Write a polynomial of least degree with integral coefficients that has the given zeros.
1.0, 5, 2
2.-3,-5,3,-1
5. 2 mult.2, -4
3.-5, 2 + i
4.-1, 2i

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.

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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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 following values of x, makes the set of ratios equivalent:

2: 3 = 6: 9

4: 7 = 24: 42

(6*2)12: 48 = 3: 12

12: 15 = 16: 20

The ratio can be used to determine how much of one item is contained in the other by comparing two sums of the same units. Ratios fall into two different groups.

Whereas the second is a part to whole ratio, the first is a part-to-part ratio. The part-to-part ratio demonstrates the link between two independent entities or organisations.

Now here in the 1st set:

2:3 = 6:x

Now, x = 6×3/2

⇒ x = 9

Similarly,

4:7=x:42

⇒ x = 24

The next ratio we have:

2x:48= 3:12

⇒ x = 6

Now, the last ratio,

12:15 = x:20

⇒ x = 16

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10⁻³ is equal to 1/1000 or 0.001.

What are Exponents?

Exponents are a shorthand way of representing repeated multiplication of a number by itself. They are indicated by a superscript number placed to the right and above the base number.

The superscript number represents the number of times the base number is multiplied by itself. For example, 2³ means 2 multiplied by itself three times, which equals 8.

Exponents are used to simplify large and small numbers, and are fundamental to algebraic and mathematical calculations. Exponents have several rules, such as the power of a power rule, product rule, quotient rule, and negative exponents rule.

10⁻³ can be evaluated as:

1 / 10^3 = 1 / 1000

Therefore, 10⁻³is equal to 1/1000 or 0.001.

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To find the equation for a line parallel to y = 2x + 1 and passing through the point (1,5), we need to remember that parallel lines have the same slope.

Since the slope of y = 2x + 1 is 2, the slope of the parallel line will also be 2.

Using the point-slope form of a linear equation, we can plug in the given slope and point to find the equation of the parallel line:

y - y1 = m(x - x1)

y - 5 = 2(x - 1)

Simplifying this equation gives us the equation for the parallel line:

y = 2x + 3

So, the equation for the line parallel to y = 2x + 1 and passing through the point (1,5) is y = 2x + 3.

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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.

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

(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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a) The purchase price of the new equipment is $20,531.76.

b) The amount of interest that will have to be paid is $6,948.24.

The purchase price of the new equipment for New Bread Bakery can be found using the formula for the present value of an annuity:

PV = PMT * [(1 - (1 + i)^(-n)) / i]

Where PV is the present value (or purchase price), PMT is the monthly payment, i is the monthly interest rate, and n is the number of payments.

Plugging in the given values:

PV = 458 * [(1 - (1 + 0.092/12)^(-5*12)) / (0.092/12)]

PV = 458 * [(1 - (1 + 0.00767)^(-60)) / 0.00767]

PV = 458 * [(1 - 0.6887) / 0.00767]

PV = 458 * 40.4624

PV = 18,531.76

The purchase price of the new equipment is $18,531.76. However, this does not include the down payment of $2000. So, the total purchase price is:

PV + Down Payment = 18,531.76 + 2000 = $20,531.76

To find the amount of interest that will have to be paid, we can subtract the purchase price from the total amount paid over the five years:

Interest = (458 * 5 * 12) - 20,531.76 = 27,480 - 20,531.76 = $6,948.24

Therefore, the amount of interest that will have to be paid is $6,948.24.

(a) The purchase price of the new equipment is $20,531.76. (b) The amount of interest that will have to be paid is $6,948.24.

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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:

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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In the given figure by using the alternative angles rule we know that x = 82°.

Alternate angles are a unique type of angle in geometry.

The collection of non-adjacent angles on either side of the transversal is known as alternate angles.

Alternative Interior Angles: Angles are created on the inside, or interior, of two other lines when a third line known as the transversal crosses them. These other lines are typically parallel.

The alternate internal angles are those that are perpendicular to one another.

So, in the given figure:

∠ABD = ∠BDC = 35° (Alternate angles)

Then, ∠DBC will be:

82 + 35 + x = 180

117 + x = 180

x = 180 - 117

x = 63°

Then, ∠DBC = ∠BDA = 63° (Alternate angles)

Now, ∠DAB = 63 + 35 + x = 180

= 63 + 35 + x = 180

= 98 + x = 180

= x = 180 - 98

= x = 82°

Therefore, in the given figure by using the alternative angles rule we know that x = 82°.

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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 final answer length of the other dimension of the garden is 9x units.

To find the length of the other dimension of the garden, we need to use the formula for the area of a rectangle:

Area = Length x Width

We are given the area and one dimension, so we can plug those values into the formula and solve for the other dimension:

[tex]81x^2-126x[/tex] = (9x-14)(Length)

To solve for the length, we need to divide both sides of the equation by (9x-14):

Length =[tex](81x^2-126x)/(9x-14)[/tex]

Now we can simplify the right side of the equation by factoring out a common factor of 9x:

Length = (9x)(9x-14)/(9x-14)

The (9x-14) terms cancel out, leaving us with:

Length = 9x

So the length of the other dimension of the garden is 9x units.

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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.

The true statement about the polynomials is (b) No, it's only with polynomials with a degrees of 1

Given that the polynomials f and g have a degree of 3

The composition of two functions, f ∘ g (read as "f composed with g"), is not commutative in general, meaning that f ∘ g is not necessarily equal to g ∘ f.

This holds true for polynomials of degree 3 as well.

In fact, if f and g are two different polynomials of degree 3, then f ∘ g and g ∘ f will be different polynomials in general.

The equation f ∘ g = g ∘ f holds true is when f and g are constant polynomials, that is, polynomials of degree 0 or 1.

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Answer:

Step-by-step explanation:

a=70

b=45

c=65

d=45

e=70

f=110

make sure to add degree symbol

Enjoy :)

The answer is \(a+b+c+d = 10\).

To find \(a+b+c+d\), we can use matrix multiplication to solve for each variable. Matrix multiplication is performed by multiplying the elements of each row of the first matrix by the corresponding elements of each column of the second matrix, and then summing the products.

So, we can set up the following equations:

\(10 = 1a + 2c\)

\(1 = 1b + 2d\)

\(-6 = 3a - 3c\)

\(-6 = 3b - 3d\)

Solving for each variable, we get:

\(a = 6 - 2c\)

\(b = (1 - 2d)/1\)

\(c = (6 + 3a)/(-3)\)

\(d = (3b + 6)/(-3)\)

Substituting the values of \(a\) and \(b\) into the equations for \(c\) and \(d\), we get:

\(c = (6 + 3(6 - 2c))/(-3)\)

\(d = (3((1 - 2d)/1) + 6)/(-3)\)

Solving for \(c\) and \(d\), we get:

\(c = -2\)

\(d = -1\)

Substituting these values back into the equations for \(a\) and \(b\), we get:

\(a = 6 - 2(-2) = 10\)

\(b = (1 - 2(-1))/1 = 3\)

So, \(a+b+c+d = 10 + 3 + (-2) + (-1) = 10\).

Therefore, the answer is \(a+b+c+d = 10\).

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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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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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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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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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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!!!

The number of yards of ribbon Lynn used to make a bow is 1/16 yards.

To find out how many yards of ribbon Lynn used to make a bow, we need to subtract the amount of ribbon she had left from the amount she started with and then divide by the number of bows she made. We can do this using the following steps:

1. Convert the mixed numbers to improper fractions: 1(5)/(8) = 13/8 and 1(1)/(4) = 5/4
2. Subtract the two fractions: 13/8 - 5/4 = 13/8 - 10/8 = 3/8
3. Divide the result by the number of bows: (3/8) / 6 = 3/8 x 1/6 = 3/48 = 1/16

Therefore, Lynn used 1/16 yards of ribbon to make a bow.

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Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

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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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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