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The simplified standard form of (3.05 x 10⁻⁷) (8.67 x 10⁴) is 2.642 x 10⁻¹.

To simplify (3.05 x 10⁻⁷) (8.67 x 10⁴) and leave the answer in standard form to 3 decimal places:

1: Multiply the decimal numbers:
3.05 * 8.67 = 26.4245

2: Add the exponents:
-7 + 4 = -3

3: Combine the result and exponent in standard form:
26.4245 x 10⁻³

4: Adjust the decimal to have only one non-zero digit to the left of the decimal point and adjust the exponent accordingly:
2.64245 x 10² x 10⁻³

5: Simplify by combining exponents:
2.64245 x 10⁻¹

6: Round to 3 decimal places:
2.642 x 10⁻¹

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The area of one garden using each side of the lounging area is 15 feet long is equal to 56.25 square feet.

Shape of the garden landscape is square.

If the lounging area is a square with sides of length 15 feet,

Area of lounging area

= (15 feet) × (15 feet)

= 225 square feet

Four congruent sections of the landscape plan .

Three indoor gardens and one walkway.

Divide the lounging area into four equal square sections.

Each of the congruent sections has an area equal to,

Area of lounging area = 4 × area of one garden

Let's call the area of one garden be x.

⇒225 = 4x

Solving for x, we divide both sides by 4

⇒x = 225/4

⇒x  = 56.25 square feet

Therefore, the area of one garden is 56.25 square feet.

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the wire has uniform density, the center of gravity is located at the centroid of the quarter-circle, which is (4/3, 4/3).

The center of gravity (x¯,y¯) of the wire lies on the line of symmetry, which passes through the origin and the centroid of the quarter-circle.

The centroid of a quarter-circle with radius 6 is located at (4/3, 4/3) from the origin (as derived using calculus). Thus, the line of symmetry passes through the origin and (4/3, 4/3).

The equation of the line passing through two points (x1, y1) and (x2, y2) is given by:

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

Substituting (x1, y1) = (0, 0) and (x2, y2) = (4/3, 4/3), we get:

(y - 0) / (x - 0) = (4/3 - 0) / (4/3 - 0)

Simplifying, we get:

y = x

Therefore, the center of gravity (x¯,y¯) is located on the line y = x.

Since the wire has uniform density, the center of gravity is located at the centroid of the quarter-circle, which is (4/3, 4/3).

Hence, x¯=y¯=4/3.

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Using the compound interest formula, the amount in Russ' account after 4 years is $ 12588.15

To find how much will be in Russ' account after 4 years, we use the compound interest formula.

A = P(1 + r)ⁿ where

Given that

So, substituting the values of the variables into the equation, we have that

A = P(1 + r)ⁿ

A = $8000(1 + 0.12)⁴

A = $8000(1.12)⁴

A= $8000(1.5735)

A= $ 12588.15

So, the amount is $ 12588.15

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The decimal fraction 3.003 can be expressed as the sum of fractions 3,003/1,000.

To express the decimal fraction 3,003 as a sum of fractions with a denominator that is a power of 10, we first need to determine the number of decimal places in the fraction. In this case, there are three decimal places, so we can write:

3,003 = 3 + 0.0 0 3

To express 0.003 as a fraction, we can write it as:

0.003 = 3/1000

So, we can write:

3,003 = 3 + 3/1000

To express this as a fraction with a denominator that is a power of 10, we can write:

3,003 = 3,000/1,000 + 3/1,000

Simplifying this expression, we get:

3,003 = 3,000/1,000 + 3/1,000 = (3,000 + 3)/1,000 = 3,003/1,000

Therefore, the decimal fraction 3,003 can be expressed as a sum of fractions with a denominator that is a power of 10 as 3,003/1,000.

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Answer:

Step-by-step explanation:

To find when the ball reaches its maximum height, we need to find the vertex of the quadratic function h(t) = 76t - 16t^2.

The vertex of a quadratic function of the form y = ax^2 + bx + c is at the point (-b/2a, f(-b/2a)), where f(x) = ax^2 + bx + c.

In this case, a = -16 and b = 76, so the time at which the ball reaches its maximum height is given by:

t = -b/2a = -76/(2*(-16)) = 2.375

Rounded to the nearest hundredth, the ball reaches its maximum height after 2.38 seconds (Option D).

The exact cost of the 100th pair of jeans. The approximate cost of the 101st pair of jeans. The approximate cost of the 100th pair of jeans. The exact cost of the 101st pair of jeans The exact cost of the 99th pair of jeans.

The marginal cost function of  C(x) = 2300 + 5x + 0.01x2 + 0.0002x is $3100

Process of finding marginal cost:

(a) To find the marginal cost function, we need to take the derivative of the cost function C(x) with respect to x. This gives us:

C'(x) = 5 + 0.02x + 0.0006x^2

So the marginal cost function is:

MC(x) = 5 + 0.02x + 0.0006x^2

(b) To find C'(100), we simply plug in x = 100 into the marginal cost function we just found:

C'(100) = 5 + 0.02(100) + 0.0006(100)^2 = 11

This predicts the exact cost of manufacturing the 101st pair of jeans.

The approximate cost of the 101st pair of jeans can be found by plugging in x = 101 into the original cost function C(x):

C(101) = 2300 + 5(101) + 0.01(101)^2 + 0.0002(101) ≈ $3120.02

The approximate cost of the 101st pair of jeans.

The exact cost of the 100th pair of jeans can be found by plugging in x = 100 into the original cost function C(x):

C(100) = 2300 + 5(100) + 0.01(100)^2 + 0.0002(100) = $3100

Hence the marginal cost is $3100

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The value of x is 5/3.

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator.

We have equation in fraction are:

[tex]\frac{3x-2}{3x+1} = \frac{1}{2}[/tex]

To solve the value of x

In the above equation, Solve by cross multiplication:

2(3x - 2) = 3x + 1

Open the bracket and multiply by 2 :

6x - 4 = 3x +1

Combine the like terms:

6x - 3x = 1 + 4

Add and subtract the terms:

3x = 5

x = 5/3

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The score that marks the 11% of all scores is approximately 56.875 .

To find the score that marks the 11% of all scores, we need to use the standard normal distribution table, also known as the Z-table, since the given distribution is a normal distribution.

The first step is to find the Z-score that corresponds to the 11th percentile, which is given by: Z = invNorm(0.11) ≈ -1.225

Here, "invNorm" represents the inverse of the standard normal cumulative distribution function, which can be computed using statistical software or a calculator.

The second step is to use the Z-score formula to find the raw score that corresponds to this Z-score:Z = (X - μ) / σ

where X is the raw score we want to find, μ is the mean of the distribution, and σ is the standard deviation. Plugging in the values we have:

-1.225 = (X - 63) / 5

Solving for X, we get:

X = -1.225 * 5 + 63 = 56.875

Therefore, the score that marks the 11% of all scores is approximately 56.875

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Answer:

y=f(x) = log7x

Just trust me

The graph best represents the function y = f(x) = 7x, an exponential function.

The graph represents the function y = 7x, which is an exponential function. In an exponential function, the variable x is the base, and the exponent is a constant, which in this case is 7. This means that the function grows rapidly as x increases, creating a steep curve on the graph.

The other two options, y = f(x) = log7x and y = f(x) = x7, are not represented by the given graph.

The function y = f(x) = log7x is a logarithmic function, which has a different shape on the graph, with a horizontal asymptote and the x-axis acting as its asymptote.

The function y = f(x) = x7 is a polynomial function, where x is raised to the power of 7, and it would have a different pattern on the graph compared to the exponential function shown.

Thus, the graph best represents the function y = f(x) = 7x, an exponential function.

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There is no solution to the given system of equations and the lines are parallel which has been obtained by using the substitution method.

What is the substitution method?

When solving simultaneous linear equations in algebra, the substitution approach is a common technique. As the name of the procedure suggests, one variable's value from one equation is switched in the second equation.

We are given equations as -2x + 2y = 7 and -x + y = 4.

Now, using the second equation, we get

⇒ -x + y = 4

⇒ y = 4 + x

Now, on substituting this in the first equation, we get

⇒ -2x + 2y = 7

⇒ -2x + 2 (4 + x) = 7

⇒ -2x + 8 + 2x = 7

⇒ 8 ≠ 7

So, there is no solution to the given system.

This means that the two lines in the system are parallel which means they will never meet.

A graph depicting the same has been attached below.

Hence, there is no solution to the given system.

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The integer that represents a credit of $30 if zero represents the original balance is +30.

A credit represents an increase in funds, while a debit represents a decrease. In this case, a credit of $30 means that $30 has been added to the account, increasing the balance. Since zero represents the original balance, adding $30 results in a positive balance of $30, which is represented by the integer +30.

Therefore, +30 represents a credit of $30 if the original balance is zero. The reasoning behind this is that a credit increases the balance, so a positive integer is used to indicate the amount by which the balance has increased. In this case, it is an increase of $30, hence +30.

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The wood flooring for the floor will cost $14,175.

To calculate the cost of replacing the wooden floor at Greg's gym, we first need to find the area of the rectangular floor. The area of a rectangle can be found using the formula: area = length × width. In this case, the length is 45 feet and the width is 35 feet.

Area = 45 feet × 35 feet = 1575 square feet

Since the cost of wood flooring is $9 per square foot, we can now calculate the total cost:

Total cost = area × cost per square foot = 1575 square feet × $9/square foot = $14,175

So, the wood flooring will cost Greg $14,175 to replace the floor at his gym.

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Answer:

V=3456, SA= 1008

Step-by-step explanation:

V=b*h*L (Formula)

8*18*24=3456 (sub, alg)

SA=30*8+24*18+24*8+8*18=54*8+32*18=1008 (Formula; sub, alg)

Answer:

To find the number of smaller pieces that can be obtained, we need to divide the total length of the wood by the length of each smaller piece:

Number of pieces = Total length ÷ Length of each piece

Number of pieces = 7.2 m ÷ 0.12 m

Number of pieces = 60

Therefore, 60 smaller pieces can be obtained from the 7.2 m long piece of wood.

Answer:

60

Step-by-step explanation:

To determine how many smaller pieces can be obtained from a 7.2 m long piece of wood, we need to divide the total length of the wood by the length of each smaller piece.

Total length of wood = 7.2 m

Length of each smaller piece = 0.12 m

Number of smaller pieces = Total length of wood / Length of each smaller piece

Number of smaller pieces = 7.2 m / 0.12 m

Number of smaller pieces = 60

Therefore, 60 smaller pieces can be obtained from a 7.2 m long piece of wood, with each smaller piece being 0.12 m in length.

When we convert the given 54 square feet into square yards we get 6 square yards by using two unit multipliers to convert.

A fraction that equals 1 and is used to convert one set of units to another one is a unit multiplier. The fraction numerator and denominator contain equivalent measurements in different units.

We need to convert the 54 square feet to square yards by using two unit multipliers. by using the two-unit multipliers

given standards :

1 yard = 3 feet

1 square yard = 9 square feet

To convert the 54 square feet to square yards we need to multiply 54 square feet by two unit multipliers which are (1 yard / 3 feet) and (1 yard / 3 feet). Then the equation can be written as:

= 54 square feet × (1 yard / 3 feet) × (1 yard / 3 feet)

= 6 square yards

Therefore, 54 square feet is equal to 6 square yards.

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To find dx dy, we need to take the derivative of y with respect to x. Using the chain rule, we have:

dy/dx = d(Vx)/dx = V * d(x)/dx + x * d(V)/dx

Since we are given y = Vx, we can substitute and simplify:

dy/dx = y/x * d(V)/dx + V

Now we can plug in the given values: y = 8, dt/dx = 1.75. We also need to find V:

y = Vx, so V = y/x = 8/x

Now we can substitute and simplify again:

dy/dx = 8/x * d(V)/dx + 8/x

We need to find d(V)/dx. We know that t = f(x,V), so we can use the chain rule again:

dt/dx = df/dx + df/dV * dV/dx

Since t and V are independent, df/dV = 0. So we have:

dt/dx = df/dx + 0 * dV/dx

dt/dx = df/dx

We also know that dt/dx = 1.75. Therefore:

1.75 = df/dx

Now we can find d(V)/dx:

d(V)/dx = d/dx (y/x) = (dy/dx * x - y * dx/dx) / x^2

Since y = 8, we have:

d(V)/dx = (dy/dx * x - 8) / x^2

Substituting what we know, we get:

d(V)/dx = (8/x * 1.75 - 8) / x^2 = 8(1.75 - x) / x^3

Now we can substitute everything into the formula we derived earlier:

dy/dx = 8/x * d(V)/dx + 8/x

dy/dx = 8/x * (8(1.75 - x) / x^3) + 8/x

Simplifying, we get:

dy/dx = 14/x^2 - 1.75

Therefore, when y = 8 and dt/dx = 1.75, dx/dy = 1/(dy/dx) is:

dx/dy = 1 / (14/x^2 - 1.75) = x^2 / (14 - 1.75x^2)
Given y = √x, we first need to find dy/dx, the derivative of y with respect to x. Using the power rule, we can rewrite y = x^(1/2), and the derivative will be:

dy/dx = (1/2)x^(-1/2)

Now, we are given that y = 8, so we need to find the corresponding value of x:

8 = √x
64 = x

Next, we are given dt/dx = 1.75. We need to find dt/dy, which can be calculated by taking the reciprocal of dy/dx:

dt/dy = 1 / (dy/dx)

Now, we substitute x = 64 into the derivative:

dy/dx = (1/2)(64)^(-1/2) = (1/2)(8)^(-1) = 1/16

Finally, we can find dt/dy by taking the reciprocal of dy/dx:

dt/dy = 1 / (1/16) = 16

So, the value of dt/dy when y = 8 and dt/dx = 1.75 is 16.

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Answer:

x>3

Step-by-step explanation:

i assume you're solving for x so,

1) rearrange terms,

5x+4>19

2)subtract 4 from both sides

5x+4-4>19-4

3) Simplify

5x>15

4) divide both sides by 5, because they are same factor

\frac{5x}{5} > \frac{15}{5}

5) Finally, the answer is

x>3

The loan future value is $7726.73.

To find the loan future value, we need to calculate the total amount that Robert will owe at the end of the 2-year loan term, including both the principal (initial loan amount) and the interest.

To begin, we can use the formula for calculating compound interest:

[tex]A = P(1 + r/n)^{(nt)[/tex]

where A is the final amount, P is the principal, r is the interest rate, n is the number of times the interest is compounded per year, and t is the time in years.

In this case, we know that the principal is $7200, the interest rate is 4.3% (or 0.043 as a decimal), the loan term is 2 years, and the interest is compounded once per year (n = 1).

Substituting these values into the formula, we get:

A = 7200(1 + 0.043/1)²

A = 7200(1.043)²

A = 7726.73

Therefore, the loan future value is $7726.73. This means that at the end of the 2-year loan term, Robert will owe a total of $7726.73, which includes the original $7200 loan amount and $526.73 in interest.

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The total surface area of the television is 21,584 square centimeters.

To find the total surface area of the television, we need to calculate the area of all six sides and add them up.

The front and back sides have the same dimensions and area, so we can find the area of one and multiply it by two. The same goes for the left and right sides.

The area of the front/back sides is:

120 cm x 68 cm = 8160 sq cm

Multiplying by 2 gives us the total area of both front/back sides:

2 x 8160 sq cm = 16,320 sq cm

The area of the left/right sides is:

68 cm x 14 cm = 952 sq cm

Multiplying by 2 gives us the total area of both left/right sides:

2 x 952 sq cm = 1904 sq cm

The area of the top and bottom sides is:

120 cm x 14 cm = 1680 sq cm

Multiplying by 2 gives us the total area of both top/bottom sides:

2 x 1680 sq cm = 3360 sq cm

Adding up all six sides, we get:

16,320 sq cm + 1904 sq cm + 3360 sq cm = 21,584 sq cm

Therefore, the total surface area of the television is 21,584 square centimeters.

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To find the equation of the plane that passes through the point (0, 9, 0) and is perpendicular to the vector n = -2i ÷ 4k, we first need to find the normal vector of the plane.

Since the plane is perpendicular to the given vector, the normal vector will be parallel to it. So, we can take the given vector and multiply it by -1 to get a vector in the opposite direction, which will be normal to the plane.

n = -2i ÷ 4k = -1/2i ÷ k

Multiplying by -1 gives us:

n = 1/2i ÷ k

Now we can use the point-normal form of the equation of a plane:

r · n = d

where r is the position vector of any point on the plane, n is the normal vector, and d is the distance of the plane from the origin (since the normal vector is normalized, d will be the signed distance of the plane from the origin).

Substituting the given point (0, 9, 0) and the normal vector n = 1/2i ÷ k into the equation, we get:

(0, 9, 0) · (1/2i ÷ k) = d

0 + 9(1/2) + 0 = d

d = 4.5

So the equation of the plane is:

x/2 + z/2 = 4.5

or, multiplying by 2 to eliminate fractions:

x + z = 9

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A function of x that performs the operations  y = f(x) = 6x^9 + 4, the inverse to the function found in part (a). x = g (y) =  ((y - 4) / 6)^(1/9)

The function that performs the operations of raising x to the ninth power, multiplying by 6, and adding 4 is

f(x) = 6x^9 + 4

To find the inverse function, we need to solve for x in terms of y

y = 6x^9 + 4

Subtract 4 from both sides

y - 4 = 6x^9

Divide both sides by 6

(x^9) = (y - 4) / 6

Take the ninth root of both sides

x = ((y - 4) / 6)^(1/9)

Therefore, the inverse function is

g(y) = ((y - 4) / 6)^(1/9)

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Answer:

  46 inches

Step-by-step explanation:

You want the perimeter of ABCD, where AB and BC are tangent to circle D, and AB = 15 inches, BD = 17 inches.

The attachment shows the figure. Radii DA and DC are perpendicular to the tangens, so each triangle is a right triangle. The hypotenuse BD is given as 17 inches, and the leg AB is given as 15 inches. The other leg is found from the Pythagorean theorem (or from your knowledge of Pythagorean triples). It is ...

  AD = √(DB² -AB²)

  AD = √(17² -15²) = √(289 -225) = √64

  AD = 8

The perimeter is the sum of side lengths. The kite shape is symmetrical, so the perimeter is ...

  P = 2(AD +AB) = 2(8 +15) = 46 . . . . inches

The perimeter of ABCD is 46 inches.

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Kaden will earn $729.38 in interest in 30 months.

First, we need to calculate the annual interest rate equivalent to 2.5% for 1 year:

[tex]1 + r = (1 + 0.025)^1[/tex]

1 + r = 1.025

r = 0.025

So, Kaden's account earns 0.025 or 2.5% interest per year.

Next, we can calculate the amount of interest Kaden will earn in 30 months, which is 2.5 years:

n = 2.5 (number of years)

P = $5,000 (principal)

r = 0.025 (annual interest rate)

We can use the compound interest formula to calculate the final amount A:

[tex]A = P(1 + r)^n[/tex]

[tex]A = 5000(1 + 0.025)^2^.^5[/tex]

A = $5,729.38

The interest earned is the difference between the final amount and the principal:

Interest = A - P

Interest = $5,729.38 - $5,000

Interest = $729.38

Therefore, Kaden will earn $729.38 in interest in 30 months.

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Answer:

2[tex]\sqrt{17}[/tex]

Step-by-step explanation:

Use the distance formula to determine the distance between the two points.

Distance = [tex]\sqrt{(7-(-1))^{2} + (4-2)^{2} }[/tex]

Simplify, and you will get the answer

2[tex]\sqrt{17}[/tex]

To convert to polar coordinates, we need to express x and y in terms of r and θ. We have:

x = r cos θ

y = r sin θ

Also, we need to change the limits of integration. The region of integration is the circle centered at the origin with radius 8, so we have:

-π/2 ≤ θ ≤ π/2 (for the upper half of the circle)

0 ≤ r ≤ 8

Now we can express the integrand in terms of r and θ:

[tex]x^2 + y^2 = r^2[/tex] (by Pythagoras)

[tex]20(x^2 + y^2) = 20r^2[/tex]

So the integral becomes:

∫-π/2π/2∫[tex]08r^3 cos^2 θ sin θ dr dθ[/tex]

We can simplify cos^2 θ sin θ using the identity cos^2 θ sin θ = (1/3)sin^3 θ, so we get:

∫-π/2π/2∫[tex]08r^3 (1/3)sin^3 θ dr dθ[/tex]

The integral with respect to r is easy to evaluate:

∫0^8r^3 dr = (1/4)8^4 = 2048

The integral with respect to θ is also easy to evaluate using the fact that sin^3 θ is an odd function:

∫-π/2π/2(1/3)[tex]sin^3[/tex] θ dθ = 0

Therefore, the value of the iterated integral is:

2048(0) = 0

The volume of the solid is zero. This makes sense because the integrand is an odd function of y (or sin θ) and the region of integration is symmetric with respect to the x-axis.

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The probability of spinning fewer than four nines is 1,626,101,367 / 1073741824, which simplifies to approximately 1.514%.

To find the probability of spinning fewer than four nines, we need to first calculate the total number of possible outcomes. The spinner can land on any of the eight sections on the board, and it is spun 10 times. So, the total number of possible outcomes is 8^10, which is 1073741824.

Next, we need to calculate the number of outcomes where fewer than four nines are spun. We can do this by finding the number of outcomes with 0, 1, 2, or 3 nines, and adding them up.

To find the number of outcomes with 0 nines, we need to find the number of ways to choose from the non-nine sections on the board. There are 5 non-nine sections, and we need to choose 10 of them. This is a combination problem, and the number of outcomes is 252.

To find the number of outcomes with 1, 2, or 3 nines, we need to use a similar approach. We can use combinations to find the number of ways to choose the nines and the non-nines, and then multiply them together. The number of outcomes with 1 nine is 9 x 5^9, with 2 nines is 9 x 9 x 5^8, and with 3 nines is 9 x 9 x 9 x 5^7.

Adding up all these outcomes, we get 252 + 9 x 5^9 + 9 x 9 x 5^8 + 9 x 9 x 9 x 5^7 = 1,626,101,367.

So, the probability of spinning fewer than four nines is 1,626,101,367 / 1073741824, which simplifies to approximately 1.514%.

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The unit price for a child ticket is $2.50 and the unit price for an adult ticket is $3.

To find the unit price for a child ticket and an adult ticket, we can set up a system of equations based on the given information. Let x be the unit price for a child ticket and y be the unit price for an adult ticket.

From the first sentence, we know that:

4x + y = 13 ...(1)

From the second sentence, we know that:

3y + 2x = 14 ...(2)

Now we have a system of equations with two variables, which we can solve using either substitution or elimination method. For simplicity, we will use the elimination method.

Multiplying equation (1) by 3, we get:

12x + 3y = 39 ...(3)

Subtracting equation (2) from equation (3), we get:

10x = 25

x = 2.50

Substituting x = 2.50 into equation (1), we get:

4(2.50) + y = 13

y = 3

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The trinomial can now be represented by the square of the binomial (0.123 + 10c)²

To insert a monomial so that the trinomial may be represented by the square of a binomial, consider the trinomial 0.0152 + ... + 100c².

1: Identify the square root of the first and last terms, which are √0.0152 and √100c². The square roots are 0.123 and 10c, respectively.

2: Determine the middle term by multiplying the square roots together and doubling the result. (0.123)(10c)(2) = 2.46c.

3: Insert the middle term into the trinomial, forming the complete trinomial: 0.0152 + 2.46c + 100c².

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Answer: To solve for x in the equation X/y=z-8, we need to isolate x on one side of the equation.

Multiplying both sides by y, we get:

X = y(z-8)

Therefore, the solution for x is:

X = y(z-8)

Step-by-step explanation: