Part A: Write the polynomial function with zero { -2, 0, 3√2 }
Part B: Write the polynomial function with zero { -1, 3, 2i }

The rectangular prism's dimensions are 3:2:1 in terms of length, breadth, and height. The prism's length can be computed as 24 cm using its volume, 48 cm3, as input.

Volume = Length × Width × Height

48 cm3 = L × 2 × 1

L = 24 cm

A rectangular prism is a solid 3D object that has six faces, eight vertices and twelve edges. The length, width and height of a rectangular prism can be expressed in a ratio of 3:2:1 respectively. Knowing this ratio and the volume of the prism, which is 48 cm3, it is possible to calculate the length of the prism. To calculate the length of the prism, first the volume of the prism must be expressed in terms of the length. This can be done by using the formula Volume = Length × Width × Height. Therefore, 48 cm3 = L × 2 × 1. Solving this equation for L gives the length of the prism as 24 cm. Therefore, the length of the rectangular prism with a volume of 48 cm3 and a ratio of 3:2:1 is 24 cm.

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Answer:

OQ = 4

Step-by-step explanation:

the ratios of the segments OP : PQ : QR = 1 : 1 : 3 = x : x : 3x ( x is a multiplier)

then

OP + PQ + QR = OR , that is

x + x + 3x = 10

5x = 10 ( divide both sides by 5 )

x = 2

Then

OQ = OP + PQ

      = x + x

     = 2x

     = 2 × 2

     = 4

Julio needs to prove that two sides of the two triangles are congruent, in addition to the hypotenuse and one set of legs that are already congruent, to use the SAS Triangle Congruence Theorem.

Julio needs to prove that the two triangles have congruent sides in order to use the SAS Triangle Congruence Theorem. This means that he needs to show that one side of one triangle is congruent to a corresponding side of the other triangle and the same applies to the other two sides. This can be done by using methods such as measuring the sides, using algebraic equations, or using geometric constructions.

According to Julio statement, he has already constructed two right triangles to have congruent hypotenuses and one set of congruent legs, which means he has already proved that one side of one triangle is congruent to a corresponding side of the other triangle (hypotenuse) and one set of legs are congruent.

Therefore, Julio need to prove the remaining side of the triangle congruent to the corresponding side of the other triangle. Once he proves this, he can use the SAS Triangle Congruence Theorem to state that the two triangles are congruent.

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Answer:

Ryan did

Step-by-step explanation:

7/8 is .875 which is about 87

To compare the score of Ryan and Sam, we need to convert the fractions to decimals.

Ryan got 7/8 problems correct, which is equivalent to 0.875 when expressed as a decimal.

Sam got 80% correct, which is equivalent to 0.8 when expressed as a decimal.

So, Ryan got a better score

a. the difference in the two data provided =31072940 - 24658823 = 6414117

b. the sum of the two data to the nearest thousand hundred = 31072940 - 24658823 = 55731763

nearest to Thousand hundred = 55730000

The expression that represents the total amount of change she should receive is y = 20 - 3x.

An algebraic expression that uses either a constant or a variable raised to the first power for each term is known as a linear expression. This means that none of the exponents can be greater than 1.

The price of x boxes of cereal $3 each = 3x

Let y be the extra cash she paid

Total cash she paid = $20

Then we have

3x + y = 20

And for expression that represents the total amount of change she should receive

y = 20 - 3x

Thus, The expression that represents the total amount of change she should receive is y = 20 - 3x.

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So, each platter will have 25 legs and 25 wings.

To determine the greatest number of platters the kitchen staff can make, you need to find the least common multiple of 25 and 50. This is because each platter must have the same number of legs and wings, so you need to find the smallest number of legs and wings that can be divided evenly into both 25 legs and 50 wings.

The least common multiple (LCM) of 25 and 50 is 50. This means that the greatest number of platters the kitchen staff can make is 50/25 = 2 platters.

Therefore, each platter will have 25 legs and 25 wings.

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Find the least frequent multiple of 25 and 50 to determine the maximum number of platters the kitchen staff can produce. Finding the fewest number of legs and wings that can be equally divided into 25 legs and 50 wings is necessary because each platter must have the same number of legs and wings.

25 and 50 have a least common multiple (LCM) of 50. The maximum amount of platters the kitchen staff is capable of producing is 50/25, or 2 platters.

Therefore, there will be 25 legs and 25 wings on each plate.

The length x will be 23.994615468 ft or rounded approximately 24 feet.

The length x is the distance from the center of the roof to the edge of the roof.

        x = 15 + (15 * tan(25°)) + 1

        tan(25°) = 0.466307658

        x = 15 + (15 * 0.466307658) + 1

        x = 15 + 6.994615468 + 1

        x = 23.994615468 ft

So, the length x = 23.994615468 ft, or approximately 24 feet.

The problem is about finding the length x, which is the distance from the center of the roof to the edge of the roof of a grain bin with a radius of 15 ft and a recommended slant of 25° for the roof. The roof is also required to overhang the edge of the bin by 1 ft. The length x was calculated using trigonometry and found to be approximately 24 feet.

Complete Problems (Question):

Carlos plans to build a grain bin with a radius of 15 ft. The suggested slant of the roof is 25°. He wants the roof to overhang the edge of the bin by 1 ft. What should the length x be? Give your answer in feet and inches.

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We can find the solution of y = -2x + 6 by graphing the equation by plotting the intercepts of the equation.

Here we can solve the equation by calculating the x and y intercepts of the equation.

This is done by equating the other coordinate to 0 to get the intercept.

For the x-intercept, we will take y to be 0 to get

-2x + 6 = 0

or, 2x = 6

or, x = 3

Hence one intercept will be (3 , 0)

For the y-intercept, we will let x be 0 to get

y = 6

Hence getting the other intercept to be (0 , 6)

Now we can plot the graph by simply plotting these points and drawing a straight line passing through it

To get any unique solution, another equation needs to be plotted and the intersection point of the 2 lines will give us the required answer.

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Complete Question

How do you solve y = -2x + 6?

(0,3) , (4,0) are two solution of equation 3x + 4y = 12.

An equation is a mathematical statement that asserts the equality of two expressions. It typically consists of two parts, separated by an equal sign (=), with the expressions on either side representing the same value.

Given Linear equation in two variables:

3x + 4y = 12 ----( 1 )

Substitute x = 0 , in equation ( 1 ) ,

3 × 0 + 4y = 12

=> 4y = 12

=> y = 12/4

y = 3

Therefore ,

( x , y ) = ( 0 , 3 )

Substitute y = 0 in equation ( 1 ) ,

3x + 4 × 0 = 12

=> 3x = 12

=> x = 12/3

x = 4

Therefore,

( x , y ) = ( 4 , 0 )

Required two solutions are ( 0 , 3 ) , ( 4 , 0 )

Therefore, (0,3) , (4,0) are two solution of equation 3x + 4y = 12.

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Answer:

No

Step-by-step explanation:

In the given Rhombus ABCD, the measure of side AE = 27.85.

Verify that the two diagonals are parallel to one another. The diagonal lines are parallel. A rhombus is what it is. The parallelogram is a rectangle, rhombus, and square since the diagonals are all congruent and perpendicular to one another.

Area can be used to determine the area of a rhombus because it is a parallelogram, and its area can be determined from the length of its base and perpendicular height.

Here, we construct an alternate formula for the area of a rhombus that uses the lengths of its diagonals. Find the length of the other diagonal if one of the diagonals is 8 units long. We already know how to compute the area of a rhombus using its diagonals: Area = (1/2) (diagonal1 diagonal2) 256 = (1/2) (8 diagonal2).

AB = 26

BD = 20

BD/2 = 10

Using Pythagorean theorem:

[tex]AE = \sqrt{26^2 + 10^2}[/tex]

AE = 27.85

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Answer:

2 in

Step-by-step explanation:

If im not wrong, each side should be 2 inches, as it would have to be 2x2x2 for a volume of 8 inches cubed

To write 8 more than a number, we use the mathematical operation of addition and the notation 8+ Number = N+8.

To write 8 more than a number, we need to use the mathematical operation of addition. Addition is the process of combining two or more numbers to find the total or sum.

In this case, we are given the number 5 and we are asked to find the number that is 3 more than it. To do this, we can use the mathematical notation: 8 + Number = N+8.

This notation means that we are adding 8 to a number, which results in N+8. The "+" symbol is the addition operator and it is used to indicate that we are performing an addition operation. The "=" symbol is used to indicate that the result of the addition is N+8.

Another way to write 8 more than a number is to use the phrase "8 plus a number". This phrase indicates that we are adding 8 to a number to get N+8.

Therefore, In short, to write 8 more than a number, we use the mathematical operation of addition and the notation 8 + Number = N+8. This means that we are adding 8 to a number, resulting in N+8. It can also be written as "8 plus N", indicating the same operation.

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The solution to the equation 7x - 9 = 16 is x = 25/7. This can be achieved by using the addition property of equality and simplifying the equation.

The equation 7x - 9 = 16 can be solved by using The equation's solution can be changed by adding the same amount to either side of the equation, according to the addition property.

To both sides of the equation, add 9.

7x - 9 + 9 = 16 + 9

Simplify the equation.

7x = 25

Divide both sides of the equation by 7.

7x/7 = 25/7

Simplify the equation.

x = 25/7

Therefore, the solution to the equation 7x - 9 = 16 is x = 25/7.

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The sum of a regular polygon's exterior angles will always equal 360 degrees.

Exterior angles are those that are parallel to a polygon's inner angles but are on the outside of it. The sum of two internal opposite angles equals the measure of an exterior angle. The Exterior Angle is the angle formed by any side of a shape and a line drawn from the opposite side. Another example: When we add up the Interior Angle and Exterior Angle we get a Straight Angle (180°), so they are "Supplementary Angles". An exterior angle of the triangle is a nonstraight angle (one that is not just an extension of a side) outside the triangle but adjacent to an interior angle (Figure 1 ).

Here,

The sum of the exterior angles of a regular polygon will always equal 360 degrees.

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Answer:

y = -3/2 x + 2

Step-by-step explanation:

3x + 2y = 8

2y = -3x + 8

y = -3/2 x + 4

slope of given line = m = -3/2

Parallel lines have equal slopes.

Slope of parallel line through point (-2, 5), m = -3/2.

y = mx + b

m = -3/2

y = -3/2 + b

point: (-2, 5)

5 = (-3/2)(-2) + b

5 = 3 + b

b = 2

Equation: y = -3/2 x + 2

Answer:

10 1/8

Step-by-step explanation:

25 3

8

+

-15 1

4

=  (25 + -15) + (

3

8

+

-1

4

)

=  10 +

3

8

+

-1 × 2

4 × 2

=  10 +

3

8

+

-2

8

=  10 +

3 + -2

8

=  10 +

1

8

=  

10 1

8

Answer:

The correct statements describing the process of converting z = 2 + 3i to polar coordinates using technology are:

Write the complex number as a point in the complex plane: (2, 3i)

Substitute a = 2 and b = 3 for the real and imaginary parts respectively.

Using radians for θ, record the result as r = 3.606 and θ = 0.983 as your answer in polar coordinate form: (3.606, 0.983).

To convert a complex number in the form of z = a + bi to polar coordinates using technology, we can use the following steps:

Write the complex number as a point in the complex plane, with the real part as the x-coordinate and the imaginary part as the y-coordinate.

Substitute a for the real part and b for the imaginary part.

Using the Pythagorean theorem, we can find the distance from the origin to the point, which is the magnitude or modulus of the complex number, represented by r.

Using the tangent function, we can find the angle of the point from the positive x-axis, which is the argument or phase of the complex number, represented by θ.

Record the result in polar coordinates as (r, θ), where r is the magnitude and θ is the argument, given in radians.

It's also worth noting that polar coordinates can also be represented in the form of (r, θ ) or (r, arg(z)) or (r, angle(z))

Answer:

z = 2 + 3i

Step-by-step explanation:

The Law of Sines says that in any given triangle, the ratio of any side length to the sine of its opposite angle is the same for all three sides of the triangle. This is true for any triangle, not just right triangles.

The law of sines relates the ratios of side lengths of triangles to their respective opposite angles. This ratio remains equal for all three sides and opposite angles. We can therefore apply the sine rule to find the missing angle or side of any triangle using the requisite known data.

The ratio of the side and the corresponding angle of a triangle is equal to the diameter of the circumcircle of the triangle. The sine law is can therefore be given as,

[tex]\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C}[/tex]

In a right triangle, the sine of an angle is the ratio of the length of the opposite side divided by the length of the hypotenuse.

The Law of Sines says that in any given triangle, the ratio of any side length to the sine of its opposite angle is the same for all three sides of the triangle. This is true for any triangle, not just right triangles.

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Answer:

Step-by-step explanation:

Given similar triangles DEF and GHF, and side lengths DE = 6, EF = 10, GH = 21, FG = 28, you want the lengths of y=FH and x=FD.

Corresponding sides of similar triangles are proportional. This means ...

  DE/GH = EF/HF = FD/FG

  6/21 = 10/y = x/28

We can multiply by 28 to solve for x:

  x = 28(6/21) = 8

Multiplying by 21y/6 will give the value of y:

  y = (21/6)(10) = 35

The values of x and y are 8 and 35, respectively.

__

Additional comment

These are both 3-4-5 right triangles. The smaller is multiplied by 2; the larger is multiplied by 7 to give 6-8-10 and 21-28-35 triangles.

Answer:

9

Step-by-step explanation:

2x + 3y - 2

Putting x=1; y=3

(2x1) + (3x3) - 2

2 + 9 - 2

Now, according to BODMAS, we shall add first.

11 - 2

9

Fast food chains that use plastic or styrofoam containers in selling their products are contributing to the global plastic pollution crisis. Styrofoam and plastic containers, which are not biodegradable, take up to 1000 years to decompose.

Every year, an estimated 8 million metric tons of plastic end up in the ocean, and the majority of it is from single-use plastic products such as those used by fast food chains. This plastic pollution is having a devastating effect on the environment, with marine life ingesting and becoming entangled in the plastic. In addition, the production of styrofoam and plastic containers is highly energy intensive and contributes to the emission of greenhouse gases. This is a problematic situation that needs to be addressed urgently.

The energy intensity of production for styrofoam and plastic containers can be calculated using the formula:

Energy Intensity (EI) = Energy Used (EU) / Output (O)

For example, if it takes 50 kWh of energy to produce a unit of output, the energy intensity of production would be 50 kWh/unit. This highlights the environmental impact of styrofoam and plastic containers, and the urgent need to reduce their use in fast food chains.

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The expression is simplified to y⁹/12x². Option A

The index form of a number is simply described as a number written as an exponential expression.

It is described as a single number  raised to another number.

Index forms are also described as standard forms and scientific notation.

From the information given, we have;

3x^⁻⁴y⁵/(2x³y⁻⁷)⁻²

Now, expand the bracket of the denominator and multiply the values

3x^⁻⁴y⁵/2x⁶y⁻¹⁴

Divide the expression , we have;

3/-4 (x^⁻⁴y⁵/2x⁶y⁻¹⁴)

To determine the quotient, subtract the exponents of the denominator from the numerators

3× -4(x⁻⁴⁺⁶y⁵⁻¹⁴)

Now, add or subtract the exponential values, we get;

-12 (x⁻²y⁻⁹)

y⁹/12x²

Hence, the value is y⁹/12x²

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Answer:512

Step-by-step explanation:

hi, I'm no bot just in case...

the grapgh of the line shows y intercept of -9 and rate of change by 4

SoThe equation of the lline will be: [tex]y=4x-9[/tex]

A partial sum limit is the sum of the series.

A function may get close to two distinct limits. There are two scenarios: one in which the variable approaches its limit by values larger than the limit, and the other by values smaller than the limit.

A partial sum is the total of a limited number of the series' terms. To see how the infinite sum behaves, we can examine a collection of these sums. The index of the final term in the sum is used to denote each of these partial sums.

When a group of numbers, known as addends or summands, are added together in mathematics, the outcome is their sum or total.

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Answer: we would need 7 bags of fertilizer to cover the area of the triangle.

Step-by-step explanation:

To find the area of a triangle, we can use Heron's formula. Heron's formula states that the area of a triangle can be found by taking the square root of the semi-perimeter multiplied by the difference of the semi-perimeter and each side length.

The semi-perimeter of the triangle is (2.1+1.8+2.7)/2 = 2.7

The area of the triangle is sqrt(2.7*(2.7-2.1)(2.7-1.8)(2.7-2.7)) = sqrt(2.70.60.9*0) = 1.35

Each bag of fertilizer covers 0.2 square miles, so we need to divide the area of the triangle by the area covered by each bag to find how many bags are needed: 1.35 / 0.2 = 6.75

Rounding up to the nearest whole number, we would need 7 bags of fertilizer to cover the area of the triangle.

The probability that Marshall wins a prize on his second spin =  0.1875

Consider an event X = the number of spins until Marshall wins a prize.

Given that a prize wheel with 4 segments of equal size, one of which is labeled winner.

So, the sample space n = 4

For given event x, the possible outcomes = 1

Using the formula of probability,

p = x/n

p = 1/4

p = 0.25

So, the probability of success p = 0.25

q = 1 - p

q = 1 - 0.25

q = 0.75

To find the probability that Marshall wins a prize on his 2nd spin.

Using formula, [tex]P(X = k) = (1 - p)^{k-1}p[/tex]

For  k = 2,

[tex]P(X = 2) = (1 - 0.25)^{2-1}\times 0.25[/tex]

P(X = 2) = 0.75 × 0.25

P(X = 2) = 0.1875

Thus, the required probability is  0.1875

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