a rectangle has an area of 16ft squared, every dimension is multiplied by a scale factor, and the new rectangle has an areaof 64 ft squared, what was the scale factor? ...?
Answer:
Scale factor is 2
Step-by-step explanation:
A rectangle has an area of 16ft²
That is
Length₁ x Breadth₁ = 16 ft²
Every dimension is multiplied by a scale factor, let the scale factor be s.
New dimensions are
Length₂ = s x Length₁
Breadth₂ = s x Breadth₁
New area is given by
Area = Length₂ x Breadth₂ = s x Length₁ x s x Breadth₁
Area = s² x Length₁ x Breadth₁
64 = s² x 16
s² = 4
s = 2
So scale factor is 2
What is the maximum number of turns in the graph of f(x)=2x^3-2x^2+7x-25 ?
The maximum number of turns in the graph of f(x) is:
2
Step-by-step explanation:Turning Point of a graph--
The turning point of a graph is a point where the graph changes it's behavior i.e. it changes from increasing to decreasing and from decreasing to increasing.
The polynomial of degree n has atmost " n-1 " turning points.
Here we are given a polynomial f(x) as:
[tex]f(x)=2x^3-2x^2+7x-25[/tex]
The polynomial is of degree 3.
Hence, the maximum number of turning points of the function f(x) is: 3-1=2
It takes carl 2/3 of an hour to clean his room every day. How many hours did he spend cleaning his room in the month of May?
for the normal (perpendicular) line to the curve y= square root of 8-x^2 at (-2,2) would the slope be 1/2? ...?
The slope of the normal line to the curve y = sqrt(8 - x^2) at the point (-2, 2) is -1/2.
Explanation:The question asks for the slope of the normal line to the curve y = sqrt(8 - x^2) at the point (-2, 2). To find the slope of the normal line, we need to find the derivative of the given curve and evaluate it at the given point. The derivative of y with respect to x is d/dx [sqrt(8 - x^2)]. Using the chain rule, the derivative is -x / sqrt(8 - x^2).
To find the slope of the normal line, we take the negative reciprocal of the derivative. So the slope of the normal line is 1 / (x / sqrt(8 - x^2)). Evaluating this at x = -2, we get the slope of the normal line as -1/2.
What is the absolute value of 4+7i is equal to the square root of ______
Answer:
The absolute value of 4+7i is equal to [tex]\sqrt{4^{2}+7^{2}}[/tex].
The absolute value of the 4+7i be [tex]\sqrt{65}[/tex].
Step-by-step explanation:
The absolute value is given by .
|a + bi| = [tex]\sqrt{a^{2}+b^{2}}[/tex]
Now find the absolute value of the 4+7i.
|4+ 7i|= [tex]\sqrt{4^{2}+7^{2}}[/tex]
|4+ 7i| = [tex]\sqrt{16+49}[/tex]
|4+ 7i| = [tex]\sqrt{65}[/tex]
Therefore the absolute value of the 4+7i is [tex]\sqrt{65}[/tex] .
A rectangular piece of metal is twice as long as it is wide. Squares with sides 4 inches long are cut from the four corners and the flaps are folded upward to form a box. If the volume is 1536 inches cubed, what were the original dimensions of the piece of metal? ...?
A $5000 investment earns $550 annual simple interest in one year. What is the annual interest rate?
A group of 140 tourist are going on a tour the tour guide rents 15 vans. each van holds 9 people. what is a division problem that could be used to find how many vans they need to hold every one?
The slope of diagonal AB is , _ and its equation _ is .
Find the multiplicative inverse of 6 + 2i.
SOS
Answer:
[tex]\frac{3}{20}-\frac{1}{20}i[/tex]
Step-by-step explanation:
Find the multiplicative inverse of a complex number using the process described below:
The inverse is found by reciprocating the original complex number. The reciprocal of the complex number (6+2i) is [tex]\frac{1}{6+2i}[/tex]. Multiply the numerator and denominator of the reciprocal by conjugate of the denominator and simplify:
[tex]\frac{1}{6+2i}*\frac{6-2i}{6-2i}[/tex]
You get: [tex]\frac{3}{20}-\frac{1}{20}i[/tex]
Hope this helps!!
Write the equation of the line perpendicular to 3x + y = -8 that passes through (-3,1) . Write your answer in slope-intercept form. Show your work.
How many times does 41 go into 278?
As a salesperson at Roaring Waves Beach Supplies, Carissa receives a monthly base pay plus commission on all that she sells. If she sells $500 worth of merchandise in one month, she is paid $385. If she sells $1,000 of merchandise in one month, she is paid $470.
Find Carissa's salary when she sells $1,900 worth of merchandise. ...?
Answer:
$623
Step-by-step explanation:
Let us suppose that the
Earning = y
Fixed payment = c
Commission paid = m per unit
Case 1.
When 500 units are sold, Earning y = $385
Earning = Fixed Payment + Commission paid per unit * Number of units
385=c+m*500
385=c+500m ________(a)
Case 2.
When 1000 units are sold earning y = $470
Earning = c+m*1000
470=c+1000m _________(b)
Subtracting (a) from (b) we get
85=500m
[tex]m=\frac{85}{500}\\=0.17[/tex]
Putting this value of m in (a)
[tex]385=c+\frac{85}{500} * 500[/tex]
385=c+85
c=300
Hence the fixed payment is $300 and the commission given is $0.17 per unit
Case 3 :
Number of Units sold = 1900
Earning = 300+0.17*1900
Earning = 300+323
Earning = 623
Hence The earning will be $623
Jeremy baked 9 cakes for the bake sale. He sifted 2 cups of powdered sugar evenly on the tops of the cakes. How much powdered sugar is on each cake?
Describe the variation 3xy = 5.
A. y varies inversely as the square of x.
B. y varies inversely as x.
C. y varies directly as x.
D. y varies directly as the square of x.
Answer:
The answer is the option B
y varies inversely as x.
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]yx=k[/tex] or [tex]y=k/x[/tex]
In this problem we have
[tex]3xy=5[/tex] -----> rewrite
[tex]xy=5/3[/tex]
The value of k is equal to [tex]k=\frac{5}{3}[/tex]
therefore
y varies inversely as x.
Your cell phone company started a rewards club. For every three texts sent, you get 15 points. You need 1800 points for a prize. How many texts do you need to send to get that prize
Answer:
360 texts
Step-by-step explanation:
Given,
The points given for 3 texts = 15,
So, the points given for 1 text = [tex]\frac{15}{3}[/tex] = 5,
If x text are sent,
Then the number of points earned = x × points for 1 text
= 5x
According to the question,
5x = 1800
[tex]\impilies x = \frac{1800}{5} = 360[/tex]
Hence, 360 texts needs to send to get 1800 points.
For what values of r does the function y= e^rx satisfy the differential equation 2y"+y'-y=0?
...?
Answer:
r = 1/2, -1
Step-by-step explanation:
First, you need to find the 1st and 2nd derivatives for the function y = e^rx:
y' = re^rx
y'' = r^2e^rx
Next, you substitute them into the differential equation 2y'' + y' - y = 0:
2(r^2e^rx) + re^rx - e^rx = 0
Factor e^rx out:
e^rx(2r^2 + r - 1) = 0
Divide both sides by e^rx:
2r^2 + r - 1 = 0
Factor the left side:
(2r - 1)(r + 1) = 0
Solving both of the equations, you get:
2r - 1 = 0
2r = 1
r = 1/2
r + 1 = 0
r = -1
Values: r = 1/2, -1
PLEASE HELP! WILL UPVOTE!
Which ordered pair is the solution to the system of equations?
{2x−y=−5
{x+3y=22
(7, 19)
(4, 9)
(8, 21)
(1, 7)
An observer in a lighthouse 350 feet above sea level observes two ships directly offshore. The angles of depression to the ships are 4° and 6.5°. How far apart are the ships?
A copy machine makes 114 copies in 4 minutes and 45 seconds. How many copies does it make per minute?
To determine the number of copies made per minute, the total time of 4 minutes and 45 seconds is first converted to 4.75 minutes. Dividing the total copies (114) by the total time in minutes (4.75) gives us 24 copies per minute.
Calculating Copies Per Minute
To find out how many copies the machine makes per minute, we need to convert the total time into minutes. There are 4 minutes and 45 seconds. Since there are 60 seconds in a minute, we can convert 45 seconds into minutes by dividing by 60, which gives us 0.75 minutes. Therefore, the total time in minutes is 4 + 0.75 = 4.75 minutes.
Now, we use the given information that the copy machine makes 114 copies in 4.75 minutes to calculate the number of copies it makes per minute:
Copies per minute = Total copies / Total time in minutes
Copies per minute = 114 copies / 4.75 minutes
Copies per minute = 24 copies per minute (rounded to the nearest whole number)
you roll two dice what is the probability that the sum of the dice is less than 5 and one dice shows a 2? ...?
What is the conclusion of the following statement?
A number is even if the number is divisible by 6.
A. A number is even if the number is divisible by 6.
B. A number is divisible by 6 if the number is even.
C. A number is divisible by 6.
D. The number is even.
Answer: Hello mate! The correct answer is D.
the statement is "A number is even if the number is divisible by 6."
Here the hipotesis is "the number is divisible by 6", and this hipotesis implies the conclussion, wich is "a number is even". This is because the statement implies that te first thing we check is if the number is divisible by 6, and then we can know if the number is even or not.
this can be written as
"if a number is divisible by 6, then the number is even"
where is more easy to see wich one is the conclussion of the statement.
Then you can see that the right answer is D "the number is even"
The range of f(x) = logb x is the set of all negative real numbers.
a.true
b.false
Answer:
Statement is false .
Step-by-step explanation:
Given : The range of f(x) = [tex]log_{b}(x)[/tex] is the set of all negative real numbers.
To find : Statement is true or false.
Solution : We have given that function f(x) = [tex]log_{b}(x)[/tex].
Range : range of logarithm function is all real numbers (-∞, ∞)
Therefore, Statement is false .
Solve for a: y= -1/2ax-5, m=5/2
Final answer:
To solve for 'a' in the equation y = -1/2ax - 5 with a given slope of 5/2, we compare it to the standard linear equation format and find that 'a' is equal to -5.
Explanation:
To solve for a, we need to look at the equation y = -1/2ax - 5 given that the slope (m) is 5/2. In a linear equation of the form y = mx + b, m represents the slope. Comparing it to the given equation, we can see -1/2a is the slope in our case. Therefore, to find a, we set -1/2a equal to the given slope of 5/2 and solve:
-1/2a = 5/2
To isolate a, we first multiply both sides by -2:
a = -2(5/2)
Multiplying this out, we find:
a = -5
Thus, in the context of a linear equation and assuming the slope m provided is indeed intended to be the value of the direct variation component, the value for a is -5.
Which line segment is a chord of circle E in the diagram below?
a) DE
b) BC
c) AB
d) CD
Answer
Find out the which line segment is a chord of circle E in the diagram below.
To prove
As given
Definition of a chord
A chord is the striaght line whose endpoints are lies in the circle.
Now as shown in the diagram given in the question.
CD is the striaght line whose endpoints lies in the circle E .
Therefore CD is a chord of circle E.
Option (d) is correct.
What is the answer to 3/4-3/8?
To solve 3/4 - 3/8, convert 3/4 to 6/8 and then subtract 3/8 from 6/8. The result is 3/8.
To find the answer to 3/4 - 3/8, follow these steps:
Find a common denominator for the fractions. The denominators here are 4 and 8. The least common multiple of 4 and 8 is 8.Convert 3/4 into a fraction with a denominator of 8. Since 3/4 = (3 * 2) / (4 * 2), it becomes 6/8.Now, subtract the fractions: 6/8 - 3/8.Perform the subtraction: 6/8 - 3/8 = 3/8.Thus, the answer to 3/4 - 3/8 is 3/8.So, 3/4 - 3/8 = 3/8.
Evaluate a + b ÷ 2, if we know a = 3 and b = 6. A. 4 B. 6 C. 1 D. 4.5
Select all the statements that are true about the linear equation. y = 4x - 3
a. The point (1,1) is on the graph of the equation.
b. The point (0,3) is on the graph of the equation.
c. 4x - y = -3 has the same graph.
d. The graph of the equation is the set of all points that are solutions to the equation.
e. The graph of the equation is a single point, representing one solution to the
equation.
Think that be is an answer but not sure.
Need help asap! It's a multiple answer choice worth a lot of points.
The correct statements for this question would be:
a) The point (1, 1) is on the graph of the equation."
d) The graph of the equation is the set of all points that are solutions to the equation.
Option (a) and (d) are true.
What is linear expression?
A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.
Given that;
The linear equation;
y = 4x - 3
Now, By option a;
To check the point (1, 1) is on the graph of the equation.
We can substitute x = 1 and y = 1 in the equation of line as;
y = 4x - 3
1 = 4 × 1 - 3
1 = 4 - 3
1 = 1
Thus, The point (1,1) is on the graph of the equation.
For option b;
Since, The point (0, 3) is not satisfy the equation y = 4x - 3.
Hence, Option b is not true.
For option c;
Since, The y - intercept of the line 4x - y = -3 and line y = 4x - 3 is not same.
Hence, Both have different graph.
Clearly, By the graph of y = 4x - 3 is is the set of all points that are solutions to the equation.
So, Option d is true.
Thus, The correct statements for this question would be:
a) The point (1, 1) is on the graph of the equation."
d) The graph of the equation is the set of all points that are solutions to the equation.
Option (a) and (d) are true.
Learn more about the equation of line visit:
https://brainly.com/question/13763238
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to calculate a rewards program incentive, you?
Final answer:
Rewards program incentives are calculated by considering the alignment between the rewards offered and the needs and values of the participants. These incentives must balance the trade-off between work and compensation, adhering to principles of effort and fair compensation.
Explanation:
Understanding Rewards Program Incentives
To calculate a rewards program incentive, one must consider the various factors that influence both the likelihood and the extent to which individuals participate in the program. Such a program typically aims to increase desired behaviors - for example, increasing purchases or promoting consistent work performance - by offering some form of reward or compensation. The effectiveness of these incentives is often determined by how well they align with participants' values and needs.
In contexts where these incentives might impact work behavior, one must consider the trade-offs individuals face. If a program reduces government assistance dollar for dollar as earnings increase, this could diminish the incentive to work. Conversely, if the program allows individuals to maintain a level of government assistance even as they earn income, some might choose to work fewer hours (choice S) but still maintain or increase their total income. Others might continue to work the same number of hours (choice R) or even more, depending on how the incentives align with their personal circumstances and preferences.
There are also principles of effort and compensation to consider. Ideally, a well-designed incentive program rewards individuals according to the effort they put in and the costs they incur. However, the balance between maximizing efficiency for the program and providing adequate motivation for the participants can be complex and requires careful calibration.
To calculate a rewards program incentive, it's important to analyze the relationships among work hours, income, and effort. Changes in incentives may influence individuals to adjust their work hours to maximize benefits. The goal is to find the sweet spot where the incentive structure aligns with the desired behavior, whether that's working more, the same, or fewer hours for optimal compensation.
Explanation:To calculate a rewards program incentive, you need to assess the different factors that influence choice and compensation. For instance, when a program provides financial incentives without reducing them entirely as earnings increase, individuals might alter their work hours to maximize overall income. This could mean choosing a point on the budget line, like S, where they work fewer hours but have greater income, or a point like R, maintaining the same work effort, or even increasing their hours, depending on the incentives.
The decision-making process regarding work hours and income can be complex, involving considerations of effort and compensation. These are guided by incentives and how individuals weigh the trade-offs between labor and leisure. Furthermore, such choices reflect the underlying principle that rewards should ideally align with the effort and costs involved in a person's work activity.
Changes in incentives can lead to different choices. If rewards or penalties for certain actions are adjusted, individuals may shift their decisions accordingly to maximize their benefits. For example, if a program becomes more generous without penalizing additional earnings, some may opt to work less, as they could still maintain or increase their income levels. Conversely, if the program became less generous or introduced greater penalization for earnings, individuals might be inclined to work more to achieve the same level of income.
Find the mode.19, 1, 17, 19, 3, 20, 5, 2
The mode of this set is 19.
1. **List the Numbers**: Start by listing out all the numbers in the set.
[tex]\[ 19, 1, 17, 19, 3, 20, 5, 2 \][/tex]
2. **Count Frequency**: Count how many times each number appears in the list.
- 19 appears twice.
- 1 appears once.
- 17 appears once.
- 3 appears once.
- 20 appears once.
- 5 appears once.
- 2 appears once.
3. **Identify the Most Frequent Number**: The mode is the number that appears most frequently. In this case, 19 appears twice, which is more than any other number in the set. Therefore, the mode of this set is 19.