In circle F, m/GFH = 140° and the area of the shaded sector = 14π. Find the length of FG.

The equation y = 3x - 1 and x² + y² = 73 then x = -1, y = -2.

Simultaneous linear equations are a pair of linear equations in two or three variables that are solved simultaneously to arrive at a single answer.

Simultaneous equations are two or more algebraic equations that share the same unknown variables and have the same solution for each of them. The simultaneous equations must therefore have a single solution, according to this.

Add together the equations if the signs vary. Subtract the indications from one another if they match. Different Add, Same Subtract, or DASS, is a simple way to remember this.

Substitute y = 3x + 1 in [tex]$x^2+y^2=5$[/tex]

[tex]$$x^2+(3 x+1)^2=5 \quad \Rightarrow \quad 10 x^2+6 x-4=0$$[/tex]

Hence

[tex]$$\begin{aligned}& 5 x^2+3 x-2=0 \Rightarrow 5 x^2+5 x-2 x-2=0 \quad \\\& 5 x(x+1)-2(x+1)=0 \quad \Rightarrow \quad(5 x-2)(x+1)=0\end{aligned}$$[/tex]

Hence, either [tex]$x=\frac{2}{5}, y=3 \times \frac{2}{5}+1=\frac{11}{5}$[/tex]

or [tex]$x=-1, y=3 \times(-1)+1=-2$[/tex].

The complete question is:

How do you solve the simultaneous equations [tex]$x^2+y^2=5$[/tex] and y=3x+1?

To learn more Simultaneous equations refer to:

https://brainly.com/question/16763389

#SPJ1

Answer:

-4

Step-by-step explanation:

a1 is 2

a2 = a1^2-5 = 4-5 = -1

a3 is a2^2-5 = 1-5 = -4

How to Name a Graph: Tips for Writing Great Chart Captions

Now, According to the question:

The title should concisely tell the reader what is in the graph. Avoid the obvious use of “vs.” or “versus” or the word “plotted” in the title. Graphs that will appear as a figure in a publication or in a formal laboratory report will not have a title (the information is given in the figure caption).

Learn more about Graph at:

https://brainly.com/question/29670230

#SPJ4

Logarithmic functions are important largely because of their relationship to exponential functions.

What is logarithm ?

In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x. For example, since 1000 = 10³, the logarithm base 10 of 1000 is 3, or log₁₀ = 3.

The first section explains the meaning of the logarithmic function f (x) = c·loga(x - h) + k. It describes how to evaluate logarithms and how to graph logarithmic functions. This section also addresses the domain and range of a logarithmic function, which are inverses of those of its corresponding exponential function.

The next section presents two special logarithmic functions--the common logarithmic function and the natural logarithmic function. The common logarithm is log10x, and it corresponds to the "log" button on most calculators. The natural logarithm is logex, and it corresponds to the "ln" button on most calculators. The natural log has a particular use in economics--it is used to perform calculations involving compound interest.

Logarithmic functions are important largely because of their relationship to exponential functions.

To learn more about logarithm visit : brainly.com/question/30085872

#SPJ4

Answer:

Solution

slope = 2

Step-by-step explanation:

calculate the slope m using the slope formula

m = \frac{rise}{run}

run

rise

= \frac{y_{2}-y_{1} }{x_{2}-x_{1} }

x

2

−x

1

y

2

−y

1

with (x₁, y₁ ) = (- 1, - 5) and (x₂, y₂ ) = (2, 1) ← 2 points on the line

m = \frac{1-(-5)}{2-(-1)}

2−(−1)

1−(−5)

= \frac{1+5}{2+1}

2+1

1+5

= \frac{6}{3}

3

6

= 2

A possible second point with a y-coordinate of 8 is equal to 5.

In Mathematics, the slope of a straight line can be calculated by using this this mathematical expression;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

From the information provided above, we have the following slope and data points on the line:

Points on x-axis = (1, 2).

Points on y-axis = (_, 8).

Slope, m = 3/2

Substituting the given points into the slope formula, we have the following;

Slope, m = (y₂ - y₁)/(x₂ - x₁)

3/2 = (8 - 2)/(x₂ - 1)

3/2 = 6/(x₂ - 1)

Cross-multiplying, we have:

3(x₂ - 1) = 12

x₂ - 1 = 12/3

x₂ - 1 = 4

x₂ = 4 + 1

x₂ = 5

In conclusion, we can logically deduce that the second point (x₂) is 5.

Read more on slope here: brainly.com/question/3493733

#SPJ1

The amount that the store donate will be $50

It should be noted that a word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

In this case, for every camera sold in February the store donated $2 to a charity. If 25 cameras are sold, the amount that the store donate will be:

= 25 × $2

= $50

Learn more about word problem on:

brainly.com/question/21405634

#SPJ1

Complete question

For every camera sold in February the store donated $2 to a charity. If 25 cameras are sold, how much did the store donate ?

Answer:

B) USA

Step-by-step explanation:

USA is in North America

Try graphing the function to determine the range if you are unable to solve for x. Vertex of x² - 3 / 2 :  Minimum (0,-3/2) .

f(x)=x^2 -3/ 2

When you solve the equation for x, you get something of the form x=g. Write down y=f(x) after that.

The range of f(x) is determined by the domain of g(y), which you should find.

Try graphing the function to determine the range if you are unable to solve for x.

Domain of x² - 3 /2:

Solution : -∝ < x < ∝

Interval Notation ; ( - ∝ ,∝)

Range of x² - 3 / 2 :

Solution :f(x) ≥ - 3 / 2

Interval Notation : -3/2 ,∝

Axis interception points of x² - 3 /2 :

X intercepts : ( √3,0) , ( - √3,0)

Y intercepts : (0,-3/2)

Vertex of x² - 3 / 2 :

Minimum (0,-3/2) .

To Learn more About  range refer To:

https://brainly.com/question/2264373

#SPJ1

We can write the measurements as -

Given is a right angled triangle.

We can write -

{ 1 } -

sin (A) = a/c

a = c sin(A)

a = 12 sin(40°)

a = 12 x 0.65

a = 7.8

{ 2 } -

cos (A) = b/c

b = c cos(A)

b = c cos(40°)

b = 12 x 0.77

b = 9.24

{ 3 } -

tan (B) = b/a

tan (B) = 9.24/7.8

tan (B) = 1.19

(B) = 50°

Therefore, we can write the measurements as -

To solve more questions on Trigonometric equations, visit the link below-

brainly.com/question/1041084

#SPJ1

Answer: The answer is 4 units(AD=4)

Step-by-step explanation:

basically we are given two similar shapes. We know that OM = 2  and OK = 1, so we already know the scale factor: 2. Therefore, we multiply BC by two to get 4 which is AD.

Answer:

your answer is 4

Step-by-step explanation:

yeah whatever it said above.

Transformation of the parent function it represents, linear translation down 3 units.

By modifying the value of x (for example, y(x) = x + 2) or by multiplying x by a constant (for example, y(x) = 3x), you can examine the graphs of linear functions. Do not forget that y(x) = x is the linear parent function. Its most fundamental and straightforward form is this.

The graph of y = f (x - h) is translated h units to the RIGHT of the graph of the parent function if h > 0, and it is translated h units to the LEFT if h 0.

as in f(x) = ( x – 3)

The graph of y=f(x-h) is a translation of |h| units to the LEFT of the graph of the parent function if h 0; otherwise, it is a straight line.

Example: f(x) = (x + 4).

To learn more about Transformation refer to:

https://brainly.com/question/4289712

#SPJ1

Answer:

I believe the answer to be increasing by increments of times 3 x3

A linear equation for the total monthly cost of long-distance calls, C, for t minutes is C = 50 + 0.1t.

A linear equation is an algebraic or mathematical equation.

Linear equations are written in the form of  y=mx+b.

In this linear equation, y equals the value of the equation, m is the slope (unit rate), x represents the variable (a first-order term), and b is the y-intercept (fixed rate), which is always a constant.

The fixed cost monthly for long-distance phone calls = $50

The charge per minute = $0.10

Let the minutes of long-distance calls = t

Let the total monthly cost = C

C = 50 + 0.1t

Learn more about linear equations at https://brainly.com/question/2030026

#SPJ1

Answer:

15/16

Step-by-step explanation:

3/8 = 6/16

6/16+3/16=9/16

9/16+3/16=12/16

12/16+3/16=15/16

Answer: 450 inches

Step-by-step explanation:

The domain of the function f(x) = x² is all real numbers, including negative numbers, zero, and positive numbers.

The domain of a function is the set of all values for which the function is defined. For the function f(x) = x², the domain is all real numbers. This includes negative numbers, zero, and positive numbers. This means that the function is defined for any real number, no matter how large or small. In other words, the domain of f(x) = x² is the set of all real numbers, {x ∈ R}. This is because the square of any real number is still a real number, and so the function is defined for all real numbers. Thus, the domain of f(x) = x² is all real numbers.

Learn more about domain here

https://brainly.com/question/13113489

#SPJ4

The degree of financial leverage for Foggy Futures Weather Forecasters

is 1.06

Degree of Financial leverage (DFL) = (EBIT) / (EBT)

Earnings Before Interest and Taxes (EBIT) = $750,000

Amount to be given as loan on $1000000

$1,000,000 x 4.5% = $1,000,000 x 4.5/100

= $45000

To find EBT ( Earnings Before Tax),

EBT = EBIT - 45000

       = 750000 - 45000

EBT = 705000

∴ DFL =  (EBIT) / (EBT)

          = 750000/705000

 DFL = 1.06

The DFL is a percentage that accountants and financial professionals use to show changes in a company's net income due to changes in its profits before interest and taxes (EBIT).

Earnings before interest and taxes (EBIT) is a measurement of a company's profit in accounting and finance that takes into account all revenues and costs (both operating and non-operating), with the exception of interest costs and income tax costs.ve

Learn more about Degree of Financial Leverage :

https://brainly.com/question/23841033

#SPJ4

the scale factor will be √5.

What is dilation?

resizing an object is accomplished through a change called dilation. The objects can be enlarged or shrunk via dilation. A shape identical to the source image is created by this transformation. The size of the form does, however, differ. A dilatation ought to either extend or contract the original form. The scale factor is a phrase used to describe this transition.

The scale factor is defined as the difference in size between the new and old images. An established location in the plane is the center of dilatation. The dilation transformation is determined by the scale factor and the center of dilation.

The given figure ABCD dilated to A'B'C'D'

take DC =√ (9-13)² + (4-7)²

DC = √16+9= 5

D'C' = √(4-6)²+(3-4)²

= √5

Hence the scale factor will be √5.

Learn more about scale factor, by the following link

https://brainly.com/question/30215119

#SPJ1

When k = -1/2, the equation has real and equal roots of x = 2.

An equation is a mathematical statement that two expressions are equal. It consists of two expressions, one on each side of an equal sign. Equations are used to solve problems in mathematics, chemistry, physics, engineering, and other sciences. They can also be used to define relationships between different variables or constants. Equations are an important tool for understanding the world around us.
The value of k in the given equation is -1/2. This is because when k is equal to -1/2, the equation has real and equal roots of x = 2. This can be verified by substituting k = -1/2 and x = 2 into the given equation:

KX² + 5x + 4 = 0
(-1/2) (2²) + 5(2) + 4 = 0
(-1) + 10 + 4 = 0
9 = 0

Therefore, when k = -1/2, the equation has real and equal roots of x = 2.

To know more about Equation click-
https://brainly.com/question/2972832
#SPJ4

Answer:

A) angle

Step-by-step explanation:

This is a definition.

Solving a formula for a variable means rewriting the formula so that the variable is Isolated to one side.

Solving a formula for a particular variable entails placing that variable alone with a coefficient of 1 on one side of the equals sign. The other side of the equals sign represents all other variables and constants.

A formula is a mathematical representation of how two variables relate to one another. In the sciences, including physics, biology, and chemistry, formulas are also employed. They are employed in medicine to do computations for calculating body mass index or distributing medication. Calculations are done using formulas in spreadsheet systems.

To learn more about variable here:

https://brainly.com/question/29521826

#SPJ4

Answer:

30 m/s

i believe

Answer:30 m/s

Step-by-step explanation:It travels 150 m in 5 seconds. What is its average speed ? Thus, the average speed of the car is 30 m/s.

Answer:

759 [tex]\frac{1}{9}[/tex]

Step-by-step explanation:

Convert the mixed numbers into fraction ( to make it easier )

Equation:

[tex]\frac{29}{3}[/tex] x [tex]\frac{244}{3}[/tex]    <—- Remember these are mixed number ;)

Now we make it into this..

28 x 244

————-

 3 x 3

Multiply the top : 6832

Multiply the bottom : 9

Make to fraction——-/\

( [tex]\frac{6832}{9}[/tex] )

Simplify the answer to:

759 [tex]\frac{1}{9}[/tex]

This is an incorrect question.

The correct question should be as:

Simplify: [tex]9^{\frac{1}{3}} *81^{\frac{1}{3}}[/tex]

Step-by-step Solution:

[tex]9^{\frac{1}{3}} *81^{\frac{1}{3}}[/tex]

⇒[tex]9^{\frac{1}{3} }[/tex]  is the same as [tex]\sqrt[3]{9}[/tex]

⇒[tex]81^{\frac{1}{3} } \\[/tex]  is the same as [tex]\sqrt[3]{81}[/tex]

⇒[tex]\sqrt[3]{9*81}[/tex]

⇒[tex]\sqrt[3]{3*3*9*9}[/tex]

⇒[tex]\sqrt[3]{3*3*3*3*3*3}[/tex]

Pull out groups of 3 from underneath the radical:

⇒[tex]\sqrt[3]{9}[/tex] * [tex]\sqrt[3]{81}[/tex]

⇒[tex]\sqrt[3]{729}[/tex]

⇒ 9

Therefore, the correct solution to this question is: 9

To learn more about "simplification" here:

brainly.com/question/28595186

Answer:

factor out the GCF

Step-by-step explanation:

The volume of the right circular cylinder of height 6 inches and base radius 3 inches is about 169.6 cubic inches.

A right circular cylinder is a solid that has two parallel circular plane surfaces at the top and bottom part of the cylinder, and a curved closed surface perpendicular to and joining the top and bottom circular surfaces

The volume of a right circular cylinder can be found using the formula;

V = π·r²·h

Where;

r = The radius of the cylinder

h = The height of the cylinder

π = 3.14

The dimensions of the cylinder are 6 inches and 3 inches

Whereby the height of the cylinder, h = 6 inches, and the radius of the cylinder, r = 3 inches, we get;

Volume of the right circular cylinder, V = 3.14 × 3² × 6 ≈ 169.6

The volume of the right circular cylinder, V = 169.6 in³

Learn more on finding the volume of regular figures here: https://brainly.com/question/25238219

#SPJ1

The required values of slope and y-intercept are 10 and 15.

The formula for these lines is y = mx + b, where m denotes the slope and b the y-intercept. Our line has a slope of 3 and a y-intercept of -5, which we know from the question. By entering these numbers, we obtain the equation of our line as y = 3x - 5.

We have,

y = 10x + 15

On comparing with general equation of line.

Y = mx + c

m is slope of line, c is y-intercept.

Then,

m = 10

And

y-intercept = 15

Thus,the required values of slope and y-intercept are 10 and 15.

To know more about Equation of line visit:

brainly.com/question/21511618

#SPJ4

The set of polynomials is not closed under division.

A polynomial is a mathematical statement made up of exponents, constants, and variables that are mixed using addition, subtraction, multiplication, and division operations. Polynomial means "many terms" since it combines the words poly-, which means "many," and -nomial, which in this context means "term." A polynomial may have exponents (like the 2 in y2), constants (like x and y), variables (like the x and y exponents), and other terms, but only those that can be mixed using addition, subtraction, multiplication, and division are permitted. Constants, variables, and exponents are all permitted in polynomials, but variable division is never permitted.

In addition, they are now only limited to a finite number of terms, which can be one or more.

The dividend appears at the top of the division at first, similar to how long multiplication is written.

For such more questions on Polynomials:

brainly.com/question/11536910

#SPJ4

The equations for both Khalil's and Ronda's purchase is given below:

The price of one loaf of bread is $3.44

4 cans and 3 loaves=11.67

8 cans and 1 loaf= 12.89.

Set up the equation:

These are the equations for both Khalil's and Ronda's purchases.

If we solve for x in the equation, the answer would be $3.44

Read more about systems of equations here:

https://brainly.com/question/13729904

#SPJ1

A grocery store is offering a sale on bread and soup. Khalil buys four cans of soup and

three loaves of bread for $11.67. Ronda buys eight cans of soup and one loaf of bread for $12.89.

Homework. Help

a. Write equations for both Khalil's and Ronda's purchases.

b. Solve the system to find the price of one can of soup and the price of one loaf of bread