Find the equation of the circle shown in the figure.

Answer:

x y

1 2

2 2

3 2

4 2

5 2

To write the equation y = -2x + 6 as a table, we need to substitute different values of x into the equation and solve for y. Here is an example of a table with some values of x and the corresponding values of y:

x y

1 4

2 2

3 0

4 -2

5 -4

Step-by-step explanation:

Answer: B. f(x) = (x - 2)^2 - 3

Step-by-step explanation:

After the discount and the tax is applied, Megan will pay 29.10 dollars for the sweater.

We know that originally, the sweater costs $34.00, and there is a 20% decrease on that cost and a tax of 7%.

The decrease of 20% is written as a factor (1 - 20%/100%) = (1 - 0.2)

And an increase of 7% is written as a factor (1 + 7%/100%) = (1 + 0.07)

Then the amount that Megan pays for the sweater is:

P = $34.00*(1 - 0.2)*(1 + 0.07)

P = $34.00*(0.8)*(1.07)

P = $29.10

She pays 29.10 dollars for the sweater.

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The equation of the vertical line that passes through (-4, 3) is x = -4.

This means that all points on the line have an x-coordinate of -4 and a y-coordinate of any value. To prove this, we can plug in -4 for x in the standard form of an equation of a line: y = mx + b. Since the line is vertical, the slope (m) is undefined, so the equation becomes 0 = 0 + b, which simplifies to b = 0.  Since m is undefined, the equation simplifies to just x1 = -4, meaning that the x-intercept of the line is -4. The equation of the line is then y = 0x - 4, which simplifies to y = -4. Therefore, the equation of the vertical line that passes through (-4, 3) is x = -4

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The equation of the line that passes through the points (0, -1) and (1, 2) is y = 3x - 1.

The equation of a straight line in slope - intercept form is -

y = mx + c

{m} - slope.

{c} - intercept along the y - axis.

Given is the line passes through the y - axis at (0, -1) and through the point (1, 2).

We can write the slope of the line as -

m = (2 + 1)/(1 - 0)

m = 3

So, we can write the equation as -

y = 3x + c

For the point (0, - 1), we can write -

- 1 = 3 x 0 + c

c = - 1

Therefore, the equation of the line that passes through the points (0, -1) and (1, 2) is y = 3x - 1.

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The mathematical proof is given below. Then the claims are correct.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

The triangle ΔABC is a right-angle triangle. And line CD is perpendicular to line AB.

In triangles ΔABC, ΔACD, and ΔCDB, we have

∠ACB = ∠ADC = ∠BDC                     (Right angle)

∠ABC = ∠ACD = ∠CBD                     (Corresponding angles)

Then the triangles ΔABC, ΔACD, and ΔCDB will be similar to each other. And in triangle ΔABC by the Pythagoras theorem is written as,

AB² = AC² + BC²

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On solving the system of linear equations y = -x + 2 and 3x - y = 6, the point of solution is obtained as option 3: (2,0).

What is a linear equation?

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

The system of linear equations are -

y = -x + 2....(1)

3x - y = 6....(2)

Writing equation (2) in standard form y = mx + b -

- y = -3x + 6....(3)

Now solving the equation (1) and (3) by adding -

y + (-y) = -x + 2 + (-3x + 6)

0 = -4x + 8

4x = 8

x = 2

Now, substituting the value of x = 2 in equation (1) -

y = -x + 2

y = -(2) + 2

y = -2 + 2

y = 0

Therefore, the values for x and y are 0 and 2 respectively.

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The drummer buys 4 pair of sticks and 2 pair of brushes.

Let x be the number of pairs of brushes the drummer buys.

We know that the number of sticks he buys is twice the number of brushes so, 2x is the number of pairs of sticks

The total cost of the brushes is 24x dollars and the total cost of the sticks is 10.5*2x = 21x dollars

We know that the total cost of all the sticks and brushes is 90 dollars

So we have the equation:

24x + 21x = 90

45x = 90

x = 2

So the drummer bought 2 pairs of brushes and 2*2 = 4 pairs of sticks

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Marcella is incorrect. A trapezoid is a quadrilateral with exactly one pair of parallel sides, while a rectangle is a quadrilateral with four right angles. Since the definition of a rectangle requires four right angles, it is not possible for a trapezoid to be a rectangle as they have only one pair of parallel sides.

A square is a special type of rectangle, where all four sides are of equal length. Therefore, it is possible for a square to be a rectangle.

Answer:

Step-by-step explanation:

1 Remove parentheses.

3x-4-x+5

2 Collect like terms.

(3x-x)+(-4+5)

3 Simplify.

2x+1

The answer is 2x+1.

Hope this helps. :D

Therefore , the solution of the given problem of slope comes out to be

m =-1/5 and b =5 units.

The slope of a line determines how steep it is. A characteristic of a color filter equation is a gradient overflow. The horizontal distance disparities (run) between two points are divided by the average vertical differences (rise) between the exact two points to determine the slope. The equation y = mx + b, which is known as the hill type equation, is used to express the fixed path issue. If grading is m, a = b, and the line's y-intercept is located there (0, b).

Here,

Given :

From the given graph we get

Points(0,5)  and (1,0)

So,

Slope m = 1-0 /0-5

=> m= -1/5

and

For b

=> b = 5 units.

Therefore , the solution of the given problem of slope comes out to be

m =-1/5 and b =5 units.

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An inverse log is defined as the anti-log of a log function raised to a negative value.

Enter a number and a base into the calculator.

The calculator will display the inverse log of the number and base entered.

The base of the natural log is equal to e=2.71828. The standard base for the log is base 10.

The following formula is used to calculate the inverse log of a number and base.

㏒[tex]b^{-1}[/tex](y) = [tex]b^{y}[/tex]

Where x is the value you are calculating

b is the base

and y is the number to take the log of

To calculate an inverse log, raise the base value to the power of the number being taken in the log.

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Answer:

  Emille's soccer team

Step-by-step explanation:

You want to know the higher win/loss ratio of Emille's 9/12 or Grant's 10/15.

One way to compare the fractions is to subtract one from the other:

  9/12 -10/15 = (9·15 -12·10)/(12·15) = (135 -120)/(12·15) = 1/12

This is a positive number, so the fraction 9/12 is higher.

Emille's team's win/loss ratio is higher because subtracting the win/loss ratio of Grant's team gives a positive result.

__

Additional comment

Grant's team's ratio reduces to 2/3, which can be expressed as 8/12. This is clearly lower than 9/12.

The number of students in the class is 29.

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, A teacher buys a fruit cup for $2.50 and a monthly planner for $9.00 for each student in their classroom. The teacher spends a total of $333.50 for all the fruit cups and monthly planners.

Let the numbers of students be a,

Therefore, total spend on fruit cups for a students = 2.50a

And, total spend on planner for a students = 9a

Therefore, establishing the equations,

2.5a + 9a = 333.5

11.5a = 333.5

a = 29

Hence, there are 29 students in the class.

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Answer: The answer is D.369 miles

Step-by-step explanation:

To solve this problem, you can use the formula: distance = rate x time.

We know that Chris and Nikoletta start at the same point, and they drive in opposite directions, so the total distance between them is the sum of the distance that each of them travels.

If Chris travels at a rate of 54 mph, and he drives for 3 hours, then the distance he travels is:

distance = rate x time = 54 mph x 3 hours = 162 miles

Similarly, if Nikoletta travels at a rate of 69 mph, and she drives for 3 hours, then the distance she travels is:

distance = rate x time = 69 mph x 3 hours = 207 miles

So the total distance between Chris and Nikoletta is the sum of the distance that each of them travels:

distance = 162 miles + 207 miles = 369 miles.

So the answer is D.369 miles

Answer:

22 units

Step-by-step explanation:

3

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 5x + 3 ← is in slope- intercept form

with y- intercept c = 3

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

to find the equation of the line from the table

y = mx + c

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (4, 15) and (x₂, y₂ ) = (10, 66) ← 2 ordered pairs from the table

m = [tex]\frac{66-15}{10-4}[/tex] = [tex]\frac{51}{6}[/tex] = 8.5 , then

y = 8.5x + c ← is the partial equation

to find c substitute any ordered pair from the table into the partial equation

using (6, 32 ) , then

32 = 8.5(6) + c = 51 + c ( subtract 51 from both sides )

- 19 = c ← the y- intercept

to calculate the distance between the y- intercepts c = 3 and c = - 19

find the absolute value of the difference, that is

distance = | - 19 - 3 | = | - 22 | = | 22 | = 22

or

distance = | 3 - (- 19) | = | 3 + 19 | = | 22 | = 22

then distance between the y- intercepts is 22 units

✓

3. x⁶× x × x³ = x⁶+³ = x⁹

x⁹ is not factorable with rational numbers

6+1+3 = 10

x⁶× x × x³ = x¹⁰

✓ ✓

4. 3⁴×2³ = 6⁴+³

6⁴+³ is not factorable with rational numbers

3⁴×2³ = 3³ × 2³ × 3 = (3×2)³ × 3 = 6³ × 3¹

Answer:Acute Angle

Step-by-step explanation:

The slope of line passing through the points (3, 8) and (-1, 0) is 2.

In the given question, we have to find the slope of the line that passes through the points (3, 8) and (-1, 0).

The point-slope approach is typically used when two points that sit on a specific line are specified.

A line's equation is written as y - y(1) = m(x - x(1)), where y(1) is the Y-axis coordinate, m is the slope, and x(1) is the X-axis coordinate.

m = [tex]\frac{y(2)-y(1)}{x(2)-x(1)}[/tex]

From the given points x(1) = 3, y(1) = 8, x(2) = -1, y(2) = 0.

Now putting the value

m = [tex]\frac{0-8}{-1-3}[/tex]

Now solving

m = [tex]\frac{-8}{-4}[/tex]

m = 2

Hence, the slope of the line passing through the points (3, 8) and (-1, 0) is 2.

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According to the division property of equality, if both sides of an equation are divided by a common real integer that is not zero, the quotients remain equal.

Commutative property, associative property, distributive property, and identity property are the four number properties. Only the algebraic operations addition, subtraction, multiplication, and division are linked with number characteristics.

The four key terminology used in the division process are dividend, divisor, quotient and remainder. Dividend Divisor = Quotient + Remainder is the formula for dividing two numbers.

Commutative property, associative property, distributive property, and identity property are the four number properties. Only the algebraic operations addition, subtraction, multiplication, and division are linked with number characteristics.

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The angles (6·x + 17)° and (4·x + 23)°, which are same side interior angles, indicates that the measure of the angle (6·x + 17)° is 101°

Same side interior angles are angles formed on the same side of a transversal to two lines and on the interior part of two two lines.

The possible diagram in the question obtained from a similar online question and created with MS Word is attached.

The possible question is to find the measure of the angle with a measure of (6·x + 17)°

From the attached drawing, we get;

Angle 6·x + 17 and angle 4·x + 23 are same side interior angles

Same side interior angles are supplementary, therefore;

6·x + 17 + 4·x + 23 = 180° (definition of supplementary angles)

(10·x + 40)° = 180°

10·x = 180° -  40° = 140°

x = 140° ÷ 10 = 14°

x = 140° ÷ 10 = 14°

x = 14

The measure of the angle (6·x + 17)° is therefore;

(6·x + 17)° = (6 × 14 + 17)° = 101°

The possible question is to find the measure of the angle (6·x + 17)°

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Answer:

Step-by-step explanation:

The number of tickets that she has bought is 6000-5520 = 480 tickets.

What is probability ?

Probability is a measure of the likelihood of a certain event happening. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. A probability of 0.5 represents an event that is equally likely to happen or not happen, while a probability of 0.8 represents an event that is more likely to happen than not happen.

Probability can be expressed as a decimal, fraction, or percentage. For example, a probability of 0.5 can also be expressed as 1/2 or 50%.

If the probability of her winning the prize in a lottery is 0.08, then the probability of her not winning the prize is 1-0.08 = 0.92.

If 6000 tickets are sold, and the probability of her not winning the prize is 0.92, then the number of tickets that she has not bought is 0.92*6000 = 5520.

Therefore, the number of tickets that she has bought is 6000-5520 = 480 tickets.

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The total area of the composite figure is;  94.485 sq.units

The given composite shape is made up of a rectangle and the quadrant of a circle.

Formula for area of rectangle is;

A_r = Length * Width

Thus;

A_r = 8 * 7

A_r = 56 sq.units

The formula for the area of the quadrant of a circle is;

A_quad = ¹/₄πr²

Thus;

A_quad = ¹/₄π * 7²

A_quad = 38.485 sq.units

Total area of composite figure = 56 sq.units + 38.485 sq.units

= 94.485 sq.units

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The value of variable x that makes -4x-(-10 - 8x) = -(12x-14) true is 1/4. thus, option c is correct.

An equation's unknown numerical value is represented by a symbol (typically a letter) called a variable in algebra. X and Y, which are real-number unknowns, as well as z, which are complex-number unknowns, as well as t, r, and s are frequently used variables (arc length).

Given

-4x-(-10 - 8x) = -(12x-14)

-4x + 10 + 8x = -12x + 14

4x + 10 = 14 - 12x

4x + 12x = 14 - 10

16x = 4

x = 4/16

x = 1/4

Thus, Option C is correct, x = 1/4

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Two rays that share the same endpoint and form a line are called opposite rays. These rays move in opposite directions.

In mathematics, a ray is defined as a line which has a fixed starting point but does not have an endpoint.

Opposite rays can be defined as two rays which have the same endpoint, forms the line and rays move in the opposite direction to each other.
The line can be defined as the continuous extent of dots without any thickness or breadth. It is endless.

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According to the Number line:

0 will be the number after that negative 1

Now, According to the question:

What is the number line?

A number line is a horizontal line that has equally spread number increments. The numbers included on the line will determine how the number on the line can be answered. The question that goes with the number determines how it will be used, for example, plotting a point.

So, According to the Number line:

0 will be the number after that negative 1

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