7.4y-2.9y

pls lmk....

Answers

Answer 1

4.5y

subtract 2.9y from 7.4y, and you get 4.5y


Related Questions

the graph shows the preimage shaded in grey and the image outlined in black. what is the scale factor of the dilation?

Answers

The scale factor of dilation of the shaded in gray to the shaded in black is 3

Calculating the scale factor dilation

Given that

The preimage = shaded in gray

The image = shaded in black

From the graph, we have the following values on the image and the preimage

The preimage = shaded in gray = 4

The image = shaded in black = 12

The scale factor of dilation is then calculated as

Scale factor = shaded in black/shaded in gray

So, we have

Scale factor = 12/4

Evaluate

Scale factor = 3

Hence, the scale factor dilation is 3

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Freddie plays baseball. If we assume the probability of him getting a base hit is 0.305, what is the probability that he gets 4 base hits in a row?

Answers

So, the probability of Freddie getting 4 base hits in a row is approximately 0.0088, or 0.88%.

What is Probability?

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

by the question.

Assuming that each at-bat is independent of the others, the probability of Freddie getting a base hit in one at-bat is 0.305.

To find the probability that he gets 4 base hits in a row, we can use the multiplication rule for independent events. This rule states that the probability of two or more independent events occurring together is the product of their individual probabilities.

Therefore, the probability of Freddie getting 4 base hits in a row is:

0.305 x 0.305 x 0.305 x 0.305 = 0.0088 (rounded to four decimal places)

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A large equilateral triangle pyramid stands in front of the city's cultural center. Each side of the base measures 40 feet and the slant height of each lateral side of the pyramid is 50 feet.

A painter can paint 100 square feet of the pyramid in 18 minutes.

How long does it take the painter to paint 75% of the pyramid?

Answers

Answer:

A large equilateral triangle pyramid stands in front of the city's cultural center. Each side of the base measures 40 feet and the slant height of each lateral side of the pyramid is 50 feet.

A painter can paint 100 square feet of the pyramid in 18 minutes.

How long does it take the painter to paint 75% of the pyramid?

Step-by-step explanation:

The total surface area of the pyramid can be calculated using the formula for the lateral surface area of a pyramid:

Lateral surface area = (1/2) × perimeter of base × slant height

Since the base is an equilateral triangle, the perimeter is 3 times the length of one side:

Perimeter of base = 3 × 40 feet = 120 feet

Lateral surface area = (1/2) × 120 feet × 50 feet = 3000 square feet

To paint 75% of the pyramid, the painter needs to paint:

0.75 × 3000 square feet = 2250 square feet

Since the painter can paint 100 square feet in 18 minutes, the time required to paint 2250 square feet can be calculated as:

2250 square feet ÷ 100 square feet per 18 minutes = 225 ÷ 10 × 18 minutes = 405 minutes

Therefore, the painter would need 405 minutes or 6 hours and 45 minutes to paint 75% of the pyramid.

Use the rational zeros theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. f(x) = x^3 - x^2 - 37x - 35 Find the real zeros of f. Select the correct choice below and; if necessary, fill in the answer box to complete your answer. (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any rational numbers in the expression. Use a comma to separate answers as needed.) There are no real zeros. Use the real zeros to factor f. f(x)= (Simplify your answer. Type your answer in factored form. Type an exact answer, using radicals as needed. Use integers or fractions for any rational numbers in the expression.)

Answers

By using rational zeros theorem, we find that there are no real zeros of the polynomial function f(x) = x^3 - x^2 - 37x - 35, so we cannot factor f(x) over the real numbers.

To find the real zeros of the polynomial function f(x) = x^3 - x^2 - 37x - 35, we can use the rational zeros theorem, which states that any rational zeros of the function must have the form p/q, where p is a factor of the constant term (-35) and q is a factor of the leading coefficient (1).

The possible rational zeros of f are therefore ±1, ±5, ±7, ±35. We can then test each of these values using synthetic division or long division to see if they are zeros of the function. After testing all of the possible rational zeros, we find that none of them are actually zeros of the function.

Therefore, we can conclude that there are no real zeros of the function f(x) = x^3 - x^2 - 37x - 35.

However, we could factor it into linear and quadratic factors with complex coefficients using the complex zeros of f(x). But since the problem only asks for factoring over the real numbers, we can conclude that the factored form of f(x) is:

f(x) = x^3 - x^2 - 37x - 35 (cannot be factored over the real numbers)

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Suppose we want to choose 5 letters, without replacement, from 15 distinct letters

Answers

[tex]\text{order does not matter}[/tex]

[tex]\text{sample space}= \text{15 letters}[/tex]

[tex]\text{no repetition}[/tex]

[tex]\text{P(A)}= \text{15C5}= \text{3003 ways}[/tex]

f the random walk starts in the center, on average how many steps does it take to return to the center?

Answers

Total number of steps taken by an average man in a year while walking with 7192 steps a day is equals to 2,625,080 steps/year.

Number of steps taken by average man in a day is equals to  7192

Then the total number of steps he takes in a year is equals to,

Calculate it by multiplying the average number of steps per day by the number of days in a year.

There are different ways to define a year,

But assuming a regular calendar year of 365 days, the calculation would be,

Total number of days in a year = 365 days

Total number of steps in a year

= 7192 steps/day x 365 days/year

= 2,625,080 steps/year

Therefore, on average the man would walk about 2,625,080 steps in a year.

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The given question is incomplete, I answer the question in general according to my knowledge:

If a man walks with random steps and the average man takes 7192 steps a day about how many steps does the average man take in a year?

A invested Rs 4500 for 3 years at the rate of 8% annual compound interest and B invested the
same amount for same time at the rate of per month per rupee I paisa simple interest. Calculate
(i) The interest received by A. (ii) The interest received by B.

Answers

The calculation of the interest received by Investor A and Investor B is as follows:

Investor A = $1,168.70 (Compound)Investor B = $1,620 (Simple).

What is the difference between compound and simple interest?

Compound interest is based on the system of charging interest on accumulated interest and principal for each period.

Simple interest is charged on only the principal for each period.

A's Investment at 8% Annual Compound Interest:

N (# of periods) = 3 years

I/Y (Interest per year) = 8%

PV (Present Value) = $4,500

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $5,668.70

Total Interest = $1,168.70

B's Investment at Paisa 1 per R1.00 Monthly Simple Interest:

N (# of periods) = 3 years

r = 1 paisa per rupee per month

= 1÷100*100 = 1%

Annually rate =1%*12 = 12%

PV (Present Value) = $4,500

Results:

Total Interest = $1,620 (R4,500 x 12% x 3)

Future Value (FV) = $6,120.

Thus, while Investor A receives $1,168.70 at the end of 3 years, Investor B receives $1,620.

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What is the difference between the questionnaire and an interview?

Answers

Answer: Questionnaire refers to a research instrument, in which a series of question, is typed or printed along with the choice of answers, expected to be marked by the respondents, used for survey or statistical study. It consists of aformalisedd set of questions, in a definite order on a form, which are mailed to the respondents or manually delivered to them for answers. The respondents are supposed to read, comprehend and give their responses, in the space provided.

A ‘Pilot Study’ is advised to be conducted to test the questionnaire before using this method. A pilot survey is nothing but a preliminary study or say rehearsal to know the time, cost, efforts, reliability and so forth involved in it.

The interview is a data collection method wherein a direct, in-depth conversation between interviewer and respondent takes place. It is carried out with a purpose like a survey, research, and the like, where both the two parties participate in the one to one interaction. Under this method, oral-verbal stimuli are presented and replied by way of oral-verbal responses.

It is considered as one of the best methods for collecting data because it allows two way exchange of information, the interviewer gets to know about the respondent, and the respondent learns about the interviewer. There are two types of interview:

Personal Interview: A type of interview, wherein there is a face to face question-answer session between the interviewer and interviewee, is conducted.

Telephonic Interview: This method involves contacting the interviewee and asking questions to them on the telephone itself.

A questionnaire is considered a voting type of process while an interview is discussing a topic

how many one-to-one functions are there from a set with five elements to sets with the following number of ele- ments? a) 4 b) 5 c) 6 d) 7

Answers

a) Number of one-to-one functions are equal to the zero, because n< m.

b) Number of one-to-one functions are equal to the ⁵P₅ = 120.

c) Number of one-to-one functions are equal to the ⁶P₅ = 720.

c) Number of one-to-one functions are equal to the ⁷P₅ = 2250.

One to one function is a special form of function that defined from one set to another and maps every element of the range to exactly one element of its domain unique output. As we know a set A has m elements and set B has n elements, then

Number of one-to-one functions from set A to Set B = P(n,m) or ⁿPₘ , n≥ m and number of one-to-one functions from set A to Set B = 0 , n< m.

Now, we have a domain set with five elements, m = 5

a) Here, another set (co-domain) has 4 elements, n = 4. So, Number of one-to-one functions = 0 , n<m.

b) number of elements in another set,n= 5

So, Number of one-to-one functions = ⁵P₅ = 5!/(5 - 5 )! ( permutation formula)

= 5!/0! = 120

c) Number of elements in another set, n= 6

So, Number of one-to-one functions= ⁶P₅

= 6!/(6 - 5)!

= 6!/1! = 720

d) Number of elements in another set, n

= 7

So, Number of one-to-one functions

= ⁷P₅ = 7!(7 - 5)!

= 7!/2! = 2250

Hence, required value is 2250.

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The sum of the ages of father and son at present is 45 years. If both live on until the son's age becomes equal to the father's present age, the sum of their ages then will be 95 years. Find their present ages.

Answers

Answer:

father age 45 son age 0 this is answer

how do you find the simplest radical form for this please help me i got a (f) and i really need help that’s why i’m up this late trying to do all of my missing assignments.

Answers

Answer:

[tex]14 {y}^{2} \sqrt{ {x}^{3} {z}^{9} }[/tex]

Step-by-step explanation:

[tex] \sqrt{196 {x}^{3} {y}^{4}{z}^{9} }= \sqrt{196} \times \sqrt{ {x}^{3} } \times \sqrt{ {y}^{4} } \times \sqrt{ {z}^{9} } \\ \sqrt{196} = 14 \\ \sqrt{ {x}^{3} } = {x}^{ \frac{3}{2} } \\ \sqrt{ {y}^{4} } = {y}^{2} \\ \sqrt{ {z}^{9}} = {z}^{ \frac{9}{2} }[/tex]

A fractional exponent is not necessarily simpler so just take out the 1st and 3rd parts of the term which simplify nicely:

[tex] \sqrt{196 {x}^{3} {y}^{4}{z}^{9} } = 14 {y}^{2} \sqrt{ {x}^{3} {z}^{9} } [/tex]

x±Z./
x±t./
A highway safety researcher is studying the design of a freeway sign and is interested
in the mean maximum distance at which drivers are able to read the sign. The
maximum distances (in feet) at which a random sample of 9 drivers can read the sign are as follows:
400 600 600 600 650 500 345 500 440
The mean of the sample of 9 distances is 512 feet with a standard deviation of 105
feet.
(a) What assumption must you make before constructing a confidence interval?
•The population distribution is Uniform.
•The population distribution is Normal.
(b) At the 90% confidence level what is the margin of error on your estimate of the true mean maximum distance at which drivers can read the sign.
Answer= feet (round to the nearest whole number)
(c) Construct a 90% confidence interval estimate of the true mean maximum
distance at which drivers can read the sign.
Lower value= feet (round to the nearest whole number)
Upper value= feet (round to the nearest whole number)
(d) There is a 10% chance the error on the estimate is bigger than what value?
Answer= feet (round to the nearest whole number)
(e) The researcher wants to reduce the margin of error to only 15 feet at the 90% confidence level. How many additional drivers need to be sampled? Assume the sample standard deviation is a close estimate of the population standard deviation.
Answer=

Answers

In response to the stated question, we may state that The margin of error function is equal to the highest mistake on the estimate.

what is function?

In mathematics, a function is a connection between two sets of numbers in which each member of the first set (known as the domain) corresponds to a single element in the second set (called the range). In other words, a function takes inputs from one set and produces outputs from another. Inputs are commonly represented by the variable x, whereas outputs are represented by the variable y. A function can be described using an equation or a graph. The equation y = 2x + 1 represents a linear function in which each value of x yields a distinct value of y.v

(a) The population distribution must be assumed to be normal before generating a confidence interval.

(b) The margin of error with 90% confidence is provided by:

Error Margin = Z (/2) * (/n)

Where Z (/2) is the confidence level/2 crucial value, is the population standard deviation (unknown), and n is the sample size.

Error Margin = t (/2, n-1) * (s/n)

Where t (/2, n-1) is the critical value for the degrees of freedom /2 and n-1, and s is the sample standard deviation.

(d) The margin of error is equal to the highest mistake on the estimate.

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An instructor is administering a final examination. She tells her class that she with give an A grade to the 10% of the students who earns the highest marks. Past experience with the same examination has yielded grades that are normally distributed with a mean of 70 and a standard deviation of 10. If present class runs true to form, what numerical score would a student need to earn an A grade?

Answers

To earn an A grade, a student needs to score at least 82.8 , calculated using the inverse normal cumulative distribution function with a mean of 70, a standard deviation of 10, and a 10th percentile of 0.10.

Given that the grades are normally distributed with a mean of 70 and a standard deviation of 10.

We need to find the score which is at the 10th percentile of the distribution.

Using the standard normal distribution table, we can find the z-score that corresponds to the 10th percentile.

From the table, we can see that the z-score is approximately -1.28.

Using the formula for standardizing a normal distribution:

z = (x - μ) / σ

where z is the z-score, x is the raw score, μ is the mean, and σ is the standard deviation.

Substituting the given values, we have:

-1.28 = (x - 70) / 10

Solving for x, we get:

x = (-1.28 * 10) + 70

x = 82.8

Therefore, a student would need to earn a score of approximately 82.8 to receive an A grade.

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If 5 is increased to 9, the increase is what percentage of the original number

Answers

Answer: It's a 80% increase

Step-by-step explanation:

Help please! I have no idea!!!! PLEASEE

Answers

To highlight the line y = 0 on the graph in black/grey, draw a straight line passing through all points whose y-coordinate is 0.

What is graph?

In mathematics, a graph is a visual representation of a set of data, typically as a set of points or lines on a coordinate plane. Graphs are used to represent various types of data, such as numerical values, functions, relationships, and patterns.

Assuming that the graph is a coordinate plane with the x-axis and y-axis, do the following:

To highlight the point (9, 8) on the graph in red, locate the point (9, 8) on the coordinate plane and mark it with a red color.

To highlight the point (20, f(20)) on the graph in green, you need to know the value of f(20) first. Once you have that value, locate the point (20, f(20)) on the coordinate plane and mark it with a green color.

To highlight the line y = 5 on the graph in blue, draw a straight line passing through all points whose y-coordinate is 5. This line should be parallel to the x-axis and should be marked with a blue color.

Therefore To highlight the line y = 0 on the graph in black/grey, draw a straight line passing through all points whose y-coordinate is 0. This line should be parallel to the x-axis and should be marked with a black/grey color.

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Model the pair of situations with exponential functions f and g. Find the approximate value of x that makes​ f(x) =​ g(x). ​f: initial value of 500 decreasing at a rate of ​6% ​g: initial value of 90 increasing at a rate of ​6%
The value of x that makes ​f(x)​g(x) is x

Answers

Answer:

Step-by-step explanation:

u got this

If n is an integer and n > 1, then n! is the product of n and every other positive integer that is less than n. for example, 5! = 5 x 4 x 3 x 2 x 1a. Write 6! in standard factored formb. Write 20! in standard factored formc. Without computing the value of (20!)2, determine how many zeros are at the end of this number when it is written in decimal form. Justify your answer

Answers

a. 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720. b. 20! = 20 x 19 x 18 x ... x 2 x 1. c. There are 16 zeros at the end of the decimal representation of (20!)2.

a. 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720

b. 20! = 20 x 19 x 18 x ... x 2 x 1. To write this in factored form, we can identify the prime factors of each number and write the product using exponents. For example, 20 = 2² x 5, so we can write 20! as:

20! = (2² x 5) x 19 x (2 x 3²) x 17 x (2² x 7) x 13 x (2 x 2 x 3) x 11 x (2³) x (3) x (2) x 7 x (2) x 5 x (2) x 3 x 2 x 1

Simplifying, we get:

20! = 2¹⁸ x 3⁸ x 5⁴ x 7² x 11 x 13 x 17 x 19

c. The number of zeros at the end of (20!)² in decimal form is determined by the number of factors of 10, which is equivalent to the number of factors of 2 x 5. Since there are more factors of 2 than 5 in the prime factorization of (20!)², we only need to count the number of factors of 5. There are four factors of 5 in the prime factorization of 20!, which contribute four factors of 10 to the square. Therefore, (20!)²ends in 8 zeros when written in decimal form.

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Let G
be a group. Say what it means for a map φ:G→G
to be an automorphism. Show that the set-theoretic composition φψ=φ∘ψ
of any two automorphisms φ,ψ
is an automorphism. Prove that the set Aut(G)
of all automorphisms of the group G
with the operation of taking the composition is a group.

Answers

a) An automorphism of a group G is a bijective map φ:G→G that preserves the group structure. That is, φ(ab) = φ(a)φ(b) and φ(a⁻¹) = φ(a)⁻¹ for all a, b ∈ G.

b) The set-theoretic composition φψ of any two automorphisms φ, ψ is an automorphism, as it preserves the group structure and is bijective.

c) The set Aut(G) of all automorphisms of G, with the operation of composition of maps, is a group. This is because it satisfies the four group axioms: closure, associativity, identity, and inverses. Therefore, Aut(G) is a group under composition of maps.

An automorphism of a group G is a bijective map φ:G→G that preserves the group structure, meaning that for any elements a,b∈G, we have φ(ab) = φ(a)φ(b) and φ(a⁻¹) = φ(a)⁻¹. In other words, an automorphism is an isomorphism from G to itself.

To show that the set-theoretic composition φψ is an automorphism, we need to show that it satisfies the two conditions for being an automorphism. First, we have

(φψ)(ab) = φ(ψ(ab)) = φ(ψ(a)ψ(b)) = φ(ψ(a))φ(ψ(b)) = (φψ)(a)(φψ)(b)

using the fact that ψ and φ are automorphisms. Similarly,

(φψ)(a⁻¹) = φ(ψ(a⁻¹)) = φ(ψ(a))⁻¹ = (φψ)(a)⁻¹

using the fact that ψ and φ are automorphisms. Therefore, φψ is an automorphism.

To show that Aut(G) is a group, we need to show that it satisfies the four group axioms

Closure: If φ,ψ∈Aut(G), then φψ is also in Aut(G), as shown above.

Associativity: Composition of maps is associative, so (φψ)χ = φ(ψχ) for any automorphisms φ,ψ,χ of G.

Identity: The identity map id:G→G is an automorphism, since it clearly preserves the group structure and is bijective. It serves as the identity element in Aut(G), since φid = idφ = φ for any φ∈Aut(G).

Inverses: For any automorphism φ∈Aut(G), its inverse φ⁻¹ is also an automorphism, since it is bijective and preserves the group structure. Therefore, Aut(G) is closed under inverses.

Since Aut(G) satisfies all four group axioms, it is a group under composition of maps.

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12. What is the height of the trapezoid in yards? (Hint: Use the formula
A = 1/2h (b 1, + b2,) (Lesson 2)

Answers

Answer:

height = 7 yards

Step-by-step explanation:

the area (A) of a trapezoid is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )

where h is the perpendicular height between the 2 parallel bases

here b₁ = 12 , b₂ = 9 and A = 73.5 , then

[tex]\frac{1}{2}[/tex] h(12 + 9) = 73.5 ( multiply both sides by 2 to clear the fraction )

h(21) = 147

21h = 147 ( divide both sides by 21 )

h = 7 yards

Triangle ABC is similar to triangle DEF. What is AC?

Answers

Answer:

i think side AC is 14 because if you do subtract BC (18) from EF(12) you get 6, so u add 6 to DF(8) and get 14.

if its confusing ask me questions!!

Answer:

12

Step-by-step explanation:

When triangles are similar, their side ratios are the same. The ratio of EF to BC is 18/12, or 3/2. To find the side AC, we would multiply the corresponding part of DEF by 3/2, the same ratio. The corresponding part of DEF would be DF. DF = 8. 8 times 3/2 is 12. So AC is 12.

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If "f" is differentiable and f(1) < f(2), then there is a number "c", in the interval (_____, _____) such that f'(c)>_______

Answers

If "f" is differentiable and f(1) < f(2), then there is a number "c", in the interval  (1, 2)  such that f'(c)>  0.

How do we know?

Applying the  Mean Value Theorem for derivatives, if a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one number c in the interval (a, b) such that:

f'(c) = (f(b) - f(a)) / (b - a)

In the scenario above, we have that f is differentiable, and that f(1) < f(2).

choosing a = 1 and b = 2.

Then applying the Mean Value Theorem, there exists at least one number c in the interval (1, 2) such that:

f'(c) = (f(2) - f(1)) / (2 - 1)

f'(c) = f(2) - f(1)

We have that f(1) < f(2), we have:

f(2) - f(1) > 0

We can conclude by saying that there exists a number c in the interval (1, 2) such that:

f'(c) = f(2) - f(1) > 0

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Calculate the following limits?

Answers

The answer of the given question based on the limits the answers are as follows, (a)  lim f(x) = 1 , (b)  lim f(x) = 3 , (c)  lim f(x) = 3.

What is Graph?

A graph is  visual representation of data that shows the relationship between two or more variables. Graphs can be used to display  wide variety of information, including numerical data, functions, and networks. The most common types of graphs like line graphs, bar graphs, scatter plots, and pie charts.

Graphs are widely used in many fields, like science, economics, engineering, and social sciences, to help people understand and analyze complex data. They are  powerful tool for visualizing trends, patterns, and relationships, and are often used to communicate findings to wider audience.

a) The limit of f(x) as x approaches 2 from the left:

We can see from the graph that as x approaches 2 from the left, f(x) approaches 1. Therefore, we can write:

lim f(x) = 1

x→2-

b) The limit of f(x) as x approaches 2 from the right:

Similarly, as x approaches 2 from the right, f(x) approaches 3. Therefore:

lim f(x) = 3

x→2+

c) The limit of f(x) as x approaches 2:

Since the limit from the left and the limit from the right exist and are equal, we can say that the limit of f(x) as x approaches 2 exists and equals the common value of the left and right limits. Therefore:

lim f(x) = 3

x→2

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Given the coordinates shown and given that SU = 10, what are the coordinates of U if STUV is a kite?

A) (10, 18)
B) (0, 28)
C) (18, 28)

Answers

The calculated coordinates of U if STUV is a kite is (10, 18)

Calculating the coordinates of U if STUV is a kite?

From the question, we have the following parameters that can be used in our computation:

The figute of a kite

Also, we have

S = (0, 18)

And the distance SU to be

SU = 10

If the quadrilateral STUV is a kite, then the coordinates S and U are on the same horizontal level (according to the figure)

So, we have

U = (0 + 10, 18)

Evaluate

U = (10, 18)

Hence, the coordinates of U if STUV is a kite is (10, 18)

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The number 0 is an element of the set of natural numbers.
OA. True
B. False
SUBI

Answers

it is false. 0 is not a natural number. it is a whole number

PLEASE HELP !
Use the figure below to answer the questions

Answers

From the figure 1. Two line segments are LA and EP. 2. Two rays are EC and AH. 3. Two lines are b and AP.

What are rays, line segment and line?

A ray is a segment of a line with a single endpoint and unlimited length in a single direction. A ray cannot be measured in terms of length.

The ends of a line segment are two. These endpoints are included, along with every point on the line that connects them. A segment's length can be measured, while a line's length cannot.

A line is a collection of points that extends in two opposing directions and is endlessly long and thin.

From the given figure we observe that,

1. Two line segments are LA and EP.

2. Two rays are EC and AH.

3. Two lines are b and AP.

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given a function f(x), find the critical values and use the critical values to find intervals of increasing/deacreasing, maxes and mins.

Answers

The critical values, the intervals of increasing or decreasing and the maximum and minimum points of the f(x) is (-1.5, -16), x < -1.5 and x = -1.5 and for b (4,6) and (2,10), (2,4).

A) Critical values

We will find out the critical value by solving for f ' (x) = 0

therefore, taking the derivative of given function we get,

f ' (x) = 4(2x) + 12 = 0

        = 8x + 12 = 0

therefore, 8x = -12

                 x = -12/8

                 x= -1.5

x = -1.5 is the only critical value in x-coordinate. Now to determine the y-coordinate, simply put the value of x in the function f(x) = 4x2 + 12x - 7

we get, f(-1.5) = 4(-1.5)2 + 12 (-1.5) - 7

                      = 4(2.25) - 18 - 7

                      = 9 - 25 = -16  

therefore, the critical value of the function f(x) = 4x2 + 12x - 7 is (-1.5, -16)

f(x) =x3 - 9x2 + 24x - 10.

Intervals of increasing and decreasing function is i.e. f decreases for

x < -1.5.

Therefore, f has minimum value at x = -1.5.

B) Critical values

We will find out the critical value by solving for f ' (x) = 0

therefore, taking the derivative of given function we get,

f '(x) = 3x2 - 9(2x) + 24

       = 3x2 - 18x + 24 = 0

therefore, 3 ( x2 - 6x + 8) = 0

   i.e x2 - 6x + 8 = 0

        (x-4) (x-2) = 0

So, x = 4 or x = 2 are the two critical values in x-coordinate. Now to determine the y-coordinate, simply put the values of x in the function f(x) =x3 - 9x2 + 24x - 10

we get, Substituting x = 4

f(4) = 43 - 9 (4)2 +24 (4) -10

     = 64 - 144 + 96 - 10

     = 6

Now, Substituting x = 2

f(2) = 23 - 9(2)2 + 24(2) - 10

     = 8 - 36 + 48 - 10

     = 10

Therefore, the critical values of the function f(x) =x3 - 9x2 + 24x - 10 are (4,6) and (2,10).

Intervals of increasing and decreasing functions is f decreases in (2,4).

therefore, f has minimum at x = 4 and maximum at x = 2.

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Complete question:

For each function determine: i) the critical values ii) the intervals of increasing or decreasing iii) the maximum and minimum points.

a. f(x) = 4x²+12x–7 (3 marks)

b. F(x) = x°-9x²+24x-10 (3 marks)

Show your solution ( 3. ) C + 18 = 29

Answers

Answer:

Show your solution ( 3. ) C + 18 = 29

Step-by-step explanation:

To solve the equation C + 18 = 29, we want to isolate the variable C on one side of the equation.

We can start by subtracting 18 from both sides of the equation:

C + 18 - 18 = 29 - 18

Simplifying the left side of the equation:

C = 29 - 18

C = 11

Therefore, the solution to the equation C + 18 = 29 is C = 11.

A home has gone up in value over several
decades and is now worth 1354% of its
original sale price of $23,000. What is the
value now?

Answers

Answer:

$31,142

Step-by-step explanation:

To convert a percentage into a decimal, you move the decimal two places to the left. 1354% converted into a decimal is 13.54.

$23,000 * 13.54 = $31,142

Maximize z = 3x₁ + 5x₂
subject to: x₁ - 5x₂ ≤ 35
3x1 - 4x₂ ≤21
with. X₁ ≥ 0, X₂ ≥ 0.
use simplex method to solve it and find the maximum value​

Answers

Answer:

See below.

Step-by-step explanation:

We can solve this linear programming problem using the simplex method. We will start by converting the problem into standard form

Maximize z = 3x₁ + 5x₂ + 0s₁ + 0s₂

subject to

x₁ - 5x₂ + s₁ = 35

3x₁ - 4x₂ + s₂ = 21

x₁, x₂, s₁, s₂ ≥ 0

Next, we create the initial tableau

Basis x₁ x₂ s₁ s₂ RHS

s₁ 1 -5 1 0 35

s₂ 3 -4 0 1 21

z -3 -5 0 0 0

We can see that the initial basic variables are s₁ and s₂. We will use the simplex method to find the optimal solution.

Step 1: Choose the most negative coefficient in the bottom row as the pivot element. In this case, it is -5 in the x₂ column.

Basis x₁ x₂ s₁ s₂ RHS

s₁ 1 -5 1 0 35

s₂ 3 -4 0 1 21

z -3 -5 0 0 0

Step 2: Find the row in which the pivot element creates a positive quotient when each element in that row is divided by the pivot element. In this case, we need to find the minimum positive quotient of (35/5) and (21/4). The minimum is (21/4), so we use the second row as the pivot row.

Basis x₁ x₂ s₁ s₂ RHS

s₁ 4/5 0 1/5 1 28/5

x₂ -3/4 1 0 -1/4 -21/4

z 39/4 0 15/4 3/4 105

Step 3: Use row operations to create zeros in the x₂ column.

Basis x₁ x₂ s₁ s₂ RHS

s₁ 1 0 1/4 7/20 49/10

x₂ 0 1 3/16 -1/16 -21/16

z 0 0 39/4 21/4 525/4

The optimal solution is x₁ = 49/10, x₂ = 21/16, and z = 525/4.

Therefore, the maximum value of z is 525/4, which occurs when x₁ = 49/10 and x₂ = 21/16.

I will mark you brainiest!

A concave polygon can never be classified as a regular polygon.

A) True
B) False

Answers

Answer:

False.

Step-by-step explanation:

A concave polygon can never be a regular polygon as it can never be equiangular. Each side of a regular polygon must be the same length, and all interior angles must also be equal.

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