Solve the following rational equation: If no solution exists then state that. Show complete work. y/y−2y+ 4/y-3 = 4/ y2−5y+6

Answer: 12 no caculator needed

Step-by-step explanation:

The monthly house payment will be $375.84. The annual payment  for A farmer that purchased 265 acres of land for $4,300/acre  will be $75,436.20. The annual payment  of  Larry purchased a new combine that cost $240,500will be $64,514.88.

To calculate the monthly house payment for a home loan of $55,000 at 5.25% APR for 20 years, we can use the formula:

M = P * (r / (1 - (1 + r)^(-n)))

Where M is the monthly payment, P is the principal amount, r is the monthly interest rate, and n is the number of monthly payments.

In this case, P = $55,000, r = 5.25% / 12 = 0.004375, and n = 20 * 12 = 240.

Plugging in these values, we get:

M = $55,000 * (0.004375 / (1 - (1 + 0.004375)^(-240)))

M = $375.84

Therefore, the monthly house payment will be $375.84.

#2
To calculate the annual payment for a loan of 265 acres of land at $4,300/acre with a 25% down payment and 6.75% APR over 20 years, we can use the same formula as above, but with different values for P, r, and n.

In this case, P = 265 * $4,300 * (1 - 0.25) = $845,625, r = 6.75% / 12 = 0.005625, and n = 20 * 12 = 240.

Plugging in these values, we get:

M = $845,625 * (0.005625 / (1 - (1 + 0.005625)^(-240)))

M = $6,286.35

Since this is the monthly payment, we can multiply it by 12 to get the annual payment:

A = $6,286.35 * 12 = $75,436.20

Therefore, the annual payment will be $75,436.20.

#3
To calculate the annual payment for a loan of $240,500 for a new combine with a rebate of $4,500, a trade-in of $9,500, and a down payment of $5,000 at 8% APR over 4 years, we can use the same formula as above, but with different values for P, r, and n.

In this case, P = $240,500 - $4,500 - $9,500 - $5,000 = $221,500, r = 8% / 12 = 0.006667, and n = 4 * 12 = 48.

Plugging in these values, we get:

M = $221,500 * (0.006667 / (1 - (1 + 0.006667)^(-48)))

M = $5,376.24

Since this is the monthly payment, we can multiply it by 12 to get the annual payment:

A = $5,376.24 * 12 = $64,514.88

Therefore, the annual payment will be $64,514.88.

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The solution of the absolute value inequality is (-∞,-5] U [-3,∞) in interval notation and x ≥ -3 or x ≤ -5 in algebraic notation.

Step 1: To solve the absolute value inequality, we need to isolate the absolute value expression on one side of the inequality. We can do this by adding 1 to both sides of the inequality:

|x + 4| ≥ 1

Step 2: Now, we can split the inequality into two separate inequalities:

x + 4 ≥ 1 and x + 4 ≤ -1

Step 3: Solve each inequality for x:

x ≥ -3 and x ≤ -5

Step 4: Express the solution in interval notation and algebraic notation. In interval notation, the solution is (-∞,-5] U [-3,∞). In algebraic notation, the solution is x ≥ -3 or x ≤ -5.

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those are opposite angles therefore they are equal

3x - 3 = 2x + 13

solve for x

x = 16

Answer:

See below.

Step-by-step explanation:

We are asked to find the value of x.

We should know that the 2 angles given are Vertical Angles.

Vertical Angles are angles that are opposite of each other. These angles are equal to each other if 2 or more lines are straight.

Let's set the angles equal to each other.

[tex]3x-3=2x+13[/tex]

Simplify:

[tex]x=16[/tex]

The value of x is 16.

Answer:

X = 1

Step-by-step explanation:

[tex]2x + 8 = 4x + 6 \\ collect \: the \: like \: terms \\ 8 - 6 = 4x - 2x \\ 2 = 2x \\ x = 1[/tex]

Answer:

x = 1

Step-by-step explanation:

first subtract 6 from both sides

2x + 8 = 4x + 6

     -6           -6

2x + 2 = 4x

Now get the variable on to one side by subtracting 2x from both sides

2x + 2 = 4x

-2x         -2x

2 = 2x

Now divide both sides by two to get the value of x

2 (÷ 2) = 2x (÷ 2)

1 = x

x = 1

to check your work, plug in one for x

2x + 8 = 4x + 6

2(1) + 8 = 4(1) + 6

2 + 8 = 4 + 6

10 = 10

this statement is true which means the solution is true

Hope this helps!

14. x = -1 or x = -7

17. x = 0, x = 3, x = -3

18. x = (-3 + 4√2)/2 or x = (-3 - 4√2)/2

The solutions and verification for the given equations are explained below:Solution 1:Given equation is x2 + 8x + 7 = 0.Let's solve the above equation by using the quadratic formula.The quadratic formula isx = [ -b ± sqrt(b2 - 4ac) ] / 2aIn the given equation, a = 1, b = 8, and c = 7x = [-8 ± sqrt(82 - 4(1)(7))] / 2*1x = [-8 ± sqrt(64 - 28)] / 2x = [-8 ± sqrt(36)] / 2Therefore, the solutions are x = -4 + 3 or -4 - 3i.e., x = -1 or x = -7Solution 2:Given equation is x3 – 9x = 0.The given equation can be rewritten as x(x2 - 9) = 0.We know that a * b = 0 if either a = 0 or b = 0.Using this concept, we can say that either x = 0 or x2 - 9 = 0Therefore, x2 = 9 => x = ± 3So the solutions for the given equation are x = 0, x = 3, x = -3Solution 3:Given equation is (x + 6)(x - 3) = 10.The given equation can be rewritten as x2 + 3x - 28 = 0.Let's solve the above equation by using the quadratic formula.The quadratic formula isx = [ -b ± sqrt(b2 - 4ac) ] / 2aIn the given equation, a = 1, b = 3, and c = -28x = [-3 ± sqrt(32)] / 2Therefore, the solutions are x = (-3 + 4√2)/2 or x = (-3 - 4√2)/2Solutions for the given equations are:x = -1, -7, 0, 3, -3, (-3 + 4√2)/2, (-3 - 4√2)/2.Verification:Let's verify the solutions of the given equations.Verification for x2 + 8x + 7 = 0When x = -1, -7, x2 + 8x + 7 = 0 satisfies.Verification for x3 – 9x = 0When x = 0, 3, -3, x3 – 9x = 0 satisfies.Verification for (x + 6)(x – 3) = 10When x = (-3 + 4√2)/2, (-3 - 4√2)/2, (x + 6)(x – 3) = 10 satisfies.

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Convert the expression as follows:

To Show:-

Answer:-

The ratio given to us is ,

[tex]\implies (y + 2) : ( y + 7) = k : 1 \\[/tex]

In fraction form we can write it as ,

[tex]\implies \dfrac{y+2}{y+7}=\dfrac{k}{1} \\[/tex]

Now solve for y , by cross multiplying,

[tex]\implies 1( y + 2 ) = k( y + 7) \\[/tex]

Simplify the brackets,

[tex]\implies y + 2 = ky + 7k \\[/tex]

Subtract ky on both sides ,

[tex]\implies y - ky + 2 = 7k \\[/tex]

Subtract 2 on both sides,

[tex]\implies y - ky = 7k - 2 \\[/tex]

Take out y as common from LHS ,

[tex]\implies y ( 1 - k ) = 7k - 2 \\[/tex]

Divide both the sides by (1-k) ,

[tex]\implies \underline{\underline{ \green{y =\dfrac{7k-2}{1-k}}}} \\[/tex]

Hence Proved !

and we are done!

The missing angle as labelled in the task content and required to be determined is; 33°.

It follows from the task content that the missing angle is to be determined from the task content.

By the use of trigonometric ratios;

The missing angle, x can be determined as follows;

tan (x) = 9.09 / 14

x = tan-¹ (9.09/14).

x = 32.995°

The missing angle is therefore; 33°.

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The equipment will be worth approximately $3,145.73 after 7 years.

To find the value of the printing equipment after 7 years, we need to first determine the common ratio (r) of the geometric sequence.

We can do this by dividing any term by the preceding term. Let's divide the value in year 2 by the value in year 1:

r = 9,600/12,000 = 0.8

Now we can use the formula for a geometric sequence to find the value of the equipment after 7 years:

a₇ = a₁r⁶

where;

Plugging in the values we have:

a₇ = 12,000 x 0.8⁶

a₇ ≈ $3,145.73

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1. Independent Variable: Group (No News or watch news)

Dependent Variable: Depression Scores

2. Null Hypothesis: μ = 0

Alternative Hypothesis: μ < 0

3. Yes, you can reject the null hypothesis at a = 0.05 because there is a considerable difference in the depression ratings of the two groups

1. According to the information provided, the score for depression depends on whether a group watches the news or not.

Group is an independent variable (No News or watch news).

Depression scores are a dependent variable.

2. Null Hypothesis: The two groups do not differ in their depression levels, which is the null hypothesis.

Alternate Hypothesis: Those who don't read or watch the news will score less depressed than people who receive therapy as usual.

μ = 0 is the null hypothesis.

Between the two groups, there is no difference in depression scores.

Differential Hypothesis:  μ < 0

Those who don't read or watch the news will score less depressed than people who receive therapy as usual.

3. Due to the p-value of (0.024) < α(0.05) at α = 0.05, we can rule out the null hypothesis.

The rejection zone of the t-distribution with 12 degrees of freedom has the t-score of -2.58.

As a result, it is clear that there is a considerable difference in the depression ratings of the two groups, with the group that does not watch or read the news scoring significantly lower on the depression scale than the group that continues to get therapy as usual.

The proper response is "Yes".

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The complete question is:

Dr. Z is interested in discovering if there is a difference in depression scores between those who do not watch or read the news and those who continue with therapy as normal. She divides her clients with depression into 2 groups. She asks Group 1 not to watch or read any news for two weeks while in therapy and asks Group 2 to continue with therapy as normal. The dataset score is a record of the results of the measure, administered after 2 weeks.

Independent Samples T-Test

                                   t                          df                          p

Score                      -2.580                    12                      0.024

1. Identify IV and DV.

2. State the null hypothesis and the directional (one-tailed) alternative hypothesis

3. Can you reject the null hypothesis at a = 0.05?

The y-intercept of the continuous function in the table is (0, –6) which can be determined by looking at the first point, (0, –6).

A continuous function is a function that is defined for all values of its independent variable, and whose graph is a continuous line without breaks or gaps. It typically means that a function's value for an input can be calculated without having to consider the values of the function for other inputs.

The y-intercept of a continuous function is the point at which the graph of the function crosses the y-axis. It is the point where the x-coordinate is zero. In other words, it is the point where the graph of the function intersects the y-axis.

In the given table, the y-intercept can be determined by looking at the first point, (0, –6). This means that the y-coordinate is –6 when the x-coordinate is 0. Therefore, the y-intercept of the continuous function in the table is (0, –6).

The y-intercept also helps us to determine the slope of the function. The slope is the rate at which the function changes as we move along the x-axis. The slope can be calculated by looking at the change in the y-coordinate for a given change in the x-coordinate.

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The y-intercept οf the cοntinuοus functiοn in the table is (0, –6) which can be determined by lοοking at the first pοint, (0, –6).

A cοntinuοus functiοn is a functiοn that is defined fοr all values οf its independent variable, and whοse graph is a cοntinuοus line withοut breaks οr gaps. It typically means that a functiοn's value fοr an input can be calculated withοut having tο cοnsider the values οf the functiοn fοr οther inputs.

The y-intercept οf a cοntinuοus functiοn is the pοint at which the graph οf the functiοn crοsses the y-axis. It is the pοint where the x-cοοrdinate is zerο. In οther wοrds, it is the pοint where the graph οf the functiοn intersects the y-axis.

In the given table, the y-intercept can be determined by lοοking at the first pοint, (0, –6). This means that the y-cοοrdinate is –6 when the x-cοοrdinate is 0. Therefοre, the y-intercept οf the cοntinuοus functiοn in the table is (0, –6).

The y-intercept alsο helps us tο determine the slοpe οf the functiοn. The slοpe is the rate at which the functiοn changes as we mοve alοng the x-axis. The slοpe can be calculated by lοοking at the change in the y-cοοrdinate fοr a given change in the x-cοοrdinate.

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Complete question:

Which is a y-intercept of the continuous function in the table?

Answer:

Step-by-step explanation:

2-Bs:  4 x 3.8 = 15.2     2 x 15.2 = 30.4 m²

2-Cs:  11.5 x 3.8 = 43.7   2 x 43.7 = 87.4 m²

Total S.A. = 92 + 30.4 + 87.4 = 209.8 m²

Answer: 2.98m squared i think im not sure im just guessing im still not fully awake yet bro.

Step-by-step explanation:

Answer:

Step-by-step explanation:

41+x=81

x=40

The rabbits score 40 points in the second half.

Answer:

55

Step-by-step explanation:

The value of r when 2^(r)=(1)/(32) is -5. This can be derived by taking the logarithm of both sides of the equation. Since log2 (2^r) = r and log2 (1/32) = -5, then r = -5.

In order to work out the value of r when 2^(r) = 1/32, we need to use logarithms. Logarithms are a way of expressing a number as the power of another number. Specifically, the logarithm of a number x is the exponent y to which a given base must be raised to equal x.

In this case, the base is 2, so log2 (2^r) = r. Therefore, to work out the value of r, we need to find the logarithm of 1/32. This can be done by dividing 1 by 32 and taking the logarithm of the result. We get log2 (1/32) = -5. Therefore, r = -5.

Since the question specifies that we should give the answer as an integer or as a fraction in its simplest form, we must conclude that the answer is -5. It is impossible to reduce this fraction any further, so it is already in its simplest form.

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Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

The amount in the second case is more. Then the better job is the second one.

In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.

If he can make $2,000 worth of sales per week. Then the total amount in the first case is given as,

⇒ $31,200 + $2,000 x 0.09 x 52

⇒ $40,560

And the total amount in the second case is given as,

⇒ $26,000 + $2,000 x 0.15 x 52

⇒ $41,600

The amount in the second case is more. Then the better job is the second one.

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The given equation is x2−9/18​−x−3/12​=x+3/x

(a) The restrictions on x are that x cannot equal 0, 6, or -4. This is because if x were to equal any of these values, the denominator of one of the fractions in the equation would equal 0, which is undefined.

(b) The least common denominator of the fractions in the equation is 36. This is because 36 is the smallest number that is divisible by 18, 12, and x.

(c) To solve the equation, we can multiply each term by the least common denominator to eliminate the fractions:

36x2 - 18(9) - 36x - 3(3) = 36x + 3(36)

Simplifying and rearranging the terms gives us:

36x2 - 72x - 207 = 0

Using the quadratic formula, we can find the values of x:

x = (-(-72) ± √((-72)2 - 4(36)(-207)))/(2(36))

Simplifying gives us:

x = (72 ± √12960)/72

So the solutions are x = (72 + √12960)/72 and x = (72 - √12960)/72.

However, we must check these solutions against the restrictions on x. The first solution, (72 + √12960)/72, is approximately 6.8, which does not violate any of the restrictions. The second solution, (72 - √12960)/72, is approximately -0.8, which also does not violate any of the restrictions. Therefore, the solutions to the equation are x = (72 + √12960)/72 and x = (72 - √12960)/72.

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the total cost of the clarinet, including shipping and handling, is $600.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Given, Jordan bought a clarinet priced at $517. Shipping and handling cost an additional 16% of the price.

The cost of shipping and handling is 16% of the price of the clarinet, which is:

0.16 * $517 = $82.72

the total cost of the clarinet including shipping and handling, we need to add the cost of the clarinet and the cost of shipping and handling:

Total cost = $517 + $82.72 = $599.72

Rounding this to the nearest dollar, we get:

Total cost = $600

Therefore, the total cost of the clarinet, including shipping and handling, is $600.

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Answer:

0.07

Step-by-step explanation:

Percentages are on a scale of 1. 100% is 1, 1% is 0.01

we can convert percentage to decimal by moving the decimal point 2 places left.

Therfore, the answer is 0.07

The graphs of y = x and y = -1 are related to each other because they intersect at the point (-1, -1)

An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.

The standard equation of a linear equation is:

y = mx + b

where m is the rate of change and b is the y intercept

Given the graphs of y = x and y = -1.

As we can see from the graphs, they intersect at the point (-1, -1)

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Answer:

4 to power of 3 in expanded form is 4 x 4 x 4.

HOPE THIS HELPS :)

The statistical measures are:

Min: 2

Q1: 4

Med: 8

Q3: 13

Max: 15

The box and whiskers plot is attached.

Box and whiskers plot is a simple way of representing statistical data on a plot in which a rectangle is drawn to represent the second and third quartiles, usually with a vertical line inside to indicate the median value.

The lower and upper quartiles are shown as horizontal lines on either side of the rectangle.

The statistical measures are as follows:

The minimum value is the lowest number in the data set. Thus:

Min = 2

The lower quartile (Q1) is the value under which 25% of data points are found when they are arranged in increasing order. That is:

2, 2, 3, 4, 5, 5, 8

Q1 = 4

The median is the value in the middle of an ordered set of

numbers.

2, 2, 3, 4, 5, 5, 8, 8, 10, 10, 11, 13, 15, 15, 15

Med = 8

The upper quartile (Q3), is the value under which 75% of data points are found when arranged in increasing order.

10, 10, 11, 13, 15, 15, 15

Q3 = 13

The maximum value is the highest number in the data set. Thus:

Max = 15

Check the attached for image of the plot.

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The two positive, consecutive, even numbers are 12 and 14.

To find the two numbers, we need to use algebra to solve the equation given in the question.

Let x be the first even number and x + 2 be the second even number, since they are consecutive.

According to the question, the square of the sum of these two numbers exceeds the sum of their squares by 336. So we can write the equation as:

[tex](x + x + 2)^{2} - (x^2 + (x + 2)^2) = 336[/tex]

Simplifying the equation gives:

4x^2 + 8x + 4 - x^2 - x^2 - 4x - 4 = 336

2x^2 + 4x - 336 = 0

Dividing the equation by 2 gives:

x^2 + 2x - 168 = 0

Using the quadratic formula, we can find the value of x:

x = (-2 ± √(2^2 - 4(1)(-168)))/(2(1))

x = (-2 ± √676)/2

x = (-2 ± 26)/2

The two possible values of x are:

x = 12 or x = -14

Since we are looking for positive even numbers, we can disregard the negative value of x.

So the first even number is 12 and the second even number is 12 + 2 = 14.

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Answer:

[tex]\boxed{R:-40.48}[/tex]

Step-by-step explanation:

Rewriting the statement we have:

[tex]-44+22 \times\frac{ 16}{100}[/tex]

According to the order of operations, we solve:

simplify:

[tex]-44+22 \times\frac{ 4}{25}\\=-44 +\frac{88}{25} \\=\frac{-44(25)+88}{25} = \frac{-1012}{25} \approx -40.48[/tex]

Answer:

Height = 8

Volume = 48

Step-by-step explanation:

(4x4)x3 = 48

So the values of a, h, and k in the vertex form of the parabola are a = 6/11, h = -1/2, and k = 3.

A parabola's vertex form is given by:

y = a(x - h)^2 + k

where an is a constant that governs the parabola's shape and (h, k) is the parabola's vertex.

The vertex is (-1/2, 3), and the directrix is x = -13/24, according to the information provided.

The value of a can be calculated using the common parabola formula:

4a = 1/ (distance from vertex to directrix) (distance from vertex to directrix)

4a = 1 / (|(-1/2) - (-13/24)|)

4a = 1 / (11/24)

4a = 24/11\sa = 6/11

The vertex form of the parabola can now be simplified by substituting the vertex and a values:

y = (6/11)(x + 1/2)^2 + 3

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Answer:

In the image

Hope this helps!

Step-by-step explanation:

The angle between the vectors "[−12​] and [6−1​]α" is approximately 2.03 radians.

To find the angle between the vectors, we can use the formula:

cos(α) = ([tex]V{1}[/tex] • [tex]V{2}[/tex]) / (||[tex]V{1}[/tex]|| ||[tex]V{2}[/tex]||)

Where v1 and v2 are the two vectors, and ||[tex]V{1}[/tex]|| and ||[tex]V{2}[/tex]|| are the magnitudes of the vectors.

For the given vectors:

[tex]V{1}[/tex] = [−1 2] and [tex]V{2}[/tex] = [6 −1]

[tex]V{1}[/tex]• v2 = (−1)(6) + (2)(−1) = −6 + −2 = −8

||[tex]V{1}[/tex]|| = √((-1)^2 + 2^2) = √(5)

||[tex]V{2}[/tex]|| = √(6^2 + (-1)^2) = √(37)

cos(α) = (−8) / (√(5) √(37)) = −8 / √(185)

α = cos^-1(−8 / √(185))

α ≈ 2.03 radians

Therefore, the angle between the vectors is approximately 2.03 radians.

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Option a) t= 4 years. The effective interest rate for the specified account is 9.31%. This is because the effective interest rate is the rate that actually applies to the balance in the account, taking into account the compounding frequency. The formula for the effective interest rate is:

Effective interest rate = (1 + nominal yield / compounding frequency) ^ compounding frequency - 1

In this case, the nominal yield is 9% and the compounding frequency is 2 (since it is compounded twice a year). Plugging these values into the formula, we get:

Effective interest rate = (1 + 0.09 / 2) ^ 2 - 1
Effective interest rate = (1.045) ^ 2 - 1
Effective interest rate = 1.092025 - 1
Effective interest rate = 0.092025

Converting this to a percentage, we get:

Effective interest rate = 9.31%

Therefore, the correct answer is 9.31%.

For the second part of the question, we can use the formula for future value to find the missing quantity. The formula is:

A = P(1 + rt)

Plugging in the given values, we get:

5580 = 4500(1 + 0.06t)

Solving for t, we get:

5580 = 4500 + 270t
1080 = 270t
t = 4

Therefore, the correct answer is t = 4 years, or choice A.

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