The required solutions are x = 2-i and x = 2+i to the given quadratic function.
What is a quadratic function?
The quadratic function is defined as a function containing the highest power of a variable is two.
We have been given that quadratic function as
-2x² + 8x - 10 = 0
Compare the given function to the standard quadratic function f(x) = ax² + b x + c.
We get a = -2, b = 8 and c = -10
Using the quadratic formula to solve the above quadratic function
[tex]x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\dfrac{-8\pm \sqrt{8^2-4\left(-2\right)\left(-10\right)}}{2\left(-2\right)}[/tex]
[tex]x=\dfrac{-8\pm \:4i}{2\left(-2\right)}[/tex]
[tex]x=\dfrac{-8+4i}{2\left(-2\right)},\:x=\dfrac{-8-4i}{2\left(-2\right)}[/tex]
x = 2-i, x = 2+i
Thus, the required solutions are x = 2-i and x = 2+i to the given quadratic function.
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What is the rate of change between (3.4,-0.1) and (3.5,0.1)?
The rate of change between the points (3.4, -0.1) and (3.5, 0.1) is 2.
How to find rate of change?The rate of change function is defined as the rate at which one quantity is changing with respect to another quantity.
The rate of change formula gives the relationship describing how one quantity changes in relation to the change in another quantity.
Therefore,
rate of change = Δy / Δx
rate of change = y₂ - y₁ / x₂ - x₁
Hence, let's find the rate of change of (3.4,-0.1) and (3.5,0.1).
rate of change = 0.1 + 0.1 / 3.5 - 3.4
rate of change = 0.2 / 0.1
rate of change = 2
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How to write the equation of the line with m = - 3/4 that goes through (2, –5) in
Slope–Intercept Form.
Answer: y=-3/4x-3.5
Step-by-step explanation:
First, set up the equation based on the information we already know. The slope-intercept form is y=mx+b (m being the slop and b is the y-intercept)
We already know the slope, so we can substitute it.
y=-3/4x+b
Now, the only variable we need to find is b (the y-intercept)
To do this we can substitute the point that was given, (2,-5)
Substitute -5 in for y and 2 in for x.
Then you get the equation -5=-3/4(2)+b
Multiply -3/4 and 2 and you get -5=-3/2+b
Add -3/2 from both sides to isolate b
You then get b=-3.5
Substitute b back in the original equation
Your final answer is y=-3/4x-3.5
On a recent survey, students were asked if they like to fly and if they can drive. The partial results are given in the relative frequency table.
(On a recent survey, students were asked if they like to fly and if they can drive. The partial results are given in the relative frequency table.)
A frequency distribution table is a tool for structuring the provided data in a way that makes sense and facilitates comprehension.
What is a frequency distribution table in math ?In our daily lives, we come across a lot of data presented as numerical values, tables, graphs, etc. This data may include statistics on the number of goals scored in football games, local temperatures, the most popular goods among pupils in a class, and so on. Data are the gathered pieces of knowledge. The frequency of an occurrence or a value is the number of times it happens. A frequency table is a collection of objects with the frequency of each item shown in the table.A frequency distribution table is a tool for structuring the provided data in a way that makes sense and facilitates comprehension.The partial results :
Likes to fly cannot drive = 0.35 - 0.12 = 0.23Row total and likes to fly = 1 - 0.4 = 0.6Does not like to fly and can drive = 0.65 - 0.37 = 0.28Does not like to fly and cannot drive = 0.40 - 0.28 = 0.12Learn more about A frequency distribution table refer to :
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Please help me with this question
Answer:
D
Step-by-step explanation:
it is a regular pentagon.
so, all side lengths are equal, and also all cross connections between corners are equal.
that makes TR parallel to PQ.
and that makes SPQ an isoceles triangle (both legs are equally long). and the smaller triangle S to x to the angle to the right of x is similar to SPQ, which means they have the same angles.
so, the triangle interior angle at P = the triangle interior angle Q = y.
and they must be the same as the bottom 2 interior angles of the small triangle.
x and the angle right to x are equal too, as they are the triangle exterior (supplementary) angles to the bottom 2 interior angles of the small triangle.
we know that the sum of all angles of the internal trapezoid (PQ to x and its right neighbor) is 360.
and based on the EqualLogic found above these angles are
2×x + 2×y = 360°
x + y = 180°
A desk is on sale for $459, discount is 32% less than the regular price
What is the regular price?
If James Handerson wants to see a 15% increase in his bench press, and he can lift 210 pounds now, what goal weight should he shoot for?
James Handerson should shoot for 241.5 lbs.
Step-by-step explanation:Here are the steps to figuring out your problem:First, convert 15% into a decimal by moving the decimal place over twice to get 0.15.
Then, set up this equation:
0.15 x 210 = 31.5
Now, 31.5 is the percent increase, so now we add to the original weight:
210 + 31.5 = 241.5
Solution:
241.5 lbs.
I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!
Kate wants to install an in ground pool in five years. She estimates the cost will be $50,000. How
much should she deposit monthly into an account that pays 1. 6% interest compounded
monthly in order to have enough money to pay for the pool in 5 years? Round your answer to
the nearest dollar
Kate should deposit $46,158.28 monthly into an account
In this question, we have been given the amount A = $50,000,
interest rate R = 1.6%
period t = 5 years
We need to find the principal amount (P)
First, convert R as a percent to decimal
r = 1.6/100
r = 0.016
Using the formula of compound interest for P,
P = A / (1 + r/n)nt
P = 50,000.00 / (1 + 0.016/12)(12)(5)
P = $46,158.28
Therefore, Kate should deposit $46,158.28
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Mary has 96 fliers to post around town. last week she posted 1/6 of them. this week she posted 1/4 of the remaining fliers. How many fliers has she still not posted?
Answer:
Start with 60 fliers
post 1/4 of fliers so 60*.25=15
60-15=45 left
post 1/5 of remaining so 45*.20=9
45-9=36 left
Step-by-step explanation:
Last week: (had 60) (used 1/4)= (60)(1/4)= 15. So, you used 15.
You have 60-15=45 left. This is how many you have to start the week.
This week: (had 45) (used 1/5)= (45)(1/5)= 45/5=9. So, you used 9.
This means that you have 45-9= 36 left.
Mary Still did not post 60 fliers.
Total fliers Mary was having = 96
Fliers she posted last week = 1/6 = 0.16
Fliers left with Mary after posting 1/6 part last week
= 96 x 0.16
= 16
Fliers left with Mary after the posting of 1/6 of them
= 96 - 16
= 80
Now the new remaining number of fliers with Mary = 80
Fliers she posted this week = 1/4 = 0.25
Fliers left with Mary after posting 1/4 part this week
= 80 x 0.25
= 20
Fliers left with Mary after the posting of 1/4 of them this week
= 80 - 20
= 60
Therefore, the fliers that Mary still did not post = 60
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The vertices of ▲ XYZ are X (6,-5), Y (3,0), Z (-4, 9). A XYZ is translated 3 units left and 8 units up. Then, it is translated 2 units right and 6 units down. What is the final translation rule that maps the pre-image to the final image?
Answer:
After the first translation, the coordinates of the vertices of the triangle will be X (3,-13), Y (0,-8), Z (-7, 1). After the second translation, the coordinates of the vertices will be X (5,-7), Y (2,-2), Z (-5, 7).
The final translation rule that maps the pre-image to the final image is a translation of 2 units right and 6 units up. This can be written as a translation rule of the form (x, y) -> (x + 2, y + 6).
Step-by-step explanation:
After the first translation the coordinates are:
(x, y) → (x - 3, y + 8)After the second translation the coordinates are:
(x - 3, y + 8) → (x - 3 + 2, y + 8 - 6) = (x - 1, y + 2)The final translation rule is:
(x, y ) → (x - 1, y + 2)or
One unit left and 2 units up.slope is 1/4 the line passes through the point 8,5
Answer:
Go up by 1 and run 4, remeber slope: rise over run. If the point is 8,5 then find 8 on the x axis and 5 and the y, wherever they meet, that's your answer.
Step-by-step explanation:
A local company interested in marketing its new brand of headphones wants to know the best way to go about seeing the effectiveness of its recent advertising campaign. The company approached your Math III class for ideas, since you are studying statistics and probability right now. Using your knowledge from this module, your task is to create a new posting to explain to the company its options for soliciting the opinions of the general public. Make sure you identify the pros and cons of each possibility, and make your recommendation as to how the company should approach its market research
The subject of a random event is covered in the mathematical field of probability.
Statistics is a field of mathematics that deals with gathering, analyzing, interpreting, and presenting vast amounts of numerical data.
Given,
Probability;-
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
Statistics;-
Statistics are numerical representations of sample characteristics. One population parameter is the average income in the United States. On the other hand, a sample statistic is the average income for a sample taken from the United States. Although both figures correspond to the mean income, only one is a statistic.
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What is the domain of this function?(–10,3)(3,2)(0,–8)(8,–4)(7,6)
Answer:
d = {-10, 0, 3, 7, 8}
Step-by-step explanation:
the domain is the set of x values in a function
For what values of x is y=-7-|x| increasing? Decreasing?
The intervals for which the function y = -7 - |x| is increasing and decreasing is given as follows:
Increasing: x < 0.Decreasing: x > 0.How to obtain the intervals of increase and decrease?The function is defined as follows:
y = -7 - |x|.
The parent absolute value function is increasing for x > 0 and decreasing for x < 0.
For this problem, the multiplication by -1 means that the function was reflected over the x-axis, meaning that the intervals of decrease and increase were exchanged, and thus they are given as follows:
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Label the slope for each line.
Miss Muffet's Spider
Answer:
A=1 B=2 C=7
Step-by-step explanation:
Look at the graph!!!!
18. What are the zeroes of the function? (1 point)
y=(x-3)(x + 2)(x-2)
O-3, 2, -2
O-3, 2, 2
03, -2, 2
03, 2, 2
The required zeros of the function y=(x-3)(x + 2)(x-2) is given as 3, -2, and 2. Option C is correct.
Here,
Zero of the function are the values of x, for a function for which the function gives y = 0,
So let y = 0, - - - - - -(1)
Put y = (x-3)(x + 2)(x-2) in equation 1
(x-3)(x + 2)(x-2) = 0
Equating each parenthesis step by step with zero,
x - 3 = 0 ; x + 2 = 0 ; x - 2 = 0
x = 3 ; x = -2 ; x = 2
So the values that came out are 3, -2, and 2, are said to be zeros of the given function,
When we substitute any value in the function then y becomes zero such as,
Put x = 3 in function,
y = (3-3)(3+2)(3 - 2)
y = (0)(5)(1)
y = 0
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the radius of the wheel on a bike is 19 inches. if the wheel is revolving at 140 revolutions per minute, what is the linear speed of the bike, in miles per hour?
Therefore, the linear speed of the wheel on a bike is approximately 0.9π miles per hour.
What is meant by linear speed?The pace at which an object travels a specific distance in a predetermined amount of time is known as linear speed. By dividing the distance traveled by the time it takes to cover that distance, it may be used to determine how rapidly an item is travelling in a straight line. For instance, if a car moves 100 meters in 10 seconds, its linear speed is 10 meters per second. Linear speed is distinct from average speed, which takes into account any variations in velocity or direction throughout the duration of a voyage. Linear speed is also distinct from tangential speed, which is the pace at which an item travels along a circular route. Physics' fundamental idea of linear speed.
How to solve?
C=2πr,
C=2π(19)=38π.
linear speed of v=(38π/60)*5280=33.6π feet per second.
final speed of v=(33.6π/3600)*60=0.9π miles per hour.
Therefore, the linear speed of the bike is approximately 0.9π miles per hour.
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The profit a company made decreased 20% to 66 million from one year to the next. What was the profit the year before
82.5 million was the profit the year before the profit decreased 20% to 66 million from one year to the next
What does profit means ?
Profit is the term used to describe the financial gain experienced when the revenue from a commercial activity exceeds the costs, costs, and taxes associated with maintaining that activity.
Any profits generated are returned to the company's owners, who can decide whether to keep the money for themselves, pay dividends to shareholders, or reinvest it in the company.
Entire revenue less total costs equals profit.
Companies report gross profit, operational profit, and net profit for accounting purposes (the "bottom line").
Investors are drawn to profitable businesses because these businesses either distribute their earnings as dividends to shareholders or invest them back into the business, which raises stock value.
According to the question Company lost 20% from its profit and it reached to 66 million that means
let X be the total profit of the year
X - loss percent = 66 millions
X - X (20/100) = 66 million
X-0.2X = 66 million
0.8X = 66 million
X= 66/0.8 million
X = 82.5 million
So, 82.5 million was the profit the year before
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how long is the hypotenuse?
Tyler made a scale drawing of an apartment. The scale of the drawing was 1 millimeter : 2 meters. The living room is 6 meters long in real life. How long is the living room in the drawing?
In the drawing, the length of the living room is 3 millimeters.
What is a scale factor?The scale factor defines a variable in a ratio of two different measurements.
Sometimes drawings of large models are represented in a scale factor of a smaller unit.
Given, Tyler made a scale drawing of an apartment. The scale of the drawing was 1 millimeter : 2 meters.
The living room is 6 meters long in real life and assuming in the drawing it is x millimeters.
∴ 1 : 2 : : x : 6.
1/2 = x/6.
x = 6/2.
x = 3.
So, In drawing it is 3 millimeters.
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x/2 -5 = -3
Answers: A.4 B.1 C.-4 D.-16
Answer:
A. 4
Step-by-step explanation:
x/2 - 5 = -3
x/2 = 2
x = 4
Multiply both sides of the equation by 2.
x - 10 = -6Add 10 to both sides.
x = -6 + 10Add −6 and 10 to get 4.
x = 4Using the equation , describe how to create a system of linear equations with an infinite number of solutions.
In the case of coinciding lines with the same y-intercept, the number of solutions to the equation system is unlimited.
What is Equation?An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values. as in 3x + 5 = 15, for example.
There are many different types of equations, such as linear, quadratic, cubic, etc.
Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign.
It shows that the expressions printed on the left and right sides have an equal relationship. In any mathematical equation, we have LHS = RHS (left hand side = right hand side).
Equations can be solved to find the value of an unknown variable that represents an unknown quantity. If there is no "equal to" symbol in the sentence, it is not an equation.
Hence, In the case of coinciding lines with the same y-intercept, the number of solutions to the equation system is unlimited.
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Complete question-
Using the equation y = 2/3 x - 5, describe how to create a system of linear equations with an infinite number of solutions.
for a math proficiency exam, it is known that the population mean score is 1100 and the population standard deviation is 100. if the test is administered to 64 randomly selected individuals from this population, what is the probability that the sample mean will lie between 1070 and 1120? after finding the appropriate probability, indicate the interval that includes this probability. group of answer choices .7001 to .8500 .6001 to .7000 .8501 to 1.000 .0000 to .3000 .3001 to .6000
The probability that the sample mean will lie between 1070 and 1120 is .7001 to .8500.
To find the probability that the sample mean will lie between 1070 and 1120, we use the Z-score formula:
Z = (x - μ) / σ
where x is the value we are looking for (in this case 1070 or 1120), μ is the population mean (1100), and σ is the population standard deviation (100).
Using this formula, we can calculate the Z-scores for 1070 and 1120, which are -0.3 and 0.2 respectively.
We can then use a Z-table to find the probability associated with each of these Z-scores. The probability associated with a Z-score of -0.3 is 0.6179, and the probability associated with a Z-score of 0.2 is 0.7886.
The probability that the sample mean will lie between 1070 and 1120 is the difference between these two probabilities, which is 0.1707. This is equivalent to a probability of 0.7001 to 0.8500.
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Determine if (2, -1) is a solution to the system of equations:
2x−y=5
y=3x−7
Justify your answer using mathematics.
Is the coordinate a solution?
yes or no
The solution to the system of equations is (x, y) = (2, -1).
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
WE are given the system of equations
2x−y=5
y = 2x - 5
y=3x−7
Adding the two equations Then divide by 2
Subtracting the second equation from the first gives;
0 = x -2
x = 2
y = -1
therefore, The solution is (x, y) = (2, -1).
The solution to the system of equations is (x, y) = (2, -1).
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Ethan and Adrian are reading the same book. At the beginning of the month, Ethan was on page 18 and Adrian was on page 45. Ethan will read 12 pages per day and Adrian will read 9 pages per day. Let E represent the page of the book that Ethan is on at the end of t days into the month, and let A represent the page of the book that Adrian is on at the end of t days into the month. Write an equation for each situation, in terms of t,, and determine whether Ethan or Adrian is farther along in the book after 4 days.
Answer: Ethan
Step-by-step explanation:
E:A
18:45 on page
12:9 per day
48:36 after 4 days
Ethan is further along in the book after 4 days
Winston's bill at the restaurant was $32. He left a tip of 20%.
What was the tip amount? Round your answer to the nearest penny.
The round of tip amount.
Total tip = $ 7.00
Total (Bill + Tip) = $ 39.00.
How to Calculate Tip?
To calculate the tip multiply the total check by 1 plus the decimal percentage tip you'd like to leave.
If you wanted to leave a 20% tip, you would add 1 to 0.20 to get 1.20. Multiply the bill by 1.20 to get the total amount you'd leave including tip.
Decide on tip percentageAdd the decimal form of tip percentage to 1 to get your rateMultiply the bill by your rateTo calculate this, you can multiply the bill amount by the tip percentage: $32 * 0.20 = $6.40.
The tip amount was $6.40.
Hence, the round of tip amount.
Total tip = $ 7.00
Total (Bill + Tip) = $ 39.00.
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A rideshare company charges a $3 ride fee in
addition to its meter, which is $1.50 for every mile.
Write an equation for this situation in point-slope
form for a customer who went 6 miles and paid
$12 total.
A. y 6= 3(x-12)
B. y + 6 = 1.50(x - 12)
C. y - 1.50 = 3(x-6)
D. y - 12 = 1.50(x-6)
Option D, The equation that satisfy the situation is y - 12 = 1.50(x-6).
What is Coordinate Geometry?The study of geometry using coordinate points is known as coordinate geometry (also known as analytical geometry). Finding the distance between two points, breaking lines into m:n segments, locating a line's midpoint, computing a triangle's area in the Cartesian plane, and other operations are all feasible using coordinate geometry.
A straight line is represented using its slope and a point on the line using point slope form. This indicates that the point slope form is used to get the equation of a line whose slope is "m" and which passes through the points (x 1, y 1). The equation of a straight line can be expressed in several ways. Point slope shape is one of them. Y - Y 1 = m(x - X 1) is the equation for the point slope form, where (x1, y1) is a randomly chosen point on the line and m is the slope of the line.
The slope of the line is 1.5
The Point through which the equation will satisfy is (6,12)
Therefore the equation of the line in Point-Slope form is
y - y1 = m ( x- x1)
⇒ y - 12 = 1.50 ( x - 6)
Option D, The equation that satisfy the situation is y - 12 = 1.50(x-6).
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how is the accuracy rate calculated? how is the accuracy rate calculated? subtract the number of correct predictions from the total number of predictions. divide the number of true positives by the number of true negatives. divide the number of correct predictions by the total number of predictions. add the number of true positives and the number of false negatives.
Accuracy rate is equal to the difference of predicted value and true value divide it by true value and then multiply by 100 to get the rate.
Accuracy value represent the calculated value is more close to the true value.It help us to measure the statistical error.It help us to know what the error given in the measured value of the data.Divide the difference of predicted and true by the true value and then multiply it by 100 to get the accuracy rate.Accuracy test can be done different statistical methods also.Accuracy rate = [ | Predicted value - True vale|/ true value ] × 100
Therefore, the accuracy rate is the percentage of the ratio of difference of predicted value and true value to the true value.
The given question is incomplete, I answer the question in general according to my knowledge:
How is the accuracy rate calculated?
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Which graph shows a system with no solutions?
help meeeeeeeeeeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeeeeeeeeee!!!!!
Answer:
Step-by-step explanation:
a.) The population is years measured after 2000 so 2000 is 0. Any number to the 0 power is 1 so the population is 23.1 (million).
b.) 28.3 = [tex]23.1e^{0.0152t}[/tex]
1.22510823 ≈ [tex]e^{0.0152t}[/tex]
ln 1.22510823 ≈ 0.0152t
t≈13.4 MILLION
it takes avery 48 seconds to sprint 365m what is her average speed