Answers
Answer:
the answer to the question provided is y = x
Related Questions
A hostel has food for 60 days if after 15 days 500 more students joined th hostel and the food lasted for 40days only. How many students were there in hostel
Answers
Answer:
625
Step-by-step explanation:
here we are in an inverse proportion situation :
As the number of days increases
when the number of students decreases and vice versa.
__________________
Say n is the original number of students.
___________________________________________
After 15 days, the rest of food is enough for n students for 45 days,
or enough for n+500 students for 25 days.
Then
45n = 25×(n + 500)
Then
45n = 25n + 25×500
Then
45n - 25n = 25×500
Then
20n = 12500
Then
n = 12500÷20
= 625
and thus , there were 625 students in the hostel.
The population of a rural city follows the exponential growth model P(t)=3400^0.0371t where t is the number of years after 1986 . a) Use this model to approximate the population in 2030.
Answers
After answering the presented question, we can conclude that expressions Therefore, the population of the rural city in 2030 is approximately 11,014.18.
what is expression ?In mathematics, you can multiply, divide, add, or subtract. An expression is constructed as follows: Number, expression, and mathematical operator A mathematical expression is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) It is possible to contrast expressions and phrases. An expression or algebraic expression is any mathematical statement that has variables, integers, and an arithmetic operation between them. For example, the expression 4m + 5 has the terms 4m and 5, as well as the provided expression's variable m, all separated by the arithmetic sign +.
To approximate the population in 2030, we need to find the value of P(t) when t = 44, since 2030 is 44 years after 1986.
Using the given exponential growth model, we have:
\(P(t) = 3400^(0.0371t)\\P(44) = 3400^(0.0371*44)\\P(44) = 3400^1.6334\\P(44) = 11014.18\\\)
Therefore, the population of the rural city in 2030 is approximately 11,014.18.
To know more about expressions visit :-
https://brainly.com/question/14083225
#SPJ1
There are twenty-four 4 digit whole numbers that use each ofth four digits, 2, 4, 5, and 7 exactly once. Listed in numbericalorder from smallest to largest, the number in the 17th position inthe list is;
a. 4527 b. 5724 c. 5742 d. 7245 e. 7524
A straight concrete sidewalk is to be 3 feet wide, 60 feetlong and 3 inches thick. How many cubic yards of concretemust a contractor order for the sidewalk if concrete must beordered in a whole number of cublic yards?
a. 2 b. 5 c. 12 d.20 e. more than 20
Answers
The number in the 17th position in the list is 7425
We start by eliminating some of the options. The smallest possibility for the larger number is if the larger number were twice the smaller number. \($2457\times2=4914$\), since \($2457$\) the least value in the group. In order for the largest possibility to be less than or equal to 7542, the largest number in the set, when multiplied by 2, it must be twice as large as the largest number in the set.This happens to be \($2754\times2=5508$\). As a result, the number would need to be even and between 4914 and 5508. 5472 and 5274 are the only even numbers in the set and in this range. Both of these numbers are not twice a number in the set, according to a cursory check. The number cannot be four times or higher than any other number in the set because \($2457\times4=9828$\), well past the range of the set. Therefore, the number must be triple another number in the set. The least possibility is \($2457\times3=7371$\)and the greatest is \($2475\times3=7425$\), since any higher number in the set multiplied by 3 would be out of the range of the set. Reviewing, we find that the upper bound does in fact work, so the multiple is \($2475\times3=7425\).
To learn more about the upper bound click here:
brainly.com/question/22965427
#SPJ4
Answer to this equation , simplified
Answers
If the value of a = 5 and c = √21 then the value of b = 2i, b = -2i.
What is meant by simplest radical form?Simply said, simplifying a radical eliminates the need for further square, cube, fourth, etc. roots to be found. This is known as expressing in the simplest radical form. In the denominator of a fraction, it also means eliminating any radicals. The top and bottom of a fraction are said to be in its simplest form if they only share the number one. For the top and bottom to remain whole numbers, you cannot divide them further. Additionally, lowest terms, or simple form, may be used. Take the fraction, as an example.The formula goes a² + b² = c², where a and b are legs of the triangle (the non hypotenuse sides), and c is the hypotenuse (the side opposite to the right angle).In this problem, we have one leg and the hypotenuse.
Let the equation be a² + b² = c²
substitute the values in the above equation, we get
5² +b² = (√21)²
25+b²=21
Move 25 to the right side
b² = -4
For x² = f(a) the solutions are \($x=\sqrt{f(a)},-\sqrt{f(a)}$\)
\($$b=\sqrt{-4}, b=-\sqrt{-4}$$\)
simplifying the above equation, we get
\(& \sqrt{-4}=2 i \\\)
\(& -\sqrt{-4}=-2 i \\\)
b = 2i, b = -2i
Therefore, the value of b = 2i, b = -2i.
To learn more about hypotenuse refer to:
https://brainly.com/question/2217700
#SPJ1
Darren bought 3 shirts for $44.10. Each shirt cost the same amount. Which equation models the cost, y, to purchase x shirts?
Answers
Answer:
Y= 14.7x
Step-by-step explanation:
Since 3 shirts=44.10 and each shirt cost the same
⇒1 shirt = 44.10/3
1 shirt=$14.7
⇒ The equation is Y= 14.7x
For as many shirts you want to purchase,you substitute a value for x,multiply by the cost of a shirt which is 14.7 to get the total cost
Please show work with every step
Answers
Answer:
Yes, it is a function
Step-by-step explanation:
A function is a set of ordered pairs where there are no two of the same domain. The domain is the first coordinate which is x. In this question the domain is 9, 14, 0, 2 there is no two of the same domain so this is a function.
Hope This Helps :)
Question 9 of 10 Which of the following is most likely the next step in the series? OA. O B. O C. O D.
Answers
Answer: B
Step-by-step explanation:
The most likely the next pattern in the series is 2 lines with red color. Therefore, option B is the correct answer.
What is pattern?A recurring arrangement of numbers, forms, colours, and other elements constitutes a pattern in mathematics. The Pattern can be connected to any kind of occasion or thing. When a group of numbers are arranged in a particular way, the arrangement is referred to as a pattern. Patterns can also occasionally be referred to as a series.
From the given patterns
Figure 1 has 5 lines and it is blue in color.
Figure 2 has 4 lines and it is red in color.
Figure 3 has 3 lines and it is blue in color.
So, Figure 4 must has 2 lines and red in color.
Therefore, option B is the correct answer.
Learn more about the pattern here:
https://brainly.com/question/23136125.
#SPJ7
Explain the difference between a simple random sample and a systematic sample. (Select all that apply.)
(1).In a systematic sample, every sample of size n has an equal chance of being included.
(2).In a systematic sample, random samples from each strata are included.
>
(3).In a simple random sample, the only samples possible are those including every kth item from the random starting position.
(4).In a simple random sample, random samples from each strata are included.
(5).In a systematic sample, the only samples possible are those including every kth item from the random starting position.
(6).In a systematic sample, the clusters to be included are selected at random and then all members of each selected cluster are included.
(7).In a simple random sample, the clusters to be included are selected at random and then all members of each selected cluster are included.
(8).In a simple random sample, every sample of size n has an equal chance of being included.
Answer (5) and (8)
Answers
The difference between a simple random sample and a systematic sample are;
(5).In a systematic sample, the only samples possible are those including every kth item from the random starting position.
(8).In a simple random sample, every sample of size n has an equal chance of being included.
How to identify different methods of sampling?
A simple random sample is defined as a subset of a statistical population whereby each member of the subset has an equal probability or chance of being chosen or selected.
Meanwhile systematic sampling is defined as a probability sampling method where researchers select members of the population at a regular interval.
Looking at the given options, we can conclude that the correct ones are;
In a simple random sample, every sample of size n has an equal chance of being included.
In a systematic sample, the only samples possible are those including every kth item from the random starting position.
Read more about sampling methods at; https://brainly.com/question/16587013
#SPJ1
Which of the following calculations described in the following statements require that you use the addition rule?
A)Calculate the probability of black offspring from the cross AaBb × AaBb,when B is the symbol for the black allele.
B)Calculate the probability of children with both cystic fibrosis and polydactyly when parents are each heterozygous for both genes.
C)Calculate the probability of each of four children having cystic fibrosis if the parents are both heterozygous.
D)Calculate the probability of a child having only sickle-cell anemia or cystic fibrosis if each parent is each heterozygous for both traits.
Answers
If probability each parent is heterozygous for both features, determine the likelihood that a child will only have cystic fibrosis or sickle-cell anaemia.
P(Sickle-cell Anemia)
= 0.25
P(Cystic Fibrosis)
= 0.25
P(Sickle-cell Anemia or Cystic Fibrosis) = P(Sickle-cell Anemia) + P(Cystic Fibrosis)
P(Sickle-cell Anemia or Cystic Fibrosis)
= 0.25 + 0.25
P(Sickle-cell Anemia or Cystic Fibrosis)
= 0.5
The likelihood that a child will have either cystic fibrosis or sickle-cell anaemia is 0.5 or 50%. This is because both parents are heterozygous for both features. This means that each parent has a 25% chance of passing on either one of the conditions to their child. The probability of having either one of the conditions is the sum of the individual probabilities, which is 0.25 + 0.25 = 0.5 or 50%.
Learn more about probability here
https://brainly.com/question/11234923
#SPJ4
i’ll mark brainlest again! :D
Answers
Answer:
3 one
yeeeeeeeeet
Question 5
< >
A research group needs to determine a 99% confidence interval for the mean repair cost for all car insurance
small claims. From past research, it is known that the standard deviation of such claims amounts to $146.91.
a. What is the critical value that corresponds to the given level of confidence?
Round your answer to two decimal places.
b. If the group wants their estimate to have a maximum error of $16, how many small claims should they
sample?
Round your answer up to the next integer.
Submit Question Jump to Answer
Answers
A standard deviation is a measure of how widely distributed the data is in relation to the mean. The critical value is z = 1.645 and the should sample at least 228.13638 small claims.
What is meant by standard deviation?A standard deviation (or) is a measure of how widely distributed the data is in relation to the mean. A low standard deviation indicates that data is clustered around the mean, whereas a high standard deviation indicates that data is more spread out.
The square root of the average of all squared deviations is the standard deviation. A region defined by one standard deviation, or one sigma, plotted above or below the average value on that normal distribution curve would include 68 percent of all data points.
Explanation in detail:
We can calculate our ∝ level by subtracting 1 from the confidence interval and dividing it by 2. So:
\($\alpha=\frac{1-0.99}{2}=0.05\)
Now we must locate z in the Stable, as z has a p value of \($1-\alpha$\)
So z with a p value of 1-0.05=0.95 equals z=1.645, implying that the answer to question an is z=1.645.
Determine the margin of error M as follows:
\(M=z * \frac{\sigma}{\sqrt{n}}\)
In which ∝ is the standard deviation of the people and n is the size of the sample.
b)
\($16=1.645 \cdot \frac{146.91}{\sqrt{n}}\)
Expand
\($1.645 \cdot \frac{146.91}{\sqrt{n}}: \quad \frac{241.66695}{\sqrt{n}}$$$\)
\($16=\frac{241.66695}{\sqrt{n}}$$\)
Square both sides:
\($\quad 256=\frac{58402.91472 \ldots}{n}$\)
\($256=\frac{58402.91472 \ldots}{n}\)
Solve
\($256=\frac{58402.91472 \ldots}{n}: \quad n=228.13638 \ldots$\)
Verify Solutions: \($n=228.13638 \ldots$\) True
The solution is
n=228.13638...
To learn more about standard deviation, refer to:
https://brainly.com/question/475676
#SPJ13
Please use the following for the next 6 questions. Suppose that the average weekly earnings for employees in general automotive repair shops is $450, and that the population standard deviation for the earnings for such employees is $50. A sample of 100 such employees is selected at random.
1) What is the probability distribution of the average weekly earnings for employees in general automotive repair shops?
2) Find the probability that the average weekly earnings is less than $445.
3) Find the probability that the average weekly earnings is exactly equal to $445.
4) Find the probability that the average weekly earnings is between $445 and $455.
5) In answering the previous 3 questions, did you have to make any assumptions about the population distribution?
6) Now assume that the weekly earnings for employees in all general automotive repair shops is normally distributed, obtain the probability that a given employee will earn more than $480 in a given week.
Answers
1) The probability distribution of the average weekly earnings for employees in general automotive repair shops is the sampling distribution of the sample mean. According to the Central Limit Theorem, if the sample size is large enough, the sampling distribution of the sample mean is approximately normal, with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
2) To find the probability that the average weekly earnings is less than $445, we can standardize the sample mean and use a z-table. The z-score for $445 is calculated as follows: z = (445 - 450) / (50 / sqrt(100)) = -1. Using a z-table, we find that the probability that the average weekly earnings is less than $445 is approximately 0.1587.
3) Since we are dealing with a continuous distribution, the probability that the average weekly earnings is exactly equal to any specific value is zero.
4) To find the probability that the average weekly earnings is between $445 and $455, we can subtract the probability that it is less than $445 from the probability that it is less than $455. The z-score for $455 is calculated as follows: z = (455 - 450) / (50 / sqrt(100)) = 1. Using a z-table, we find that the probability that the average weekly earnings is less than $455 is approximately 0.8413. Therefore, the probability that it is between $445 and $455 is approximately 0.8413 - 0.1587 = 0.6826.
5) In answering questions 2-4, we made an assumption about the population distribution based on the Central Limit Theorem. We assumed that since our sample size was large enough (n=100), our sampling distribution would be approximately normal.
6) If we assume that weekly earnings for employees in all general automotive repair shops are normally distributed with a mean of $450 and a standard deviation of $50, then we can calculate the z-score for an employee earning more than $480 in a given week as follows: z = (480 - 450) / 50 = 0.6. Using a z-table, we find that the probability that an employee will earn more than $480 in a given week is approximately 1 - 0.7257 = 0.2743.
A 8 1/4 inch candle burns down in 11 hours how far has it burns after 8 1/2 hours
Answers
In 8 1/2 hours, the candle would burn 6 3/8 inches.
How many inches would the candle burn in 8 1/2 hours?A mixed number is a non-integer that is made up of a whole number and a proper fraction. An example of a mixed number is 8 1/4.
The first step is to determine how much of the candle burns in one hour.
Inches of candle that burns in 1 hour = 8 1/4 ÷ 11
33/4 x 1/11 = 3/4 inches
Now, multiply the inches of candle that burns in an hour by 8 1/2
Inches of candle that would burn in 8 1/2 hours = 3/4 x 8 1/2
3/4 x 17/2 = 51/8 = 6 3/8 inches
To learn more about multiplication of fractions, please check: https://brainly.com/question/1114498
#SPJ1
AABC is similar to AADE. Enter the congruence statements that must be true.
The congruence statements that must be true are
Answers
Answer:
A is congruent to A, B is congruent to D, and C is congruent to E
Step-by-step explanation:
If ABC is congruent to ADE, then that means both triangles angles are congruent in the order they are given in.
(Hopefully you can comprehend what I just explained lol-)
Find the inverse of the equation f(x)=ln(x/x-2)
Answers
Answer:
inverse of f(x) = (2e^x)/(e^(x)-1)
Step-by-step explanation:
The revenue function for a real estate agency is based on a percentage of the amount of monthly sales made by agents. The cost function for the agency is based on the commissions, paid to the agent plus the fixed monthly costs. both functions are shown below where X is the dollar amount of the monthly sales made by agents.
• Revenue function: f (x) = 0.03
• Cost function: g (x) = 0.015x + 4,600
The agency will break, even when the revenue function is equal to the cost function. For the agency to break even, what amount of monthly transactions, in dollars, must be generated by its agents?
• Between $0 and $2000
• Between $4,500 and $4,700
• Between $153,000 and $155,000
• Between $305,000 and $307,000
Answers
Answer:
D. Between $305,000 and $307,000
Step-by-step explanation:
A. This is a result of finding 4,600(0.03 + 0.015).
B. This is a result of using the y-intercept for the cost function.
C. This is a result of incorrectly solving the equation 0.03x = 0.015x + 4,600 by dividing 4,600 by 0.03
instead of 0.015 in the final step.
D. This is a result of correctly solving the equation 0.03x = 0.015x + 4,600 ⇒ 0.015x = 4,600 then dividing
4,600 by 0.015 to get approximately 306,667.
Equivalent fractions are those that simplify to the same fraction.
Provide 3 equivalent fractions for the fraction 9/12.
Answers
Answer:
\(\frac{3}{4} = \frac{6}{8} = \frac{9}{12} = \frac{18}{24} \)
Right the slope intercept form of the line that passes through (1,-2) and is parallel to the line y=4x+2
Answers
explanation: parallel lines have the same slope, which the slope here is 4. if you plug in the x value of 1 in 4(1)-6, then you get -2 which is the desired y-value.
Choose the shape that matches the definition a three dimensional shape with a circular base and a vertex opposite base.
Answers
We need to identify which is the correct shape. We are told that it has a vertex. A vertex is a point where two or more lines, curves or edges met. In three dimensional shapes a vertex is a corner of the shape. As you can see, from the three shapes we have in the picture the only one with a corner is the cone. It is also important to note that this corner is in the opposite side of the base and this base has a circular shape.
AnswerAs we discussed above the shape that meets these characteristics is the cone. Therefore the answer is the cone.
For Pharaoh Company, variable costs are 60% of sales,the fixed costs are $175,500. Managements net income goal is $67,500.
Answers
The required sales in dollars needed to achieve managements target is $607,5000.
What is the required level of sales?
Net income is total revenue less total cost. Total cost is the sum of fixed cost and variable cost. Fixed cost is the cost that remains constant regardless of the level of output. e.g. rent. Variable cost is the cost that varies with output e.g. wages.
Net income = sales - total cost
Net income = sales - (fixed cost + variable cost)
$67,500 = sales - ($175,500 + 0.6sales)
$67,500 = sales - $175,500 - 0.6sales
$67,500 + $175,500 = sales - 0.6sales
243,000 = 0.4sales
sales = 243,000 / 0.4
sales = $607,500
Here is the complete question:
For Pharaoh Company, variable costs are 60% of sales, the fixed costs are $175,500. Managements net income goal is $67,500.Compute the required sales in dollars needed to achieve managements target net income of $67.500.
To learn more about net income, please check: https://brainly.com/question/26181966
#SPJ1
▪ For every 8 multiple-choice questions on Minnie's math
test, there are 5 short-answer questions. How many multiple-choice and short-answer questions are on a test with 65 question
Answers
The number of multiple-choice and short-answer questions on a test with 65 questions will be 40 and 25 respectively.
Numerical calculationTo determine the number of multiple-choice and short-answer questions on a test with 65 questions, we can set up a proportion based on the given ratio:
Multiple-choice questions : Short-answer questions = 8 : 5
Let x be the number of multiple-choice questions.
Let y be the number of short-answer questions.
Using the proportion, we can set up the following equation:
8/5 = x/y
8y = 5x
x = (8y)/5
Since the total number of questions on the test is 65, we have the equation:
x + y = 65
Substituting the expression for x from the previous equation:
(8y)/5 + y = 65
(8y + 5y)/5 = 65
13y/5 = 65
13y = 65 * 5
13y = 325
Dividing both sides by 13:
y = 325/13
y = 25
Substituting this value of y back into the equation x = (8y)/5:
x = (8 x 25)/5
x = 40
Therefore, there are 40 multiple-choice questions and 25 short-answer questions on the test with a total of 65 questions.
More on numerical problems can be found here: https://brainly.com/question/1774761
#SPJ1
- 13 < 2z - 3 < 5
Write the solutien using interval notation.
Answers
Answer:
ok we need to foil this form,
add +3 to all we get, -13+3 <2z-3+3 <5+3
it becomes -10<2z<8,
divide all terms by 2, we get -5<z<4
in interval notation we can write this as; (-5, 4)
Write x² + 10x + 29 in the form (x + c)² + d, where c
and d are numbers.
What are the values of c and d?
Answers
Answer:Write x² + 10x + 29 in the form (x + c)² + d, where c
Step-by-step explanation:
Answer:
(x+5)² + 4, so c is 5 and d is 4
Step-by-step explanation:
x² + 10x + 29 is a quadratic equation which can be witten as x² + bx + c, where b is 10 and c is 29.
We need to complete the square to get it in the form
(x + c)² + d
Completing the square uses the form:
\((x + \frac{b}{2} ) {}^{2} - ( \frac{b}{2} ) {}^{2} + c\)
substitute b = 10 and c = 29 in this form:
\((x + \frac{10}{2}) {}^{2} - ( \frac{10}{2} ) {}^{2} + 29\)
Simplify further:
\((x + 5) {}^{2} - 25 + 29\)
\((x + 5) {}^{2} + 4\)
c = 5, d = 4
In the diagram below of triangle BCD, E is the midpoint of BD and F is the midpoint of CD. If EF = 43-4x, and BC = 32-2x, what is the measure of EF?
Answers
The measure of the length EF of the triangle is; 21
How to solve similar triangles?We are given the the triangle BCD and we are told that;
E is the midpoint of BD.
F is the midpoint of CD
Now, since we have those midpoints, it means that by the concept of similar triangles, that;
DF/DC = EF/BC
Since F is the midpoint of DC, then it means that;
2DF = DC
We are given;
EF = 43 - 4x, and BC = 32 - 2x
Thus, we now have;
DF/(2DF) = (43 - 4x)/(32 - 2x)
1/2 = (43 - 4x)/(32 - 2x)
Cross multiply to get;
32 - 2x = 43 - 4x
4x - 2x = 43 - 32
2x = 11
x = 11/2
x = 5.5
Thus;
EF = 43 - 4(5.5)
EF = 43 - 22
EF = 21
Thus, we conclude that the side length EF is 21.
Read more about similar triangles at; https://brainly.com/question/14285697
#SPJ1
For the following vectors, (a) find the dot product v•w ; (b) find the angle between v and w , (c) state whether the vectors are parallel, octagonal, or neither. V=-3i-4j, w=6i+8j
A- v•w
B-the angle between v and w is theta ^•?
C- the vectors v and w are?
Answers
B) The angle between vectors v and w can be found using the formula: cos(theta) = (v • w) / (||v|| ||w||), where ||v|| and ||w|| are the magnitudes of vectors v and w respectively.
First, we need to find ||v|| and ||w||:
||v|| = sqrt((-3)^2 + (-4)^2) = 5
||w|| = sqrt((6)^2 + (8)^2) = 10
Now, we can substitute in the values to get:
cos(theta) = (-50) / (5 * 10) = -1
theta = arccos(-1) = pi radians or 180 degrees.
Therefore, the angle between vectors v and w is 180 degrees.
C) Two vectors are parallel if their directions are the same, which can be determined by comparing their unit vectors.
The unit vector of v is:
v_hat = v / ||v|| = (-3/5)i + (-4/5)j
The unit vector of w is:
w_hat = w / ||w|| = (6/10)i + (8/10)j = (3/5)i + (4/5)j
We can see that the unit vectors are in opposite directions, which means that the vectors are anti-parallel or opposite. Therefore, the vectors v and w are neither parallel nor orthogonal.
Sue needs to drive 372 miles to visit her aunt. She stopped at a gas station one-third of the way in to her trip. How many miles has she traveled?
Answers
Answer:
Sue has traveled 124 miles.
Step-by-step explanation:
Here, the distance covered by Sue is a fraction of the total distance to be covered.
The total distance to her aunt's = 372 miles
but the gas station is at one-third of the distance to be covered.
Thus,
Miles traveled by Sue = \(\frac{1}{3}\) x 372
= 124
Miles traveled by Sue = 124 miles.
Therefore Sue has traveled 124 miles.
Instructions: Given the quadratic function, state whether the parabola opens up or down, and whether it has a maximum or minimum.
Answers
The parabola opens down and has a vertex of (1, 7) which is a maximum value
Explanation:Given:
\(y\text{ = -3x}^2\text{ + 6x + 4}\)To find:
a) if the parabola opens up or down
b) the coordinate of the vertex
c) If it is maximum or minimum
a) To determine if the parabola opens up or down, we will use the sign of the leading coefficient.
The leading coefficient 3x² is negative. when the sign is negative, it will open down. if positive, it will open up. Hence, the parabola opens down
b) To get the vertex of the parabola, we will apply the formula:
\(\begin{gathered} Vertex\text{ = \lparen h, k\rparen} \\ h\text{ = }\frac{-b}{2a} \\ k\text{ = f\lparen}-\frac{b}{2a})\text{ = f\lparen h\rparen} \end{gathered}\)\(\begin{gathered} from\text{ the quadratic equation: -3x}^2\text{ + 6x + 4} \\ a\text{ = -3, b = 6, c = 4} \\ h\text{ = }\frac{-6}{2(-3)} \\ h\text{ = }\frac{-6}{-6}\text{ = 1} \\ \\ k\text{ = f\lparen1\rparen} \\ we\text{ }will\text{ substitute for x in the given function } \\ f(1)\text{ = -3\lparen1\rparen}^2\text{ + 6\lparen1\rparen + 4} \\ f(1)\text{ = -3 + 6 + 4 = 7} \\ k\text{ = 7} \\ \\ Hence,\text{ the vertex \lparen h, k\rparen = \lparen1, 7\rparen} \end{gathered}\)
c) If a parabola opens up, the vertex will be the lowest value (minimum). If a parabola opens down, the vertex will be the highest value (maximum)>
Since our graph opens down, it has a maximum value
The parabola opens down and has a vertex of (1, 7) which is a maximum value
Please look at the graphs in the photo. Thank you!
Answers
(a). The graph of y = -f(x) is shown in the image below.
(b). The graph of y = g(-x) is shown in the image below.
How to draw the graph of the transformed functions?By reflecting the parent absolute value function g(x) = |x + 2| - 4 over the x-axis, the transformed absolute value function can be written as follows;
y = -f(x)
y = -|x + 2| - 4
Part b.
In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would determine the slope of this line;
Slope (m) = rise/run
Slope (m) = -2/4
Slope (m) = -1/2
At data point (0, 5) and a slope of -1/2, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 5 = -1/2(x - 0)
g(x) = -x/2 + 5, -4 ≤ x ≤ 4.
y = g(-x)
y = x/2 + 5, -4 ≤ x ≤ 4.
Read more on reflection here: brainly.com/question/27912791
#SPJ1
Graph the inequality.
-6 ≤y+ 2x <15
Answers
Answer:
Look Below Hope It Helps
Step-By-Step Explanation:
Answer:
Graph C.
Step-by-step explanation:
Find the area of the shaded region.
f(x)=x4-12x³ +48x², g(x) = 44x+105
340-
(-1,61)
(5,325)
co.
8
Q
Answers
Answer:
Step-by-step explanation:
To find the area of the shaded region, we need to first find the x-coordinates of the points where the two functions intersect. We can set f(x) = g(x) and solve for x:
x^4 - 12x^3 + 48x^2 = 44x + 105
x^4 - 12x^3 + 48x^2 - 44x - 105 = 0
We can use a numerical method, such as the Newton-Raphson method, to approximate the roots of this equation. Using a graphing calculator or computer algebra system, we can find that the roots are approximately:
x = -1.932, x = 0.695, x = 4.149
Note that the root x = -1.932 is outside the given interval [3, 4], so we can ignore it.
The shaded region is bounded by the x-axis, the line y = 340, and the graphs of f(x) and g(x) between x = 3 and x = 4. To find the area of this region, we can integrate the difference between the two functions over this interval:
A = ∫3^4 [g(x) - f(x)] dx
A = ∫3^4 [44x + 105 - (x^4 - 12x^3 + 48x^2)] dx
A = ∫3^4 [-x^4 + 12x^3 - 48x^2 + 44x + 105] dx
We can integrate term by term using the power rule:
A = [-x^5/5 + 3x^4 - 16x^3 + 22x^2 + 105x]3^4
A = [-1024/5 + 192 - 192 + 22 + 105] - [-81/5 + 108 - 192 + 66 + 105]
A = 347.2
Therefore, the area of the shaded region is approximately 347.2 square units.