What is the range of the following function

The dimensions of the rectangular pen to minimize the amount of material needed is 4L which gives 160ft.

The minimum length or breadth of the open space type, as measured along the longest two (2) straight lines meeting at a right angle to define the lot's maximum length and width.

With regard to the above problem,

let us say L is the lenght of the rectangle and W is the width

Based on the formula for the area of a rectangle,

L x W  = 1600ft

To minimize the perimeter, of the rectangle, we must assume that:

L = W

that is L² = 1600

If we applied square root to both sides of the equation, we'd have


L = 40

Thus the minimum perimeter is given as: 4L = 4 x 40 = 160ft.

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Answer:

A right-angled triangle

Answer:

5 hours

Step-by-step explanation:

$65 - $15 = $50

$50/$10 = 5

The distance between the two points is 8.25 units

The distance between two points in a plane is the length of the line segment separating the two locations. Typically, the equation d=((x2 - x1)2 + (y2 - y1)2) is used to calculate the distance between two locations. You may use this formula to get the separation between any two points on an x-y plane or coordinate plane.

The following is the formula for the separation between two points:

d= √(x₁-x₂)²+(y₁-y₂)²

Points (x1, Y1) and (x2, Y2)

As given in the question, the points are (-6, -6) and (-8, 2)

The distance between the two points is,

d= √(-6+8)²+(-6-2)²

d=√4+64

d=√68 units= 8.25 units

Therefore, the distance between the two points is 8.25 units

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The commission that thereal estate agency gets is $16885.

The commission that the agent gets is $76750

The selling price for a house = $ 307,000

The commission rate for real estate agency = 5.5 %

The commission rate for the agent = 25 %

So, the commission which real estate agency gets:

= 5.5 % of $307,000

= 0.055 × $ 307,000

= $16885

The commission which agent get:

= 25% of $ 382,000

= 0.25 × $ 307,000

= $76750

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Answer:

A. 5/3

Step-by-step explanation:

The line is in a positive trend we can see it because when we read it from left to write we can see it go up. The point where we start is 5 levels down from the second point  3 units to the left.

We can model this using  rise/run

Rise = 5

Run = 3

5/3

The expression that represents "10 subtracted from the quotient of 3 and a number" is D. 3 over n - 10.

An expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

Let the number be n

The expression will be:

= 3/n - 10

Therefore, the correct option is D.

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Answer:

Put one dot at (0,3) and the other dot at (1,0)

Step-by-step explanation:

Let x = 0

6x + 2y = 6

6(0) + 2y = 6

2y = 6  Divide both sides by 2

y = 3

(0,3)

Let y = 0

6x + 2y = 6

6x + 2(0) = 6

6x = 6  Divide both sides by 6

x = 1

(1, 0)

The price of a pack of balloons is 4. 39

The price of a pack of party favors is 0. 36

We have that;

Let the cost of balloons be x

Let the cost of party favors by y

From the information given, we have that;

3x + 4y = 14. 63   (1)

2x + 4y = 16. 03  (2)

Now, let's make 'x' the subject from equation (1)

x = 14. 63 - 4y/ 3  (3)

Substitute in equation (2)

3( 14. 63 - 4y/ 3) = 16. 03

expand the bracket

43. 69 - 12y /3 = 16. 03

cross multiply

43. 69 - 12y = 48. 09

collect like terms

- 12y =  - 4. 4

make 'y' the subject

y = 0. 36

substitute in equation (3)

x = 14. 63 - 4(0. 36)/ 3

x = 13. 1/ 3

x = 4. 39

Hence, the prices are 4. 39 and 0. 36 respectively.

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Step-by-step explanation:

that simply means we use one equation to express one variable by the other, and then we use that identity in the second equation (substituting one variable by the expression of the other variable. and then we solve for that remaining variable.

finally we use one of the original equations to solve for the second variable.

4x + y = 19

so, that gives us

y = 19 - 4x

we use that now in the second equation :

6x + 7(19 - 4x) = 1

6x + 133 - 28x = 1

-22x + 133 = 1

-22x = -132

22x = 132

x = 6

now, let's use e.g.

4x + y = 19

4×6 + y = 19

24 + y = 19

y = -5

Michael will be spending the cost of $ 15.652 on the Furry Fabric.

Given, that Michael is dressing up as Maggie,

He is making his costume and he needs 8.6 yards of furry fabric

The fabric costs $1.82 per yard.

So, as he needs 8.6 yards of fabric and each yard of that fabric costs him $1.82.

1 yard of Furry Fabric = $1.82

8.6 yards of Furry Fabric = $1.82 × 8.6

8.6 yards of Furry Fabric = $ 15.652

Hence, Michael will be spending the cost of $ 15.652 on the fabric.

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The street was 900m long when the speed is 15m/s and, the time is 60 seconds.

To calculate speed, divide the distance traveled by the time it took to complete the voyage, so speed = distance divided by time. To determine the distance, multiply the speed by the passage of time. These equations can be reduced as s=d/t, where s represents speed, d represents distance, and t represents time.

Distance divided by time equals speed. Distance = time * speed

To solve for speed or rate, utilize the speed formula, s = d/t, which implies speed equals distance divided by time. To solve for time, utilize the time formula, t = d/s, which implies time equals distance divided by speed.

Given,

Speed of the biker who travels down the street=15m/s

Time taken=60seconds

Distance=?

We know that,

Distance=Speed× Time

Distance=15×60

Distance=900m

Therefore, the street was 900m long

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The equation that passes (6,0) and (3,4) is -3y=4(x-6)

What are the different forms of straight lines ?

The following information about the straight line is required if we wish to obtain the equation for it.

1. The y-intercept and slope

2. Two-point and slope

3. Two things.

4. the intersection of the x- and y-axes

the straight line that passes through (6,0) and (3,4).

The equation can be expressed in a point-slope form which is ,

y/x-6=4/-3

∵ -3y=4(x-6)

Hence,

The equation that passes (6,0) and (3,4) is -3y=4(x-6)

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The system of equations with the solution (4, -3) is y = x - 7 and y = 2x - 11.

We are given a point. The coordinates of the point are (4, -3). We need to find a system of equations such that they pass through the given point.

We will use the slope-point form of a line. Let the slope of the equation of the straight line be "m". We need two equations. The general equation of a line using the slope-point form is given below.

(y - y1) = m(x - x1)

We know that both equations must pass through the given point for the solution to exist.

(y - (-3)) = m(x - 4)

(y + 3) = m(x - 4)

We just need to take any two values of the slope of the line.

First, we take m = 1. The corresponding equation is given below.

(y + 3) = m(x - 4)

(y + 3) = 1*(x - 4)

y + 3 = x - 4

y = x - 7

Next, we take m = 2. The corresponding equation is given below.

(y + 3) = m(x - 4)

(y + 3) = 2*(x - 4)

y + 3 = 2x - 8

y = 2x - 11

Hence, the system of equations is y = x - 7 and y = 2x - 11.

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Answer:

Step-by-step explanation:

A coefficient is a number before the variable that shows how many groups of the variable there are. For example, 2b would be two groups of B.

The coefficients in this expression would be 4 (as in 4x) and 8 (as in 8y).

Answer:2/5=4/10 and 1/4=2/8

Step-by-step explanation: you can simplify 4/10 to get 2/5 and same with 2/8. You would divide the fraction by two.

The information about the graph of the relationship that is given is: E. y-intercept and a point that is not an intercept.

In Mathematics, the y-intercept of any graph such as a linear, quadratic, trigonometric function, generally occurs at the point where the value of "x" is equal to zero (x = 0).

Mathematically, the slope-intercept form of a straight line is generally modeled or represented by this mathematical expression;

y = mx + c

Where:

In this context, we can reasonably infer and logically deduce that the total number of pages (y-intercept) which is equal to 180 is an information that was provided, as well as the number of hours (666 hours), which represents a data point on the x-coordinate of the graph.

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Answer: 4x+10

simplified: 2x+5

Step-by-step explanation:

Answer: 4x+10

You multiply 2 by (2x) = 4x

You multiply 2 by (5) = 10

Answer: final answer = 3/8

Step-by-step explanation:
it says 1/8 + 1/4. before you can add them you have to make sure that both fractions have the same denominator first you have to make both of the bottom denominators the same so its 1/8+2/8.
1/8+2/8=3/8

Answer:

7.416 is the answer

The solution to the inequality is x > 0

Inequality in mathematics differentiate two values,  if one is less than, greater than, or not equal to another value

Evaluate the equation by letting the unknow to be on one side

−1 − 10x < −1

-10x < -1+1

Add +1 to both sides

= -1-10x+1 < -1+1

= -10x < 0

Divide both sides by -10 same factor and flip the relation because  of negative factor

=  -10x /-10 > 0/-10

= x > 0

Therefore the solution to the inequality is x>0

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Yes this question can be proven by mathematical induction

What do you mean by induction in mathematics?

For each and every natural number n, a statement, theorem, or formula can be proved using the mathematical induction technique. By generalizing this into the "Principle of Mathematical Induction," which we would utilize to demonstrate any mathematical assertion.

Here, n ≥ 1

1/1.2 + 1/2.3 + 1/3.4 + .............. + 1/n(n +1)

We employ the idea of Sigma here.

S/1/r(r + 1) { r = 1 to n }

Sigma [1/(r + 1) - 1/(1/r)] { r = 1 to n }

put r = 1 \s1/1 - 1/(1 + 1) = 1 - 1/2

put r = 2 \s1/2 - 1/(2 +1) = 1/2 - 1/3

put r = 3 \s1/3 - 1/(3 +1) = 1/3 - 1/4

........................................................... put r = n 1/n - 1/(n + 1)

after adding

Sigma = [1/(r+1) - 1/(1/r)] {r = 1 to n } = 1 -1/2 + 1/2 -1/3 + 1/3 - 1/4 + ............1/n - 1/(n +1)

= 1 - 1/( n +1) = n/( n +1)

Consequently, 1/1.2 + 1/2.3 + 1/3.4 +... 1/n(n + 1) = n/(n + 1).

so it proved

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The total 18 numbers such  that n<150 exist, if the sum of the numbers of factors of N and N^2 is 34

Let me give you an example. 12. Both 2- 2 times and 3- 1 times are factors of 12.

Factors in total (2+1)*(1+1)=6

It will have 2- 4 times and 3-2 times for 122.

15 total factors of 5*3

Situation 1: N = xy

attempting a reverse strategy for N*N Factors in 35=5*7 are x-4 times and y-6 times.

Regarding N-x-2 and Y-3 timings.

There are a total of (2+1)*(3+1)=12 factors.

Situation 2

Since N2 has 34 factors if N2 is raised to the power of 34, there are 17 factors for N.

Consequently, 17+1 = 18 factors in total.

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Answer:

$24

Step-by-step explanation:

3(4) + 3(4) = x (the total cost)

12 + 12 = x

x = $24

aₙ=a+(n-1)d is the formula can be used to find the nth term of the sequence.

Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

Given sequence is 5,9,13,17,21

Five comma nine comma thirteen comma seventeen comma twenty one.

We need to find the nth term of the sequence.

Firstly we need to find the sequence is AP or GP.

An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same.

so 9-5=4,

13-9=4

Hence the sequence is a Aritmetic sequence.

In arithmetic sequence the nth term can be find by using the formula

aₙ=a+(n-1)d

where a is first term and d is common difference.

Hence aₙ=a+(n-1)d is the formula can be used to find the nth term of the sequence.

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The price of the share 3 years later, given the increase in value, can be found to be $43.29

The value of the Southside stock sold was $ 37 at the current age. Three years later, this value had increased by 17 %.

This means that the price of the share 3 years later would be:

= Share price currently x ( 1 + increase in value)

= 37 x ( 1 + 17 % )

= 37 x 1. 17

= $ 43. 29

The price is  $43.29

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According to the solving the area of the square is 68.0625.

As is common knowledge, a square is a four-sided, two-dimensional figure. It is also referred to as a quadrilateral. The total quantity of unit squares forming a square is referred to as the square's area. In other words, it is described as the area that the square takes up.

The box formed after cutting the square from each corner will have the dimensions as,

length = 104 - 2x, width = 39 - 2x, height = x.

∴ volume of the box = length × width × height

∴ v = (104 - 2x)(39 - 2x)(x) -----(i)

∴ v = (104 - 2x) (39x - 2[tex]x^{2}[/tex])

∴ v = 104(39x - 2[tex]x^{2}[/tex]) -2x(39x - 2[tex]x^{2}[/tex])

∴ v = 4056x - 208[tex]x^{2}[/tex] - 78[tex]x^{2}[/tex] + 4[tex]x^{3}[/tex]

∴ v = 4[tex]x^{3}[/tex] - 286[tex]x^{2}[/tex]  + 4056x

let f(x) =  4[tex]x^{3}[/tex] - 286[tex]x^{2}[/tex]  + 4056x  -----(ii)

To, find x for which f(x) is maximum,

⇒we should apply second derivative test ,

According to this test, first we should find critical points at which f'(x) = 0.

then if f''(x) < 0 for that critical point then f(x) is maximum at that critical point.

∴ let us consider, f'(x) = 0.

now, f(x) =  4[tex]x^{3}[/tex] - 286[tex]x^{2}[/tex]  + 4056x

⇒ f'(x) = 12[tex]x^{2}[/tex] - 572x + 4056.  -----(iii)

⇒ f'(x) = 4(3[tex]x^{2}[/tex] - 143x + 1014)

⇒ f'(x) = 0.

⇒  f'(x) = 4(3[tex]x^{2}[/tex] - 143x + 1014) = 0

⇒ x = (-b ± [tex]\sqrt{b^{2} - 4ac }[/tex])/2a    ; where a = 3, b = -143, c = 1014.

∴ x = (-(-143) ± [tex]\sqrt{(-143)^{2} -4(3)(1014)}[/tex])/2×3

∴ x = (143 ± [tex]\sqrt{8281}[/tex])/6.

∴ x = [tex]\frac{143 + 91}{6}[/tex]  , x = [tex]\frac{143 - 91}{6}[/tex]

⇒ x = 39, 8.25

the square of length 8.25 inch should be cut from each side to det contained with the maximum volume.

Area of the square is = [tex]x^{2}[/tex] = [tex]8.25^{2}[/tex]

∴ Area = 68.0625

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The probability that the area covered by a can of spray paint is 0.251

The variable of interest is:

X: are objects that can be painted with a single can of spray paint.

This variable has a normal distribution, with a mean of 25 feet square and a standard deviation of 3 feet square.

Symbolically:

P(X≥27)

To calculate the probability, use the standard normal distribution, so first standardize the value of X using:

Z= (X-μ)/σ

P(X≥27)= P(Z≥(27-25)/3)= P(Z≥0.67)

Now, because the Z-table contains cumulative probability information:

P(Zα≤Z₀)=1-α

you must perform the following conversion to calculate the requested probability:

1 - P(Z<0.67)= 1 - 0.749= 0.251

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