Serenity has 58 m of fencing to build a four-sided fence around a rectangular plot of land. The area of the land is 210 square meters. Solve for the dimensions (length and width) of the field.

Answer:

mode = 3

Step-by-step explanation:

the mode is the value that occurs most often in the data set

3, 7, 4, 6, 3, 5, 9, 40, 6, 3

the value 3 occurs most often , 3 times

then mode of data set = 3

The principal investment required to get a total amount of $17,757.16 from compound interest at a rate of 3.9% per year compounded continuously over 9 years is $12,500.75.

What is continuous compounding?

There is no cap on how frequently interest can accumulate thanks to continuous compounding. A balance can compound continuously an unlimited number of times, which means interest is earned on it constantly.

We have,

9 years in an account with a 3.9% annual interest rate compounded continuously,

an investment is worth a total of $17,757.16.

First, convert R as a percent to r as a decimal

r = R/100

r = 3.9/100

r = 0.039 per year,

Then, solve the equation for P

P = A / ert

P = 17,757.16 / e(0.039*9)

P = $12,500.75

Hence, the principal investment required to get a total amount of $17,757.16 from compound interest at a rate of 3.9% per year compounded continuously over 9 years is $12,500.75.

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Answer:

$12,500.75

Step-by-step explanation:

I got it right.

By using the concept of vector, it can be calculated that

Component form of vector v = (-4 , 5)

What is a vector?

Vector is anything that has magnitude and direction and follow the vector addition law. Vector is a very important tool in mathematics and physics.

Here,

The initial point of vector v is (1, -4) and the terminal point of vector v is      (-3, 1)

Component form of vector v = (-3 - 1, 1 - (-4)) = (-4 , 5)

Second option is correct

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The reasoning above makes it very evident that the hyperbola's coordinate is (8, -1)

The hyperbola is open upward and downward because the expression 'y' has a positive leading coefficient. In comparison to the usual equation, the hyperbola's center is found to be at (2, -1) and its 'a' point, 6, and 'b' point is 8. A smooth curve that lies in a plane and is classified as a hyperbola in mathematics by either its geometric characteristics or by equations for which it is the solution set. Two parts of a hyperbola, referred to as connected components or branches, are mirror reflections of one another and resemble two infinite bows.

Given,

((x-2)²/36)-((y+1)²/64)=1

We know that the standard form of a parabola is:

((x-k)²/a²)-((y-h)²/b²)=1

Center for the given hyperbola is (2, -1)

And a=6, b=8

And the coordinates for the center of the hyperbola are x=8, y= -1

Therefore, (x, y)=(8, -1)

The reasoning above makes it very evident that the hyperbola's coordinate is

(8, -1)

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Answer:

After dilation, the size of the image will change and the shape of the image will be same

Dilating an image means the changing the size of the image, but the shape of the image will be same

Dilation is the process of changing the size of the image without changing the shape of the image

The image after the dilation is called as the pre image.

The dilation can be done by using the scale factor or normally increase or decrease the size,

If the dilation of an image done by scale factor, the size is increased or decreased according to the value of scale factor. If it is greater than 1 the size increases and if it is between 0 and 1 the size decreases

Therefore, size of the image will change after the dilation

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Answer:

-x² -10x -26

Step-by-step explanation:

Substitute x in f(x) with x + 5:

f(g(x)) = - (x+5)² - 1

= - (x² + 10x + 25) -1

= -x² -10x -25 -1

= -x² -10x -26

The constant of proportionality that relates the number of servings to cups of cheese is  0.25.

According to the question,

Sarah used 2.5 cups of cheese in a dish that serves 10 people, this can be written as :

let the c be the cups of cheese : c = 2.5 cups of cheese

let n be the number of the people that is been served

Then the equation can be written as :

c ∝ n

then we can bring in the proportionality constant sign as ;

then c = kn

then we can introduce the given figures into the equation as ;

=> 2.5=k (10)

the we can determine the value of the constant as :

=> k=2.5/10 = 0.25

Hence, constant of proportionality relates the number of servings to cups of cheese is 0.25

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No, The dilation doesn't change the shape of the image

Dilation is a type of a transform where an image size either increase or decrease but has the same shape as the original. In other words, the dilation is similar to the original.

All dilations have a center and a scale factor. The center is the point of reference for the dilation (like the vanishing point in a perspective drawing)

Scale factor tells us how much the figure stretches or shrinks. A scale factor is typically labeled  "k" and is always greater than zero.  It is the ratio of the sizes of the original figure with the dilated figure

The only change in the dilation process is that the distance between the points changes. It means that the length of the sides of the original image and the dilated image may vary.

Therefore , Dilation doesn't changes the shape

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Given ▲ ABC and  ▲DEF are the examples of AAS congruence theorem.

According to the AAS, or Angle Angle Side congruence rule, two triangles are said to be congruent if two pairs of corresponding angles and the opposite or non-included sides are equal to one another.

The sides are not included between the angles but rather run in either direction of the angles, whereas the angles are sequential and corresponding in nature.

let's consider 2 triangles ▲ ABC ,  ▲DEF.

A at top B left C right . D at top E left F right side

∠B = ∠E

∠C = ∠F

AB = DE.

We can see that ∠B = E and ∠C = F if we superimpose the two triangles on top of one another. The lengths of the excluded sides, AB and DE, are also equal. As a result, we can state that ABC ≅ DEF.

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Therefore , Angela needs to fill this cup 6/7 times.

A fraction represents a component of a whole or, more generally, any number of equal parts. As in one-half, eight-fifths, and three-quarters, a fraction in conversational English denotes the number of components of a specific size.

Here,

To her dough, Angela needs to add 12 cups of milk. She only has a measuring cup that holds 14 cups.

Thus, the number of times angela needs to fill  cup are = 12/14 times

thus ,

=> 12/14 =6/7

Therefore , Angela needs to fill this cup 6/7 times.

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Perimeter of Rectangle is 44m

A perimeter is a closed path that encompasses, encircles, or delineates a one-dimensional length or a two-dimensional shape.

According to the given information

Area of Rectangle = l × b

Area of Rectangle = 105 [tex]m^{2}[/tex]

Length of one side = 7 m

Let the length of the adjacent side = b

Area of Rectangle given = 7 × b

                     105   = 7 × b

                       b    =  [tex]\frac{105}{7}[/tex]

                       b   = 15 m

Perimeter of Rectangle given = 2( l + b )

                                        = 2 ( 7 + 15 )

                                        = 2 × 22

                                        = 44m

Perimeter of Rectangle is 44m

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Answer:

A and B

Step-by-step explanation:

-(5/3) = -1.67

-5/3 = -1.67

5/-3 = -1.67

5/3 ≠ -1.67

-5/-3 ≠ -1.67

-(-5/3) ≠ -1.67

The total amount they will pay would be $95.557

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

Given that the cost of their meal was $75.99. Tax on the meal is 6.75% and they left a 19% tip on the cost of the meal.

Cost of meal = $75.99

The tax amount = 6.75% of 75.99

                  = ( 6.75/100 ) x 75.99

                  = $5.129

Tip amount = 19% of 75.99

                  = (19/100) x 75.99

                  =  $14.438

Thus, the Total amount they will pay

= $75.99 + $5.129 + $14.438 = $95.557

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Answer:

A split infinitive is a common grammatical mistake that can be hard for writers to spot. Many people think they are not a big deal, but they can often have a major impact on your writing and make it hard for a reader to understand what you have to say.

Step-by-step explanation:

Take, for example, this sentence:

I like to on a hot day eat a lot of ice cream.

Did you have to read it twice to be clear what it was saying? I know I did. But let's make just a little adjustment:

On a hot day, I like to eat a lot of ice cream.

Answer:Use it as it is or fit non-normal distribution

Step-by-step explanation:

Answer:

121°

Step-by-step explanation:

x + 6 + 3x -15 + 5x + 36 = 180

9x + 27= 180

9x = 180 - 27

9x = 153

9/9 x = 153/9

x = 17

mC = 5·17 + 36

85 + 36

121°

Answer: y = 8 , x = 4

Step-by-step explanation:

gosh darn i haven done this since algebra 1 !!

since both equations equal y, we can make them equal to each other since y = y

-2x +16 = 2x (im just gonna simplify without all the extra steps sorry)

x = 4 (this is the first answer)

now we can plug in x to find y

y = 2(4)

y = 8 (second answer)

im sorry if the grammar is horrid its 3 am

The measure of the perpendicular of the right-angle triangle will be 16.728 units.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

The sine of the angle is the ratio of perpendicular to the hypotenuse.

sin θ = Perpendicular / Hypotenuse

The angle is 42° and the measure of Hypotenuse is 25. Then the measure of the side 'x' will be given as,

sin θ = Perpendicular / Hypotenuse

sin 42° = Perpendicular / 25

Perpendicular = 25 x sin 42°

Perpendicular = 16.728

The measure of the perpendicular of the right-angle triangle will be 16.728 units.

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Answer:

[tex]b) 5^{\frac{1}{12} }[/tex]

Step-by-step explanation:

∛5 = 5^1/3

⁴√5 = 5^1/4

Then:

∛5 / ⁴√5 = (5^1/3) / (5^1/4)

              = 5^(1/3 - 1/4)

1/3 - 1/4 = 4/12 - 3/12 = 1/12          

Then:

5^(1/3 - 1/4) = 5^1/12

= [tex]5^{\frac{1}{12} }[/tex]

**** The symbol ^ means that the expression on the right is an exponent.

Example:

5^1/3

means  1/3 is an exponent,

Answer:61

Step-by-step explanation:

Answer:

200

Step-by-step explanation:

Because there were 110 people at the concert, that means only 110 seats were filled. So we can think of the problem as its own equation if we word it like this:

110     is    55%    of    how many seats

110     =   0.55    x      ?

Now to solve by dividing 110 by 0.55

110/0.55 = 200

The interval on which the graph is increasing and decreasing are ( -∞,3] and [3,∞) respectively.

There is no interval where the function is constant.

In order to solve this question we need to study the graph attached,

From the graph, we could see that the plotting of the graph is starting from the negative axes and we could observe an increasing slope in the function, and the increment stopped after reaching point B(3,0), we can also observe that the value of the y-axis increases with that of the x-axis.

The interval at B(0,3) must be wrote down as ( -∞,3]

Again we could see a sudden drop in the slope of the function of the graph as the slope of the graph this time starts decreasing and moves to infinity and again we could observe that the value of the x-axis starts decreasing with the decrease in the value of the y-axis.

The function was constant at a null interval.

Therefore, The interval on which the graph is increasing and decreasing are ( -∞,3] and [3,∞) respectively and there is no interval where the function is constant.

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Answer:

1.1667

Step-by-step explanation:

Brainliest please!

Answer:

Below

Step-by-step explanation:

y = 19/x^3       <===== solve for 'x'

x = cube rt (19/y)     < ====now switch the x and y's

y = cube rt ( 19/x)

Answer: f^-1(x) = 19^3/x

Step-by-step explanation:

Given that : f(x) = y = 19/x^3

x^3 = 19/y

y = (19)^3/x = f^-1(x)

Answer:

a value that is not yet known

Answer:

2p(6p + 5)

Step-by-step explanation:

12p² + 10p ← factor out 2p from each term

= 2p(6p + 5)

f(-2) = 254 , meaning if the company sells shirts -2 , they would make a profit of 254 dollars. This interpretation is true in the context of the problem.

f(12) = 266 , meaning if the company sells shirts 12 , they would make a profit of 266 dollars. This interpretation is true in the context of the problem.

f(17.5) = 270.25, meaning if the company sells shirts 17.5 , they would make a profit of 270.25 dollars. This interpretation is true in the context of the problem.

Based on the observations above, it is clear that an appropriate domain for the function is x ≥ - 2.

Functions and values given the function that represents elevation, in feet, of Jayden hikes expressed as:

f(x)=(x+2)²+250.

If the domain value of the function is -4, then;

f(-4)=(-4+2)²+250

f(-4) = 4 + 250

f(-4) = 254

f(-4) = 254 means If Jayden hikes 4 miles to the south, his elevation would be 254 feet. This interpretation is true in the context of the problem

If the domain value of the function is -4, then;

f(2)=(2+2)²+250

f(2) = 16 + 250

f(2) = 266

f(2) = 266 means If Jayden hikes 2 miles to the north, his elevation would be 266 feet. This interpretation is true in the context of the problem

If the domain value of the function is 2.5, then;

f(2.5)=(2.5+2)²+250

f(2.5) = 20.25 + 250

f(2.5) = 270.25

f(2.5) = 270.25 means If Jayden hikes 2.5 miles to the north, his elevation would be 270.25 feet. This interpretation is true in the context of the problem

Determining the domain

The domain exist for the value of (x+2)² ≥ 0

x + 2 ≥ 0

x ≥ - 2

Based on the observation above, it is clear that an appropriate domain of the function is x ≥ - 2

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The given equation after a translation by 2 units upwards is y = 3.5x + 2.

The rules for translating an equation in both vertical and horizontal directions are:

The given equation is y = 3.5x

The equation after translation by 2 units upward is obtained by using the rule we have y = f(x) + m.

⇒ y = 3.5x + 2

The graphs for the given equation and the translated equation are shown in the graph below.

For the pair that show translation in both equations, substituting x = 0, we get

y = 3.5x ⇒ y = 3.5(0) = 0; So, the point is (0,0)

and

y = 3.5x + 2 ⇒ y = 3.5(0) +2 = y = 2; So, the point (0,2)

Therefore, the required pair is (0,0) and (0,2).

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Answer:

$575 after 5 years

Step-by-step explanation

3% of 500= 15

15 × 5= 75

500 + 75= $575