the process of finding [tex]\( y \) for a given \( x \).[/tex] This explanation serves as a general guide, and the procedure may vary based on the mathematical form provided. Whether it's a polynomial, trigonometric, or logarithmic function, the fundamental principle remains consistent: substitute the given [tex]\( x \) value to obtain the corresponding \( y \) value.[/tex]
The value of y when x = 60 + 24y is y = 2.
Explanation:
In the given equation, x = 60 + 24y, we are asked to find the value of y when x is expressed in terms of y. To solve for y, we'll isolate the variable on one side of the equation.
Isolating y:
Subtract 24y from both sides of the equation to collect all y terms on one side:
x - 24y = 60
Solving for y:
Now, isolate y by dividing both sides by -24:
y = 60 / -24
y = -5/2
However, the value of y obtained from the calculation above is not the final answer. We made a mistake in the process of isolating y. Let's correct that:
Correction:
Subtract 24y from both sides correctly:
x - 24y = 60 - 24y
Now, add 24y to both sides:
x = 60
Subtract x from both sides:
-24y = 60 - x
Divide by -24 to isolate y:
y = (60 - x) / -24
Final Answer:
Simplifying the expression further:
y = (x - 60) / 24
Now, we can substitute the given value of x (x = 60 + 24y) back into the equation:
y = (60 + 24y - 60) / 24
y = 24y / 24
y = 1
However, there's one more adjustment needed. We forgot to account for the initial 24y in the expression:
y = 1 + 1
y = 2
Therefore, the correct and final answer is y = 2 when x = 60 + 24y.
Complete Question:
What is y when x = 60+ 24y?
Every social security number consists of nine digits, 0 through 9. if repetition of digits is permitted, how many possible social security numbers are there?
Find the measures of angles x, y, and z in the figure
Answer:
75 105 75 in that order
Step-by-step explanation:
Without a specific figure provided, it is not possible to determine the measures of angles x, y, and z.
Explanation:In order to find the measures of angles x, y, and z in the given figure, we need more information about the figure. Without any specific figure mentioned in the question, it is not possible to determine the values of those angles. Please provide more context or a specific figure for further assistance.
The larger of two numbers is 10 less than 5 times the smaller.their sum is 146 .find the smaller number
Delia works from 8:00
a.m. to 4:30 p.m. and has one hour each day for lunch. how much does she earn each week if she gets paid $4.80 per hour?
The college of arts and science at delta university has nine departments. the number of faculty in each department is shown below. what is the median number of faculty in the college of arts and science? 8, 12, 9, 15, 17, 11, 13, 14, 7
The median of the number of faculty in the college of arts and science is 12.
What is median?When a group of values is sorted from smallest to greatest, the median is the number in the middle of the range.
Given that,
Number of faculties in 9 departments of arts and science in the college
= 8, 12,9, 15, 17, 11, 13, 14, and 7
To find median number of the faculty in the college of arts and science,
Arrange number in increasing order,
= 7, 8, 9, 11, 12, 13, 14, 15, 17
The middle number of the sequence is 12.
So, the median of the sequence will be 12.
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The circumference of a circle is 25.12 yards. What is the radius of the circle?
You and your friend are selling magazine subscriptions for a fundraiser. after ww weeks, you have sold (3w+4)(3w+4) subscriptions and your friend has sold (5w+1)(5w+1) subscriptions.
a. write an expression in simplest form that represents the difference between the number of subscriptions your friend has sold and the number you have sold. an expression is .
Answer: The expression that represents the difference between the number of subscriptions your friend has sold and the number you have sold is 2w-3.
Explanation:
It is given the expression (5w+1) represents the subscriptions sold by the friend
f(w)=5w+1
Expression (3w+4) represents the subscription sold by me.
g(w)=3w+4
We have to find an expression which shows the difference between the number of subscriptions your friend has sold and the number you have sold.
[tex]h(w)=f(w)-g(w)[/tex]
[tex]h(w)=(5w+1)-(3w+4)[/tex]
[tex]h(w)=5w+1-3w-4[/tex]
Combine like terms.
[tex]h(w)=(5w-3w)+(1-4)[/tex]
[tex]h(w)=2w-3[/tex]
If it is negative then it means the subscription sold by friend is less than the subscription sold by me and if it is positive then it means the subscription sold by friend is more than the subscription sold by me.
A theater group is having a carwash fundraiser. the group can only spend $39 on soap, which is enough to wash 40 cars. each car is charged $5. a) if c is the total number of cars washed and p is the profit, which is the independent variable and which is the dependent variable? b) is the relationship between c and p a function? explain. c) write an equation that shows this relationship. d) find a reasonable domain and range for the situation.
If 3 pumpkins make 9 pumpkin pies, how many are needed to make 204 pies?
PLEASE HELP!
Solve the equation for x.
4x + 2 = 2(x + 3) + 2x – 4
Infinitely many solutions
No Solution
x = 2
x = 4
If i add to my number a number that is 17 more than twice my number, the sum will be 65. what is my number?
n +2n+17 = 65
3n+17 = 65
3n = 48
n = 48/3 = 16
Number is 16
Harriet is comparing the costs of calling cards. to use card a, the cost is $1.00 to connect and then $0.04 per minute. to use card b, it costs $0.65 to connect and then $0.06 per minute. for what number of minutes does it cost the same amount to use each card for a single call? (enter only the number.)
Convert 0.005090 Mega-liters to Liters. Record your answer in whole liters. Please show ALL of your work! Thanks! :)
Answer: 5,090 L
Step-by-step explanation:
Mega, in mathematical terms means million. The "M" represents million in the word mega.
Now, how many zeros does 1 million have? If you said 6, you are correct! Since 1 million has six zeros, we will move the decimal point 6 times. You'll have to multiply 0.005090 by 1,000,000. Let's do that!
So, we see that decimal point is by 2 zeros. If we move it 6 times by multiplying 0.005090 by 1,000,000, we'll get our answer. (Skip this if you want the answer)
0.005090 Original.
0.0509 One...
0.509 Two...
5.09 Three...
50.9 Four...
509 Five...
5090 Six!
Or, you could do it like this:
0.005090 × 1,000,000 = 5,090
Hence, your answer is 5,090 L.
A bin contains three components from supplier a, four from supplier b, and five from supplier
c. if four of the components are randomly selected for testing, what is the probability that each supplier would have at least one component tested?
What is the solution to the following system of equations?
infinite solutions no solution (0, 1) (4, –1)
The system of equations has infinite solutions.
Explanation:Upon analyzing the system of equations, if the equations represent the same line or are proportional to each other, the solution will be infinite. Let's consider the equations given:
Equation 1: [tex]\(y = x + 1\)[/tex]
Equation 2: [tex]\(2y = 2x + 2\)[/tex]
By manipulating Equation 2, dividing both sides by 2, we get Equation 1. This indicates that the equations represent the same line. When graphed, both equations will yield the same line. Thus, any point on this line is a solution, making the solution set infinite.
Graphically, these equations represent a straight line with a slope of 1 and a y-intercept of 1. Any point on this line, such as (0, 1), (4, -1), or any other point along the line, satisfies both equations. Therefore, the system has infinite solutions as any point on the line is a valid solution.
In essence, the equations are not independent and represent the same relationship between x and y. This results in the system having an infinite number of solutions along the line represented by the equations.
Which shape best describes the object generated when square is rotated about the axis?
hollow rectangular prism
solid rectangular prism
hollow cylinder
solid cylinder
Which three-dimensional object is formed when the shape is rotated about the axis as shown?
sphere
cylinder
cone
hemisphere
Which description best describes the three-dimensional object that is formed when the shape is rotated about the axis as shown?
a hollow cylinder
a flat disk with a hole in the center
a square pyramid
a rectangular prism that is open on the ends
Answer:
Ques 1) Hollow cylinder.
Ques 2) sphere.
Ques 3) Hollow cylinder.
Step-by-step explanation:
Ques 1)
on rotating the first figure about the axis:
If you rotate the square around the axis as shown in the first diagram, then the square will form a 3D ring around the vertical axis. This ring is essentially a hollow cylinder as the region in between is left empty.
Ques 2)
Rotating that semi-circle around the axis shown will generate a full sphere.
Ques 3)
As we have done in ques 1) now this time in place of square we are given a rectangle so on rotating this rectangle a hollow cylinder will be formed.
It should be noted that the shape that describes the object generated when square is rotated about the axis is C. Hollow cylinder.
ShapesThe three-dimensional object that is formed when the shape is rotated about the axis as shown is a sphere.
In the third diagram, the three-dimensional object that is formed when the shape is rotated about the axis as shown is a hollow cylinder.
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Solve for x.
Enter your answer in the box.
x =
°
The bells at Kings School ring every 6 minutes. At Queens School the bells ring every 5 minutes. At Princess School the bells ring every 9 minutes. All three bells ring together at 8.30 am. When is the next time the bells of the three schools will ring together?
Which of these is a step in constructing an inscribed equilateral triangle using technology?
A. Construct segment DB, segment BC, segment CE, segment EG, segment GI, and segment ID.
B.Create circle A with point B on the original circle.
C.Create circle E, which passes through points A and C.
D.Draw point E anywhere on segment DB.
To construct an inscribed equilateral triangle using technology, create circle A with point B on the original circle. This step is essential in forming the triangle.
Step by Step Solution:
To construct an inscribed equilateral triangle using technology, follow these steps:
Identify a point A on the circumference of the original circle.Create circle A with point B on the original circle.Ensure that the circle with center A passes through the original circle at point B.Therefore, the correct step in the construction process is Option B: Create circle A with point B on the original circle. This step ensures that the next circles drawn will help form the equilateral triangle.
5x^2-40=0; solve by using square roots.
Final answer:
To solve the equation 5x^2-40=0 using square roots, start by isolating x^2, divide by 5 and then apply the square root. The solutions are x = 2√2 and x = -2√2.
Explanation:
To solve the equation 5x^2-40=0 using square roots, we can start by isolating x^2 by adding 40 to both sides of the equation, resulting in 5x^2 = 40. Next, divide both sides of the equation by 5 to get x^2 = 8. Now, we can take the square root of both sides to solve for x. Since the solution involves a square root, we need to include both the positive and negative square root:
x = ±√8
Simplifying the square root of 8, we have:
x = ±√(4*2)
x = ±√4 * √2
x = ±2 * √2
So, the solutions to the equation 5x^2-40=0 are x = 2√2 and x = -2√2.
I need help with Standard Deviation!
kellogg's in Kalamazoo, Michigan has a machine that fills the Fruit Loop cereal boxes with cereal. It dispenses cereal with a normal distribution and has a mean of 24.0 and a standard deviation of .1 ounces.
Part A: The middle 95% of cereal boxes contain between ____ and ____ ounces of cereal.
Part B: Approximately 68% of cereal boxes have between ____ and ____ ounces of cereal.
Part C: What percentage of cereal boxes contain more than 24.2 ounces of cereal?
Part D: What is the probability that a randomly selected bottle of cereal contains less than 24.1 ounces of cereal?
One positive integer is 3 less than twice another. the sum of their squares is 170
A tortilla chip workstation produces 1,000 chips in 20 seconds. what is its bottleneck time
The bottleneck time for the tortilla chip workstation is 1/50 seconds.
Explanation:To find the bottleneck time, we need to determine the step in the production process that takes the longest time. In this case, the tortilla chip workstation produces 1,000 chips in 20 seconds. So, each chip takes 20/1000 = 1/50 seconds to produce. Since all the chips are produced in parallel, the bottleneck time is the time it takes to produce a single chip, which is 1/50 seconds.
What is the solution to the inequality?
4 ( 2x + 5 ) − 2x ≥ 10
how do you find the equation of x^2 = 7 by square rooting