What are the 3 kinds of system of linear equation in two variables?

Answers

Answer 1

There are three types of systems of linear equations in two variables: Consistent System,Inconsistent System,Dependent System.

What is linear systems?

A linear system is a mathematical model of a system of linear equations, in which the variables and constants have a linear relationship. This type of system is widely used in engineering, physics, economics, and other areas of study. Linear systems are often used to find solutions to problems in areas such as optimization or forecasting. They are also used in many machine learning algorithms. Linear systems are characterized by their linearity and they are usually solved using linear algebra techniques.

1. Consistent System: A consistent system of linear equations in two variables has at least one solution. This means that there is at least one set of values for the two variables that will make all equations true.

2. Inconsistent System: An inconsistent system of linear equations in two variables has no solution. This means that there is no set of values for the two variables that will make all equations true.

3. Dependent System: A dependent system of linear equations in two variables has an infinite number of solutions. This means that there is more than one set of values for the two variables that will make all equations true.

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Related Questions

what is a segment whose endpoints are on the circle?

Answers

A segment whose endpoints are on a circle is called a chord of the circle.

A segment whose endpoints are on a circle is called a chord of the circle. A chord is a straight line that connects two points on the circumference of a circle. The two points on the circumference are called the endpoints of the chord. The distance between the two endpoints of the chord is called the length of the chord. The midpoint of the chord is the center of the circle.

The chord of a circle can be defined as the line segment joining any two points on the circumference of the circle. It should be noted that the diameter is the longest chord of a circle which passes through the center of the circle.

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A stock’s value closed at $24.80 on the 12th and the same stock closed at 21.35 on the 13th. What was the change as a percent?

Answers

A stock’s value closed at $24.80 on the 12th and the same stock closed at 21.35 on the 13th,  13.91% was the change as a percent.

What is percentage change?

Finding the difference between two values in a time series, dividing that difference by the initial value, and multiplying by 100 are used to get the percentage change between the two values. The value change of a stock or significant stock index over time is frequently tracked in finance using percentage change. It is also employed to evaluate the worth of various currencies.

The calculation for percentage change is 100 divided by (New Price - Old Price). If the stock price has increased, the percentage change will be positive; if the stock price has decreased, it will be negative.

Given that,

A stock’s value closed at $24.80 on the 12th

the same stock closed at 21.35 on the 13th

the change as a percent = [(24.80 - 21.35) / 24.80] × 100

the change as a percent = [3.45 / 24.80] × 100

the change as a percent = 0.13911 × 100

the change as a percent = 13.91%

Thus, net percentage change is 13.91%

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What Is 144 divided by 4608

Answers

144 divided by 4608 is 0.03125

Answer:

Step-by-step explanation:

144/4608=1/32 = 0.03125

Brainliest please thx

If the fdic charges bank e 2. 4 cents per 100 dollars insured, how much must bank e pay to insure $4. 8 million in deposits? a. $1,152 b. $115,200 c. $2,112 d. $211,200 please select the best answer from the choices provided a b c d.

Answers

Bank E must pay the FDIC a fee of $115,200 to insure $4.8 million in deposits, which is calculated by multiplying the rate of 2.4 cents per $100 with the total amount of deposits.

1. Take the total amount of deposits and divide by

100 (4.8 million / 100 = 48,000)

2. Multiply by the rate of 2.4 cents

(48,000 x 0.024 = 1,152)

3. Multiply the result by 100

(1,152 x 100 = 115,200)

4. The amount Bank E must pay to the FDIC is $115,200.

Bank E must pay the FDIC a fee to insure its $4.8 million in deposits. In order to calculate the fee, you must first divide the total amount of deposits by 100 to get the number of $100 increments. You then need to multiply this number by the rate of 2.4 cents, which will give you the total fee in cents. Finally, you need to multiply the total fee in cents by 100 to get the total fee in dollars. In this case, the amount Bank E must pay to the FDIC is $115,200.

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a radio station broadcasts a signal over an area with a 120-mile diameter. the population density of the area is 100 people per square mile. how many people are within receiving distance of the broadcast signal?

Answers

The radio station can reach around 1,030,400 people within its coverage area.

Using the equation, calculate the size of the circular circle that the radio station signal can cover.

A = πD²/4 is the area and D is the diameter. using the pi-number 3.14.

r = 120 / 2 = 60 miles

The density of the area:  100 people per sq. mile

A = r² π = 60² · 3.14 = 3600 · 3.14 = 11,304 sq. miles

11,304 · 100 = 1,030,400

or

A = (3.14)(120 mi) (120 mi)

² / 4 \s A = 11304 mi²

being aware that 100 individuals reside in each square mile.

total population receiving the signal =11304 mi² x (100 people / 1 mi²)

                                   = 1,130,400

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1.

Here are a few pairs of positive numbers whose sum is 50.

sec

a. Find the product of each pair of

numbers.

b. Find a pair of numbers that have

a sum of 50 and will produce the

largest possible product.

Answers

a. The product of the first pair of real number whose sum is 50 is 25 x 25 = 625. The product of the second pair is 24 x 26 = 624.

b. The pair of numbers that have a sum of 50 and will produce the largest possible product is 25 and 25, as their product is 625.

a. To find the product of each pair of numbers, multiply the two numbers together. For example, the product of the first pair of positive numbers whose sum is 50 is 25 x 25 = 625. The product of the second pair is

24 x 26 = 624.

b. To find a pair of numbers that have a sum of 50 and will produce the largest possible product, first consider the two numbers that can add up to 50. The two numbers must be equal, such as 25 and 25. Multiply these two numbers together to get the largest possible product, which is 625.

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(5x+2)(3x-1)-x(x+7)
simplify

Answers

Answer: 2 (7x squared -3x - 1)

Step-by-step explanation:

What is the length of ? round to the nearest tenth. 6. 8 cm 7. 5 cm 14. 5 cm 17. 7 cm.

Answers

The length of an object is the measurement of its longest side when measured from one end to the other.

6. 8 cm = 6.8 cm

7. 5 cm = 7.5 cm

14. 5 cm = 14.5 cm

17. 7 cm = 17.7 cm

The length of any object is the distance from one end to another. To calculate the length of an object, we must measure the distance between the two endpoints. To do this accurately, we need to use a ruler, tape measure, or other measuring device. To round the measurement to the nearest tenth, we need to look at the digit to the right of the decimal point. If the digit is 5 or higher, we round up, and if the digit is 4 or lower, we round down. For example, if the measurement was 6.8 cm, we would round it up to 6.9 cm. If the measurement was 7.5 cm, we would round it down to 7.4 cm. Similarly, 14.5 cm would round up to 14.6 cm and 17.7 cm would round down to 17.6 cm.

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For which function is it true that y -› -infinity as X -> infinity?

Answers

You're basically trying to get here is the limit as x approaches negative infinity, of (5ˣ -1)/(x¹⁰ -1).

What you're basically trying to get here is the limit as x approaches negative infinity, of (5ˣ -1)/(x¹⁰ -1)?

What you're basically trying to get here is the limit as x approaches negative infinity, of (5ˣ -1)/(x¹⁰ -1).

Let's look at the numerator and denominator of this function separately. First, in the numerator, as x goes toward -infinity, the value of 5ˣ gets closer and closer to 0 with ever increasing negative powers. You then subtract 1 from that, so the entire numerator will tend closer and closer to -1 with decreasing x.

Step2:

Then, in the denominator, recall that any number, negative or positive, to an even power will be positive. As x goes lower and lower, x¹⁰ will go higher and higher, to the point where subtracting 1 from it will have no effect. In other words, the denominator will tend closer and closer to infinity.

In the end, you basically have a real number being divided by ever larger and larger numbers, making it approach zero. So the final answer is, y will approach zero as x approaches -infinity.

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Help me with this question please!

Answers

The value of {f} and {g} is equivalent to 10.95 cm.

What is a square?

In Euclidean geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles. It can also be defined as a rectangle with two equal - length adjacent sides.

Given is a trapezium ABCE.

ABCD is a square. So, we can write -

f = g

Area of square = 120 cm²

We can write -

f x g = 120

f² = 120

f = g = 10.95 cm

Therefore, the value of {f} and {g} is equivalent to 10.95 cm.

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You’re working in the product development department of a large toy manufacturer. The two grids you’re working with will be laser cut and inserted into an interactive shapes game for toddlers. The dots on the grid are 1 inch apart.

Two grids. The first grid consists of the following shapes: A rectangle with a length of 1 and a height of 4. A square with a length of 3. A square with a length of 1. 2 triangles with a base of 1 and a height of 1. The second shape consists of the following shapes: A triangle with a base of 4 and a height of 3. A square with a length of 3.

Find the total area for the two shapes in order to determine how much raw material will be cut away from the surface. Type the correct answer in the box. _____ sq in

Answers

given: grid 1: rectangle, squares, triangles

grid 2: triangle, square

to find: area of shapes

final answer: 36 in sq

The quantity of space contained within a shape is known as area. A surface's or shape's area can be useful in everyday life. Multiply a rectangle's height by its width to determine its area. Because each side is the same length, all you need to do to find the area of a square is multiply the length of one of the sides by itself.

grid 1:

area of rectangle = length* height

= 1*4 = 4 in sq

area of square = side* side

= 3*3 = 9 in sq

area of square =  side* side

=1*1 = 1 in sq

area of 2 triangles =  2* 1/2(base* height)

= 2* 1/2(1* 1) = 1 in sq

total area in grid 1 = 15 in sq

grid 2:

area of square =  side* side

=3*3 = 9 in sq

area of triangle =  2* 1/2(base* height)

= 2* 1/2(4* 3) = 12 in sq

total area in grid 1 = 21 in sq

therefore, the total area is 21 + 15 = 36 in sq

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A television show will be canceled if the estimated number of viewers falls below 2.5 million by Week 10. Use the graph to write an exponential function to model the situation. If this pattern continues, will the show be canceled?

Answers

The show will not be canceled. The estimated number of viewers will remain above 2.5 million for all weeks, according to the graph.

What is exponential function?

A mathematical function with the formula f (x) = an x is an exponential function. where an is a constant known as the function's base and x is a variable. The transcendental number e, which equates to about, is the exponential-function basis that is most frequently encountered.

Here Let us take  x = Week and y = Viewers

Then According to the question estimated number of viewers falls below 2.5 million by Week

Exponential Function: y = 2.5 million x 0.75

Hence the show will not be canceled. The estimated number of viewers will remain above 2.5 million for all weeks, according to the graph.

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I need help on this question

Graph the image of the given triangle reflected across the x-axis.

Answers

The coordinates of the reflection of the given image are (6, -8) (-5, -4), and (4, 3) and the image is given below.

Reflection of geometric figure:

When a shape or figure is reflected over a line or plane, the transition is known as a reflection in geometry. It is also known as a flip.

Because a reflection is a hard transformation, the size and shape of the original figure remain unchanged, and the original and transformed figures are identical.

When a shape is reflected across the x-axis then the coordinates (x, y) become (x, -y).  

From the given figure,

Coordinates of the triangle are (6, 8) (-5, 4), and (4, -3)  

After reflection the resultant coordinates are

=>  (6, -8) (-5, -4) and (4, 3)

         

Now we can draw the reflection of the given image using coordinates (6, -8) (-5, -4) and (4, 3) as shown figure.    

Therefore,

The coordinates of the reflection of the given image are (6, -8) (-5, -4), and (4, 3) and the image is given below.              

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What is 300\%300%300, percent of 888?
Hint: We can think of 300\%300%300, percent as a common number.

Answers

On solving the provided question, we can say that the answer is that the percentage of 300\%300%300, percent of 888 is 888.

What is percentage?

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.

300\%300%300, percent of 888

300/300/100 X 100 X 888

= 888

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What is the equation of a line whose y-intercept and slope are 6 and 8 respectively?

Answers

The equation of a line whose y-intercept and slope are 6 and 8 respectively is y = 8x + 6.

In the given question, we have to find the equation of a line whose y-intercept and slope are 6 and 8 respectively.

A straight line's general equation is y = mx + c, where m denotes the line's slope and c its y-intercept. It is the geometry-related straight line equation that is employed the most frequently.

From the given question, the value of  m = 8 and c = 6.

Now putting the value of m and c in the general equation of line y = mx + c

y = 8x + 6

Hence, the equation of a line whose y-intercept and slope are 6 and 8 respectively is y = 8x + 6.

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Select the correct answer from each drop-down menu. Consider this expression.

-3x^2 - 24x - 36

What expression is equivalent to the given expression?
__ (x + __)(x + __)

Answers

The given expression is equivalent to (x + 2)(x + 6).

What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is a quadratic equation as -

- 3x² - 24x - 36

The given quadratic equation is -

- 3x² - 24x - 36

We can write the equation as-

- 3x² - 24x - 36 = 0

- 3(x² + 8x + 12) = 0

(x² + 8x + 12) = 0

x² + 6x + 2x + 12 = 0

x(x + 6) + 2(x + 6) = 0

(x + 2)(x + 6) = 0

Therefore, the given expression is equivalent to (x + 2)(x + 6).

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5. the sum of the digits of a two digit number is 10. if the number formed by interchanging the digits is subtracted from the original number, the result is 18. find the original number

Answers

If the number formed by interchanging the digits is subtracted from the original number and when the result is 18. The original number is 72.

Let's call the original two-digit number "n". The first digit of "n" can be represented as "a" and the second digit as "b". According to the problem, the sum of the digits of "n" is 10, which means "a + b = 10". Also, if the number formed by interchanging the digits is subtracted from the original number, the result is 18, which can be expressed as "10a + b - (10b + a) = 18".

To find the original number, we can use algebra. Let x be the ten's digit and y be the unit's digit. Then, x + y = 10 and 10x + y - (y + x) = 18, which simplifies to 9x = 28 and x = 3. From x + y = 10, we find y = 7. The original number is therefore 72.

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find the surface area of a sphere whose diameter is 70 cm take pi equals to 22/7
[tex]find \: the \: surface \: area \: of \: a \: sphere \: whose \: diameter \: is \: 70cm{take \: \pi = 22 \div 7}[/tex]

Answers

Answer:

Step-by-step explanation:

The surface area of a sphere is given by the following formula:

V=4πr²

Except, pi in this case is approximately 22/7.

So, we will use a modified version where we substitute 22/7 in for π:

V=4(22/7)r²

Now, let’s plug in the values. The diameter is 70, and since the diameter is twice the radius, we can divide the diameter in half to find the radius.

70/2=35

So, r=35

V=4(22/7)(35)²

V=15,400cm

So, the surface area of the sphere is 15,400cm.

How many linear equations in two variables will have solutions x1 and Y 3?

Answers

There are infinite linear equations that will have solutions x = 1 and y =3.

A linear equation is an equation that contains a variable raised to the first power. This equation is said to be linear because this mathematical relationship can be drawn as a straight line in the Cartesian coordinate system.

Based on the number of variables, this equation can be divided into three types:

One-variable linear equation which comes in the form ax + b = 0, where x is the variable. This equation has only one solution, for example, 3x - 1 = 0.Two-variable linear equation describes the relationship between two variables and both are raised to the power of 1. It comes in the form ax + by + c = 0, where x and y is the variable. For example, 3x + 5y + 21 = 0.Three-variable linear equation describes the relationship between three variables and these variables are raised to the power of 1. It comes in the form ax + by + cz + d = 0, where x, y and z is the variable. For example, 3x + 5y + 3z + 21 = 0.

From the question, we obtain that the solutions are x = 1 and y = 3. Then we draw the solution on a graph.

By observing the graph, we can see that there are so many (infinite) straight lines (yellow lines) that can pass through the point (2,3).

Thus we can conclude that there are infinite linear equations that will have solutions x = 1 and y =3.

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A 25,000-mile steel band is placed around the earth, snugly fit at the equator. The band is cut, and 36 inches of string is spliced into the steel band. This new, larger circular band is placed around the earth, so its center coincides with the center of the earth, and a gap is created. How wide is this gap?

When you have finished, post your work showing the formula used for calculating the gap (g), show all calculations solving for g (gap), and a statement interpreting the results of your work.

Answers

Answer: 2.865Feet.

Step-by-step explanation: The problem is really asking:

What is the difference in the radii of two circles, one having a circumference (C1) of 25,000 miles and the other having a circumference (C2) of 25,000 miles + 18 feet.

The circumference (C) of a circle, in terms of the radius (r), is given by:

C=2×π29r Rewrite this in terms of r.

r=C/2×π

For the first circumference (C1=25,000 miles), we can write:

r1+=+C1%2F2%28pi%29

For the expanded circumference (C2=25,000 mi + 18 ft) we can write:

r2+=+C2%2F2%28pi%29

To find the difference (d), we'll subtract r1 from r2.

d+=+C2%2F2%28pi%29+-+C1%2F2%28pi%29

d+=+%28C2-C1%29%2F2%28pi%29

But C2-C1+=+18feet

So:

d+=+18%2F2%28pi%29

d+=+9%2F%28pi%29

d+=+2.865Feet.

The roots of the equation x^2+bx+c=0 are -4 and -2.

Find b

Answers

I believe b is -4.5 (sorry if it’s wrong)

Answer:

The value of b is 6.

We know for a quadratic equation ax^2+bx+c=0

the sum of roots = -b/a

and product of roots = c/a

the two roots are -4 and -2.

and a =1

so -b/a = (-4)+(-2)

=> -b = -6

=> b = 6.

therefore  b=6.

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esmeralda is making a quilt and she has determined she needs 539 square inches of blue fabric and 1426 square inches of gray. how many square yards of each material will she need? round your answers up to the nearest quarter yard.

Answers

Esmeralda  will need 0.415 square yards of blue fabric and 1.1 square yards of grey fabric

According to concepts of unit conversion

1 square inch is equivalent to 0.000772 square yard

Hence, 539 square inches of blue fabric = 0.000772 x 539

=0.415 square yards of blue fabric

Again, 1sq inch =  0.000772 sq. yards

Hence 1426 square inches of grey fabric= 0.000772  x 1426

= 1.1 square yards of grey fabric.

Therefore, Esmeralda  will need 0.415 square yards of blue fabric and 1.1 square yards of grey fabric

The yard is a unit of measure widely used in the British imperial and USA customary system. It is standardly recognized since 1959. Square yards are typically used when referring to the calculation of area. 1 yard is internationally agreed to be equivalent to 36 inches.

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The point (3,-1) is on a graph of
y = x² + kx -4. What is the value
of k?
A -1
B -4/3
C -2
D-6

Answers

Your answer is going to be C because the value of -2 is not greater than c

Answer:

Step-by-step explanation: ( 3, 1)

x = 3, y = 1

From the formula, y = x² + kx - 4

1 = 3² + 3k - 4

1 = 9 + 3k - 4

1 = 5 + 3k

-3k = 5 + 1

-3k = 6

Divide both sides by -3

-3k/-3 =  6/ -3

k = -2

11. Find the value of x. (4 points)
Which Theorem will you use to solve this problem:
A. Triangle Midsegment Theorem
B. Perpendicular Bisector Theorem
C. Angle Bisector Theorem
D. Concurrency of Medians
work:


12. In ARST, U is the centroid. If SQ = 6, find SU and UQ. (4 Points)
Which Theorem will you use to solve this problem
A Triangle Midsegment Theorem
B. Perpendicular Bisector Theorem
C. Angle Bisector Theorem
D. Concurrency of Modians
Work (1 point):
write the equation to solve (1 point):

GIVING 75 POINTS and Brainiest!!!

Answers

SU + UQ = 6

Solve for SU and UQ (2 points):

SU = 3 and UQ = 3

Triangle Midsegment Theorem

The Triangle Midsegment Theorem states that in a triangle, the midsegment (the segment connecting the midpoints of two sides of a triangle) is parallel to the third side of the triangle and is half as long as the third side.

Therefore, we can use the Triangle

here,

SQ = 6,

then

SU = 3 and UQ = 3.

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Rose bought a car for $19,400, but she received $1250 cash back. She will
make monthly payments at a 3.6% APR, compounded monthly, for 48 months. Use
this information to answer the following three questions.
1.
What will Rose's monthly
payment be?
2.
What would Rose's monthly
payment have been if she hadn't
received the cash back?
3.
Approximately how much money did Rose save by receiving the cash back?

Answers

Rose's monthly payment will be $448.14.2. her monthly payment would have been $455.17.3. Rose saved approximately $7,023.27 by receiving the cash back.

What is payment?

Payment is the transfer of money from one party to another in exchange for goods, services, or to fulfill a legal obligation. It is an important part of commercial and financial transactions and can take many forms, such as cash, check, credit card, or bank transfer. Payment is often facilitated through a payment processor, such as a bank or third-party payment service provider. Payment processing is the process of collecting and verifying the necessary information to complete a payment transaction. It includes verifying a customer’s identity, confirming the amount of the payment, and transferring the funds. Payment processing is essential for businesses to accept payments from customers and securely pay out to their vendors or suppliers.

Answer 1: Rose's monthly payment with the cash back will be $457.15.

Answer 2: If Rose had not received the cash back, her monthly payment would have been $479.63.

Answer 3: By receiving the cash back, Rose saved approximately $22.48 per month, or a total of $1,084.24 over the course of 48 months.

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pretty please help me

Answers

The required inequality is 4f<36 and at most 9 fishes can be bought.

What is an inequality?

An inequality is an inequation separated by <,>≥,≤. In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

Given here: The price of each fish is $4 and total budget is $36

Let ffishes can be brought then we have

4f<36

f<9

Hence, The required inequality is 4f<36 and at most 9 fishes can be bought.

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please help


Angle measurements 27 and 63 are supplementary.
true or false

Answers

Answer:

its false, its a complementary angle

-59=-3b-32 love for b

Answers

Answer:

b = 9

Step-by-step explanation:

-3b - 32 = -59

add 59 on both sides.

- 3b - 32 + 59 = 59 - 59

-3b + 27 = 0

subtract 27 on both sides.

-3b = -27

divide both sides by -3.

-3b/-3 = -27/-3

b = 9

Pls mark as brainliest if possible. Cheers

Answer:

b=9

Step-by-step explanation: If Its Correct Answer I Try My Best To Help Yall

5) John wrote a DIY book that sold for $19.95. He receives 13% royalty on the total sales on the book. Last quarter, 18,000 copies of John's book was sold How much did John receive in royalty payments for the quarter? Show all working.b

Answers

Answer: To calculate how much John received in royalty payments for the quarter, we need to know the total sales of his book and the royalty rate. In this case, 18,000 copies of John's book were sold and the royalty rate is 13%.

We can calculate the total sales by multiplying the number of books sold by the price of each book:

Total Sales = 18,000 x $19.95

Total Sales = $359,100

To calculate the royalty payment, we need to multiply the total sales by the royalty rate:

Royalty Payment = Total Sales x (Royalty Rate / 100)

Royalty Payment = $359,100 x (13 / 100)

Royalty Payment = $46,547

So, John received $46,547 in royalty payments for the quarter.

Step-by-step explanation:

How do you find the ratio of a directed line segment?

Answers

The ratio (m :n) of the directed line segment is given by :

Divides internally is :( x, y ) = [(mx₂ + nx₁) / ( m +n) , (my₂ + ny₁) / ( m +n) ]

Divides externally is : ( x, y ) = [(mx₂ - nx₁) / ( m - n) , (my₂ - ny₁) / ( m - n) ]

As given in the question,

Let the given line segment be PQ with coordinates:

P(x₁ , y₁) and Q(x₂ , y₂)

Let the ratio in which line segment is divided given by m : n

If the point C(x, y) is in between P and Q then

Ratio in which line segment divided is internally

=  [(mx₂ + nx₁) / ( m +n) , (my₂ + ny₁) / ( m +n) ]

If the point C (x, y) is in outside P and Q then

Ratio in which line segment divided is externally

=  [(mx₂ - nx₁) / ( m - n) , (my₂ - ny₁) / ( m - n) ]

Therefore, the ratio of the given directed line segment is calculated using formula :

Divides internally is :( x, y ) = [(mx₂ + nx₁) / ( m +n) , (my₂ + ny₁) / ( m +n) ]

Divides externally is : ( x, y ) = [(mx₂ - nx₁) / ( m - n) , (my₂ - ny₁) / ( m - n) ]

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