Find the Domain, Range, rel. Max and minimum, end behavior, and thr increasing and decreasing intervals.

EQUATION: f(x)=-x^3+8x^2-15x

Answers

Answer 1

Step-by-step explanation:

Domain: The domain of the function is all real numbers.

Range: The range of the function is all real numbers less than or equal to 8. To see this, note that the leading coefficient of the polynomial is negative (-x^3), so the function approaches negative infinity as x approaches positive or negative infinity. The largest y-value the function can attain is 8, which occurs at x = 2.

Relative maxima and minima: To find the relative maxima and minima, we find the critical points of the function, which are the values of x that satisfy f'(x) = 0 or f'(x) does not exist. The first derivative of the function f(x) is given by:

f'(x) = -3x^2 + 16x - 15

Solving f'(x) = 0, we get:

-3x^2 + 16x - 15 = 0

x = 1, 5

We also need to determine the concavity of the function near each critical point to determine whether each is a relative maximum or minimum. To do this, we find the second derivative of the function and evaluate its sign at each critical point. The second derivative of f(x) is given by:

f''(x) = -6x + 16

Since f''(x) is always negative, the function is concave down and therefore has a relative maximum at x = 1 and a relative minimum at x = 5.

End behavior: The leading term of the function is -x^3, which means the function approaches negative infinity as x approaches negative infinity and positive infinity as x approaches positive infinity. The end behavior of the function is therefore negative infinity as x approaches negative infinity and positive infinity as x approaches positive infinity.

Increasing and decreasing intervals: To find the increasing and decreasing intervals of the function, we find the critical points and the sign of f'(x) in the intervals between the critical points.

f'(x) = -3x^2 + 16x - 15

Since f'(x) is negative for x < 1 and positive for x > 1, the function is decreasing for x < 1 and increasing for x > 1. Similarly, since f'(x) is positive for x < 5 and negative for x > 5, the function is increasing for x < 5 and decreasing for x > 5. So, the increasing intervals are (negative infinity, 1) and (1, 5) and the decreasing intervals are (5, positive infinity).


Related Questions

Write 3 irrational numbers between 1.5 and 1.56.

Answers

1.511; 1.512 ;1.5113

Step-by-step explanation:

we know that there are infinite numbers.

and every decimal number is a rational number

now, extend the number upto 3 decimal or 2 decimal .

then it will become 1.500

there are numbers upto 1.599

like this we can extend upto infinite values

you can write infinite numbers, but question is asked for only 3

30 POINTS HELP PLEASE
i need help with both questions thank you!!!!

Answers

Answer:

see explanation

Step-by-step explanation:

(6)

given f(x) then - f(x) represents a reflection in the x- axis

given f(x) then f(x) + c represents a vertical translation of f(x)

• if c > 0 then a shift up of c units

• if c < 0 then a shift down of c units

thus g(x) = - | x | + 2

is a reflection over the x- axis and vertical shift up of 2 units

(7)

f(2) means value of f(x) when x = 2

x = 2 is in the interval x ≥ 2 with f(x) = [tex]\sqrt{x-2}[/tex] , then

f(2) = [tex]\sqrt{2-2}[/tex] = [tex]\sqrt{0}[/tex] = 0

I think the other person that answered the question is right

) You spin the spinner once.
6
5
7
2
Submit
3
What is P(greater than 2)?
) Write your answer as a fraction or whole number.

Answers

The value of P(Greater than 2) is 0.75

How to evaluate the probability

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

Spinner = 6 5 7 2

Using the above as a guide, we have the following:

Greater than 2 = 3

Total = 4

The probability is

P = Greater than 2/Total

Substitute the known values in the above equation, so, we have the following representation

P(Greater than 2) = 3/4

Evaluate

P(Greater than 2) = 0.75

Hence, the solution is 0.75

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A scenic train ride has one price for adults and one price for children. One family of two adult-
nd two children pays $62 for the train ride. Another family of one adult and four children pays
O. How much does it cost for one child to ride the train

Answers

Using simultaneous equations, the child ticket costs $18.

What are simultaneous equations?

Simultaneous equations are two or more equations solved concurrently or at the same time.

Simultaneous equations are also known as a system of equations.

                Family A     Family B      Total Cost

Adults            2                  2                $62

Children         1                  4                 $70

Let the ticket cost per child = x

Let the ticket cost per adult = y

Equations:

2x + 2y = 62 ... Equation 1

x + 4y = 70 ... Equation 2

Multiply Equation 1 by 2

4x + 4y = 124 ... Equation 3

Subtract Equation 2 from Equation 3:

4x + 4y = 124

-

x + 4y = 70

3x = 54

x = 18

= $18

From Equation 2, Substitute x = 18:

x + 4y = 70

18 + 4y = 70

4y = 52

y = 13

= $13

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Question Completion:

Another family of one adult and four children pays $70.

THIS IS THE OSHA 10-HOUR COURSE AND I NEED HELP WITH IT.
1. Remember not to use tools that are ________ in any way.
2. What should you do with corded tools when they are not being used?
3. This is the sudden release of electrical energy through the air when a high-voltage gap exists and there is a breakdown between conductors:
4. What electrical hazard is present in this image?
5. The longer you’re exposed to high noise levels, the more likely it is that ________ damage will occur.
6. In a situation where you expect to encounter airborne hazardous substances, but you don’t need skin protection, what level of full-body protection will you need?
7. Which of the following are struck-by falling hazards?
8. If you see an increase in traffic, step in and direct traffic to ensure safety. Is this a safe or unsafe practice?
9. In general, employers must provide fall protection to construction workers working on surfaces with unprotected sides and edges that are how many feet above the lower level?
10. When constructing a scaffold, there are specific criteria for the ________ the scaffold is built on.
11. Which of the following is the most dangerous factor among crane accidents?
12. An excavation is at risk for cave-in and water accumulation because of the excess soil that has accumulated. What type of excavation protection will address this situation?
13. Protect workers from cave-ins and other excavation-related hazards. Whose responsibility is this?

Answers

Answer:

1 harmful

Step-by-step explanation:

2 they will be not use if you not use

in python, math expressions are always evaluated from left to right, no matter what the operators are. True/False ?

Answers

True






The answer is true because it doesn’t matter how you evaluate the expression it would always be true

Triangle A B C. The length of side A C is 10, B C is 6, and A B is 8. Triangle A prime B prime C prime. Side A prime C prime has a length of 5.
Triangle ABC is dilated to get triangle A'B'C'. Which is the length of A'B'?
Options:
3
4
5
16

Answers

The measure of side A'B' for the triangle A'B'C' is equal to 4 using a scale factor of 1/2 to dilate it.

What is scale factor

Scale factor is the ratio between the scale of a given original object and a new object, which is its representation but of a different size either bigger or smaller.

The dilation if the triangle ABC implies it is bigger than the triangle A'B'C' with a scale factor 1/2 since AC = 10 and A'C' = 5

side A'B' = 8 × 1/2

side A'B' = 4

Therefore, the measure of side A'B' for the triangle A'B'C' is equal to 4 using a scale factor of 1/2 to dilate it.

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Answer:

the answer is B, 4. :)

4. Determine the kinetic energy of 1500 kg pick-up truck traveling at 31.0 m/sec. Show work thanks

Answers

Answer:

Step-by-step explanation:

The formula for kinetic energy is:

KE = (1/2) * m * v^2

where KE is the kinetic energy, m is the mass of the object, and v is the velocity of the object.

We are given the mass of the pick-up truck as 1500 kg and its velocity as 31.0 m/sec. We can plug these values into the formula to calculate its kinetic energy:

KE = (1/2) * m * v^2

= (1/2) * 1500 kg * (31.0 m/sec)^2

= (1/2) * 1500 kg * 961.0 m^2/sec^2

= 720750 J

Therefore, the kinetic energy of the pick-up truck is 720750 Joules.

r

Step-by-step explanation:

v

Phyllis invested $12,500, a portion earning a simple interest rate of
4 1/5%
per year and the rest earning a rate of 4% per year. After one year the total interest earned on these investments was $518.00. How much money did she invest at each rate

Answers

Let x be the amount invested at 4 1/5% interest rate. Then, the amount invested at 4% rate would be $12,500 - x.

The interest earned on the x amount at 4 1/5% interest rate can be calculated as x * 4.2 / 100 * 1.
And the interest earned on the ($12,500 - x) amount at 4% rate can be calculated as ($12,500 - x) * 4 / 100 * 1.

The total interest earned after a year is $518, so we can set up the following two equations:

x * 4.2 / 100 * 1 = x * 0.042 * 1

($12,500 - x) * 4 / 100 * 1 = ($12,500 - x) * 0.04 * 1

Adding the above two equations, we get:

x * 0.042 * 1 + ($12,500 - x) * 0.04 * 1 = $518

Expanding and solving for x, we get:

x = $8470

So, Phyllis invested $8470 at 4 1/5% interest rate and $12,500 - $8470 = $4030 at 4% interest rate.

Work out the volume of the cuboid below.
Remember to give the correct units.
13 m
5m
13 m
3 m

Answers

Answer:

195m^3

Step-by-step explanation:

Volume of a rectangle = Length x Width x Height

L = 5m

W = 3m

H = 13m

V = 5m x 3m x 13m

V = 195m^3

Give the domain and range of G.
Write your answers using set notation.

Answers

Domain of function =  {-3 , -4}

Range of function =  {4 , -1 , -4}

What is domain and range of a function?

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

Given,

points on graph of a function are

(-3 , 4) , (-3 , -1) , (-4 , -4)

Range is set of y-values,

Range = {4 , -1 , -4}

Domain is set of x - values

Domain = {-3 , -4}

Hence, Domain and range of function are {-3 , -4} and {4 , -1, -4} respectively.

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GEOMETRY
Find the volume of each figure. Round to the nearest tenth if necessary.

Answers

Vοlume οf the cylinder in will be 226.28 yd³, Vοlume οf Slanted cylinder is 141.37 in³ and Vοlume οf οblique cubοid is 1224 cm³.

What exactly is a cylinder?

In geοmetry, a cylinder is οne οf the fundamental 3d fοrms with twο parallel circular bases at a distance. The curving surface cοnnects the twο circular bases at a predetermined distance frοm the centre. The axis οf the cylinder is the line cοnnecting the centres οf twο circular bases. The height οf the cylinder is the distance between the twο circular bases.

A. Nοw,given that diameter οf base = 6 yd then radius=6/2=3 yd

and height will be =√10²-6²  (By Pythagοras theοrem )

= √64

= 8 yd

then vοlume οf cylinder is=πr²h

= 22/7*3*3*8

= 1584/7

= 226.28 yd³

Hence, Vοlume οf the cylinder  will be 226.28 yd³.

B. Vοlume οf Slanted cylinder is V = πr²h

V = π3²5

V = π × 3 × 3 ×5

V = 141.37 in³

Hence, Vοlume οf Slanted cylinder is 141.37 in³

C. Vοlume οf οblique cubοid is V = lwh

V = 17 × 18 × 4

V = 1224 cm³

Therefore ,Vοlume οf οblique cubοid is 1224 cm³.

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Eric and Jennifer both plan to run for a spot on the school board in their city. They must each collect a certain number of signatures to get their name on the ballot. So far, Eric has 20 signatures, but Jennifer just started and doesn't have any yet. Eric is collecting signatures at an average rate of 17 per hour, while Jennifer can get 19 signatures every hour. Assuming that their rate of collection stays the same, eventually the two will have collected the same number of signatures. How many signatures will they both have? How many hours will have gone by?

Answers

Answer:

10 hours would've gone by, and they have collected 190 signatures.

Step-by-step explanation:

pls all of them its urgent

Answers

The simplified forms of the fractions are 3 and -5 repectively

How do you simplify a fraction?

To simplify a fraction, you divide both the numerator (top number) and denominator (bottom number) by their greatest common factor (GCF) until there are no more common factors. The result will be the simplified form of the fraction.

We have to note that;

1 ) 1 + 1/2 = 3/2

Then we have;

3/2 * 2/1 = 6/2 = 3

2) 3/4 - 2 = -5/4

Then we have;

-5/4 * 4/1 = -5

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(a) Latoya lost 60 dollars from her pocket.
Write a signed number to represent this change.


(b) A car corporation produced 1180 more cars this month than last.
Write a signed number to represent this month's change in production.

Answers

Answer:

-60, +1180

Step-by-step explanation:

if a cone-shaped hole is 3 feet deep and the circumference of the base of the hole is 44 feet, what is the volume of the hole? use 22/7 for pi

Answers

The volume of the conical hole will be 154 cubic feet.

What is the volume of the cone?

The area a cone takes up in a three-dimensional plane is known as its volume. A cone's base is circular, so it is made of a radius and a diameter.

Given that a cone-shaped hole is 3 feet deep and the circumference of the base of the hole is 44 feet,

The volume of the cone will be calculated as:-

Volume = (1/3)πr²h

The circumference of the cone is,

2πr = 44

2 x ( 22 / 7 ) x r =  44

r = 7 feet

The volume of the cone will be calculated as:-

Volume = (1/3)πr²h

Volume = ( 1 / 3 )  x ( 22 / 7 ) x 7 x 7 x 3

Volume = 22 x 7

Volume = 154 cubic feet

Therefore, the volume will be 154 cubic feet.

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Find the monthly payment for a 25-year, the ballon mortgage for 375,000 at an APR of 4.5% . What will be their total interest charges after 25 years? Round to the nearest whole number?

Answers

The total interest charger after 25 years for the balloon mortgage would be = $421, 875

What is simple interest?

Simple interest is the additional sum of money that is paid to a person after a sum of money was invested for a specific amount of time.

Given:

The principal= 375,000

The time for the mortgage = 25 years

The rate = 4.5%

The formula for simple interest

= P×T×R/100

= 375,000×4.5×25/100

= 42187500/100

= $421, 875

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Compare using >, <, or =
a. 5 thirds + 2 ninths _____ 1 9/8

Answers

What is a fraction?

A fraction is a fragment of a whole number, used to define parts of a whole. The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.

The equation for this problem is this:

[tex]\frac{5}{3} + \frac{2}{9}[/tex] (> < =) [tex]1\frac{9}{8}[/tex]

First, we need to find a common denominator between  [tex]\frac{5}{3}[/tex] and [tex]\frac{2}{9}[/tex].

What is a common denominator?

A common denominator consists of two or more fractions that have the same denominator. This makes it easier to perform numeric equations, and to solve them.

To find the common denominator, we can multiply the denominators, 3 and 9.

3 × 9 = 27

Now we know that the two new fractions are going to have a denominator of 27.

[tex]\frac{?}{27} \frac{?}{27}[/tex]

Now, we can use these equations to solve for the numerator.

9 × 5 = 453 × 2 = 6

Now, the fractions look like this:

[tex]\frac{45}{27} \frac{6}{27}[/tex]

To add them together, we can use this equation:

[tex]\frac{45}{27}+ \frac{6}{27} = \frac{51}{27}[/tex]

Now, we need to convert [tex]1 \frac{9}{8}[/tex] into an improper fraction.

What is an improper fraction?

An improper fraction is a fraction that has a numerator that is greater than the denominator. For example, [tex]\frac{3}{2}[/tex] is a improper fraction.

[tex]1\frac{9}{8}[/tex] = [tex]\frac{17}{8}[/tex]

To convert [tex]\frac{51}{27}[/tex] and [tex]\frac{17}{8}[/tex] into common denominators, we need to multiply the denominators, like we did above.

8 × 27 = 216

The new fractions will look like this:

[tex]\frac{?}{216} \frac{?}{216}[/tex]

To solve for the numerators, we can use these equations:

17 × 27 = 4598 × 51 = 408

The fractions now look like this:

[tex]\frac{408}{216} \frac{459}{216}[/tex]

Now, convert them to mixed numbers.

[tex]\frac{408}{216} = \frac{17}{9}[/tex][tex]\frac{459}{216} = \frac{17}{8}[/tex]

Therefore, 5 thirds + 2 ninths < 1 9/8.

Which option is correct? Explain your working after choosing your answer

x^2 + 2x + 1

A. This polynomial could be factored by finding the GCF, then by grouping or using the perfect squares method.
B. This polynomial could be factored by using the difference of squares method, perfect squares method, or grouping.
C. This polynomial could be factored only by using the perfect squares method.
D. This polynomial could be factored only by using the difference of squares method.
E. This polynomial could be factored by using grouping or the perfect squares methods.
F. This polynomial cannot be factored by any of the methods used in this lesson.

Answers

E. This polynomial could be factored by using grouping or the perfect squares methods.

How to factor the polynomial

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

x^2 + 2x + 1

Expand

x^2 + x + x + 1

Factorize the expression

(x + 1)(x + 1)

This gives

(x + 1)^2

Hence, the solution is (e)

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What is the length of TE?

Answers

Answer: 20 units

Step-by-step explanation: Set the two half diagonal values equal to each other. When you solve for x, the value is 3. Substitute it back in and the half diagonals equal 10. Multiply it by two and the dial length is 20. You can use this length for TE because it is a diagonal. Hope this helps!

[tex]x^{3} +8 / x-2[/tex]

Answers

Answer:

[tex] {x}^{4} - 2x + 8 \div x[/tex]

Nate wants to buy a CD for $1000 that earns 3% APR and is compounded

quarterly for 5 years. He will be taxed on 20% of the interest that he earns.

What is the total amount of interest Nate will earn, after taxes?

O A. $40. 96

O B. $51. 20

O c. $161. 18

O D. $128. 94

SUBMIT

Help apex!

Answers

D. $128.94. is the total amount of money Nate will earn after taxes when he buys a CD for $1000  The formula for compound interest is:

A = P * (1 + r/n)^(nt), where A is the amount after t years, P is the principal amount, r is the interest rate as a decimal, n is the number of times interest is compounded per year, and t is the number of years.

We can use this formula to calculate the amount of money Nate will have after 5 years:

A = 1000 * (1 + 0.03/4)^(4 * 5) = 1000 * (1 + 0.0075)^20 = 1000 * 1.1629 = 1162.9

The interest earned is 1162.9 - 1000 = $162.9.

And the amount of interest taxed is 20% of $162.9, which is 20% * $162.9 = $32.58.

So, the total amount of interest earned after taxes is $162.9 - $32.58 = $130.32.

Therefore, the correct answer is D. $128.94.

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Y<1/2x-7
Y>=-x-1
Point :(,)

Answers

From the inequalities y < (1/2)x - 7 and y ≥ -x - 1 graphed, a possible solution is the point (30, 2)

What is an equation?

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

Inequalities are used to show the non equal comparison of two or more numbers and variables.

Given the inequalities:

y < (1/2)x - 7         (1)

And:

y ≥ -x - 1         (2)

From the inequalities graphed, a possible solution is the point (30, 2) which is shown in the darker region

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Which inequality represents eight less than three times a number is more than 22.

A. 3x - 8 > 22 B. 8 - 3X >22 C.3x - ≥ 22

Answers

Answer:

the answer of the equation is b

Pls help
And approximate solution to an equation is found using the itiretative formula
X _n+1 = (x_n)^3 -2 / 10 with x_1 = -1

Answers

On solving the provided question, we can say that the equation we have here is[tex]X_(n+1)= (x-n)^{3} - \frac{2}{10}[/tex] at [tex]x_1 = -1[/tex] n = 0 , [tex]x_1 = \frac{-3}{10}[/tex]

What is an equation?

Two assertions in a mathematical equation are joined by the equal sign (=), which stands for equality.

A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places a space between the variables 3x + 5 and 14.

The connection between the two sentences on either side of a letter is explained by a mathematical formula. Typically, there is only one variable, which also serves as the symbol.

A simple equation is a mathematical formula that, on both sides of the "equal to" sign, expresses the relationship between two expressions. Equations in this category include a variable, which is typically expressed as x or y. Simple equations often need to be rearranged in order to be solved.

the equation we have here is

[tex]X_(n+1)= (x-n)^{3} - \frac{2}{10}[/tex] , at [tex]x_1 = -1[/tex]

n = 0

[tex]x_1 = \frac{-3}{10}[/tex]

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Albert Einsteen is experimenting with 2 unusual clocks which both have 24-hours displays. Once clock goes at
twice the normal speed. The other clock goes backwards, but at the normal speed. Both clocks show the correct time
at 13:00. What is the correct time when the displays on the clock next agree?

Answers

The correct time when the clocks next agree is 13:00 on clock A and 11:00 on clock B, which occurs 12 hours after 13:00.

Call the clock that runs forward A and the clock that runs backward B. Clock A will display the time as 13:00 at that moment, but clock B (which is going backward from 13:00) will display the time as 11:00.

Clock A will move two hours on its display in one hour since it is operating at twice the typical speed. Clock A will display 15:00 an hour from now, at 14:00. Additionally, because clock B is going backward, its display will read 10:00 an hour from now.

The clocks will next sync up when Clock A displays 13:00 (its initial beginning time) and Clock B displays 11:00, which takes place after 12 hours (12 hours on clock A, 24 hours on clock B).

So the correct time when the clocks next agree is 13:00 on clock A and 11:00 on clock B, which occurs 12 hours after 13:00.

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If $10,000 is deposited into a savings account that pays 1.8% annual interest, how much more would the account be worth if interest were compounded monthly rather than annually over a period of 30 years? Round to the nearest dollar.

Answers

Answer:

Let's first calculate the amount of interest that would be earned if the interest were compounded annually. The formula for the future value of a single sum is:

F = P * (1 + r/n)^(nt)

Where:

F is the future value

P is the principal (the initial deposit)

r is the annual interest rate

n is the number of compounding periods per year

t is the number of years

For our calculation, we have:

P = $10,000

r = 1.8% = 0.018

n = 1 (annual compounding)

t = 30

So, the future value of the account with annual compounding is:

F = $10,000 * (1 + 0.018/1)^(1 * 30) = $10,000 * (1.018)^30 = $21,784.08

Now, let's calculate the amount of interest that would be earned if the interest were compounded monthly. The formula for the future value of a single sum is the same, but we need to use the monthly compounding rate (r/12) instead of the annual rate and the number of months (12t) instead of the number of years:

F = P * (1 + r/n)^(nt)

Where:

F is the future value

P is the principal (the initial deposit)

r is the annual interest rate

n is the number of compounding periods per year

t is the number of years

For our calculation, we have:

P = $10,000

r = 1.8% = 0.018

n = 12 (monthly compounding)

t = 30

So, the future value of the account with monthly compounding is:

F = $10,000 * (1 + 0.018/12)^(12 * 30) = $10,000 * (1.0015)^360 = $22,254.51

The difference in the two future values is $22,254.51 - $21,784.08 = $470.43.

So, the account would be worth $470.43 more if interest were compounded monthly rather than annually over a period of 30 years. Round to the nearest dollar, the answer is $470.

Step-by-step explanation:

Ranger Shoe Company manufactures two types of shoes, athletic shoes and casual shoes. The cost of manufacturing 20 pairs of athletic shoes and 10 pairs of casual shoes is $750. If 25 pairs of athletic shoes and 20 pairs of casual shoes were manufactured, the cost would be $1200. How much does it cost to manufacture each type of shoe?

Answers

The cost of the athletic shoe is $20 meanwhile the cost of the casual shoe is $35.

System of Equations

A system of equations is the given term of math for two or more equations with the same variables. The solution of these equations represents the point of the intersection.

You can solve a system of equations by substitution or adding methods. In the addition method, you eliminate a variable, on the other hand, in the substitution method you replace a variable for the other.

Firstly, you should extract the main information of the question.

Athletic shoes= ACasual shoes = Cfor 20 pairs of athletic shoes and 10 pairs of casual shoes, the total cost is $750for 25 pairs of athletic shoes and 20 pairs of casual shoes, the total is $1200.

Next,  you should convert the given text information into equations. See below.

20A+10C=750 (1)

25A+20C=1200 (2)

From the substitution method, you can solve this question by following the steps below:

1) Multiply equation 1 by the number -2. Then, you have:

-40A-20C= -1500 (1)

25A+20C=1200 (2)

2) Sum the previous equations presented in step 1.

-15A=-300

15A=300

A=300/15

A=20

3) Find the variable C from equation 2. In step 2, you find  A=20, thus.

25A+20C=1200 (2)

25*20+20C=1200

500+20C=1200

20C=1200-500

20C=700

C=700/20

C=35

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solve for x

-1 + 6x < 5

Answers

[tex]-1+6x < 5[/tex]

Simplify:

[tex]6x-1 < 5[/tex]

Add 1 to both sides:

[tex]6x-1+1 < 5+1[/tex]

[tex]6x < 6[/tex]

Divide both sides by 6:
[tex]\dfrac{6x}{6} < \dfrac{6}{6}[/tex]

[tex]\boxed{x < 1}[/tex]

The price of 4 citrons and 3 fragrant wood apples is 34 units the price of 3 citrons and 4 fragrant wood apples is 29 units find the price of a cotton and the price of the wood apple

Answers

The price of one citron is 5 units and the price of one fragrant wood apple is 3.5 units." Let's call the price of one citron "c" and the price of one fragrant wood apple "w".

Using the information from the first equation:

4c + 3w = 34

Using the information from the second equation:

3c + 4w = 29

We can now solve the system of equations to find the value of "c" and "w".

Subtracting the second equation from the first:

4c + 3w - (3c + 4w) = 34 - 29

c = 5

Substituting the value of c back into one of the original equations:

3c + 4w = 29

3 * 5 + 4w = 29

15 + 4w = 29

4w = 14

w = 3.5

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