for the given normally distributed random variable,
(a) P(16 < X < 22) = 0.7333
(b) P(X < k1) = 0.2946; such that the value of k1 = 16.625
(c) P(X > k2) = 0.8186; such that the value of k2 = 15.725
(d) The two cut-off values that contain the middle 90% of the normal curve area are -1.64 and +1.64.
What is the formula for finding the z-score?The formula for finding the z-score is
z = (X - μ)/σ
Here the mean (μ) and the standard deviation (σ) are applied.
Calculation:It is given that, a normally distributed random variable X has a mean μ = 18 and the variance σ² = 6.25.
So, its standard deviation is σ = √6.25 = 2.5
(a) P(16 < X < 22)
The z-score for X = 16 is
z = (X - μ)/σ ⇒ z = (16 - 18)/2.5 = -0.8
The z-score for X = 22 is
z = (X - μ)/σ ⇒ z = (22 - 18)/2.5 = 1.6
So, the probability becomes
P(16 < X < 22) = P(-0.8 < z < 1.6)
= P(z < 1.6) - P(z < -0.8)
From the distribution table, we have P(z < 1.6) = 0.9452 and P(z < -0.8) = 0.2119.
So, we get
P(16 < X < 22) = 0.9452 - 0.2119 = 0.7333
(b) The value of k1 such that P(X < k1) = 0.2946:
we have P(X < k1) = 0.2946
⇒ P(X < k1) = P(z < (k1 - μ)/σ) = 0.2946
From the table, we know that,
P(z < -0.55) = 0.2946
So,
(k1 - μ)/σ = -0.55
⇒ (k1 - 18)/2.5 = -0.55
⇒ k1 - 18 = -0.55 × 2.5 = -1.375
∴ k1 = -1.375 + 18 = 16.625
(c) The value of k2 such that P(X > k2) = 0.8186:
we have P(X > k2) = 0.8186
⇒ P(z > (k2 - μ)/σ) = 0.8186
⇒ 1 - P(z < (k2 - μ)/σ) = 0.8186
⇒ P(z < (k2 - μ)/σ) = 1 - 0.8186 = 0.1814
From the table, we know that P(z < -0.91) = 0.1814
So,
(k2 - μ)/σ = -0.91
⇒ (k2 - 18)/2.5 = -0.91
⇒ k2 - 18 = -0.91 × 2.5 = -2.275
∴ k2 = -2.275 + 18 = 15.725
(d) The two cut-off values that contain the middle 90% of the normal curve area are -1.64 and +1.64 since the z-score for a 90% confidence interval is 1.64.
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factor this expression 9x^2 - 18x
factor this expression 4x^2 - 9
Answer:
9 x (x - 2) and (2 x - 3) (2 x + 3)
Step-by-step explanation:
Factor the following:
9 x^2 - 18 x
Factor 9 x out of 9 x^2 - 18 x:
Answer: 9 x (x - 2)
Factor the following:
4 x^2 - 9
4 x^2 - 9 = (2 x)^2 - 3^2:
(2 x)^2 - 3^2
Factor the difference of two squares. (2 x)^2 - 3^2 = (2 x - 3) (2 x + 3):
Answer: (2 x - 3) (2 x + 3)
During one particular sales day, 75% of the store's customers paid with credit cards. If there were 60 customers that day, how many used a credit card? A. 15 B. 30 C. 45 D. 50 HINT Method 1: Set up a proportion and cross multiply. Method 2: Convert the
45 people used credit card on that particular day , this could be found out using simplified multiplication.
What is proportion?
A quantitative relation is an ordered try of numbers a and b, written a / b wherever b doesn't equal zero.
A proportion is Associate in Nursing equation within which 2 ratios ar set up to one another.
Main body:
We have been given that during one particular sales day, 75% of the store's customers paid with credit cards. There were 60 customers that day.
To find the number of people, who used credit card, we will find 75% of 60.
The number of people who used credit card = (75 / 100 )* 60
The number of people who used credit card = 0.75 *60
The number of people who used credit card = 45
Therefore, 45 people used credit card on that particular day.
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Question What is the best approximation of the solution to the system to the nearest integer values? Responses (3, 2) begin ordered pair 3 comma 2 end ordered pair (2, 3) begin ordered pair 2 comma 3 end ordered pair (3, 4) begin ordered pair 3 comma 4 end ordered pair (1, 3) begin ordered pair 1 comma 3 end ordered pair Graph of a system of linear equations. Equation 1 is 5 x plus 2 y equals 16. Equation 2 is x plus 3 y equals 12.
The best approximation to the solution of the system of equations is (2, 3)
How to determine the best approximation to the solution?From the question, we have the following parameters that can be used in our computation:
Equation 1 is 5 x plus 2 y equals 16.
Equation 2 is x plus 3 y equals 12.
Rewrite the equations properly
So, we have the following representation
5x + 2y = 16
x + 3y = 12
Make x the subject in the second equation
So, we have
x = 12 - 3y
Substitute x =12 - 3y in the equation 5x + 2y = 16
So, we have
5(12 - 3y) + 2y = 16
Open the brakects
This gives
60 - 15y + 2y = 16
Evaluate the like terms
-13y = -44
Divide both sides by -13
y = 3.39
Substitute y = 3.39 in x = 12 - 3y
x = 12 - 3 * 3.39
Evaluate
x = 1.83
Approximate the solutions
x = 2 and y = 3
Hence, the solution is (2, 3)
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Let a, b, and c be real numbers where a b c 0. Which of the following functions could represent the graph below?
Answer:
[tex]f(x)=x^2(x-a)^2(x-b)^4(x-c)[/tex]
Step-by-step explanation:
There is a double root at [tex]x=0[/tex], which corresponds to [tex]x[/tex] raised to an even power.
There are also 2 more double roots and one more single root. This corresponds to two factors raised to an even power and one factoe raised to an odd power.
The only option that satisfies this is Option 1.
The graphical representation of the polynomial function is given by the relation f ( x ) = x² ( x - a )²( x - b )⁴ ( x - c )
What is Equation of Graph of Polynomials?Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.
Identify the even and odd multiplicities of the polynomial functions' zeros.
Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.
The graphs cross or are tangent to the x-axis at these x-values for zeros with even multiplicities. The graphs cross or intersect the x-axis at these x-values for zeros with odd multiplicities
Given data ,
Let the polynomial equation be represented as f ( x )
Now , the value of f ( x ) is
f ( x ) = x² ( x - a )²( x - b )⁴ ( x - c )
The factors (x - a), (x - b), and (x - c) indicate that the function has roots at x = a, x = b, and x = c. These roots are of multiplicity 2, 4, and 1 respectively, which means that they are repeated in the factors (x - a)², (x - b)⁴, and (x - c), respectively.
The factor x² indicates that the graph of the function opens upward, since the leading coefficient is positive.
Overall, the graph of this function will have eight "humps" or "bumps" corresponding to its eight roots, and the heights and shapes of these bumps will depend on the values of a, b, and c.
Hence , the graph of the function is plotted
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please help i need it!
thank you!!
What is the domain of the function graphed?
A. {x:x > -4}
B. {x:x < -4}
C. {x:x ≥ -4}
D. all real numbers
(If you have the time, please give an explanation because I completely forgot how to solve these problems)
The correct option is D .
This is a parabola with domain all real numbers D .
PLEASE SHOW STEPS WILL MARK BRAINLIEST
The following graph shows a top-opening parabola.
What is the vertex form of the equation that represents this parabola?
Responses
y=(x−9)2−1y is equal to open paren x minus 9 close paren squared minus 1
y=(x+1)2−9y is equal to open paren x plus 1 close paren squared minus 9
y=(x+9)2−1y is equal to open paren x plus 9 close paren squared minus 1
y=(x−1)2−9
Answer:
(b) y=(x+1)²−9
Step-by-step explanation:
You want the vertex form equation of the graphed parabola, which opens upward and has its vertex at (-1, -9).
Vertex formThe vertex form equation for a parabola with vertex (h, k) is ...
y = (x -h)² +k
The vertex of the parabola shown is (h, k) = (-1, -9). Using these values in the equation gives ...
y = (x +1)² -9
__
Additional comment
The equation may include a scale factor that multiplies the square. Here, the curve rises 1 unit for 1 unit either side of the vertex, so the scale factor is 1. (The rise at ±1 from the vertex is the scale factor.)
Steps: (1) read the vertex coordinates from the graph; (2) put those coordinates in the vertex form equation; (3) check to see that the vertical scale factor is 1.
What are the missing statement and reason in step 2 of the proof?
The statement is AB=CD,BC=AD due to definition of parallelogram. The statement is AC=AC due to Reflexive property of equality.
What is parallelogram?A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size. A quadrilateral with the opposing sides parallel is called a parallelogram. A parallelogram with all right angles is known as a rectangle, and a quadrilateral with equal sides is known as a rhombus.
Here,
1. Statement: AB=CD,BC=AD
Reason: By definition of parallelogram.
2. Statement: AC=AC
Reason: Reflexive property of equality.
The definition of a parallelogram causes the sentence to be AB=CD,BC=AD. Due to the reflexive feature of equality, the assertion is AC=AC.
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Ticket sales for Six Flags White Water totaled $94,520 this summer. Tickets for the water park cost $17 each. How many tickets were sold?
The number of tickets that will be sold is 5560.
What is division?
A division is one of the fundamental mathematical operations that divides a larger number into smaller groups with the same number of components. How many total groups will be established, for instance, if 20 students need to be separated into groups of five for a sporting event? The division operation makes it simple to tackle such issues. Divide 20 by 5 in this case. 20 x 5 = 4 will be the outcome. There will therefore be 4 groups with 5 students each. By multiplying 4 by 5 and receiving the result 20, you may confirm this value.
Ticket sales for Six Flags White Water totaled $94,520 this summer.
Tickets for the water park cost $17 each.
The number of tickets sold will be = 94520/17 = 5560.
Hence, the number of tickets that will be sold is 5560.
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there is a real number n such that numerical values of sum of the edge lengths and surface area of a cube with side length n are equal. find n?
Answer:
Given:
Sum of edge lengths = TSA of cube
there are 12 edges in a cube
[tex]12n = 6 {n}^{2} \\ 6 {n}^{2} - 12n = 0 \\ 6n(n - 2) = 0 \\ 6n = 0 \\ n = 0 \\ n - 2 = 0 \\ n = 2[/tex]
n ≠ 0 (since length can't be 0)
therefore n=2
A tile is randomly selected from a bag that contains 10 tiles. The tiles are either blue, green, red, or yellow. After the color is recorded, the tile is placed back in the bag. A tile is pulled 100 times, of which 24 are blue tiles, 12 are green tiles, and 12 are red tiles.
The number of tiles in the bag of 10 that are yellow in colour are; 5 tiles
How to find the probability of selection?We are given;
Total number of tiles in bag = 10 tiles
Now, we are told that in the bag, the tiles are either blue, green, red, or yellow.
Now, after selecting a tile, we are told that it is put back and as such we have after 100 selections that we have 24 blue tiles, 12 green tiles and 12 red tiles. Thus;
Number that will be yellow = 100 - 24 - 12 - 12 = 52 yellow tiles
Thus, it means that the probability of selecting a yellow tile is;
52/100
Thus, number of tiles out of the 10 in the bag that are yellow =
(52/100) * 10 = 5.2
Approximately 5 yellow tiles
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Complete question is;
How many yellow tiles are most likely in the bag? Enter the answer in the box. A tile is randomly selected from a bag that contains 10 tiles. The tiles are either blue, green, red, or yellow. After the color is recorded, the tile is placed back in the bag. A tile is pulled 100 times, of which 24 are blue tiles, 12 are green tiles, and 12 are red tiles.
Find the equation of parabola
(i) having focus at (0,-3) its directrix is y = 3.
(ii) having end points of latus rectum (5,10) and (5,10) and which opens towards right.
(iii) having vertex at origin and focus at (0,2)
Answer:
somone in my class is literally a new York rat
Step-by-step explanation:
A total of 50 people play darts.
Each player is given 3 darts to try and
hit the bullseye. If 21 of the darts hit
the bullseye, then what percent of
the darts hit the bullseye?
The percentage of the darts hit the bullseye will be 14%.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
A sum of 50 individuals plays darts. Every player is given 3 darts to attempt to stir things up around town. Assuming 21 of the darts hit the bullseye.
The total number of dart is calculated as,
Total dart = 50 x 3
Total dart = 150
The percentage is given as,
P = (21 / 150) x 100
P = 0.14 x 100
P = 14%
The percentage of the darts hit the bullseye will be 14%.
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Which is called vertex?
A vertex is a point where two or more curves, lines, or edges meet.
In geometry, vertex generally refers to an intersection point or a corner where lines, curves or edges meet. As a consequence of this definition, the point where two lines meet to form an angle called an included angle are considered vertices. Hence, the corners of triangle, polygons and polyhedral are vertices. For example, the lines of square or rectangle intersect at four corners which are called its vertices (which is the plural of vertex). Similarly, the vertex of curve(s) is where they intersect with each other or with its line of symmetry.
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Given (x – 7)2 = 36, select the values of x.
x = 13
x = 1
x = –29
x = 42
Answer:
x = 13
x = 1
Step-by-step explanation:
The (x – 7)2 = 36 gives the value of x as 25.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
(x – 7)2 = 36
Now, dividing both side by 2
(x – 7)2/2 = 36 /2
(x – 7) = 18
Now, add 7 both side
x- 7+ 7= 18 + 7
x = 25
Hence, the value of x is 25.
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Four students were given paint supplies for an art project. The table shows the amount of paint used by each student.
Student 1 Student 2 Student 3 Student 4
seventeen twentieths 1 and one fourth 65% 0.20
Which student used the least amount of paint for their art project?
Student 1
Student 2
Student 3
Student 4
Student 4 used the least amount of paint for the art project
How to determine which student used the least amount of paint?Given:
Student 1 used seventeen twentieths => 17/20
Student 2 used 1 and one-fourth => 1 1/4 = 5/4
Student 3 used 65% = 65/100
Student 4 used 0.20 = 20/100
Since the amount of paint used for the art project has been expressed in fractions. Find the LCM:
17/20, 5/4, 65/100, 20/100
The LCM of 20, 4 and 100 is 100
Student 1: 17/20 = 85/100
Student 2: 5/4 = 125/100
Student 3: 65/100
Student 4: 20/100
Thus, student 4 used the least amount of paint
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Answer: Student 4 (d)
Step-by-step explanation:
Brainliest?
True or False: An asymptote is a line that a curve gets infinitely close to
True
False
3. The quilt is made of squares with diagonals. (Lesson 3-12)
The length of BD is 4.
a. Find the length of AE.
Using Pythagoras theorem, the length of AE in the square 2√2 unit
Length of AETo find the length of side AE, we have to use use the dimension of BD given.
In the figure given, the length of all sides are equal to one another. This implies that the sides are equidistant to one another.
In a given square, all the sides are equal to one another, but the length of the diagonal is the square root of the sum of two sides
This can be further explained as
BD = AC
Using Pythagoras theorem
BD² = AD² + BA²
4² = x² + x²
16 = 2x²
x² = 8
x = √8
x = 2√2
However, we need to find the length of AE
AE is half the length size of AD
AE = 2√2 / 2
AE = √2
The distance AE = √2
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Subtract expression 2 from expression 1
Expression 1: -9x + 8y
Expression 2: -8x - 2y
It is important to statistically compare the participants and the control groups on demographic characteristics to show that differences found in the evaluation are due to program differences and not to demographic differences. This type of statistical analysis speaks to the __________________ validity of the evaluation.
Group of answer choices
causal
interpreted
external
internal
Internal validity refers to the accuracy of the evaluation in attributing the changes identified to the program and not to other factors, such as demographic differences between the participants and the control group.
To ensure internal validity, one must compare the participants and the control groups on demographic characteristics in order to show that the differences found in the evaluation are due to program differences and not to demographic differences. This is done by conducting a statistical comparison of the two groups and calculating the probability that any differences found between them are due to the program and not to some other factor. This is done by computing the probability that the two groups are the same, given the observed mean differences, and then evaluating the results to determine if the differences are statistically significant. For example, if the two groups have different means, the probability of them being the same is calculated, and if this probability is low, then the difference is likely to be due to the program and not to some other factor. This type of statistical analysis speaks to the internal validity of the evaluation.
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1) 9x² + 4y² - 36x + 8y + 4 = 0
Write the standard form equation of each ellipse
with double-digit annual percentage increases in the cost of health insurance, more and more workers are likely to lack health insurance coverage (usa today, january 23, 2004). the following sample data provide a comparison of workers with and without health insurance coverage for small, medium, and large companies. for the purposes of this study, small companies are companies that have fewer than 100 employees. medium companies have 100 to 999 employees, and large companies have 1000 or more employees. sample data are reported for 50 employees of small companies, 75 employees of medium companies, and 100 employees of large companies. health insurance size of company yes no total small 37 13 50 medium 64 11 75 large 88 12 100 Conduct a test of independence to determine whether employee health insurance coverage is independent of the size of the company. Use = .05.
Compute the value of the 2 test statistic (to 2 decimals).
The p value is Selectless than .005between .005 and .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 2
What is your conclusion?
SelectConclude health insurance coverage is not independent of the size of the companyCannot reject the assumption that health insurance coverage and size of the company are independentItem 3
The USA Today article indicated employees of small companies are more likely to lack health insurance coverage. Calculate the percentages of employees without health insurance based on company size (to the nearest whole number).
Small %
Medium %
Large %
Based on the percentages calculated above, what can you conclude?
SelectLarge companies have a higher percentage of no coverage than medium and small companiesMedium companies have a higher percentage of no coverage than large and small companiesSmall companies have a higher percentage of no coverage than large and medium companiesSmall, medium, and large companies all have roughly the same percentage of no coverage
The value of the test statistics is , χ² = 15.3902
The value of P is less than 0.005 and the conclusion which we can draw from this is that the health insurance coverage is depending on the size of the business in point a.
The percentages of employees without health insurance based on company size for small , medium and large companies is ,
Small%= 33/50= 0.66Medium%=68/75 =0.91Large%= 88/100= 0.88We established our null hypothesis and alternate hypothesis as
H0: The availability of health insurance for employees is unrelated to the size of the business
H1 :The availability of employee health insurance is depending on the size of the business.
2) The alpha level for significance is set at 0.05.
3) The H0 test statistic is
O is the measured frequency, and E is the anticipated frequency, so that 2 = (O - E)2/E
This has a chi-square distribution that is around (3-1) (2-1)= 2 d.f.
We reject the null hypothesis that employee health insurance coverage is NOT independent of the size of the company because the calculated 2 = 15.3902 falls in the critical area 2 5.99.
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At Hamburger Heaven, they use two buns for every hamburger. The following shows how the number of buns, y, changes as the number of hamburgers, x, changes. Which equation shows this relationship?
Help me please!
The equation that shows the relationship between x and y is y = 2x. Option D is the correct option.
What is relationship between two variables?
A correlation exists between the two variables in question. A correlation coefficient is a metric that quantifies the strength of a relationship or level of correlation. A correlation coefficient is a measure of the strength and direction of a relationship expressed numerically.
The general equation of a line that passes origin is y = mx.
Find some point on the line:
The points that lie on the line are (1,2) , (2, 4), (3,6) etc.
Since the points lie on the line, thus they will be satisfy the equation of line.
Putting x = 1 and y = 2 in y = mx:
2 = m × 1
m = 2
Putting m = 2 in y = mx:
y = 2x
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Julie is considering enrolling in two courses: physics and chemistry. There is a 10% chance she will enroll in physics and a 45% chance she will not enroll in physics but enroll in chemistry. Given that her decision of enrolling in a course is independent of enrolling in other courses, find the probability she will not enroll in chemistry? Assume Event A: she enrolls in physics; Event B: she enrolls in chemistry.
If the decision of enrolling in the course in independent events, the probability of not enroll in chemistry is 0.55
The chances of enroll in physics = 10%
The chances of the not enroll in physics but enroll in chemistry = 45%
The probability is the ratio of the number of favorable outcomes to the total number of outcomes
The probability = Number of favorable outcomes / Total number of outcomes
Given that her decision of enrolling in a course is independent of enrolling in other courses
The probability of not enroll in chemistry = 1 - The probability of enroll in chemistry
Substitute the value in the equation
The probability of not enroll in chemistry = 1 - 0.45
= 0.55
Therefore, the probability of not enroll in chemistry is 0.55
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2x+2y=10 slope intercept equation
Answer:
y = -x + 5
Step-by-step explanation:
2x+2y=10 slope intercept equation
2x+2y=10
subtract 2x from both sides:
2y = 10 - 2x
rearrange right side:
2y = - 2x + 10
divide all terms by 2:
y = -x + 5
Answer:
Step-by-step explanation:
5 over 2
Please Help!!
It's urgent somebody
2) Write a word problem using the information from the given equation and inequality. Be sure to include all seven parts and an appropriate question requesting a solution for the unknown (variable).
The seven parts of a one-variable equation are as follows:
1 – correct variable term for the left side expression
2 – correct constant term for the left side expression
3 – correct operation between the terms of the left side expression
4 – correct equal sign or inequality symbol
5 – correct variable term for the right side expression
6 – correct constant term for the right side expression
7 – correct operation between the terms of the right side expression
Inequality: 58x+170>42x+320
The solution for the variable is that the variable should be greater than 9.375
How to write a word problem using an inequality?An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g 2x > 4
Given: the inequality 58x+170 > 42x+320. The unknown variable is x
In word problem, we can write:
When a variable x is multiplied by 58 and then 170 is added. The result is greater than variable x multiplied by 42 with 320 added
Solution for the unknown
58x+170 > 42x+320
58x-42x > 320-170
16x > 150
x > 150/16
x > 9.375
Thus, the solution for the unknown is that the unknown should be greater than 9.375
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please help. A camper drove 80 miles to a recreational area and then hiked 4 miles into the woods. The rate of the camper while driving was 10 times the rate while hiking. The total time spent hiking and driving was 3 hours. Find the rate at which the camper hiked
Driving is done at a 40 mph speed when a camper traveled 80 miles to a destination for recreation before doing a 4-mile stroll through the woods.
Given that,
A camper traveled 80 miles to a destination for recreation before doing a 4-mile stroll through the woods. The camper's speed while driving was ten times that of the hiker. Three hours were spent driving and hiking together.
We have to determine the camper's hiking speed.
We know that,
Let x represent the increasing rate and 10x represent the driving rate.
Time equation is
80/10x+4/x=3
Simplify
8/x+4/x=3
12/x=3
x=12/3=4
Therefore, Driving is done at a 40 mph speed when a camper traveled 80 miles to a destination for recreation before doing a 4-mile stroll through the woods.
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The vertex form of the quadratic function f (x) = x² + 8x + 7 is
f(x)= a(x-h)² + k.
What is the value of a?
What is the value of h?
What is the value of k?
Answer:
Step-by-step explanation:
The vertex form of a quadratic function is given by the equation f(x) = a(x - h)² + k, where (h, k) is the coordinates of the vertex of the parabola, and a is a constant coefficient.
To find the values of a, h, and k for the given quadratic function f(x) = x² + 8x + 7, we can first use the formula for the x-coordinate of the vertex of a quadratic function, which is given by h = -b / 2a. In this case, the quadratic function is f(x) = x² + 8x + 7, so b = 8 and a = 1. Plugging these values into the formula, we get:
h = -8 / 2(1) = -4
Therefore, the value of h is -4.
Next, we can use the formula for the y-coordinate of the vertex of a quadratic function, which is given by k = f(h) = a(h - h)² + k. In this case, we know that the value of h is -4, and we can plug this value into the original quadratic function to get the value of k:
k = f(-4) = (-4)² + 8(-4) + 7 = 16 - 32 + 7 = -9
Therefore, the value of k is -9.
Finally, we can use the equation f(x) = a(x - h)² + k to find the value of a. Since we know that the coordinates of the vertex are (-4, -9) and the equation of the quadratic function is f(x) = x² + 8x + 7, we can plug these values into the equation to solve for a:
f(x) = a(x - h)² + k
x² + 8x + 7 = a(x - (-4))² + (-9)
We can then distribute the squared term and simplify the equation to get:
x² + 8x + 7 = a(x² - 8x + 16) + (-9)
x² + 8x + 7 = a(x²) - 8a(x) + 16a + (-9)
We can then collect like terms to get:
x² + 8x + 7 = a(x²) - 8ax + 16a - 9
Comparing the coefficients of the x², x, and constant terms on both sides of the equation, we can see that a = 1.
Therefore, the values of a, h, and k for the given quadratic function f(x) = x² + 8x + 7 are a = 1, h = -4, and k = -9.
Suppose that f(3)=2 and g(-2)=6 explain how f(x) and g(x) cannot be inverse funtions of one another
If f{g(x)} = g(x) and g{f(x)} = f(x)
That means they cannot be inverse functions of one another.
What is a function?A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.
Given that f(3) = 2 and g(-2) = 6.
From the expression, f⁻¹(2) = 3 and g⁻¹(6) = -2
So now we take the composition,
f{g(-2)} = f (6) = y (let)
Then f⁻¹(y) = 6 = g (-2) , which is given.
Now, f{g(-2)} = g (-2).
And similarly g{f(3)} = g (2) = k (let)
g⁻¹(k) = 2 = f (3)
Now, g{f(3)} = f (3)
Therefore, if f{g(x)} = g(x) and g{f(x)} = f(x)
That means they cannot be inverse functions of one another.
To learn more about the function;
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If a = -2 and b = 3, what is the value of -3a²b?
Answer:
-36
Step-by-step explanation:
-3[tex]a^{2}[/tex]b Substitute -2 for a and 3 for b
-3[tex](-2)^{2}[/tex](3)
-3(4)(3)
-36
Answer:
= -36
Step-by-step explanation:
-3a²b
if:
a = -2
b = 3
Then:
= -3*-2²*3
= -3(-2*-2) * 3
= -3*4*3
= -36
