how do you simplify

After being rotated 180 degrees anticlockwise around the origin, the picture of the point (4,8) is (-4,-8).

The fixed point is referred to as the rotational centre. The quantity of the rotation is described by the term "angle of rotation," which is measured in degrees. The equivalent of turning a figure 90 degrees anticlockwise is turning it 180 degrees clockwise. Hence, the resulting image of the point is (-1, 2).

Below are the guidelines for rotation: rotation 90 degrees clockwise: (x,y) results in (y,-x) rotation of (x,y) at 90 degrees anticlockwise results in (-y,x) Rotating (x, y) 180 degrees both clockwise and anticlockwise results in (-x,-y).

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This means that there exists an element a of the ideal I, such that all other elements in the ideal can be written as a multiple of a. In other words, the ideal I can be written as I = (a) = {ar : r ∈ I}, where r is any element of the ideal I.

A principle ideal is an ideal that is generated by a single element. This means that there exists an element a of the ideal I, such that all other elements in the ideal can be written as a multiple of a. In other words, the ideal I can be written as I = (a) = {ar : r ∈ I}, where r is any element of the ideal I. This is an important concept in the study of rings and algebraic structures, as it allows us to understand how ideals are generated and how they relate to other ideals in the same ring.

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Answer:

  £67.78

Step-by-step explanation:

Given that rolls come in a package of 20 for £2.87 and ham slices come in a package of 30 for £6.32, you want the minimum cost of enough packs for more than 90 sandwiches, each of which uses 1 roll and 2 ham slices.

One package of 20 bread rolls is enough for 20 sandwiches. One package of 30 ham slices is enough for 15 sandwiches. The least common multiple of these numbers is the number of sandwiches that will use a whole number of each of the kinds of packages:

  LCM(20, 15) = 60 = 3·20 = 4·15

We want to make a number of sandwiches that is more than 90. The least multiple of 60 that is more than 90 is 120.

120 sandwiches will require 120/20 = 6 packages of bread rolls, and 120/15 = 8 packages of ham slices.

The cost of 6 packages of bread rolls and 8 packages of ham slices is ...

  6×£2.87 +8×£6.32 = £17.22 +50.56 = £67.78

The least Tina can spend on packs of bread and ham is £67.78.

The original list price for the product was $487.09.

To find the original list price for the product, we need to reverse the discounts and markup that were applied to it. Here is a step-by-step explanation:

Therefore, the original list price for the product was $487.09.

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The solution set for the absolute value equation |2x-4|=20 is {-14, 14}.

An absolute value equation is one that contains an absolute value expression, such as ||x| - 1| = 2.

These types of equations are solved by breaking them down into two separate equations and solving each one separately:

one with the original absolute value expression and a positive value for the other side, and the other with the negated absolute value expression and a negative value for the other side.

The steps to solving an absolute value equation are as follows:

1. Write the equation in the form |expression| = value, where expression is the absolute value expression and value is the constant on the right-hand side.

2. Separate the equation into two equations: expression = value and expression = -value.

3. Solve each equation for the variable.

4. Check the solution(s) to ensure that they satisfy the original equation.

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None of the options are sufficient to prove that ABCD quadrilateral is a kite.

what are quadrilaterals ?

Quadrilaterals are closed two-dimensional shapes with four straight sides and four angles. The word "quadrilateral" comes from the Latin words "quadri" which means "four" and "latus" which means "side". Some common examples of quadrilaterals include squares, rectangles, parallelograms, rhombuses, and trapezoids.

Each type of quadrilateral has its own unique set of properties and characteristics. For example, a rectangle has four right angles and opposite sides that are parallel and congruent. A parallelogram has opposite sides that are parallel and congruent, and opposite angles that are congruent. A rhombus has four congruent sides and opposite angles that are congruent.

According to the question:

Option A: OBC and DC being congruent only tells us that OBDC is a parallelogram, but it does not tell us anything about the other pair of adjacent sides, AB and BC.

Option B: OAC and DC being congruent only tells us that OACD is an isosceles trapezoid, but it does not tell us anything about the other pair of adjacent sides, AB and BC.

Option C: OAC and BC being congruent only tells us that OABC is a kite, but it does not tell us anything about the other pair of adjacent sides, AD and DC.

None of the options given are sufficient to prove that ABCD is a kite. To prove that ABCD is a kite that we need to show that two pairs of adjacent sides are congruent.

Therefore, none of the options are sufficient to prove that ABCD is a kite.

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Answer:

48 servings

Step-by-step explanation:

since there are 16 cups in a gallon and 2 cups makes 6 servings, then to find the number of servings a gallon makes we divide the amount of cups in a gallon (16) by how many you need to make the recipe (2), and 16/2=8 so now we multiply how many times we can make the recipe with a gallon (8) by how many servings the recipe makes (6) to get 8x6=48 servings

Answer:

y-intercept: 3

equation: y = -x + 3

Step-by-step explanation:

For problem #6: (-2,5) and (2,1)

Slope m = (y2 - y1)/(x2 - x1)

=>m = (1 - 5)/(2 - -2) = -4/4 = -1

Slope-intercept form is y = mx + b

Given m = -1, y = 1, x = 2

=> 1 = -1(2) + b

=> 1 = -2 + b

=> b = 1 + 2  = 3

equation: y = -x + 3

since b is the y-intercept => 3

Answer:

x= 6[tex]\sqrt{2}[/tex]

Step-by-step explanation:

The result is the mean of 3.9 miles and median of the team's distances is 3.5 miles.

Mean and median are two ways to measure the center of a set of numbers. Mean is the average of all the numbers in the set, while median is the middle number in the set. Mean is more affected by extreme values, while median is not. Mean is generally used when data is normal, and median when data is skewed.

Mean and median are both measures of central tendency, or measures of the center of a data set. Both measures are used to summarize a data set, but the mean is more affected by outliers, or extreme values, while the median is not.

The mean of the team's distances is 3.9 miles, and the median is 3.5 miles. To calculate the mean, add all the distances together (3.5 + 2.5 + 4 + 3.25 + 3 + 4 + 6) and divide by the number of distances (7). The result is the mean of 3.9 miles. To calculate the median, first order the distances from least to greatest (2.5, 3, 3.25, 3.5, 4, 4, 6) and take the middle number (3.5). The median of the team's distances is 3.5 miles.

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(a) The number of cans of spray paint that needs to be purchased is 3.

(b) The cost to paint the wooden prism is $12.00.

To determine the cost of painting the wooden prism, we need to calculate the surface area of the prism and then divide it by the coverage of each can of spray paint.

Let's assume the wooden prism has dimensions of 6 feet by 4 feet by 3 feet.

Part A:

The surface area of the prism can be calculated as follows:

The top and bottom faces have an area of 6 ft x 4 ft = 24 ft² each

The two side faces have an area of 6 ft x 3 ft = 18 ft² each

The front and back faces have an area of 4 ft x 3 ft = 12 ft² each

Therefore, the total surface area of the prism is:

2(24 ft²) + 2(18 ft²) + 2(12 ft²) = 96 ft²

Since each can of spray paint covers 40 ft², we need:

96 ft² ÷ 40 ft²/can = 2.4 cans

We can't purchase a partial can of spray paint, so we need to round up to the nearest whole can.

Therefore, we need to purchase 3 cans of spray paint.

Part B:

The cost of painting the box will be the number of cans required multiplied by the cost per can.

Since we need to purchase 3 cans, the cost will be:

3 cans x $4.00/can = $12.00

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The ratio used to depict the relationship between the dimensions of a model or scaled figure and the corresponding dimensions of the real figure or object is called the scale. On the other hand, a scale factor is a value that is used to multiply all of an object's parts in order to produce an expanded or decreased figure.

Given, A road map is drawn to a scale of 1mm: 50m

i) To find the distance on the map which represents 20 km on the road, we need to use the scale of the map.

Since 1 mm on the map represents 50 m on the road, we can set up a proportion:

1 mm / 50 m = x mm / 20,000 m

Cross-multiplying and solving for x, we get:

x = (1 mm / 50 m) * 20,000 m = 400 mm

Therefore, the distance on the map which represents 20 km on the road is 400 mm.

ii) To find the distance on the road which corresponds to 228 on the map, we can again use the scale of the map.

Since 1 mm on the map represents 50 m on the road, we can set up a proportion:

1 mm / 50 m = 228 mm / x m

Cross-multiplying and solving for x, we get:

x = (228 mm / 1) / (50 m / 1) = 4.56 km

Therefore, the distance on the road which corresponds to 228 on the map is 4.56 km.

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The answer is y=x+4

You would had the 4 to the side with the x on it.

Answer:

Below

Step-by-step explanation:

Slope-intercept form is  :    y = mx + b

y - 4 = x       add 4 to each side of the equation

y = x + 4      Done.

The initial population for this model is 12,000 and the maximum population is 24,000. The equation 12000/3+e^-.02(t) is used to model population growth.

The initial population and maximum population can be found by examining the growth population model.
The initial population is represented by the term before the exponential function, which in this case is 12000/3. This means that the initial population is 4000.

The maximum population is represented by the term in the denominator of the fraction with the exponential function. In this case, the maximum population is 3. This means that the population will never exceed 3, even as time (t) increases.
In conclusion, the initial population is 4000 and the maximum population is 3 according to the given growth population model.

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Answer:

Step-by-step explanation:

alternate interior angles

More formally:

If two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel (Since ∠1 = ∠4)

Answer: Alternate Interior Angles Converse

Step-by-step explanation:

If two lines are cut by a transversal so the alternate interior angles are congruent, then the lines are parallel.

x = 2logb(x2 + 56)/2

1. log2x = log218

log2x = 3

x = 23 = 8

2. log2×2 = log2(4x−4)

log2×2 = log2(4x)−log2(4)

log2×2 = log2(4x)−2

log2×2 + 2 = log2(4x)

log2(2×2) + 2 = log2(4x)

log2(4) + 2 = log2(4x)

4 + 2 = log2(4x)

6 = log2(4x)

26 = 4x

x = 23 = 8

3. logb(x2−56)=logbx

logb(x2−56) = logbx

logb(x2)−logb(56) = logbx

logbx2−logb56 = logbx

logbx2−logb56 + logbx = logbx + logbx

2logbx = logbx2 + logb56

2logbx − logbx2 = logb56

2logbx − logb(x2−56) = logb56

2logbx − logb(x2) + logb(56) = logb56

2logbx−logbx2 + logb(56) = logb56

2logbx = logb(x2 + 56)

2logbx = logb(x2 + 56)

logbx = logb(x2 + 56)/2

x = 2logb(x2 + 56)/2

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the value of the expression is 0.

To solve this expression, we can use the PEMDAS order of operations:

since there are no Parentheses and Exponents we move to multiplication and division

-2(-3) + 27 ÷ (-3) + 3 = 6 + (-9) + 3

6 + (-9) + 3 = 0

As a result, the equation has a value of 0.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13.

Here,

5 and 13 are expressions for 2x.

These two expressions are joined together by the sign "=".

Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero. As we can balance this by deducting the right-side expression from both sides' expressions, this won't reduce the generality. The two most well-known groups of equations in algebra are linear equations and polynomial equations. P(x) = 0 can be used to represent polynomial equations with a single variable. P is a polynomial, and axe + b = 0 is the standard form for linear equations. Here, are the parameters a and b.

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Answer:

Step-by-step explanation:

graph with the x axis labeled time in hours and the y axis labeled total distance in miles, with a line segment from 0 comma 0 to 0.25 comma 1.25, a line segment from 0.25 comma 1.25 to 0.5 comma 1.75, a line segment from 0.5 comma 1.75 to 0.8 comma 2.95, and a horizontal line segment from 0.8 comma 2.95 to 1 comma 2.95

It's B.

Explanation: I took the test

The part of the mural that Trevor has completed is 6/20 square meter.

The correct answer choice is option C.

Area of a rectangle is the measure of the extent of a surface. it is measured in square units.

Total area of the mural = 1 square meter

Rectangular part of the mural:

Length = 2/5 meter

Width = 3/4 meter

Area of the rectangular part of the mural = length × width

= 2/5 × 3/4

= 6/20 square meter

Ultimately, Trevor has completed 6/20 of the mural.

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Answer:

[tex](3m + 5n)(9m {}^{2} - 15mn + 25n {}^{2} )[/tex]

Step-by-step explanation:

Greetings!!!

Given expression

[tex]27m {}^{3} + 125n {}^{3} [/tex]

Apply exponents rule

Rewrite 27 as 3³

[tex] = 3 {}^{3} m {}^{3} + 125n {}^{3} [/tex]

Rewrite 125 as 5³

[tex] = 3 {}^{3} m {}^{3} + 5 {}^{3} n {}^{3} [/tex]

Apply exponent rule:

[tex]a {}^{m} b {}^{m} = (ab) {}^{m} \\ = 3 {}^{3} m {}^{3} = (3m) {}^{3} \\ = 5 {}^{3} n {}^{3} = (5n) {}^{3} [/tex]

Apply sum of cubes formula

[tex]x {}^{3} + y {}^{3} = (x + y) (x {}^{2} - xy + y {}^{2} )[/tex]

[tex](3m {}^{3}) + (5n {}^{3} ) = (3m + 5n)((3m) {}^{2} - 3m.5n + (5n {}^){2} ) \\ = (3m + 5n)((3m {}^{2} ) - 3m.5n + (5n {}^{2} ))[/tex]

simplify

[tex] = (3m + 5n)(9m {}^{2} - 15mn + 25n {}^{2} )[/tex]

If you have any questions tag me on comments

Hope it helps!!!

Answer: To find the coordinates of D1.5(ABCD), we need to perform a dilation with center D and scale factor 1.5 on the coordinates of each point.

The coordinates of point D are (-5, -10). To dilate point A, we can subtract the coordinates of D from the coordinates of A, multiply by 1.5, and then add the coordinates of D back:

D1.5(A) = 1.5[(2, 0) - (-5, -10)] + (-5, -10) = 1.5(7, 10) + (-5, -10) = (6.5, 5)

Similarly, we can dilate points B and C:

D1.5(B) = 1.5[(8, -4) - (-5, -10)] + (-5, -10) = 1.5(13, 6) + (-5, -10) = (14.5, -4)

D1.5(C) = 1.5[(4, -6) - (-5, -10)] + (-5, -10) = 1.5(9, 4) + (-5, -10) = (7.5, 4)

Therefore, the coordinates of D1.5(ABCD) are A'(6.5, 5), B'(14.5, -4), C'(7.5, 4), and D(-5, -10).

Step-by-step explanation:

Alex will need 150 tiles to make his mosaic.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the tiles in a two-dimensional plane is called the area of the tiles.

To determine the number of tiles needed to create the mosaic, we need to find out the area of the wall mosaic and then divide it by the area of each tile.

First, let's find the area of the wall mosaic. We can do this by counting the number of squares within the rectangular shape, which is the plan for the mosaic.

By counting, we can see that there are 30 squares in the horizontal direction and 20 squares in the vertical direction. Therefore, the area of the wall mosaic is:

Area of wall mosaic = 30 x 20 = 600 square cm

Now, let's find the area of each tile. The problem tells us that each tile is a square with a side length of 2 cm. Therefore, the area of each tile is:

Area of each tile = 2 x 2 = 4 square cm

Finally, we can find the number of tiles needed by dividing the area of the wall mosaic by the area of each tile:

Number of tiles needed = Area of wall mosaic ÷ Area of each tile

= 600 ÷ 4

= 150

Therefore, Alex will need 150 tiles to make his mosaic.

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Step-by-step explanation:

12(5x - 4.5) = 36

if that is really correct, then we solve this first by dividing both sides by 12

5x - 4.5 = 3

then we add 4.5 to both sides

5x = 7.5

and finally we divide both sides by 5

x = 1.5

The type of polynomial that - 2 / 3 x b³ is D. Cubic polynomial.

A cubic polynomial is a type of polynomial function in algebra that has a degree of three. Cubic polynomials can take many different forms and can have multiple real roots, complex roots, or no real roots at all.

A quadratic polynomial contains a degree of 2, a linear polynomial contains a degree of 1, and a quartic polynomial contains a degree of 4. In this case, the highest degree of the variable b is 3, which makes it a cubic polynomial.

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The required,
19. AB is tangent to circle C.
20. AB is not tangent.

In a right-angled triangle, its sides, such as the hypotenuse, are perpendicular and the base is Pythagorean triplets.

Here,
Form figure 19.

Applying the Pythagorean theorem,
BS² = AS² + AB²

Substitute the value in the above expression.
12² = 7.2² + [2*4.8]²    [radius = diameter /2]

144  = 51.84+92.16
144 = 144

Thus, the required AB is tangent to circle C.

Similarly,
In figure 20 AB is not tangent because,
BC² ≠ AB² + AC²

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The required linear function is (f(x) = 0.6(x - 2006) + 56) and this can be determined by using the arithmetic operations.

Given :

In 2006 the average grownup ate fifty-six kilos of birds.

the amount will increase by means of zero.6 pounds in step with yr till 2011.

To determine the linear feature f(x) following steps can be used

Let 'x' be the number of years.

Then the total number of years since 2006 will be:

= x - 2006

The amount boom in kilos in line with 12 months could be:

= 0.6(x - 2006)

Now, add 56 to the above equation.

= 0.6(x - 2006) + 56

It is a type of function that has a constant rate of change between the independent variable (usually denoted as x) and the dependent variable (usually denoted as y). The general form of a linear function is y = mx + b, where m is the slope or the rate of change, and b is the y-intercept.

Linear functions are commonly used in mathematics, economics, physics, and engineering to model real-world phenomena that have a linear relationship between two variables. For example, the cost of producing a certain number of units of a product may be modeled by a linear function, where the slope represents the cost per unit and the y-intercept represents the fixed costs.

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The expression |x+3|5x-2|-(x+3)(4x+3)| can be rewritten as (x+3)|x-5|.

Consider the expression |x+3|5x-2|-(x+3)(4x+3)|. To rewrite this expression in the form (x+3)|ax+b|, we will need to use the distributive property and combine like terms.

First, let's distribute the (x+3) term:

|x+3|5x-2| - (x+3)(4x+3) = |5x^2 + 13x - 2| - |4x^2 + 15x + 9|

Next, let's combine like terms:

|5x^2 + 13x - 2| - |4x^2 + 15x + 9| = |x^2 - 2x - 11|

Now, we can factor the expression inside the absolute value:

|x^2 - 2x - 11| = |(x+3)(x-5)|

Finally, we can rewrite the expression in the form (x+3)|ax+b|:

|(x+3)(x-5)| = (x+3)|x-5|

So, the expression |x+3|5x-2|-(x+3)(4x+3)| can be rewritten as (x+3)|x-5|.

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In the parallelogram given the value for the variable x is deduced as 25°.

What is a parallelogram?

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side.

According to the properties of a parallelogram, the vertically opposite angles of a parallelogram is always equation.

The first angle measures 2x + 50°.

The second angle measures 3x + 25°.

They both are placed vertically opposite to each other.

So, the equation will be -

2x + 50° = 3x + 25°

Collect the like terms -

2x - 3x = 25° - 50°

- x = - 25°

x = 25°

Therefore, the value of x is obtained as 25°.

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Answer:

D. x > 0, x ≤ 4, y ≥ 1 and y < 4

Answer:

Step-by-step explanation:

from top to bottom:

1,200

0.012

120

0.00012

If the exponent is positive, move the decimal to the RIGHT the number of spaces equal to the exponent.

If the exponent is negative, move the decimal to the LEFT the number of spaces equal to the exponent.