Sam is moving bags of soil from a loading dock into a storeroom. The topsoil
weighs 40 pounds per bag, and the mulch weighs 20 pounds per bag. The
cart Sam uses to move the bags can only carry up to 480 pounds.
Which graph represents the number of topsoil bags and mulch bags that Sam
can move in a single trip? Graphed

The polynomials that match with other equivalent expressions are :(a) → (iii), (b) → (ii), (c) → (iv), (d) → (i)

Consider the polynomials,

(a) 4x² + 18x                                (i) 2x(2x + 1)

(b) 4x² + 2x + 18x +9                   (ii) (2x + 1)(2x +9)

(c) (2x + 3)(2x + 3)                       (iii) 2x(2x + 9)    

(d) 4x² + 2x                                   (iv) 4x² + 12x + 9

Now,

Consider the polynomial 2x(2x + 1),

2x(2x + 1) = 2x(2x) + 2x(1)

2x(2x + 1) = 4x² + 2

Therefore, (d) is equal to (i).

Consider the polynomial 2x(2x + 9),

2x(2x + 9) = 2x(2x) + 2x(9)

2x(2x + 9) = 4x² + 18x

Therefore, (a) is equal to (iii).

Consider the polynomial (2x + 1)(2x +9) ,

(2x + 1)(2x +9)  = (2x)(2x) + (2x)(9) + (2x)(1) + 9

(2x + 1)(2x +9) = 4x² + 18x + 2x + 9

Therefore, (b) is equal to (ii).

Consider the polynomial (2x + 3)(2x + 3),

(2x + 3)(2x + 3) = (2x)(2x) + (2x)(3) + (3)(2x) + 9

(2x + 3)(2x + 3) = 4x² + 12x + 9

Therefore, (c) is equal to (iv).

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Answer:

vjjvwplast

Step-by-step explanation:

past I 1 days its just is right

The equation expressing the relationship between the amount of sale of statin, x years after 1998, S - 1.3·x = 5.5, indicates that the amount spent on statin in 2018 is $31,500,000,000

An equation expresses the relationship of equivalence between values or variables.

The equation that gives the amount of statin in billions of dollars is presented as follows;

Where;

S = The amount of sale of statin in billions of dollars

x = The number of years after 1998

The amount people in the U.S. will/did spend on statins in 2018 is found as follows;

S  = 1.3·x + 5.5

In 2018, x = 2018 - 1998 = 20

Therefore;

S  = 1.3 × 20 + 5.5 = 31.5

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For given triangles, The correct proportion will be 16/12=18/x.

What is a triangle?

In Geometry, triangles are the type of polygons, which have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is considered a 3-sided polygon. The sum of all the three angles of a triangle is equal to 180°. The triangle is contained in a single plane. Based on its sides and angle measurement, the triangle has six types.

Based on the sides of a triangle, a triangle is classified into 3 types, namely:

Scalene Triangle – All the sides are of different measures.

Isosceles Triangle – Two sides of a triangle are of the same measure and the remaining side has a different measure.

Equilateral Triangle – All the 3 sides of a triangle are of the same measure.

Based on the angles of a triangle, a triangle is classified into 3 types, namely:

Acute Angle Triangle – All the angles of a triangle is less than 90°.

Obtuse Angle Triangle – One of the angles of a triangle is greater than 90°.

Right Angle Triangle – One of the angles of a triangle is equal to 90°.

Now,

For given triangles ABC and DEF

as ABC ≅DEF

Then AB=DE, BC=EF AND AC=DF

given BC=16, EF=12 and DE=18 then AB=?

Let AB=x then

16/12=18/x as ABC ≅DEF

Hence,

          The correct proportion will be 16/12=18/x.

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The square root -6 -9 in complex number notation is √6i - 9

A complex number is a number of the form a + bi, where a and b are real numbers.

Given that, rewrite square root -6 -9 in complex number notation

We know that, the principal square root of a negative number is a positive number times i.

Therefore,

√-6 = √6i

Therefore, the mathematical notation will be

√6i - 9

Hence, the square root -6 -9 in complex number notation is √6i - 9

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Let's call the sales tax rate as t (in decimal form).

The cost of a $10 sweater with the sales tax included is $10 + $10 * t = $10.90.

We can set up an equation to solve for t:

$10 * t = $0.90

Dividing both sides by $10:

t = 0.09

So the sales tax rate is 0.09, which is equivalent to 9%.

The value of x is 30 degrees as it is a complimentary angle. When two angles' measurements add up to 90 degrees, they are said to be complimentary. When two angles' measures sum up to 180 degrees, they are said to be supplementary.

Complementary angles are two angles with a combined angle of 90 degrees, whereas supplementary angles have a combined angle of 180 degrees.

Reflex angles are those that are larger than 180 degrees and less than 360 degrees. So 270 degrees is a reflex angle.

Since it is a right angle triangle,

hence

[tex](2x+1)+29=90\\2x+1=61\\2x=60\\x=30[/tex]

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Rounding to the nearest day, the answer is 37 days.

Interest is a fee charged by a lender to a borrower for the use of money. It is typically a percentage of the amount borrowed and is paid periodically, such as monthly or annually. Interest is calculated based on the principal amount, which is the original sum of money borrowed, and the interest rate, which is the percentage charged for borrowing the money. Interest is a way for lenders to earn income on their investments, and for borrowers to pay for the use of money they do not currently have. There are different types of interest, such as simple interest, which is calculated only on the original principal, and compound interest, which is calculated on both the principal and any accumulated interest.

To find out how long it will take for Don's investment to earn $205 in interest, you can use the formula:

time = (interest earned) / (annual interest rate * balance)

First, you need to convert the interest rate from a percentage to a decimal by dividing it by 100: 5.5% ÷ 100 = 0.055.

Next, you can plug in the values:

time = $205 / (0.055 * $5500)

time = 0.03727272727 years, or approximately 37.2727272727 days.

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Answer:

Below

Step-by-step explanation:

Interval is -1 to 2 = 3 units

value at -1     2(-1)^2 = 2

value at 2      2 (2^2) = 8      

  (8-2) / 3 = 6/3 = 2 /unit   rate of change

Answer:

  (a)  3x +y = 2

Step-by-step explanation:

You want the equation y = -3x +2 written in standard form.

The standard form of a linear equation is ...

  ax +by = c

where a, b, c are mutually prime integers with a ≥ 0. If a=0, then b > 0.

To put the given equation into that form, we can add 3x to both sides:

  3x +y = 3x -3x +2

  3x +y = 2

The probability that the mean of a sample of 36 people is less than 13 is approximately 0.744.

Cumulative probability refers to the sum of probabilities of all possible outcomes that are less than or equal to a specific value. It is used to calculate the probability of observing a value less than or equal to a given value. For example, if we have a cumulative probability distribution function (CDF), we can use it to find the probability that a random variable is less than or equal to a particular value. The cumulative probability is the area under the probability density function (PDF) to the left of the specified value. It provides a complete picture of the distribution of a random variable, and it can also be used to calculate probabilities for ranges of values.

To find the probability that the mean of a sample of 36 people is less than 13, we need to calculate the z-score associated with the value of 13, and then look up the corresponding cumulative probability in a standard normal table.

The z-score is given by:

z = (13 - 12) / (3.2 / √(36)) = 0.625

Using a standard normal table, we can find that the cumulative probability associated with a z-score of 0.625 is approximately 0.744.

So, the probability that the mean of a sample of 36 people is less than 13 is approximately 0.744.

For the second part of the question, the probability that the mean of a sample of 36 people is greater than 13 can be calculated as 1 minus the cumulative probability associated with a z-score of 0.625, which is approximately 1 - 0.744 = 0.256.

For the last part of the question, the probability that the mean of a sample of 36 people is between 11 and 12 can be calculated by subtracting the cumulative probabilities associated with the z-scores corresponding to 11 and 12 from a standard normal table.

z1 = (11 - 12) / (3.2 / √(36)) = -0.938

z2 = (12 - 12) / (3.2 / √(36)) = 0

Using a standard normal table, we find that the cumulative probability associated with z1 = -0.938 is approximately 0.172, and the cumulative probability associated with z2 = 0 is 0.5.

So, the probability that the mean of a sample of 36 people is between 11 and 12 is approximately 0.5 - 0.172 = 0.328.

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Answer:

Andre's fraction of goals made to kicks taken is 4/6 or 2/3.

For Tom to make an equivalent fraction, he needs to make 4 goals out of a larger number of kicks than 6.

Two possible fractions for Tom would be 8/20 or 12/30. These both reduce to 2/5, which is equivalent to Andre's 2/3.

I need a bat a hit ball with this sport.

The word "sport" refers to Baseball game.

Baseball is a team ball game played by two teams, namely the pitcher team and the batter team. The game begins when the pitcher throws the ball to the batter who is called the batter. Baseball is almost the same as softball, but the size of the tools used and the fields are different.

Baseball is included in small ball games and is often included in sports lessons at school. In order to play proper baseball, there are several rules that need to be observed. In addition, the complete protection needs to be met so that players can avoid injury.

Baseball game was first created in Coperstown, New York in 1883 by Abner Doubleday. But the first baseball rules made in 1845 by Alexander J. Cartwright.

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The percent of people that preferred vanilla ice cream is equal to 25%.

In Mathematics, a percentage can be defined as any number that is expressed as a fraction of hundred (100). This ultimately implies that, a percentage indicates the hundredth parts of any given number.

In order to determine the number of people that prefer vanilla ice cream, we would develop an expression to multiply the fraction of the number of people by 100 as follows;

Number of people who prefer vanilla ice cream = 9/36 × 100

Number of people who prefer vanilla ice cream = 0.25 × 100

Number of people who prefer vanilla ice cream = 25%.

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Answer:

It is 35 degrees that is the answer

Answer:

A

Step-by-step explanation:

We need to know that angles in a rhombus add up to 360!

To find m∠JKM we have to divide m∠JML by 2.

This is because opposite angles in a rhombus must be equal meaning that the line going from one end of the rhombus to the other end must be exactly in half!

We are told that m∠JML = 70°...

Have a lovely day :)

Answer:

Step-by-step explanation:

In accordance with the Remainder theorem,  the given part means that the given polynomial has the roots of 1, -2 and 2.

So we write these three equations expressing this fact

   2A*1^4    - B*1^3    - C*1     - 16 = 0

   2A*(-2)^4 - B*(-2)^3 - C*(-2)  - 16 = 0

   2A*2^4    - B*2^3    - C*2     - 16 = 0

or

   2A -  B -  C = 16    (1)

  32A + 8B + 2C = 16    (2)

  32A - 8B - 2C = 16    (3)

Adding equations (2) and (3), you get

  64A           = 32,   which implies  A = 32%2F64 = 0.5.

Then from (1) and (2), substituting A = 0.5 there, you get

    B +  C = -15        (4)

   8B + 2C =   0        (5)

Expressing  B = -15 - C  from (4)  and substituting it to (5), you get

   8*(-15 -C) + 2C = 0,    or

   -120 - 8C +  2C = 0

        - 6C = 120

           C = - 20.

Then from equation (4),  B = -15 - (-20) = -15 + 20 = 5.

ANSWER.  A = 0.5;  B = 5,  C = -20.

We have three factors: (x-1),(x+2) and (x-2)

However, we have a quartic polynomial, since the degree (largest exponent) is 4

So we need a fourth factor. Let's call that x-p, for some real number p.

Let's expand out the following

(x-1)(x+2)(x-2)(x-p)

(x+2)(x-2)(x-1)(x-p)

(x^2-4)(x^2-px-x+p)

x^2(x^2-px-x+p)-4(x^2-px-x+p)

x^4-px^3-x^3+px^2-4x^2+4px+4x-4p

x^4+(-px^3-x^3)+(px^2-4x^2)+(4px+4x)-4p

x^4+(-p-1)x^3+(p-4)x^2+(4p+4)x-4p

Compare that result to 2Ax^4-Bx^3-Cx-16

Match up the corresponding terms, and we have the following equations

2Ax^4 = 1x^4 which leads to 2A = 1 and solves to A = 1/2 = 0.5

(-p-1)x^3 = -Bx^3 which leads -p-1 = -B and solves to B = p+1

(4p+4)x = -Cx which leads to 4p+4 = -C and solves to C = -4p-4

-4p = -16 which solves to p = 4

Use that value of p to find the other coefficients

B = p+1 = 4+1 = 5

C = -4p-4 = -4*4-4 = -20

The polynomial 2Ax^4-Bx^3-Cx-16 turns into x^4-5x^3+24x-16 after we plug in those A,B, and C values.

Answers:

A = 1/2 = 0.5

B = 5

C = -20

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The center of the circle is (13, 2)

The radius of the circle is 9

To find the center and radius of the circle described by the equation:

(x + 13)² + (y + 2)² = 81

We can compare with the standard form of the equation of the circle which is

(x - h)² + (y - k)² = r²

it can be deduced that

-h = 13, h = -13

-k = 2, k = -2

r² = 81, r = 9

This is the equation for a circle with center at (13, 2) and radius 9. So the center of the circle is (13, 2) and the radius is 9.

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Answer:

Center = (-13,-2)
Radius = 9

The domain of the equation is equal to: B. all real numbers.

The range of the equation is equal to y ≥ -4 or {-4, ∞}.

In Mathematics, a domain is the set of all real numbers for which a particular function is defined.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph shown in the image attached below, we can reasonably and logically deduce the following domain and range:

Domain = {-∞, ∞} or all real numbers.

Range = {-4, ∞} or {y|y ≥ -4}.

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The coordinates of point {B} would be (7,3).

Given is the point A(-3,-5) and its midpoint M(2,-1).

We can write as -

2 = (- 3 + x)/2

x - 3 = 4

x = 7

- 1 = (- 5 + y)/2

y - 5 = - 2

y = 3

Therefore, the coordinates of point {B} would be (7,3).

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Answer:

C

Step-by-step explanation:

The correct answer is C. Although Laura knew the creek was full of leeches, she pushed Nelly in anyway. Laura was tired of Nelly's arrogance and bragging.

The number of solutions each equation has are one solution, No solution,  Infinitely many solutions.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Given;

-1/2(12x-2)=-6x-1

1/2 (12x − 4) = 6x - 2

1/2 (12 x − 2) = −6x - 2

Now

-1/2(12x-2)=-6x-1; one solution

1/2 (12x − 4) = 6x - 2; No solution

1/2 (12 x − 2) = −6x - 2; Infinitely many solutions

Therefore, the solutions of the equations will be one solution, No solution,  Infinitely many solutions.

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The equation connecting a and d where a is the first term and d is the common difference​ is; a + d = 0

The formula for the nth term of an arithmetic sequence is expressed as;

aₙ = a + (n - 1)d

where;

a is first term

d is common difference

n is position of term

Thus;

a₈ = a + 7d

a₄ = a + 3d

The 8th term of an A.P is three times the 4th term. Thus;

a + 7d = 3(a + 3d)

a + 7d = 3a + 9d

3a - a = 7d - 9d

2a = -2d

a = -d

a + d = 0

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Answer:

  the direction changes if the coefficient is negative

Step-by-step explanation:

You want an explanation of the way you know the direction of the inequality symbol without solving the inequality.

If you have an inequality of the form ...

  ax < ( )

where the contents of ( ) has no terms containing x, then you know the solution is obtained by dividing both sides by 'a'.

You know that if 'a' is negative, that division will mean the inequality symbol is reversed:

  x > ( )/a . . . . . . . . for a < 0

When making this assessment, you only need to consider the sign of 'a', the coefficient of x. The rest of the inequality is immaterial.

__

Additional comment

Just as the sign of the variable coefficient tells you where the number line shading is relative to the boundary value, so the variable sign(s) can tell you where the shading is for a two-variable inequality.

For example, the inequality ...

  x -3y > 2

has a positive coefficient for x, so the shading will be to the right of the line (where x-values are greater than those on the boundary.)

The coefficient of y is negative, so this can be rewritten as ...

  y < ( )

meaning that shading is below the boundary line (where y-values are less than boundary values).

This inequality will have a boundary line with positive slope such that "right of the line" is the same as "below the line."

Answer:

Five divided by 206 is 0.02426

Answer:

41.2

Step-by-step explanation:

The correct statement about an odd function is:

B) It has line symmetry about the line y = –x.

Here we know that the function f(x) is an odd function, then we know that:

f(x) = -f(-x)

So, if we change the sign of the argument, we also change the sign of the of the output of the function, then there will be symmetry around the line:

y = -x

Then the correct option is B;

It has line symmetry about the line y = –x.

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The slope-intercept equation of the line that includes the points (0, 12) and (4, 36) is y = 6x + 12.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

Next, we would determine the linear equation representing the line which passes through the points (0, 12) and (4, 36) by using the point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 12 = (36 - 12)/(4 - 0)(x - 0)

y - 12 = 6(x - 0)

y = 6x + 12

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Answer: 882

Hope this helps :)

Step-by-step explanation:

Since there is only one other term in the parenthesis, there will only be one step.

Distribute the 9 to 98.

9 * 98 = 882

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{9(98)}\\\mathsf{= 98(9)}\\\mathsf{= 98 + 98 + 98 + 98 + 98 + 98 + 98 + 98 + 98}\\\mathsf{= 196 + 196 + 196 + 196 + 98}\\\mathsf{= 392 + 392 + 98}\\\mathsf{= 784 + 98}\\\mathsf{= 882}\\\\\\\\\huge\text{Therefore your answer should be:}\\\\\huge\boxed{\mathsf{882}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer: its either 6, 8, 2 or 8, 2. I don't know its one of these. bc ill show u how I got these.

Step-by-step explanation:

this could be:

plus,

times,

subtract,

or divide.

The inverse relationship between the two variables is indicated by a negative slope. In this case, the y value falls as the x value rises. As an alternative, we may see that the y value rises as the x value falls.

You can tell if (0,0) is on the line if it crosses the origin. It is known that a line has a slope of m=0.5 if it is perpendicular to the equation y=2x+3. This is the slope's negative reciprocal. Using the provided information, solve for y=0.5x+b to get the answer.

A graph with a negative slope and a left-to-right tilt is produced by a declining linear function.

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The ordered pair that completes the function is (0, 0)

From the question, we have the following parameters that can be used in our computation:

((15,21), (17,26). (21,37), (25,40), (30,45)

Missing pair = 1

Total pairs = 6

For a relation to be a function, the x values must point to different y values

This means that the pair (0, 0) can complete the function

This is so because it does not stop the relation from being a function

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