Let a function f: R → R is defined by f(x) = x² - 4x +3. (a) Write the name the locus of the curve represented by the function f(x). (b) find domain of the function f(x). (c) Find the vertex of the curve represented by f(x).
Answers
(a) The locus of the curve represented by the function is a parabola.
(b) The domain of the function f(x) is the set of all real numbers.
(c)The vertex of the parabola is (2, -1).
f(x) = x² - 4x + 3, Specifically, it is an upward-facing parabola, since the coefficient of the quadratic term (x²) is positive.
Since there are no restrictions on the input values for this function. In other words, we can plug in any real number for x, and the function will output a corresponding real number.
(c) The vertex of the curve represented by f(x) can be found by completing the square:
f(x) = x² - 4x + 3
= (x - 2)² - 1
The vertex corresponds to the minimum point of the parabola, since the coefficient of the quadratic term is positive. Therefore, the graph of f(x) is an upward-facing parabola that opens upwards, with the vertex at the point (2, -1).
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Related Questions
i thought of a number, multiplied it by 2 1 2 , divided the result by 1 1 5 , subtracted 7 18 from it, and got 1 5 6 . what was my number?
Answers
To determine the number you thought of, let's work backward from the given result of 156. We determined that the number you thought of was 490.
By following the steps in reverse order, we can calculate the original number. We start with the given result of 156. To reverse the subtraction, we add 7 18 to it, which gives us 8 7 4. Moving further, to reverse the division, we multiply 8 7 4 by 1 1 5, resulting in 1 0 0 5 6 0. Now, to reverse the multiplication, we divide 1 0 0 5 6 0 by 2 1 2, yielding 4 9 0. Hence, the number you initially thought of was 4 9 0.
In summary, by working backward from the given result of 156, we determined that the number you thought of was 490.
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the test in an if function must evaluate to either a true or a false.
Answers
Yes, the test in an "if" function must evaluate to either a True or a False value.
An "if" function, also known as a conditional statement, is used to perform specific actions based on whether a certain condition is met or not. The test or condition within the "if" function needs to be evaluated as either True or False in order for the program to decide which action to execute. If the test evaluates to True, the program will perform the action within the "if" block, and if it evaluates to False, it will either execute the action in the "else" block (if present) or simply skip the "if" block.
When using an "if" function in programming, it is essential for the test or condition within the statement to result in a boolean value, which is either True or False. This is because the program needs to determine whether the condition is met or not, so it can decide which set of actions to execute. If the condition evaluates to True, the code within the "if" block will be executed, while if it evaluates to False, the code within the "else" block (if present) will be executed, or the "if" block will be skipped altogether.
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Which equation demonstrates the multiplicative identity property? (negative 3 + 5 i) + 0 = negative 3 + 5 i (negative 3 + 5 i ) (1) = negative 3 + 5 i (negative 3 + 5 i) (negative 3 + 5 i) = negative 16 minus 30 i (negative 3 + 5 i) (3 minus 5 i) = 16 + 30 i
Answers
Answer:
(-3 + 5 i) (1) = (-3 + 5 i)
Step-by-step explanation:
The multiplicative identity property says you can multiply anything by 1 without changing its value. That is demonstrated by the equation above.
Answer:
EDGE2020 is B
Quadrilateral H' is the image of quadrilateral H after a sequence of transformations. If quadrilateral His congruent to
quadrilateral H, which transformations could have been used?
O a dilation by a scale factor of 2 followed by a reflection
O a rotation followed by a dilation by a scale factor of
O a reflection, a translation of 1 unit left, and then a dilation by a scale factor of 3
O a translation of 6 units down, a rotation, and then a reflection
Answers
When quadrilateral H' is the image of quadrilateral H after a sequence of transformations. If quadrilateral H is congruent to quadrilateral H, the transformations used is
a translation of 6 units down, a rotation, and then a reflectionWhat is rigid transformation?A rigid transformation also known as an isometry, is a type of transformation in mathematics that preserves the size, shape, and orientation of a geometric object. It involves moving or transforming an object without changing its overall structure or measurements.
In other words, the parts remain congruent after transformations.
Rigid transformations include three main types
translations, rotations andreflections.Dilation is not among and this is present in all other options
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For each of the counting questions, find the correct computation from the list below. Answers may be used multiple times or not at all. Explain your reasoning for partial credit. P(10,4) 104 410 (13 10 None of these 4 (a) How many passwords can be made from 4 digits (using the numerals 0 through 9) with repetition of digits allowed? (b) How many passwords can be made from 4 digits (using the numerals from 0 through 9) if all the digits must be distinct? (c) How many passwords can be made from 4 digits (using the numerals from 0 through 9) if the digits must be strictly increasing? For example, 1234 would work but 0117 would not work because the second to third digits are not increasing. (d) How many passwords can be made from 4 digits (using the numerals from 0 through 9) if the digits must be in non-decreasing order? For example, 0117 would work but 7708 would not work because the third digit is less than the second digit. go How many lattice paths are there from (0,0) to (10,4)?
Answers
The number of lattice paths is given by the binomial coefficient\(C(10+4, 4) = C(14, 4) = 14! / (4! * (14-4)!) = 14! / (4! * 10!) = 1001.\) Thus, there are 1,001 lattice paths from (0,0) to (10,4). \((a) P(10,4) = 10^4 = 10,000, (b) C(10,4) = 2,520, (c) C(10,4) = 2,520, (d) C(13,4) = 715\)
Lattice paths from (0,0) to (10,4) can be calculated using the combinatorial concept of binomial coefficients. The number of lattice paths is given by the binomial coefficient \(C(10+4, 4) = C(14, 4) = 14! / (4! * (14-4)!) = 14! / (4! * 10!) = 1001\). Thus, there are 1,001 lattice paths from (0,0) to (10,4).
(a) The number of passwords that can be made from 4 digits (using the numerals 0 through 9) with repetition of digits allowed is determined by the number of choices for each digit. Since there are 10 possible choices (0 through 9) for each of the 4 digits, the computation is 10^4 = 10,000.
(b) If all the digits must be distinct, the computation involves selecting 4 different digits out of 10. This can be calculated using the combination formula:\(C(10,4) = 10! / (4! * (10-4)!) = 10! / (4! * 6!) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1) = 2,520\).
(c) For the digits to be strictly increasing, we need to choose 4 digits in ascending order from 0 to 9. This is equivalent to selecting 4 digits out of 10 without repetition, which can be calculated using the combination formula: \(C(10,4) = 10! / (4! * (10-4)!) = 2,520\).
(d) If the digits must be in non-decreasing order, we need to choose 4 digits in ascending order with repetition allowed. This can be calculated using the combination with repetition formula: \(C(4+10-1, 4) = C(13, 4) = 13! / (4! * (13-4)!) = 13! / (4! * 9!) = 715\).
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The median of the data set below is 3.7. Find the mean
1.1 1.7 2 k 4.3 6.4 7.9 8.6.
Hint: First find the missing values, K. Give an exact answer.
Answers
The missing value, k, is -6.1.To find the missing value, k, we need to determine the number in the data set that corresponds to the median.
The median is the middle value when the data set is arranged in ascending order. Since we have 8 numbers in the data set, the median will be the 4th value when arranged in ascending order.
Given that the median is 3.7, we can determine that the 4th value in the data set is also 3.7.
So, we can rewrite the data set in ascending order:
1.1, 1.7, 2, k, 3.7, 4.3, 6.4, 7.9, 8.6
The mean of a data set is the sum of all the values divided by the number of values.
To find the mean, we need to calculate the sum of all the values. We know that the median is 3.7, so the sum of the data set without the missing value, k, is:
1.1 + 1.7 + 2 + 3.7 + 4.3 + 6.4 + 7.9 + 8.6 = 35.7
Since there are 8 numbers in the data set (including the missing value, k), the sum of all the values including k is:
35.7 + k
To find the mean, we divide the sum by the number of values, which is 8:
Mean = (35.7 + k) / 8
Since we want the mean to be equal to the median, which is 3.7, we can set up the equation:
(35.7 + k) / 8 = 3.7
Now we can solve for k:
35.7 + k = 29.6
k = 29.6 - 35.7
k = -6.1
Therefore, the missing value, k, is -6.1.
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a bag of chips costs $3.79 including tax. mr. connor wants to purchase chips for his class and has a $15 budget. write an inequality to solve for the number of bags of chips mr. connor can purchase with his budget
Answers
Answer: if I am not right I am sorry but think it is $0.25
Step-by-step explanation:
Sketching a Function from its Derivatives A In this post, you will use the first and second derivatives of a function (along with a few other pieces of information) to sketch the graph of a function. Sketch the graph of a single function f (x) that satisfies all of the following conditions. Use the techniques that we have learned in this course to do so. f'(x)= 16(x + 2) (6 - x) ³ 32(x + 6) f"(x) = (6 x - x) 4 The domain of fis (-[infinity], 6) U (6,[infinity]) x = 6 is a vertical asymptote of f lim f(x) = 1, lim f(x) = 1 x→→[infinity]0 f(2)= 1 8个
Answers
Here, x = 6 is a vertical asymptote of f, so the function approaches infinity as x approaches 6 from both sides.
Let's start by integrating f'(x) to get f(x). We have:
f'(x) = 16(x+2)(6-x)³ - 32(x+6)
Integrating both sides with respect to x:
f(x) = ∫[16(x+2)(6-x)³ - 32(x+6)] dx
Simplifying the integral, we get:
f(x) = -2(x+2)²(6-x)⁴ + 16(x+6) + C
where C is the constant of integration.
Next, we can find the critical points of f(x) by setting f'(x) = 0:
f'(x) = 16(x+2)(6-x)³ - 32(x+6) = 0
Solving for x, we get x = -2 and x = 6 as critical points.
Now, we can use the second derivative f''(x) to determine the concavity of the function. We have:
f''(x) = (6x-x)⁴ = x⁴
Since the second derivative is always positive for x > 0, the function is concave up on the interval (6, ∞).
Similarly, since the second derivative is always negative for x < 0, the function is concave down on the interval (-∞, -2).
At x = -2 and x = 6, the function has an inflection point.
Finally, we know that x = 6 is a vertical asymptote of f, so the function approaches infinity as x approaches 6 from both sides.
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Graph 3x + y = – 1.
Answers
Answer:
(0, - 1). thats the answer
A quadratic equation has zeros at -6 and 2. Find standard form
Answers
The quadratic equation with zeros at -6 and 2 is y² + 4y - 12 = 0. This is in standard form, which is ax² + bx + c = 0, with a = 1, b = 4, and c = -12.
To find the quadratic equation with zeros at -6 and 2, we can start by using the fact that if a quadratic equation has roots x₁ and x₂, then it can be written in the form
(y - x₁)(y - x₂) = 0
where y is the variable in the quadratic equation.
Substituting the given values of the zeros, we get
(y - (-6))(y - 2) = 0
Simplifying this expression, we get
(y + 6)(y - 2) = 0
Expanding this expression, we get
y² - 2y + 6y - 12 = 0
Simplifying this expression further, we get
y² + 4y - 12 = 0
So the quadratic equation with zeros at -6 and 2 is
y² + 4y - 12 = 0
This is the standard form of a quadratic equation, which is
ax² + bx + c = 0
where a, b, and c are constants. In this case, a = 1, b = 4, and c = -12.
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are lines y=3+5x and y=5x-1 parallel perpendicular or neither
Answers
Answer:
Step-by-step explanation:
y=mx+b is the standard form
m= slope
If the slopes are the same they are parallel
If the slopes are Opposite signed and reciprocals, then they are perpendicular
both of the slopes are 5, so the lines are parallel
what is x if 2/9+x=11/18?
Answers
Answer:
x = 7/18
Step-by-step explanation:
what is x if 2/9+x=11/18?
2/9 + x = 11/18
x = 11/18 - 2/9
x = 63/162
x = 7/18
check
2/9 + 7/18 = 11/18
11/18 = 11/18
the answer is goodThe future value of $900 saved each year for 10 years at 8 percent. (round time value factor to 3 decimal places and final answer to 2 decimal places.)
Answers
The future value of $900 saved each year for 10 years at 8 percent is approximately $12,585.90.
To calculate the future value, we can use the formula for the future value of an ordinary annuity:
FV = P * ((1 + r)^n - 1) / r,
where:
FV is the future value,
P is the annual payment or deposit ($900 in this case),
r is the interest rate per compounding period (8% or 0.08),
and n is the number of compounding periods (10 years).
Substituting the given values into the formula:
FV = 900 * ((1 + 0.08)^10 - 1) / 0.08,
FV ≈ $12,585.90.
Therefore, the future value of saving $900 each year for 10 years at an 8% interest rate is approximately $12,585.90.
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45x12=________
15x10=________
35x15=________
43X14=________
Answers
Answer:45 x 12 = 450
15 x 10 = 150
35 x 15 = 525
43 x 14 = 602
Step-by-step explanation:
15 x 10 = 150
35 x 15 = 525
43 x 14 = 602
Solve the inequality for x and identify the graph of its solution.
4|x + 3| < 8
Choose the answer that gives both the correct solution and the correct graph.
A.
Solution: x < 1 or x > 5; graph:
B.
Solution: x < –5 or x > –1; graph:
C.
Solution: x > –5 and x < –1; graph:
D.
Solution: x > –5 and x < –1; graph:
Answers
Answer:
D
Step-by-step explanation:
^^^
Can someone please help me with math.
Answers
Answer:
13.C
14.C
Step-by-step explanation:
Hello There!
For 13
The question is asking, which percentage would Darian most likely receive if he had studied for 9 hours.
The line of best fit would be used to determine the percentage he would most likely score based on the amount of hours he studied
Looking at the line of best fit we notice that at 9 hours Darian would most likely score a 78% on the test
Thus the answer is C
For 14
The question want you to find the graph that has a constant rate of change and has a y intercept of (0,0) so essentially
The question is asking "which graph best represents a proportional relationship."
If a relation is proportional it would have a straight line and it would go through the origin (0,0)
Looking at C we notice that the line is straight ( meaning it has a constant rate of change) and it also goes through the origin therefore C is your answer
The Cortez family is traveling from Miami to Washington, D.C. They plan to average 55 miles per hour on their trip.
About how many drive hours will it take the Cortez family to make the trip?
Answers
Step-by-step explanation:
Miami is approximately 1,054 mi away from Washington DC. assuming the Cortez family is driving in a straight line the time they will be on the road is
\(let \: h = hrs\)
\( 1054mi \div \frac{55mi}{h } \\ \frac{1054mi}{1} \times \frac{h}{55mi} \\ = \frac{1054mi(h)}{55mi} \)
The miles unit, mi cancels and leaves us with hours, h
\( \frac{1054 \: h}{55} \: \: \: \: is \: approx. \: \: \: \: 19.16 \: \: hrs\)
Help me with this, it’s due in a bit!
Answers
Answer:
64 square centimeters
Step-by-step explanation:
The surface are of a pyramid is found by finding the sum of the area of the four sides and the base.
Finding the triangular face:
Area of triangle = \(\frac{1}{2} b h\) = \(\frac{1}{2}*4*6 = 12\)
12 * 4 (4 sides) = 48 square cm
Finding the Base = \(w * l = 4 * 4 = 16\)
Finally, we add it together. 48 + 16 = 64
A number multiplied by 2 is no more than 12
X > 12
x < 12
2<_12
2x > 12
Answers
completely factor: 4t + 2rt + 8st
Answers
I hope this helps
Answer:
2t(2 + r + 4s)
On a menu, 1/10 of 60 dishes are chicken, 1/6 are beef, 1/3 are pork, and the rest are vegetarian. If Sergei doesn’t like beef or pork, how many dishes can he choose from on this menu?
Answers
Explanation:
If 1/10 of the 60 dishes are chicken, that means 6 of the dishes are chicken.
1/10 * 60 = 6
If 1/6 of the 60 dishes are beef, that means 10 dishes are beef.
1/6 * 60 = 10
If 1/3 of the 60 dishes are pork, that means 20 dishes are pork.
1/3 * 60 = 20
If you add up all the non-vegetarian options you would get 36, that means there are 24 vegetarian options.
So if Sergei doesn’t like beef or pork, we can subtract 30 dishes from the 60 dishes in total, which is 30.
That means Sergei can choose 30 dishes from this menu.
Alternative/faster way:
Add up the pork and beef fractions;
1/6 + 1/3
Common denominator
1/6 + 2/6 = 3/6
Simplify
3/6 = 1/2
Now just find half of the 60 dishes and that would be 30.
60 - 30 = 30
We still get the same answer, he can choose 30 dishes from this menu.
anyone her watch technoblade
1+1
Answers
Answer:
Yes.
Also, 1 + 1 = 2
Also:
Someday, I will beat him. He is revealing all of his secrets in his U-Toob videos, the fool, the moron.
Answer:
yes technoblade never dies
1+1=2
If an analysis of variance produces SS between = 20 and SS within = 40, then η 2 = 0.50.
true or false
Answers
Since η² ≈ 0.33 and not 0.50, the statement "If an analysis of variance produces SS between = 20 and SS within = 40, then η² = 0.50" is false.
ANOVA, or Analysis of Variance, is a statistical method used to compare the means of two or more groups to determine if there are any statistically significant differences between them. It is commonly used in experimental and observational studies to analyze the variance between group means and within-group variability.
ANOVA tests the null hypothesis that the means of the groups are equal, against the alternative hypothesis that at least one of the group means is different. It calculates the F-statistic, which compares the between-group variability to the within-group variability. If the F-statistic is large enough and exceeds a critical value, it indicates that there is evidence to reject the null hypothesis and conclude that there are significant differences between the group means.
We can determine if η² = 0.50 is true or false by calculating the effect size η² using the provided SS between and SS within values.
η² = SS_between / (SS_between + SS_within)
η² = 20 / (20 + 40)
η² = 20 / 60
η² = 1/3 ≈ 0.33
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True, the eta-squared value is indeed 0.50, indicating that 50% of the total variance is accounted for by the between-group variation.
The formula to calculate eta squared (η2) is:
η2 = SSbetween / (SSbetween + SSwithin)
If SSbetween = 20 and SSwithin = 40, then:
η2 = 20 / (20 + 40) = 0.5
Therefore, η2 = 0.50, which means that 50% of the total variance in the dependent variable can be attributed to the independent variable (or factor) being analyze. The statement "If an analysis of variance produces SS between = 20 and SS within = 40, then η 2 = 0.50" is true. To determine η 2 (eta-squared), you'll need to calculate the proportion of total variance explained by the between-group variation. This can be done using the formula η 2 = SS between / (SS between + SS within). In this case, η 2 = 20 / (20 + 40) = 20 / 60 = 0.50. Therefore, the eta-squared value is indeed 0.50, indicating that 50% of the total variance is accounted for by the between-group variation.
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Soledad buys 5 ounces of frozen yogurt for $2.25. What is the unit price of the frozen yogurt in dollars per ounce?
Answers
Answer:
0.45
Step-by-step explanation:
You divided 2.25 by 5
hence, you divide 2.25 by 5.
George is a candle maker. Each 14cm long candle he makes burns for 7 hours. If George makes a 46cm long candle, how long would it burn
Answers
14cm candle burns 7 hours
1cm candle burns 7/14 **since it is 1cm so it will burn less
46cm candle burns 7*46/14 = 23 hours
It took the Phillips family 6 hours to drive to their vacation destination. Due to traffic, it took them 8. 7 hours to drive home
Answers
When it takes 6 hours to travel and 8.7 hours to return home, there is a 45% increase in travel time.
What is percent?A percentage is a number or ratio expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent sign, "%," is frequently used to indicate it. A percentage is a number without dimensions and without a standard measurement. In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).
Here,
Time take to arrive at vacation destination=6 hours
Time take to arrive at home=8.7 hours
percent increase=(8.7-6)/6*100
=45%
The percent increase in the time taken to come back to home is 45% when they took 6 hours to reach and 8.7 hours to comeback.
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Complete question:
It took the Phillips family 6 hours to drive to their vacation destination. Due to traffic, it took them 8 hours and 42 minutes to drive home. Percentage for Increase or Decrease!!
With reference to the various sampling methods, ________ is used when it is important to control where the sample is delivered and when the products are of a perishable nature.
Answers
Door to door sampling is used when it is important to control where the sample is delivered and when the products are of a perishable nature.
What is sampling?The term sampling selecting refers to the selection of a small proportion of the population extrapolating the results the results obtained from this small group to represent the characteristics of the entire population. This sample is chose in a manner as to reflect the properties the generality of the population.
Hence, door to door sampling is used when it is important to control where the sample is delivered and when the products are of a perishable nature.
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Hellp me plz now yeyeyey
Answers
Answer:
step two
explanation:
the first 17.8 (-17.8) he was supposed to use was negative but the 17.8 (17.8) he used was not
Find the coordinates of M, the midpoint of UV, for U(-4, 2) and V(6, 10).
OM(-5,-4)
OM(-1,8)
OM(1,6)
OM(2, 12)
Answers
The Coordinates of M, the midpoint of UV is (1, 6).
What is coordinates?Coordinates are numbers which determine the position of a point or a shape in a particular space (a map or a graph).
To calculate the coordinates of M, the midpoint of UV, use the formula below.
Coordinates of M (x,y) = [(x₁+x₂)/2,(y₁+y₂)/2)]..................... Equation 1
Where:
x₁, x₂ = x coordinates of U and Vy₁, y₂ = y coordinates of U and VFrom the question,
Given:
x₁ = -4x₂ = 6y₁ = 2y₂ = 10Substitute these values into equation 1
Coordinates of M (x,y) = [(-4+6)/2, (2+10)/2]Coordinates of M (x,y) = [(2/2), (12/2)]Coordinates of M (x,y) = (1, 6)Hence, the Coordinates of M is (1, 6).
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Can somebody help me with this question
Answers
Answer:
900°
Step-by-step explanation:
The interior angles sum = 180° ( n - 2 )
~~~~~~~~
n = 7
180° ( 7 - 2 ) = 900°
Answer:
900 degrees
Step-by-step explanation:
just apply the formulas discussed in class !
The sum of interior angles in a triangle is 180°. To find the sum of interior angles of a polygon, multiply the number of triangles in the polygon by 180°.
The number of triangles in each polygon is two less than the number of sides.
The formula for calculating the sum of interior angles is:
(n−2)×180∘ (where n is the number of sides)
in our case we have 7 sides.
so, we could split this polygon into 5 triangles.
each of these triangles would have an angle sum of 180°.
so, the angle sum of the polygon is
5×180 = 900°