ABCD is a rectangle.

B, E and C are points on the straight line P with the equation x+2y=10

The volume of Economy Barrel is 785 litres.

The volume of Oceanview Barrel is 1766.25 litres.

The volume of Rainforest Barrel is 2649.375 litres.

The volume of Mountain Flow Barrel is 4710 litres.

The florist should buy Rainforest Barrel to have 2000L capacity without going bigger than needed.

What is volume?

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

The radius of Economy Barrel is = 50 cm

The height of Economy Barrel is = 100 cm

The formula for volume of a cylinder is -

Volume = πr²h

Substitute the values into the equation -

Volume = 3.14 × (50)² × 100

Volume = 3.14 × 2500 × 100

Volume = 785000 mL

Now converting it into litres -

785000 / 1000 = 785 Litres

Therefore, Economy barrel can hold 785 litres.

The radius of Oceanview Barrel is = 75 cm

The height of Oceanview Barrel is = 100 cm

The formula for volume of a cylinder is -

Volume = πr²h

Substitute the values into the equation -

Volume = 3.14 × (75)² × 100

Volume = 3.14 × 5625 × 100

Volume = 1766250 mL

Now converting it into litres -

1766250 / 1000 = 1766.25 Litres

Therefore, Oceanview barrel can hold 1766.25 litres.

The radius of Rainforest Barrel is = 75 cm

The height of Rainforest Barrel is = 150 cm

The formula for volume of a cylinder is -

Volume = πr²h

Substitute the values into the equation -

Volume = 3.14 × (75)² × 150

Volume = 3.14 × 5625 × 150

Volume = 2649375 mL

Now converting it into litres -

2649375 / 1000 = 2649.375 Litres

Therefore, Rainforest barrel can hold 2649.375 litres.

The radius of Mountain Flow Barrel is = 100 cm

The height of Mountain Flow Barrel is = 150 cm

The formula for volume of a cylinder is -

Volume = πr²h

Substitute the values into the equation -

Volume = 3.14 × (100)² × 150

Volume = 3.14 × 10000 × 150

Volume = 4710000 mL

Now converting it into litres -

4710000 / 1000 = 4710 Litres

Therefore, Mountain Flow barrel can hold 4710 litres.

Therefore, the florist should go with Rainforest barrel.

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The set of values of k for which the curve y = (k + 1) x² - 3x + (k + 1) lies below the X axis is k > 1/2 and k < -5/2.  

Quadratic functions are polynomial functions of second degree.

The general form of a quadratic function is f(x) = ax² + b x + c.

Given function is y = (k + 1) x² - 3x + (k + 1).

If the curve lies below the X axis, then the curve will not touch the X axis.

This means that, there will be no zeroes for the quadratic function.

So the discriminant will be negative.

Discriminant = [tex]\sqrt{b^{2}-4ac }[/tex] , for f(x) = ax² + b x + c.

So, for the function given,

Discriminant = [tex](-3)^{2} -[4*(k+1)*(k+1)][/tex]

                     = [tex]9-4(k+1)^{2}[/tex]

                     = 9 - 4(k² + 2k + 1)

                     = 9 - 4k² - 8k - 4

                     = -4k² - 8k + 5

-4k² - 8k + 5 < 0

4k² + 8k -5 > 0

Find the zeroes of 4k² + 8k - 5.

Zeroes are, k = [ -8 ± [tex]\sqrt{8^2-(4*4*-5)}[/tex] ] / (2 × 4)

                      = [ -8 ± [tex]\sqrt{144}[/tex] ] / 8

                      = [-8 ± 12] / 8

Zeroes are k = 4/8 = 1/2 and k = -20/8 = -5/2

4k² + 8k -5 = 0 when k = 1/2 and k = -5/2

4k² + 8k -5 > 0, when k > 1/2 and k < -5/2

Hence the values of k are k > 1/2 and k < -5/2 for which the function lies below the X axis.

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The trigonometric function, the identity is verified.

is trigonometric function?

The functions of an angle in a triangle are known as trigonometric functions, commonly referred to as circular functions. In other words, these trig functions provide the relationship between a triangle's angles and sides. There are five fundamental trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.

Here the given identity is,

=> [tex](cos \theta-5sin\theta)^2+(5cos\theta+sin\theta)^2=26[/tex]

Now using formula [tex](a-b)^2=a^2-2ab+b^2[/tex] and [tex](a+b)^2=a^2+2ab+b^2[/tex] then L.H.S

=> [tex]cos^2\theta-10cos\theta sin\theta+25sin^2\theta + 25cos^2\theta+10cos\theta sin\theta+sin^2\theta[/tex]

=> [tex]25sin^2\theta+25cos^2\theta+sin^2\theta+cos^2\theta[/tex]

=> [tex]25(sin^2\theta+cos^2\theta)+(sin^2\theta+cos^2\theta)[/tex]

We know that [tex]sin^2\theta+cos^2\theta=1[/tex] then,

=> 25(1)+1

=> 25+1

=> 26 = 26

L.H.S = R.H.S

Hence the given identity is verified.

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The value of d when p = 28 is 12. The solution has been obtained by using the concept of proportions.

What is proportion?

A comparison of two numbers mathematically is called a proportion. Two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio, according to the law of proportion.

We are given that p varies directly with d.

This means that they are directly proportional to each other.

When d = 3, then p = 7

So, when p = 28, then d is

⇒d/28 = 3/7

⇒d = 3*4

⇒d = 12

Hence, the value of d when p = 28 is 12.

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Answer:

To calculate the total amount Tyler will have paid to the bank, you can use the formula for simple interest:

I = Prt

Where:

I = Interest (the amount Tyler will pay to the bank)

P = Principal (the original amount borrowed)

r = Interest rate (expressed as a decimal)

t = Time (in years)

Plugging in the given values, we have:

I = 42,000 * 0.05 * 15

I = 42,000 * 0.75

I = 31,500

So, Tyler will have paid a total of $31,500 in interest to the bank once he paid the loan back in full after 15 years.

Answer:

Step-by-step explanation:

we’ll I don’t know if this is right but I will try my best first I divide what ever I have then divide or multiply it by the next number

The variable is x, the coefficient is 5, and the constant is -8 and 12.

A linear algebraic equation is an equation whose degree of the highest variable is 1. In an algebraic equation, we have variables, coefficients, and the constant.

An algebraic equation may be expressed as ax + b = 0 or ax + by + c = 0, where a, b, and c are real integers and x and y are variables with a maximum degree of one.

In 5x - 8 = 12

The variable is x, the coefficient is 5 i.e. the number prior(before) the variable, and the constant is -8 and 12.

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Answer:

Below

Step-by-step explanation:

In simplistic wording in this question, a term is a letter associated with a number

I see an m, i, s, and p in the equation. 4 different letters, so there are 4 different terms

Coefficients are the numbers associated with the term.

Counting left to right, The third one in the equation is 10s. That means the coefficient is 10

The required value of x for the  rational expression x-4/4+x to become undefined is x = -4

Rational expressions are defined as fractions of algebraic expressions, such as ax + b / cx + d.

Here,
A fraction to become undefined must consist of zero in its denominator,
So
Given expression = x - 4 / 4 + x
The above expression can be undefined if and only if 4 + x = 0
x = -4

Thus, the required value of x for the rational expression x-4/4+x to become undefined is x = -4.

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Ken's age can be calculated as follows: x x x = maximum target heart range − - − resting heart rate x = 139 − 73 = 66 x = 139 - 73 = 66 x=139−73=66.

Based on your age, you may calculate your maximum heart rate. Subtract your age from 220 to get a ballpark idea of your maximal age-related heart rate.

For instance, the predicted maximum age-related heart rate for a 50-year-old person would be computed as 220 - 50 years = 170 beats per minute (bpm).

15 seconds are needed to take your pulse. For beats per minute calculation, multiply this number by 4.

The highest rate is determined by deducting your age from 220. Therefore, the maximum heart rate for a 50-year-old is 220 minus 50, or 170 beats per minute.

Therefore, at a 50% level of effort, your goal would be 50% of that maximum, or 85 beats per minute.

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Answer:

Step-by-step explanation:

So 3a + 10c = 125 is translation of first sentence. Second part says a = c+7, "more than" indicating addition.

Substitute the 1st equation's a with c+7

So 3(c+7) + 10c = 125

Distribute.*+

3c + 21 +10c = 125

*Remember that 3(c+7) means to add up

c+ 7

c + 7

c + 7

‐-----------------

3c + 21

Combine 3c + 10c as 13c

So 13c + 21 = 125. Subtract 21 on each side (always treat left and right sides equally, believe in equality for all!!)

13c = 104. Divide each side by 13 (opposite of x)

c = 8........this is cost of each children's ticket

($8). Check: adult ticket is c +7 or $15. Does 3 adult tickets x $15 + 10 child tickets × 8 = 125? 45. + 80 = 125

Ssolution is correct. Can also be graphically to see where 3x + 10y = 125 crosses line x = y + 7

x being cost adult and y being cost of kids ticket, look at y (kids price) of point of intersection

The missing term when using the square root method is the discriminant. The discriminant is a number that is calculated from the coefficients of a quadratic equation.

A quadratic equation is a type of mathematical equation that can be written in the form of ax² + bx + c = 0, where a, b, and c are real numbers, a cannot equal 0. It is called a quadratic equation because it has a second-order term, which is the x² term. This type of equation has two solutions, which are referred to as the roots. These roots can be found by using the quadratic formula, which is x = -b ± √(b² - 4ac) / 2a. This equation can be used to solve a wide variety of problems, including finding the length of a side in a right triangle, calculating the area of a circle, finding the maximum or minimum of a function, and solving systems of linear equations.

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The area of Nick's grandfather's yard is 8/15 m²

A rectangle is a closed 2-D shape, having 4 sides, 4 corners, and 4 right angles (90°). The opposite sides of a rectangle are equal and parallel.

Given that, Nick's grandfather grows tomatoes in a section of his yard that is 4/5 meter long and 2/3 meter wide.

We have to find the area of the section,

Considering the section as a rectangular section,

Area of a rectangle = length × width

= 4/5 × 2/3

= 8/15

Hence, the area of Nick's grandfather's yard is 8/15 m²

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Answer:

40

Step-by-step explanation:

Answer: 40

Step-by-step explanation:

The function that represent the function g(x) is g(x) = f(x) + 4.

Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.

The graph of the function f(x) is given.

We know that, a linear function in slope intercept form can be represented as, y = mx + d, where m is slope and d is the y intercept.

y intercept is the y coordinate of the point where the line touches with the Y axis. At this point x coordinate is 0.

From the graph, we have f(x) = y = -1 when x = 0.

So y intercept, d = -1

Take two points from the graph (1, 0) and (0, -1).

Slope, m = (-1 - 0) / (0 - 1) = -1 / -1 = 1

f(x) can be represented in slope intercept form as f(x) = x - 1

We have a second function g(x) from the transformation of f(x).

y intercept of g(x) = 3

f(x) + 4 = x - 1 + 4 = x + 3 which can be g(X), since y intercept is 3.

Hence g(x) = f(x) + 4 is the function that represents the transformation of f(x) with y intercept 3.

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Answer:

Step-by-step explanation:

before the discount is $25

tax  rate 7.5%

set books price as X

X×(1+7.5%) = 25

X = 23.25

lets say the subtotal price already apply the discount rate

(X×(1-12%))×(1+7.5%)=25

x= 26.42

no answer match you given

The expression 3 ^ 2 * 3 ^ −5   equivalent to  is  1 / 27  .

What is Algebraic expression ?

Algebraic expression can be defined as the combination of variables and constants.

Given expression,

3 ^ 2 * 3 ^ −5

so,

3 ^ 2 * 3 ^ −5

=3 ^2 / 3 ^5

we know that a^m * a ^n  = a ^ ( m+n )

so we get,

= 3 ^ ( 2-5 )

= 3 ^ -3

= 1 / 3 ^3

Therefore, The expression 3 ^ 2 * 3 ^ −5   equivalent to  is 1 / 27  .

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Answer:

[tex]5x\leq 20[/tex]

[tex]$4[/tex] [tex]dollars[/tex]

Step-by-step explanation:

For the first question, since the maximum cost is $20, it has to be [tex]5x\leq 20[/tex] because less than or equal to 20 is the maximum.

For the second question, we solve:

[tex]5x\leq 20[/tex]

[tex]\frac{5x}{5} \leq \frac{20}{5}[/tex]

[tex]x\leq 4[/tex]

[tex]Answer[/tex] [tex]is[/tex][tex]:[/tex] [tex]4[/tex] [tex]dollars[/tex]

Answer:

a) The area of the rectangle is given by the product of its length and width. Thus:

Area = (4x - 3) * 2

Area = 8x - 6

b) The perimeter of a rectangle is the sum of the lengths of all four sides. The perimeter of this rectangle can be expressed as:

Perimeter = 2 * (length) + 2 * (width)

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

Perimeter = 8x - 6 + 4

Perimeter = 8x

Answer:

10 inches

Step-by-step explanation:

The surface area of a cylinder is equal to 2 times the area of the base circles plus the height times the circumference.

[tex]SA=2A+Ch[/tex]

[tex]SA=2\pi r^2+2\pi rh[/tex]

Now substitute given values of radius and surface area

[tex]78\pi =2\pi (3)^2+2\pi (3)h[/tex]

Simplify.

[tex]78\pi =18\pi +6\pi h\\60\pi =6\pi h\\10=h[/tex]

The height is 10 inches.

The number of possible ways in which 3 beds, 1 desk and 4 dressers can be arranged are 12.

Given is that green family is selecting a furniture set there are 3 beds 1 desk and 4 dressers.

The total number of possible ways in which 3 beds, 1 desk and 4 dressers can be arranged are -

{x} = 3 x 4 x 1

{x} = 12

Therefore, the number of possible ways in which 3 beds, 1 desk and 4 dressers can be arranged are 12.

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The number of labor hours required to install the ceiling is 24.528 labor hours.

What is ceiling?

Ceiling is the overhead surface of a room, typically flat and finished with paint, wallpaper, or tiles. It is the highest point or top part of a room, and can be made up of different materials including drywall, plaster, tiles, or even wood. Ceilings also help to separate the room from the outside air and create a space that is more comfortable and insulated. Ceilings can be used to add visual interest to a room, as they can be decorated with different colours and textures. Ceilings can also be used to conceal mechanical and electrical systems, such as wiring, piping, and ductwork.

The number of labor hours required to install the ceiling is 24.528 labor hours. This is determined by multiplying the area of the ceiling (1,856 square feet) by the productivity rate (0.013 labor hours per square foot) and then multiplying that result by the productivity factor (0.95).

1,856 square feet x 0.013 labor hours per square foot x 0.95 productivity factor = 24.528 labor hours.

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If A and B matrices have linearly independent column vectors, then the column vectors of C = AB will also has linearly independent column vectors.

Linearly independent vectors are defined when there exists no non-trivial linear combination of the vectors that equals the zero vector. We have, A∈ Rᵐ × Rⁿ and B∈ Rⁿ × Rʳ and C = AB . If both A and B both have linearly independent column vectors. So, A and B are invertible matrix . Then, Cᵀ = Aᵀ Bᵀ where the column vectors of A and B are row vectors of Aᵀ and Bᵀ matrices respectively. Also, the independence of A and B implies the independence of Aᵀ and Bᵀ. As we see Cᵀ = Aᵀ Bᵀ ,then Cᵀ is linearly independent. That means C is invertible matrix . So, the columns of matrix C is also be linearly independent.

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After listening to the excerpts we can say that, excerpt z is exposition subject soprano, excerpt x is middle entries episode and excerpt y is closing

In music, a fugue is a contrapuntal compositional technique in two or more voices that is based on a subject (a musical theme) that is introduced at the beginning in imitation (repetition at different pitches) and that recurs frequently throughout the composition.

It should not be confused with a fuguing tune, a type of song that was popularized by early American music and West Gallery music and is primarily restricted to those genres. A fugue typically consists of three main sections: an exposition, a development, and a final entry that features the subject returning in the tonic key of the fugue. Recapitulations are included in some fugues.

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Downtown Shopping stock photos, pictures and royalty-free images from iStock.

What is public parking?

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The 95% confidence interval for the mean daily income of a parking garage is between $5123.48 and $5134.52, indicating that the average daily income will be within this range.

Mean is a form of average that is calculated by adding all of the numbers in a set and then dividing the total number of numbers in the set by the total number of numbers in the set. It is sometimes referred to as the arithmetic average.

Assuming the assumptions given in section a) are correct, the 95% confidence interval for the mean daily income generated by this parking garage may be computed using the method for calculating the confidence interval for a population mean. This confidence interval is computed by taking the sample mean, 5129, and multiplying it by 1.96 times the standard error of the mean, which is the standard deviation divided by the square root of the sample size. As a result, the 95% confidence interval is (5123.48, 5134.52).

This 95% confidence range implies that we can be 95% certain that the average daily income generated by this parking garage will be between $5123.48 and $5134.52. To put it another way, we may be 95% positive that the average daily income in this parking garage is generated.

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The potential roots of f(x) = 3x³ - 13x² - 3x + 45 are given as follows:

A. +1/3

B. +5

C. +5/3

D. +9

E. +1

F. +15

G. +3

To obtain the possible rational zeros of the function, we use the Rational Zero Theroem.

The rational zero theorem states that all the possible rational zeros of a function are given by plus/minus the factors of the constant by the factors of the leading coefficient.

The parameters for this function are given as follows:

The factors are given as follows:

Hence the possible roots are given as follows:

±1/3, ±1, ±3, ±5, ±5/3, ±9, ±5, ±15.

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I don’t know Answer:

Step-by-step explanation: