The area of a rectangle is 294 in². The ratio of the length to the width is 3:2. Find the length and the width.

To get Desmos to show both square roots, you can use the formula y = √x + √(-x).  Desmos can then graph this equation, showing both the positive and negative square roots.

To get Desmos to show both square roots, you can use the formula y = √x + √(-x).This formula can be used to graph two square roots. The first square root is √x, which is the positive square root of x. The second square root is √(-x), which is the negative square root of x. To calculate the roots, you would take the square root of both x and -x. For example, if x is 4, the two roots would be √4 = 2 and √(-4) = 2i, where i is the imaginary unit. Desmos can then graph this equation, showing both the positive and negative square roots.

Learn more about square root here:

https://brainly.com/question/16880173

#SPJ4

Since [tex]1 - \sin^{2}{\theta} = \cos^{2}{\theta}[/tex], the trigonometric expression [tex]\frac{\sin{\theta}}{\sqrt{1 - \sin^{2}{\theta}}} = \tan{\theta}[/tex] is proven.

The trigonometric expression for this problem is defined as follows:

[tex]\frac{\sin{\theta}}{\sqrt{1 - \sin^{2}{\theta}}} = \tan{\theta}[/tex]

The identity used for the proof is given as follows:

[tex]\sin^{2}{\theta} + \cos^{2}{\theta} = 1[/tex]

Hence:

[tex]1 - \sin^{2}{\theta} = \cos^{2}{\theta}[/tex]

Replacing on the left side of the expression, we have that:

[tex]\frac{\sin{\theta}}{\sqrt{1 - \sin^{2}{\theta}}} = \frac{\sin{\theta}}{\sqrt{cos^{2}{\theta}}}[/tex]

Taking the square root:

[tex]\frac{\sin{\theta}}{\sqrt{1 - \sin^{2}{\theta}}} = \frac{\sin{\theta}}{\cos{\theta}}[/tex]

The tangent is given as the division of the sine by the cosine, hence:

[tex]\frac{\sin{\theta}}{\cos{\theta}} = \tan{\theta}[/tex]

More can be learned about trigonometric identities at https://brainly.com/question/7331447

#SPJ1

The terminal value formula helps estimate the value of a business beyond the explicit forecast period,

the terminal value formula = FCFF 6 / (WACC – Growth Rate)

We can say that in a DCF model with a five-year free cash flow projection, the terminal value formula = FCFF 6 / (WACC – Growth Rate)

It could be accountable that in finance, the terminal value (also known as “continuing value” or “horizon value” or "TV") of a security is the present value at a future point in time of all future cash flows when we expect stable growth rate forever. It is most likely often used in multi-stage discounted cash flow analysis and also allows for the limitation of cash flow projections to a several-year period; see Forecast period (finance). Forecasting results beyond such a period is impractical and exposes such projections to a variety of risks limiting their validity, primarily the great uncertainty involved in predicting industry and macroeconomic conditions beyond a few years.

To learn more about terminal value, click here:

brainly.com/question/28304505

#SPJ4

For the given function,

Vertical asymptote = -5/4

Horizontal asymptote = -5/4

Domain =  (-∞,-5/4) ∪ (-5/4,∞)

Range =  (-∞,-5/4) ∪ (-5/4,∞)

What is a function?

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

The given function is

[tex]f(x) = \frac{-5x+2}{4x+5}[/tex]

The given function has a vertical asymptote at x = -5/4. This is because the function tends to ∞ as x tends to -5/4.

The horizontal asymptote of the function is when x tends to ∞ .

[tex]\lim_{x \to \infty} \frac{-5x+2}{4x+5} = \frac{-5+2/x}{4+5/x} = \frac{-5}{4}[/tex]

The horizontal asymptote of function is at y = -5/4.

Since at x = -5/4, the function becomes undefined.

The domain is all real numbers except x = -5/4

Domain =  (-∞,-5/4) ∪ (-5/4,∞)

Since the function is not defined at y = -5/4 as well, the range is also

(-∞,-5/4) ∪ (-5/4,∞) .

Therefore for the given function,

Vertical asymptote = -5/4

Horizontal asymptote = -5/4

Domain =  (-∞,-5/4) ∪ (-5/4,∞)

Range =  (-∞,-5/4) ∪ (-5/4,∞)

To learn more about functions, follow the link.

https://brainly.com/question/11624077

#SPJ1

76 degrees Fahrenheit was found to be equal to approximately 24.4 degrees Celsius using the formula of conversion.

To convert Fahrenheit to Celsius, you can use the following formula:

Celsius = (Fahrenheit - 32) x 5/9

Plugging in 76 degrees Fahrenheit, we get:

Celsius = (76 - 32) x 5/9

Celsius = 44 x 5/9

Celsius = 220/9

Celsius ≈ 24.4

Therefore, 76 degrees Fahrenheit is approximately 24.4 degrees Celsius.

On the Fahrenheit scale, water freezes at 32 degrees Fahrenheit (°F) and boils at 212 °F, at standard atmospheric pressure.

On the Celsius scale, the freezing point of water is defined as 0 degrees Celsius (°C), and the boiling point of water is defined as 100 °C, at standard atmospheric pressure.

Learn more about Fahrenheit scale here brainly.com/question/31139

#SPJ4

Answer:

Step-by-step explanation:

The expression whose value is a rational number will be √(4)² and √225+ √169. Then the correct options are A and C.

If the value of a numerical expression is terminating then they are the rational number then they are called a rational number and if the value of a numerical expression is non-terminating then they are called an irrational number.

Let's check all the options, then we have

A. √(4)² = 4, is a rational number.

B. √49 + √7 = 7 + √7, is an irrational number.

C. √225+ √169 = 25 + 13, is a rational number.

D. √2 x √121 = 11√2, is an irrational number.

E. √11 x 16 = 4√11, is an irrational number.

The expression whose value is a rational number will be √(4)² and √225+ √169. Then the correct options are A and C.

More about the rational number link is given below.

https://brainly.com/question/9466779

#SPJ1

Answer:

Step-by-step explanation:

=  5 /100  * 78 =  39 /10  = 3.9

$3.90

In this equation, the value of x is fixed at 2, which means that every point on the graph will have the same x-coordinate value of 2. This creates a vertical line that passes through the point (2, y), where y can be any real number.

Therefore, the proper equation for the graph presented is:

[tex]x=2[/tex]

There will be 360 different ways without using the same airline or shipping line.

A combination in mathematics is a selection of items from a set with distinct members, where the order of selection is irrelevant.

Let's first consider the number of ways the man can choose his outbound journey. He has 6 airlines to choose from, and once he has made his choice of airline, he has 4 shipping lines to choose from.

Therefore, there are 6 × 4 = 24 ways he can choose his outbound journey.

For his return journey, he cannot use the same airline or shipping line that he used for his outbound journey.

This means he now has 5 airlines and 3 shipping lines to choose from. Therefore, there are 5 × 3 = 15 ways he can choose his return journey.

The total number of ways he can make his journey is:

24 × 15 = 360

Therefore, he can make his journey in 360 different ways without using the same airline or shipping line.

To know more about combinations follow

https://brainly.com/question/11732255

#SPJ9

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

The required formula is :

[tex] \qquad \dashrightarrow \sf \: A = P \times \dfrac{{\bigg(1 + \dfrac{APR}{n} \bigg) }^{ny} - 1}{\dfrac{APR}{n}}[/tex]

Now, plug in the values ~

[tex] \qquad \dashrightarrow \sf \: A = 250 \times \dfrac{{\bigg(1 + \dfrac{0.04}{12} \bigg) }^{(12 \times 10)} - 1}{\dfrac{0.04}{12}}[/tex]

[tex] \qquad \dashrightarrow \sf \: A = 250 \times \dfrac{{\bigg(1 + 0.0033 \bigg) }^{(12 0)} - 1}{0.0033}[/tex]

[tex] \qquad \dashrightarrow \sf \: A = 250 \times \dfrac{{\bigg(1.0033 \bigg) }^{(12 0)} - 1}{0.0033}[/tex]

[tex] \qquad \dashrightarrow \sf \: A = 250 \times \dfrac{1.4908- 1}{0.0033}[/tex]

[tex] \qquad \dashrightarrow \sf \: A = 250 \times \dfrac{0.4908}{0.0033}[/tex]

[tex] \qquad \dashrightarrow \sf \: A = 250 \times 147.249[/tex]

[tex] \qquad \dashrightarrow \sf \: A = 250 \times 147.2498[/tex]

[tex] \qquad \dashrightarrow \sf \: A = 250 \times 147.2498[/tex]

[tex] \qquad \dashrightarrow \sf \: A =\$ 36812.45[/tex]

That's the required value ~

Answer:-117

Step-by-step explanation:

-13x-143+12x=-26

-x=-26+143=117

x=-117

The zeros of the function f(x) = x² - 4x - 5 are given as follows:

x = -1 and x = 5.

The quadratic function for this problem is defined as follows:

f(x) = x² - 4x - 5

The coefficients are given as follows:

a = 1, b = -4, c = -5.

Then the discriminant is given as follows:

D = b² - 4ac

D = (-4)² - 4(1)(-5)

D = 36

Hence the zeros are given as follows:

More can be learned about quadratic functions at https://brainly.com/question/1214333

#SPJ1

Answer: x=-4, y=4

Step-by-step explanation:

We can use elimination method to solve this problem.

Let's eliminate y.

In equation 2, use the coefficient of y (i.e 5) to multiply equation 1. DO the same for other equation. Thus,

5(10x+7y=-12)

7(9x+5y=-16)

=> 50x+35y=-60

     63x+35y= -112

clearly, y can be eliminated by subtraction.

Therefore,

-13x = 52  [-63+50  and 112-60)]

x = -4.

When x = -4,

9x+5y =-16

9(-4) +5y =-16

5y = 36-16

y=4.

The required equivalent expression is 3 · z³ to the given expression 3/4 x ( z^3 x 4). which is the correct answer .

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

her, we have,

We have been given expression as:

3/4 x ( z^3 x 4)

To determine the equivalent expression to the given expression

3/4 x ( z^3 x 4)

⇒ 3* z^3

Here the variable z has an exponent is 3 which is positive,

Rearrange the terms of variables z  in the above expression

⇒3 · z³

Therefore, the required equivalent expression is 3 · z³ to the given expression 3/4 x ( z^3 x 4).

Learn more about the algebraic expression here :

brainly.com/question/21751419

#SPJ9

Anwser : 23.8

Step 1: Subtract 5% from 25.

25 - (5% of 25) = 25 - (0.05 x 25)

Step 2: Simplify the equation.

25 - (0.05 x 25) = 25 - 1.25

Step 3: Subtract 1.25 from 25.

25 - 1.25 = 23.75

Answer to question 1 is   [tex]\text{y} \le -\frac{2}{5}\text{x}+100[/tex]

=========================================================

Explanation:

The first task is to find the equation of the line through the given points in the table.

Pick any two points you want. I'll pick (0,100) and (50,80)

Determine the slope:

[tex](x_1,y_1) = (0,100) \text{ and } (x_2,y_2) = (50,80)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_{2} - \text{y}_{1}}{\text{x}_{2} - \text{x}_{1}}\\\\m = \frac{80 - 100}{50 - 0}\\\\m = \frac{-20}{50}\\\\m = -\frac{2}{5}\\\\[/tex]

The slope is -2/5.

The y intercept is b = 100 because of the point (0,100)

We go from [tex]\text{y} = m\text{x}+b[/tex] to [tex]\text{y} = -\frac{2}{5}\text{x}+100[/tex]

Each point from the table is found on this line. For instance, let's check the point (140,44)

[tex]\text{y} = -\frac{2}{5}\text{x}+100\\\\44 = -\frac{2}{5}*140+100\\\\44 = -56+100\\\\44 = 44\\\\[/tex]

This confirms (140,44)

I'll let you check the other points.

------------------

Any point on the line mentioned represents a scenario where César spends all of the $50.

If he goes above the line, then he'll spend more than $50. If he goes below, he spends less than $50.

This means we want to shade the region below the boundary line [tex]\text{y} = -\frac{2}{5}\text{x}+100[/tex]

We'll replace the equal sign with a "less than or equal" sign

We arrive at [tex]\text{y} \le -\frac{2}{5}\text{x}+100[/tex] as the final answer to question 1.

Answer: Answer to question 1 is   =========================================================Explanation:The first task is to find the equation of the line through the given points in the table. Pick any two points you want. I'll pick (0,100) and (50,80) Determine the slope:The slope is -2/5.The y intercept is b = 100 because of the point (0,100)We go from  to Each point from the table is found on this line. For instance, let's check the point (140,44)This confirms (140,44)I'll let you check the other points.------------------Any point on the line mentioned represents a scenario where César spends all of the $50.If he goes above the line, then he'll spend more than $50. If he goes below, he spends less than $50.This means we want to shade the region below the boundary line We'll replace the equal sign with a "less than or equal" signWe arrive at  as the final answer to question 1.

Step-by-step explanation:

Using the fact that the two triangles must be similar, we will see that d = 7.5 ft

To find the distance d we will use the fact that the two triangles must be similar triangles.

That means that the quotients between the legs must be equal.

For the triangle on the left side, the quotient is:

50ft/30ft

For the triangle on the right side, the quotient is:

d/height of the student.

We know that the height of the student is 4.5ft, so that quotient is:

d/4.5ft

Now we can write the equation:

d/4.5ft = 50ft/30ft

Solving this for d, we will get:

d = 4.5ft*(50ft/30ft) = 7.5 ft

Learn more about similar triangles at:

https://brainly.com/question/14285697

#SPJ1

Answer:

a) [tex]W(x) = 0.50 (3^x)[/tex]

W = tickets worth in $
x  = number of balloons popped

b) For 8 balloons popped, number of tickets = 6,561

Tickets worth = [tex]\$ 3,280.50[/tex]

Step-by-step explanation:

The relation between number of balloons popped(x) and the number of tickets is  
[tex]f(x) =3 ^ x\\\\f(1) = 3^1 = 3\\\\f(2) = 3^2 = 9\\\\f(3) = 3^3 = 27\\\\f(4) = 3^4 = 81[/tex]

each ticket is worth 50 cents

So for x  tickets

[tex]W(x) = 0.50 (3^x)[/tex]

Number of tickets for 8 balloons popped
f(x) = 3^8

= [tex]f(x) = 3^8 = 6,561[/tex]

Ticket worth = [tex]0.5 \times 6,561 = \$ 3,280.50[/tex]

The expressions 1/3(36m+12) and 12m+4  are equivalent

Equivalent expressions are defined as algebraic expressions that have the same solution but differ in the mode of the arrangement of values.

These expressions are known to have variables, constants, terms, coefficients, and factors.

They are also made up of mathematical operations.

We have the expression;

1/3(36m+12)

Now, expand the bracket

36m/3 + 12/3

Divide the values

12m + 4

Hence, the expression is 12m + 4

Learn about algebraic expressions at: https://brainly.com/question/4344214

#SPJ1

The sum of the distinct prime factors is (b) 14

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

distinct prime factors of the number 560

The distinct prime factors of the number 560 are

Factors = 2, 5, 7.

When these numbers are added, we have

Sum = 2 + 5 + 7

Evaluate

Sum = 14

Hence , the sum is (b) 14

Read more about GCF at

https://brainly.com/question/12232865

#SPJ1

By the help of congruent , the measure of angle f g h is 64 degrees and the measure of angle e g d is (4 x + 8) degrees and the value of x is 14

Things that have precisely the same size and shape are said to be congruent. The shapes and sizes need to hold true regardless of how we flip, spin, or rotate the forms. Two triangles that are identical in size and shape are said to be congruent triangles. Even if we flip, turn, or rotate one of two congruent triangles, the other two remain congruent.Two triangles must have the same angles and, as a result, must be congruent if their sides are the same.The equal sides and angles may not be in the same location if there is a turn or flip, but they are still there.

The are congruent So,

4x+8=64

Solve for x

X=14

Learn more about congruent

brainly.com/question/12413243

#SPJ4

The numeric values for each of the expressions are given as follows:

1. 9.8t² + 20t + 8:

2. -3(2.1x - 7.9):

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

Then the numeric values are given as follows:

1. 9.8t² + 20t + 8:

2. -3(2.1x - 7.9):

Learn more about the numeric values of a function at brainly.com/question/28367050

#SPJ1

The value of the x in the given triangle is 7.5 units.

Proportion definition, comparative relation between things or magnitudes as to size, quantity, number.

Given is a triangle having sides, 12, 4 and 10 there is a missing side x we need to find is value,

Using the concept of parallel lines crest a proportion,

x / 10 = 12 / 16

x = 120 / 16

x = 7.5

Hence, the  value of the x in the given triangle is 7.5 units.

Learn more about proportion, click;

https://brainly.com/question/30657439

#SPJ1

Answer:

x = 3

Step-by-step explanation:

5x + 1 = 2x + 10

1.) Subtract 2x from both sides to get 2x on the other side

5x - 2x + 1 = 10

2.) Subtract 1 from both sides to get 1 to the other side

5x - 2x = 10 - 1

3.) Combine like terms

3x = 9

4.) Divide 3 on each side to get x by itself

x = 3

The person with the largest container is Julie and the person with the smallest container is Jeff.

The volume of each container has to be determined.

Volume of a cylinder = πr²h

Where:

Volume of Ms. Liu's container:

3.14 x 3² x 12 = 339.12 in³

Volume of Ms. Julie's container:

Volume = 3.14 x 3² x 24 = 678.24 in³

Volume of Jeff's container:

Volume = 3.14 x 1² x 24 = 75.36 in³

To learn more about to determine the volume of a cylinder, check: https://brainly.com/question/9624219

#SPJ1

The total distance covered by the Ferris wheel after 6 rotations is 2616π feet

An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.

The Ferris wheel has a radius of 218 feet. The total distance covered if the Ferris wheel makes one rotation is the perimeter of the wheel.

Perimeter = 2π * radius = 2π * 218 feet = 436π

For 6 rotations:

Total distance covered = 6 * 436π = 2616π

The total distance is 2616π feet

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1