slove for the equation for x 3x + 12 = 36

If Naya is filling up the gas tank in her motorcycle she puts 4.145 gallons of gas in the tank if the gas cost $2.57 per gallon then she spend $10.65

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given,

The cost of one gallon of gas =$2.57

The quantity of gas she puts in the tank = 4.145 gallons

Apply unitary method

Then, the cost of 4.145 gallons of gas = Cost of one gallon of the gas × Quantity of gas

The cost of 4.145 gallons of gas= 2.57×4.145= $10.65

Hence, If Naya is filling up the gas tank in her motorcycle she puts 4.145 gallons of gas in the tank if the gas cost $2.57 per gallon then she spend  $10.65

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Answer:

3/2

Step-by-step explanation:

Answer: Natasha is 17 and Ravi is 25

Step-by-step explanation:

Let n = Natasha’s age and r = Ravi’s age

We can write an equation then substitute: 42=n+r

We know that Ravi is 8 years older than Natasha, so Ravi’s age is equal to n+8. We can substitute that in, so 42= n+(n+8)

Simplify:

42=n+(n+8)

42= 2n+8

42-8=2n+8-8 (subtract 8 from both sides to isolate n)

34=2n

34/2=2n/2 (divide both sides by two)

17=n

Natasha is 17, and Ravi is 8 years older. 17+8= 25, Ravi is 25. You can double check by adding 25 and 17 together, which brings you back to 42 :]

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\((4y - 4) + 3y = 52\)

\(4y - 4 + 3y = 52\)

Collect like terms

\(7y - 4 = 52\)

Add sides 4

\(7y - 4 + 4 = 52 + 4\)

\(7y = 56\)

Divide sides by 7

\( \frac{7y}{7} = \frac{56}{7} \\ \)

\(y = 8\)

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Thus ;

\(Angle \: \: W = 4y - 4\)

\(Angle \: \: W =4(8) - 4 \)

\(Angle \: \: W = 32 - 4\)

\(Angle \: \: W =28 °\)

_________________________________

\(Angle \: \: X = 3y\)

\(Angle \: \: X = 3(8)\)

\(Angle \: \: X = 24°\)

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\(f(x) = 4tan(8\pi) + 4sec^2(8\pi)(x - 8\pi) + 8sec^2(8\pi)tan(8\pi)(x - 8\pi)^2/2!\)

This expression represents the first three nonzero terms of the Taylor series expansion for f(x) = 4tan(x) centered at c = 8π.

What is the trigonometric ratio?

the trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others.

To find the first three nonzero terms of the Taylor series for the function f(x) = 4tan(x) centered at c = 8π, we can use the definition of the Taylor series expansion.

The general formula for the Taylor series expansion of a function f(x) centered at c is:

\(f(x) = f(c) + f'(c)(x - c)/1! + f''(c)(x - c)^2/2! + f'''(c)(x - c)^3/3! + ...\)

Let's begin by calculating the first three nonzero terms for the given function.

Step 1: Evaluate f(c):

f(8π) = 4tan(8π)

Step 2: Calculate f'(x):

f'(x) = d/dx(4tan(x))

= 4sec²(x)

Step 3: Evaluate f'(c):

f'(8π) = 4sec²(8π)

Step 4: Calculate f''(x):

f''(x) = d/dx(4sec²(x))

= 8sec²(x)tan(x)

Step 5: Evaluate f''(c):

f''(8π) = 8sec²(8π)tan(8π)

Step 6: Calculate f'''(x):

f'''(x) = d/dx(8sec²(x)tan(x))

= 8sec⁴(x) + 16sec²(x)tan²(x)

Step 7: Evaluate f'''(c):

f'''(8π) = 8sec⁴(8π) + 16sec²(8π)tan²(8π)

Now we can write the first three nonzero terms of the Taylor series expansion for f(x) centered at c = 8π:

f(x) ≈ f(8π) + f'(8π)(x - 8π)/1! + f''(8π)(x - 8π)²/2!

Simplifying further,

Hence, \(f(x) = 4tan(8\pi) + 4sec^2(8\pi)(x - 8\pi) + 8sec^2(8\pi)tan(8\pi)(x - 8\pi)^2/2!\)

This expression represents the first three nonzero terms of the Taylor series expansion for f(x) = 4tan(x) centered at c = 8π.

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Answer:

C

Step-by-step explanation:

(D) R’(3, 3), S’(9, 24), and T’(15, 3) set of points represents a dilation from the origin of triangle RST respectively.

Dilation means changing the size of an object without changing its shape.

The size of the object can be increased or decreased based on the scaling factor.

In mathematics, a dilation is a function f from a metric space M to itself that satisfies the identity d = rd for every point x,y \ in M.

Where d is the distance from x to y and r is a positive real number. In Euclidean space, such extensions are spatial similarities.

So, stretching from the origin is the same as multiplying all coordinates by a number.

Only D satisfies this. We know that we multiply all the coordinates by 3 to create this set of points.

Therefore, (D) R’(3, 3), S’(9, 24), and T’(15, 3) set of points represents a dilation from the origin of triangle RST respectively.

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Complete question:

Triangle RST has the coordinates R(1, 1), S(3, 8), and T(5, 1). Which of the following sets of points represents a dilation from the origin of triangle RST?

A. R’(3, 1), S’(3, 24), T’(15, 1)

B. R’(4, 4), S’(6, 11), T’(8, 4)

C. R’(3, 1), S’(9, 8), T’(15, 1)

D. R’(3, 3), S’(9, 24), T’(15, 3)

Answer:

Answer is D.

\(y=9(\frac{1}{3} )^x\\ y=9(\frac{1}{3} )^2\\\\y=1\\\\\)

Step-by-step explanation:

The interpretation is that 18% of the variation in the dependent variable can be explained by the variation in the independent variable.

Coefficient of determination R²

The percentage of variance in the dependent variable that is explained by the independent variable is shown by the coefficient of determination.  R² value is always in the range between 0 and 1. As opposed to 1, which shows that the independent variable fully explains the variation in the dependent variable, 0 means that the independent variable is utterly ineffective at predicting the variance in the dependent variable. It is stated as a percentage.

Interpretation of

R²=0.18

Since

R² is expressed in percentage terms,

R²=0.18

=18/100

=18%

Accordingly, the variation in the independent variable can account for 18% of the variation in the dependent variable. 82% of the variance is unaccounted for and cannot be attributed to the independent variable.

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The full question would be

How do you interpret a coefficient of determination, r 2, equal to 0.18 A? The interpretation is

Answer:

Step-by-step explanation:

The motorist drove at a distance of 90km at a constant speed for the first 40km, and then 20 km/hr faster for the rest of the journey.

The whole journey took him 1hr.

Let S denotes the average speed (in km/hr) for the first 40 km.

Hence we get the following relation,

40/S + (90 - 40)/(S + 20) = 1

or 50/(S + 20) = 1 - 40/S = (S - 40)/S

or (S + 20)(S - 40) = 50S or S^2 - 70S - 800 = 0 or (S - 80)(S + 10) = 0

or S = 80 (km/hr) [Ans]

[S cannot be negative value]

The derivative of the given function using the Fundamental Theorem of Calculus, Part 1, is -2sinx * cosx.

In mathematics, the derivative of a function of a real variable measures the sensitivity to a change in the function value with respect to a change in its argument. Derivatives are a fundamental tool of calculus.

To find the derivative using the Fundamental Theorem of Calculus, Part 1, for the function \(d/dx(\int_{0}^{(sinx)} (1 - t^2) dt)\), proceed as follows:

1. Identify the function within the integral:

f(t) = 1 - t²
2. Take the derivative of the function with respect to t:

f'(t) = -2t
3. Replace the t variable with the upper limit of the integral, which is sinx:

f'(sinx) = -2sinx
4. Multiply the result by the derivative of the upper limit with respect to x:

d/dx(sinx) = cosx
5. Multiply the results from steps 3 and 4:

-2sinx * cosx

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Answer:

x=10

y=5

Step-by-step explanation:

replace x in «-4x+11y=15» with 2y so it goes that way till you get y=5

a. The initial amount of money deposited into the account is $1575.

b. The annual interest rate being paid on the account is 4.5%.

c. The amount of money in the account after 15 years is approximately $2946.27.

d. It will take approximately 20 years for the account to reach a balance of at least $4000.

To answer these questions, let's analyze the given equation:

A(1) = 1575 * (1.045)^t

a. The initial amount of money deposited into the account is $1575. This is evident from the equation, where A(1) represents the amount of money after 1 year.

b. To determine the annual interest rate, we can compare the given equation with the general formula for compound interest:

A = P * (1 + r)^t

Comparing the two equations, we can see that the interest rate in the given equation is 4.5% (0.045) since (1 + r) is equal to 1.045.

c. To find the amount of money in the account after 15 years, we can substitute t = 15 into the equation and calculate the result:

A(15) = 1575 * (1.045)^15 ≈ $2946.27 (rounded to the nearest dollar)

Therefore, after 15 years, the amount of money in the account will be approximately $2946.

d. To find the number of years it will take for the account to have at least $4000, we need to solve the equation for t. Let's set up the equation and solve for t:

4000 = 1575 * (1.045)^t

To solve this equation, we can take the logarithm of both sides (with base 1.045):

log(4000) = log(1575 * (1.045)^t)

Using logarithm properties, we can simplify the equation:

log(4000) = log(1575) + log((1.045)^t)

log(4000) = log(1575) + t * log(1.045)

Now, we can isolate t by subtracting log(1575) from both sides and then dividing by log(1.045):

t = (log(4000) - log(1575)) / log(1.045)

Calculating this expression, we find:

t ≈ 19.56 (rounded to two decimal places)

Therefore, it will take approximately 20 years (rounded to the nearest whole year) for the account to have at least $4000.

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Answer:

v ≈ 6.8

Step-by-step explanation:

Step 1: Write equation

v² = 46

Step 2: Square root both sides

v = √46

Step 3: Evaluate

v = 6.78233

Step 4: Round

v ≈ 6.8

Answer:

Operations Inverse operations

Addition             Subtraction

Subtraction      Addition

Multiplication      Division

Division           Multiplication

Step-by-step explanation:

i hope this will help you

Answer: Yes.

This bowler is an outlier in the data set. In statistics, an outlier is a data point that differs significantly from other observations. In which this case, the bowler is significantly different than that of the other average scores.

The volume of the region in the first octant cut from the solid sphere \(\leq 5\) by the half-planes = 6 and = 3 is 11.67 cubic units.

To find the volume of the region in the first octant, we need to consider the intersection of the solid sphere and the two half-planes. The equation of the solid sphere is\(x^2 + y^2 + z^2 \leq 5\). The first half-plane, x = 6, intersects the sphere outside of the first octant and does not contribute to the volume. The second half-plane, y = 3, intersects the sphere in the first octant. We need to find the volume of the portion of the sphere that lies within the first octant and below the plane y = 3.

The intersection of the sphere and the plane y = 3 forms a circular disk. The radius of this disk can be found by substituting y = 3 into the equation of the sphere: \(x^2 + 9 + z^2 = 5\). Simplifying this equation, we get \(x^2 + z^2 = -4\), which indicates that there is no intersection. Therefore, the region in the first octant cut from the solid sphere \(\leq 5\) by the half-planes = 6 and = 3 is empty, and its volume is zero.

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The probability of escape on top at a is 50%.

A random walk is a mathematical process that involves taking a series of steps, each of which is equally likely to be in any direction. In the case of the upper bound and lower bound of a random walk being a=8 and b=-4, this means that the random walk can either go up or down.

The probability of the random walk escaping on top at a is the same as the probability of it never reaching b. Since the random walk can only go up or down, and the probability of it going up is equal to the probability of it going down, the probability of it never reaching b is 50%.

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In this case, the experimental probability is D. 0.860

First, note that Experimental probability, also known as Empirical probability, is founded on real experiments and adequate documentation of events.

In the table we can see that he rolled the cube 1000 times, and he recorded that 140 of those times he rolled a 5.

Then, the probability of rolling a 5 will be equal to:

P1 = 140/1000 = 0.14

Now, the probabilty of NOT rolling a 5, is equal to the rest of the probabilities, this is:

P2 = 1 - 0.14 = 0.86

then the correct option is D

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Full Question:

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

Jimmy rolls a number cube multiple times and records the data in the table above. At the end of the experiment, he counts that he had rolled 140 fives. Find the experimental probability of not rolling a five, based in Jimmy’s experiment. Round the answer to the nearest thousandth.

A. 0.140

B. 0.167

C. 0.667

D. 0.860

The statement provides two quantities, A and B, expressed as ratios of positive integers c and d. The relationship between the quantities A and B cannot be determined from the information given.

The statement provides two quantities, A and B, expressed as ratios of positive integers c and d. However, no specific values or constraints are given for c and d. Without knowing the specific values or any relationship between c and d, it is impossible to determine the relationship between A and B.

The relative magnitudes of A and B will depend on the values of c and d. If the value of c is greater than d, then A would be greater than B. Conversely, if the value of d is greater than c, then B would be greater than A. However, without any information about the values of c and d or any relationship between them, we cannot determine the relationship between A and B.

Therefore, based on the given information, the relationship between quantities A and B cannot be determined.

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Required area of the composite figure is 69 cm²

What is area of a composite shape?

the area covered by any composite shape. A composite shape is a shape in which some polygons are put together to form the required shape is called the area of composite shapes . These figures can consist of combinations of triangles, rectangles, squares etc. To determine the area of composite shapes, divide the composite shape into basic shapes such as square, rectangle,triangle, hexagon, etc.

Basically, a compound shape consists of basic shapes put together. This is also called a "composite" or "complex" shape. This mini-lesson explains the area of compound figures with solved examples and practice questions.

Here in this figure, we have two figures.

First one is rectangle and second one is triangle.

Length and breadth of the rectangle are 12 cm and 4 cm respectively.

So, area = Length × Breadth = 12 × 4 = 48 cm²

Again height of the triangle is (11-4) = 7 cm and base of the triangle is (12-6) = 6 cm.

So, area of the triangle = 1/2 × 7 × 6 = 3×7 = 21 cm²

Now if we add both area of rectangle and triangle then we will get area of the composite figure.

So, required area of the composite figure is ( 48+21) = 69 cm²

Therefore, option A is the correct option.

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An inequality that can be written in the form ax + by < c (where a and b are not both zero) is called a linear inequality in two variables.

An inequality that represents a line in a two-dimensional coordinate system is referred to as a linear inequality. The set of points that satisfies the inequality is a half-plane bounded by a line that may be dashed or solid.

In contrast to a linear equation, which represents a line, a linear inequality represents a half-plane. The points on one side of the line, rather than the points on the line, are solutions to the inequality.

The method of shading is used to graph a linear inequality in two variables. First, graph the boundary line, which is usually represented by a solid or dashed line, and then select a test point on one side of the line. Shaded regions of the half-plane containing the test point satisfy the inequality.

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a) The augmented matrix of the system and elementary row operations to find an equation relating a, b, and c so that the given system is always consistent.

b) The solution to the system is x = (17 - 7w)/6, y = -2w - 3, z = -1 + 2w, and w is a free parameter.

The given linear system of equations can be written in an augmented matrix form as:

\(\begin{bmatrix}2 & -1 & -2 & 2 & a + 1 \\-3 & -2 & 1 & -2 & b - 1 \\1 & -4 & -3 & 2 & c\end{bmatrix}\)

Since the matrix is in row echelon form, we can see that the system is consistent if and only if there is no row of the form [0 0 ... 0 | b] where b is nonzero. This condition is equivalent to the equation 2c - 2a - b + 1 = 0. Thus, the relation we were asked to find is:

2c - 2a - b + 1 = 0

To answer part (b) of the question, we can substitute the values a = -2, b = 3, and c = -1 into the augmented matrix:

\(\begin{bmatrix}2 & -1 & -2 & 2 & -1 \\-3 & -2 & 1 & -2 & 2 \\1 & -4 & -3 & 2 & -1\end{bmatrix}\)

We can then perform row operations to bring the matrix into row echelon form:

\(\begin{bmatrix}2 & -1 & -2 & 2 & -1 \\0 & -4 & -5 & 4 & 1 \\0 & 0 & 1 & -2 & -1\end{bmatrix}\)

We can see that the matrix is in row echelon form, and there are no rows of the form [0 0 ... 0 | b] where b is nonzero. Therefore, the system is consistent, and we can use back substitution to find the solution. Starting from the last row, we have:

z - 2w = -1

Multiplying the third equation by 4 and adding it to the second equation, we get:

-4y - 5z + 4w = 1

Substituting the value of z from the third equation, we have:

-4y - 5(-1 + 2w) + 4w = 1

Simplifying the expression yields:

-4y - w = 6

Finally, multiplying the first equation by 2 and adding it to 2 times the third equation, we get:

4x - 2y - 4z + 4w + 2x - 8y - 6z + 4w = -2

Simplifying the expression yields:

6x - 10y - 5z + 8w = -1

Substituting the value of z from the third equation and the value of y from the second equation, we have:

6x - 10(-2w - 3) - 5(-1 + 2w) + 8w = -1

Simplifying the expression yields:

6x + 7w - 17 = 0

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Here is my solution. I hope it is helpful.

Answer:

cos C

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos C = \(\frac{adjacent}{hypotenuse}\) = \(\frac{BC}{AC}\) = \(\frac{12}{13}\)

The explicit rule for the sequence is f(n) = a(3)^n-1

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

a_(n)=a_(n-1)*3

The above definitions imply that we simply multiply the current from by 3 to get the next term

This means that the function is a geometric function with the following parameters

Common ratio, r = 3

So, the function is

f(n) = a(3)^n-1

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Answer:

x=12

Step-by-step explanation:

(x-6)=6

x=12

Answer:

Step-by-step explanation:

\(f(x) = \frac{2x + 6}{3x} \\ \\ g(x) = \frac{ \sqrt{x} - 8}{3x} \)

To find ( f - g)(x) , subtract g(x) from f(x)

That's

\(( f - g)(x) = \frac{2x + 6}{3x} - \frac{ \sqrt{x} - 8}{3x} \)

Since they have a common denominator that's 3x we can subtract them directly

That's

\( \frac{2x + 6}{3x} - \frac{ \sqrt{x} - 8}{3x} = \frac{2x + 6 - ( \sqrt{x} - 8) }{3x} \\ = \frac{2x + 6 - \sqrt{x} + 8 }{3x} \\ = \frac{2x - \sqrt{x} + 6 + 8 }{3x} \)

We have the final answer as

Hope this helps you

Assume that there exists a smallest positive real number, call it x. Then, consider the number x/2. Since x is the smallest positive real number, x/2 is not positive, which is a

contradiction.

To prove that there does not exist a smallest positive real number, we will use a proof by contradiction. Suppose that there exists a smallest positive real number, call it x. Then, consider the number x/2. Since x is positive, x/2 is also positive. However, x/2 is smaller than x, which contradicts the assumption that x is the smallest positive real number. Therefore, our assumption that there exists a smallest positive

real number

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