To make a shade of paint called Jasper green mix 4 quarts of green paint with 2/3 cups of black paint how much green paint should be mixed with 4 cups of black paint to make Jasper green?

a) length = 24 + 2x

   width = 16 + 2x

b) The area of the new garden space = 384 + 48x + 4x².

c) The area of the border can be represented by the polynomial expression 32x+2x².

What is a polynomial expression?

A polynomial expression is a mathematical expression that is a sum of terms, each term consisting of a constant coefficient multiplied by one or more variables raised to a non-negative integer power.

a.) Let x represent the width of the border. The length of the new garden space would be 24 feet + 2x (since the border is added to both the length and width). The width of the new garden space would be 16 feet + 2x (since the border is added to both the length and width).

length = 24 + 2x

width = 16 + 2x

b.) The area of the new garden space can be represented by the trinomial (24+2x)(16+2x) = (24*16) + (48x) + (4x^2)

c.) The area of the border can be represented by the polynomial expression 2x(16+x) = 32x + 2x^2.

Hence,

a) length = 24 + 2x

   width = 16 + 2x

b) The area of the new garden space = 384 + 48x + 4x².

c) The area of the border can be represented by the polynomial expression 32x+2x².

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Pedro had 1744 hits and Ricky had 1469 hits.

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The price one year from now would be $3.10.

The price a year ago would be $2.87.

The equation that models the information is Price in a year = present price x (1 + inflation rate). It represents an exponential growth.

The year I would expect the price of to be $3.50 is 4.02 years.

Inflation is the rate at which the general price levels in an economy increases.

Price in a year = present price x (1 + inflation rate)

Price in a year = 2.98 x (1 + 0.04)

Price in a year = 2.98 x 1.04 = $3.10

Price last year = price this year / (1 + inflation rate)

= 2.98 / 1.04 = $2.87

Year the price would be $3.50 = (IN FV / PV) / r

(IN 3.50 / 2.98) 0.04 = 4.02 years

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Answer:

Step-by-step explanation:

write k for the divisor

write the coefficients of the dividend.

Bring the leading coefficient down.

Multiply the leading coefficient by k.

Add the terms of the second column.

Multiply the result by k.

Repeat steps 5 and 6 for the remaining columns

Answer:

2

Step-by-step explanation:

Say that 1 represents Ai Mi and 2 represents Malika. It could go like 1 2 or 2 1. Because there is only two of them, there isn't any other way that they could stand. Hope this helps!

The fabric that Terry need to make flags for the whole team will be 42 yards.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

In this case, Terry used 14 yards of fabric to make flags for one-third of the drill team and we want to know the fabric that Terry would need to make flags for the whole team.

The fabric that Terry need to make flags for the whole team will be the total yards of fabric divided by the fraction given. This will be:

= 14 ÷ 1/3.

= 14 × 3

= 42 yards

Therefore, 42 yards will be needed for the whole team.

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Answer:

5 and -15

Step-by-step explanation:

5 × -15 is -75.

5 + -15 is -10

The number of scores by the Eagles is 45.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Cowboys scores = x

Eagles scores = y

y = 2x - 7 _____(1)

Now,

x + y = 71 ______(2)

From (1) and (2) we get,

x + 2x - 7 = 71

3x - 7 = 71

3x = 71 + 7

3x = 78

x = 26

Now,

y = 2x - 7

y = 2 x 26 - 7

y = 52 - 7

y = 45

Thus,

The eagles scored 45.

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45.500 square units make up the region between the graph of y=x2-2 and the x-axis between x=0 and x=7.

The area between the graph of y=x^2-2 and the x-axis between x=0 and x=7 is calculated by first finding the area beneath the graph. This can be done by using the formula

A = ∫f(x)dx.

This integral is equal to

A = ∫(x^2-2)dx,

which when solved yields

A = (x^3/3)-2x.

Plugging in the values for x=0 and x=7 yields

A = (343/3)-(14)= 45.500.

To find the area between the graph and the x-axis, we subtract the area beneath the x-axis from the area beneath the graph. The area beneath the x-axis is 0, so the final answer is 45.500.This area is calculated by finding the area beneath the graph and subtracting the area beneath the x-axis.

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Lisa needs 39 cards to sell on Friday to make a profit.

Algebra is a study of mathematical expressions, in which numbers and quantities are represented in formulas and equations by letters and other universal symbols.

Given that,

Lisa makes a profit when sells 140 cards.

Number of cards sold by Lisa from Monday to Thursday are 15, 7, 14, 45.

Total number of cards sold by Lisa from Monday to Friday = 15 + 7 + 14 + 45 = 81

Since, Lisa makes profit after selling 140 cards.

Therefore, Lisa needs to sell cards on Friday = 140 - 81 = 39

Hence, Lisa needs to sell 39 cards to make a profit.

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The equation x = 77 can be found on the line perpendicular to the y-axis that passes through the coordinates (77,88).

The equation of the line passing through the point (2,4) and perpendicular to the line y= 1/3 x+6 is y = 3x - 2.The slope of the line connecting the coordinates (1, 4), (1, 3) is not known.

The graph is shown below, and the line's equation is x = -1.The equation of a line in slope-intercept form is:y = mx + cwhere the slope is m

C is the y-intercept.For the line that passes through the point and is perpendicular to the y-axis (77, 88)The slope is infinite and the equation is of the form x = k because the line is parallel to the y-axis.

Line that is perpendicular to the line has the equation y= 1/3 x+6 through the location (2,4). Line perpendicular to y= 1/3 x+6 has a slope of m = 3.

y - y1 = m is the equation of a line in point-slope form (x- x1)

y= -4 = 3(x-2) (x-2)

y= 3x - 6 +4\sy= 3x -2

Calculate m= -3 -4 /-1- to determine the slope of the line going through the points (1, 4), (1, 3). (1)

M is endless.Undefined is the slope of the line.x = -1 is the line's equation.As a result, x = 77 is the equation of the line parallel to the y-axis passing through the coordinates (77,88).

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Answer: Divide

Step-by-step explanation: (Don't look at this if you are taking a test) :)

Hello! What you do to answer this question is divide 5100 grams by 2.5 grams.  You would do this because you want to divide the weight of all the pennies by the weight of a single penny to find the number of pennies.  This is because number of pennies multiplied by 2.5 grams (weight of a penny) = 5100 grams (weight of all pennies).  You will be able to figure out what the answer is by dividing 5100 by 2.5.  

I will give you an example problem if you need help dividing decimals:

3000/1.5

Move the decimal space over one to get 3000/15

15 √3000

30 divided by 15 is 2

        2

15√3000

15 x 2 = 30

       200

15 √3000

      - 30      bring down two zeroes
__________________

       000
Since there are two extra zeroes that you took, down your answer is 200. Since you already moved the decimal space one space to the right, move it to the right again and you will get 2000.  Your answer for the example problem is 2000.

Looking at the triangles in the figure, the difference in the x coordinates of points Q and R is 10

This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent

Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions

Examining the figure shows that pair of equivalent sides are

ST and QR, UT and SR.

The solution is worked out using sides ST and QR, UT and SR.

ST / QR = UT / SR

5 / QR = 3 / (4 - (-2))

5 / QR = 3 / 6

cross multiplying

3 * QR = 30

QR = 10

hence  QR = 10

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The HL theorem, also known as the Halpern-Lehman theorem, is a theorem in propositional logic which states that, given a set of premises, the conclusion of an argument is logically valid if and only if the premises are consistent and the conclusion follows logically from the premises.

The HL theorem is a fundamental concept in propositional logic which states that a conclusion is logically valid if the premises are consistent and the conclusion follows logically from the premises. The theorem is based on the principle of deduction, which states that if a set of premises is true, then any conclusion drawn from them must also be true. In other words, if the premises are consistent and the conclusion follows logically from them, then the conclusion must be accepted as valid. The HL theorem is important because it helps to determine the validity of an argument, and is thus a useful tool for evaluating logical arguments.

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A logarithmic graph has a curved shape, with its vertical axis increasing exponentially, and its horizontal axis increasing in a logarithmic scale. The graph is useful for plotting data with a wide range of values, as it can be used to compress the data into a smaller range.

A logarithmic graph is a type of graph that is used to represent data with a wide range of values. It has a curved shape, with its vertical axis increasing exponentially and its horizontal axis increasing in a logarithmic scale. This scale compresses the data into a smaller range, which makes it easier to visualize and compare values that span a large range. It is useful for plotting data that grows or decreases exponentially, such as population growth or exponential decay. Logarithmic graphs are also used to graph values that have a very large range, such as the size of galaxies. The graph helps to compress the data into a smaller range, making it easier to visualize and compare values.

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The double integral of 6y * 4x^5 + 1 over the region D = {(x, y) | 0 ≤ x ≤ 1, 0 ≤ y ≤ x^2} is 20/3

A double integral is used to calculate the total amount of a quantity that is distributed over a two-dimensional region. In this case, the quantity being integrated is 6y*4x^5 + 1. To evaluate the integral, we need to integrate with respect to x and y.

The first step is to evaluate the inner integral with respect to y. The limits of integration for y are 0 and x^2.

The second step is to evaluate the outer integral with respect to x. The limits of integration for x are 0 and 1.

Therefore, the double integral of 6y*4x^5 + 1 over the region D = {(x, y) | 0 ≤ x ≤ 1, 0 ≤ y ≤ x^2} is 20/3.

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Randy's error is that he did not arrange the terms of the dividend in descending order of power

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

                 2x²+x+3

x²–2x+1) 2x²-3x³-3x² +7x-3

This means that

Dividend = 2x²-3x³-3x² +7x-3

Divisor = x²–2x+1

Quotient = 2x²+x+3

See that the terms of the dividend are not properly represented

The proper representation is -3x³-3x²+2x² +7x-3

Hence, the mistake is in the order of the dividend terms

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The solution of the system of linear equations are,

1) (2.2, -1.4).

2) (1.33, 1)

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Here, We have to given that;

Two lines, with their corresponding equations are given and we have to find the solution to the system of equations.

The given lines are:

Equation of Line 1 is,

⇒ y = - 7/4x + 5/2

And, This line passes through the points (0, 2.5) and (2.2, -1.4).

Equation of Line 2 is,

⇒ y = 3/4x - 3

And, This line passes through the points (0, -3) , (2.2, -1.4)

By looking at the graph/given data we have to find the solution of these linear equations as;

Remember that the solution of linear equations is an ordered pair, through which both the lines pass i.e. the point at which both the given lines intersect is the solution of the linear equations.

So, From the given data we can see that both the lines pass through one common point, (2.2, -1.4).

Since, both lines pass through this point, this means this is the point of intersection of the lines and hence there solution.

So, The answer to this questions is (2.2, -1.4)

For the second question;

The given equations are:

⇒ y = 1.5x - 1     .. (i)

⇒ y = 1              .. (ii)

Now, We can solve these equations by method of substitution.

So, Substituting the value of y from Equation 2, in Equation 1, we get:

1 = 1.5x - 1

1 + 1 = 1.5x

2 = 1.5x

x = 2/1.5

x = 1.33

And, y = 1

Thus, The solution of the given linear equations is, (1.33, 1)

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By subtracting the sum of the two known angles from 180, we can find the measure of the unknown angle. In this example, the size of angle ABC is 105 degrees.

105 degrees

To find the size of angle ABC, use the formula 180 - (A + B) = C.

A = 30 degrees

B = 45 degrees

Therefore, C = 180 - (30 + 45) = 105 degrees

Therefore, the size of angle ABC is 105 degrees to the nearest degree.

To find the size of angle ABC, use the formula 180 - (A + B) = C. In this case, A = 30 degrees and B = 45 degrees. Therefore, C = 180 - (30 + 45) = 105 degrees. The size of angle ABC is then 105 degrees, rounded to the nearest degree. This can be useful when trying to calculate the measure of an angle in a triangle. Knowing the measure of the other two angles, you can use this formula to find the measure of the third angle. By subtracting the sum of the two known angles from 180, we can find the measure of the unknown angle. In this example, the size of angle ABC is 105 degrees.

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The percentage of temperatures that are below 55° include the following: D. 25%.

In Mathematics, a box plot is sometimes referred to as box-and-whisker plot and it can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.

Based on the box-and-whisker plot (box plot) shown above, the five-number summary for the given data set include the following:

Generally speaking, the first quartile is also referred to as the 25th percentile and it is the value at which 25% of a value in a data set lies below and 75% of the answers lie above in a box plot.

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The general solution will be y(t) = (4c1 + 5c2)*e^((2+sqrt(5))t) + (10c1 + 9c2)*e^((2-sqrt(5))t).

What is differentiate ?

Differentiation is a concept in calculus that involves finding the rate of change of a function with respect to one of its variables. It is represented by the symbol ∂/∂x or ∂/∂y or ∂/∂t (where x, y and t are the variables of the function). The process of differentiation allows us to find the slope of a curve, the instantaneous rate of change, and the maximum or minimum points of a function.

The general solution of the system of differential equations dx/dt = 4x + 5y and dy/dt = 10x + 9y is given by ,

x(t) = c1e^((2+sqrt(5))t) + c2e^((2-sqrt(5))t)

y(t) = (4c1 + 5c2)*e^((2+sqrt(5))t) + (10c1 + 9c2)*e^((2-sqrt(5))t)

Where c1 and c2 are arbitrary constants determined by the initial conditions,

The general solution will be y(t) = (4c1 + 5c2)*e^((2+sqrt(5))t) + (10c1 + 9c2)*e^((2-sqrt(5))t).

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Yes, 'Rounding to the nearest cent means to round off the amount to the hundredths place' is the correct definition for Rounding to Nearest Cent.

Rounding to the nearest cent is a method of rounding an amount to the hundredths place. This means that any decimal value will be rounded up or down depending on the value of the decimal point.

For example, if the value is 0.45, it will be rounded down to 0.00 and if the value is 0.55, it will be rounded up to 1.00. This method of rounding can be used in accounting, finance and other business calculations.

Rounding to the nearest cent is a common practice used to accurately estimate an amount. It involves rounding off the amount to the hundredths place, so if the number is something like 12.356, it would be rounded off to 12.36.

Although a part of your question is missing, you might be referring to this question:

Is Rounding to the nearest cent means to round off the amount to the hundredths place the correct definition of Rounding to Nearest Cent.

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10 candies treats is Kayla still keeping for herself when Kayla had twenty candies. Kayla gave her sister one-fifth of the candies.

Given that,

Kayla had twenty candies. Kayla gave her sister one-fifth of the sweets. She gave her pal 3/8 of the remaining funds.

We have to find how many treats is Kayla still keeping for herself.

We know that,

20 candies are in Kayla's candy collection.

The amount Kayla gave her sister was equal to 1/5 of 20.

= 1/5 ×20

= 4 candies

The number of sweets Kayla has left over after sharing them with her sister = 20-4 = 16 candies

From the leftover candies, the friend received 3/8 of 16 candies.

= 3/8 × 16

= 6 candies

Kayla has 16 candies left after subtracting 6 for herself.

= 10 candies.

Therefore, 10 candies treats is Kayla still keeping for herself when Kayla had twenty sweets. Kayla gave her sister one-fifth of the sweets.

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The property states that when two vectors a and b are multiplied together, the result is equal to the negative of b multiplied by a. This can be shown by multiplying the components of both vectors and then multiplying the result by -1.

a×b = (a2*b3 - a3*b2, a3*b1 - a1*b3, a1*b2 - a2*b1)

= (a2*b3 - a3*b2, a3*b1 - a1*b3, a1*b2 - a2*b1)

= (−1) * (a2*b3 - a3*b2, a3*b1 - a1*b3, a1*b2 - a2*b1)

= (−1) * (b2*a3 - b3*a2, b3*a1 - b1*a3, b1*a2 - b2*a1)

= − b × a.

The property a × b = − b × a states that when two vectors a and b are multiplied, the result is equal to the negative of b multiplied by a. This can be proven by first expanding the components of both vectors. For a vector a=(a1,a2,a3) and b=(b1,b2,b3), the expanded form of a×b is (a2*b3 - a3*b2, a3*b1 - a1*b3, a1*b2 - a2*b1). This can then be multiplied by -1 to get the expanded form of -b×a, which is (b2*a3 - b3*a2, b3*a1 - b1*a3, b1*a2 - b2*a1). Since this is equal to the original form of a×b, this proves the property.

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A graph of each function is shown in the image attached below.

The number of weeks after which Valeria and Jackson would have the same amount of money is 5 weeks.

In order to graphically solve the equation, we would write an equation that models the situation by assigning variables to the amount of money Valeria and Jackson have saved respectively, and then translate the word problem into algebraic equation as follows:

Since Valeria had $20 in savings and saved an additional $15 each week at the beginning of the year, an equation which models this situation is given by;

T = 15V + 20

Since Jackson had $70 in savings and saved an additional $5 each week at the beginning of the year, an equation which models this situation is given by;

T = 5J + 70

Next, we would use an online graphing calculator to plot the above system of equations with a point of intersection at (5, 95) as shown in the image attached below.

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The expression that can be used to determine the amount of money that will be in the account after 4 years is 600 + (600 × 2.4% × 4).

An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. in this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.

In this case, Emily was given $600 for her high school graduation. She invested it in an account that earns 2.4% interest per year

The expression to find the amount of money will be:

600 + (600 × 2.4% × 4)

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The total surface area of the hemisphere is 235.71cm²

A hemisphere is simply called half of a sphere.  A sphere is an object that is purely round in shape

The given parameters that will help to calculate to total surface area of the hemisphere are

Diameter =2r,  This implies that r=10/2 = 5

taking the r as the radius = 5 then

The total surface area of the hemisphere is given by

Total surface area = 3пr²

Total surface area = (3*22*5*5)/7

TSA =1650/7

Therefore the total surface area = 235.71 cm²

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ΔQRS, r = 10.32 cm.

Solved by using the concept of triangle.

Three straight sides and three angles make up a triangle, a two-dimensional form. Three vertices, three angles, and three sides define a triangle. In a triangle, the lengths of its two longest sides are always bigger than its third side's length.

A triangle seems to be a three-sided polygon with three vertices. There is a 180-degree angle created inside the triangle. In other words, a triangle's internal angles add up to 180 degrees.

Triangles can be categorized into one of three groups, namely Scalene, Isosceles, or Equilateral, depending on how long their sides are.

In ΔQRS,

given that,

s = 4.2 cm

∠R = 160°

∠S = 8°

From, ΔQRS

As we know,

r / sin A = s / sin B

∠Q = 180° - 160° - 8°

∠Q = 12°

now, putting the values we get -

r = 10.32 cm

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Change in Paula's elevation/altitude per minute is 8.4m.

There are numerous variations of altitude.

Now,

Given Change in Paula's elevation in 4.5 minutes=-37 4/5 m or -189/5m

- shows decrease in elevation.

so, for change in one minute = 189/5*4.5=189/22.5=8.4m

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