Find the value of the variable y when

the sum of fractions [tex]\frac{y+1}{y-5}[/tex] and [tex]\frac{10}{y+5}[/tex] is equal to their product.

The expression when evaluated is 256

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

8 power of 8/3

Mathematically, this can be expressed as

8^(8/3)

When evaluated using a calculator, we have

8^(8/3) = 256

Hence, the solution is 256

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The x-intercepts of R(x) are (-3,0), (1,0), and (-2,0), and the y-intercept is (0,-24).

To find the x-intercepts of R(x) = (2x+6)(x-1)(4-2)(x+2), we need to set R(x) equal to 0 and solve for x:
0 = (2x+6)(x-1)(4-2)(x+2)
This equation can be simplified to:
0 = (2x+6)(x-1)(2)(x+2)
We can use the zero product property to find the x-intercepts:
2x+6 = 0, x-1 = 0, 2 = 0, x+2 = 0
Solving for x, we get:
x = -3, x = 1, x = -2
So, the x-intercepts are (-3,0), (1,0), and (-2,0).
To find the y-intercepts, we need to set x equal to 0 and solve for R(x):
R(0) = (2(0)+6)(0-1)(4-2)(0+2)
R(0) = (6)(-1)(2)(2)
R(0) = -24
So, the y-intercept is (0,-24).

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The greatest common factor of 8m2 and 7b3 is the largest monomial that can divide both 8m2 and 7b3. So, the greatest common factor of 8m^(2) and 7b^(3) is 1.


The greatest common factor (GCF) of two monomials is the product of the greatest common factor of their coefficients and the greatest common factor of their variables. In this case, the greatest common factor of the coefficients is 1, since 8 and 7 have no common factors other than 1. The GCF of the variables is 1, since m and b have no common factors. Therefore, the GCF of 8m^(2) and 7b^(3) is 1*1 = 1.

Here is a step-by-step explanation:
1. Find the GCF of the coefficients: GCF(8,7) = 1
2. Find the GCF of the variables: GCF(m^(2),b^(3)) = 1
3. Multiply the GCF of the coefficients and the GCF of the variables: 1*1 = 1
4. The GCF of 8m^(2) and 7b^(3) is 1.

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The linear function for the given values can be written as: f(x) = -x/2

The equation of a straight line is a relationship between x and y coordinates, The two point form of the equation of a straight line is:

y-y₁ = (y₂-y₁)/(x₂-x₁)*(x-x₁)

Given that,

f (-4)=2 and f (6)= -3

The linear function  = ?

we can consider input value as x and output value as y,

then the linear function can be estimated by using two point form of straight line.

y - 2 = (-3 - 2)/(6 - (-4))*(x - (-4))

y - 2 = -1/2 (x + 4)

y   =  - x/2 - 2 + 2

    =  - x/2

Hence, the linear function is f(x) = -x/2

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The solution to the set of equations is (x, y) = (8, 17).

What is system of linear equations?

A system of linear equations is a set of two or more equations with two or more variables that are to be solved simultaneously. Each equation in the system is linear, meaning it can be written in the form of ax + by + cz + ... = d, where a, b, c, and d are constants and x, y, z, and other variables are unknowns.

The goal of solving a system of linear equations is to find the values of the variables that satisfy all of the equations in the system. The solution of a system of linear equations is a set of values for the variables that make all of the equations true.

There are different methods to solve systems of linear equations, such as substitution method, elimination method, and matrix method. These methods involve manipulating the equations in the system to isolate one variable, substitute its value into another equation, and eventually find the values of all the variables.

Systems of linear equations are used in many areas of mathematics, science, engineering, and economics to model real-world situations and solve practical problems.

To find the solution to the set of equations, we need to determine the values of x and y that satisfy both equations simultaneously. One way to do this is to use substitution or elimination methods.

However, the given answer choices do not seem to be the steps of a solution process. We need to use both equations to find a solution. Here is one possible way to do it:

Equation S: y = x + 9

Equation T: y = 2x + 1

Since both equations equal to y, we can set them equal to each other:

x + 9 = 2x + 1

Simplifying this equation, we get:

x = 8

Now that we know the value of x, we can substitute it into either Equation S or Equation T to find the value of y. Let's use Equation S:

y = x + 9

y = 8 + 9

y = 17

Therefore, the solution to the set of equations is (x, y) = (8, 17).

None of the given answer choices matches this solution process.

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We can see here that the experimental probability that it will snow in March is:

Experimental probability is the probability that an event will occur based on actual experiments or observations.

It is calculated by performing an experiment or conducting observations, counting the number of times the event of interest occurs, and dividing that count by the total number of trials or observations.

Mathematically, the formula for the experimental probability is defined by:

Probability of an Event P(E) = Number of times an event occurs / Total number of trials.

Number of times it snowed = 2

Total number of trials = 5.

Thus, the experimental probability will be: 2/5.

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Answer: 941.33 inches squared

Step-by-step explanation:

You will find the area of each shape separately, then add them together.

The area of a square is s²

26² = 676

Area of a semicircle is 1/2(πr²)

1/2((3.14)(13)²)

1/2((3.14)(169))

1/2(530.66)

265.33

676 + 265.33 = 941.33 inches squared

Hope this helps!

we have that

1) cot 70=x/12

Cot 70=[opposite side]/[adjacent side]=x/12

The option 1 is correct

2) cot 70=12/x

Cot 70=[opposite side]/[adjacent side]=x/12

The option 2 is not correct

3)sec 20=x/12

Sec 20 =1/cos20

Cos 20==[opposite side]/[hypotenuse]=12/z

1/(1/cos20)-------> 1/(12/z)------> z/12

The option 3 is not correct

4) sec 20=12/x

Sec 20 =1/cos20

Cos 20==[opposite side]/[hypotenuse]=12/z

1/(1/cos20)-------> 1/(12/z)------> z/12

The option 4 is not correct

the correct value is

1) cot 70=x/12

Answer: it is - 13

Step-by-step explanation: it is -13 because it either can be less or more

Answer:

isosceles triangle.

Step-by-step explanation:

To classify triangle WXY by its sides, we need to determine whether all three sides are equal, two sides are equal, or all three sides are different. We can do this by calculating the lengths of the sides using the distance formula:

Side WX:

sqrt[(x2 - x1)^2 + (y2 - y1)^2] = sqrt[(-1 - 4)^2 + (-3 - (-10))^2] = sqrt[5^2 + 7^2] = sqrt(74)

Side WY:

sqrt[(x2 - x1)^2 + (y2 - y1)^2] = sqrt[(11 - 4)^2 + (-5 - (-10))^2] = sqrt[7^2 + 5^2] = sqrt(74)

Side XY:

sqrt[(x2 - x1)^2 + (y2 - y1)^2] = sqrt[(11 - (-1))^2 + (-5 - (-3))^2] = sqrt[12^2 + 2^2] = sqrt(148)

Since the lengths of sides WX and WY are equal, but the length of side XY is different, we can classify triangle WXY as an isosceles triangle. Specifically, it is an isosceles triangle with sides WX and WY equal.

Answer:

x = 50

Step-by-step explanation:

sin 40º = 32 / x

0.64 = 32 / x

x = 32 / 0.64

x =~ 50

The solution set for the inequality 6x + 1 ≤ 4x + 1 is x ≤ -3/2 can be written in interval notation as (-∞, 0].

To solve the inequality 6x + 1 ≤ 4x + 1, we need to isolate the variable on one side of the inequality. Here are the steps to do so:

1. Subtract 4x from both sides of the inequality: 6x + 1 - 4x ≤ 4x + 1 - 4x
2. Simplify: 2x + 1 ≤ 1
3. Subtract 1 from both sides of the inequality: 2x + 1 - 1 ≤ 1 - 1
4. Simplify: 2x ≤ 0
5. Divide both sides of the inequality by 2: 2x/2 ≤ 0/2
6. Simplify: x ≤ 0

The solution set in interval notation is (-∞, 0]. This means that any value of x less than or equal to 0 will satisfy the inequality.

"

Prper question:

Solve the inequality. Write the solution set in interval notation.

6x + 1 ≤ 4x + 1

"

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The distance between the x and y intercepts of that line is √13/2. The correct answer is (B).

To find the distance between the x and y intercepts of a line, we can use the distance formula:
d = √((x₂ - x₁)² + (y₂ - y₁)²)

First, we need to find the x and y intercepts of the line. The x intercept is where the line crosses the x-axis, so we can set y to 0 and solve for x. Similarly, the y intercept is where the line crosses the y-axis, so we can set x to 0 and solve for y.

Using the point-slope form of a line, we can find the equation of the line passing through the points (1,2) and (−0.5,1):
y - 1 = (1 - 2)/(−0.5 - 1)(x - (-0.5))
y - 1 = -2(x + 0.5)
y = -2x - 1

Now we can find the x and y intercepts:
For the x intercept, set y to 0:
0 = -2x - 1
2x = -1
x = -1/2

For the y intercept, set x to 0:
y = -2(0) - 1
y = -1

So the x intercept is (-1/2, 0) and the y intercept is (0, -1). Now we can use the distance formula to find the distance between these two points:
d = √((-1/2 - 0)² + (0 - (-1))²)
d = √((-1/2)² + (1)²)
d = √(1/4 + 1)
d = √(5/4)
d = √13/2

Therefore, the distance between the x and y intercepts of the line is √13/2.

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Answer:

35

Step-by-step explanation:

(7/20) *100=35

This is why because if 20 percent is equal to 7, so 40 % will be 14, 80% 28 and 100% will be 35

Answer: 35 dolls

Step-by-step explanation:

7/x and 20/100

20 times 5 is 100

and 7 times 5 is 35. Therefore 35 dolls are in Anita’s collection

The domains amortized expense be after one year is $27.80, the correct option is C

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

We are given that;

The expenditure of sami= $250

Now,

To calculate the amortized expense of the domain name, we need to divide the total cost by the number of years before it needs to be renewed or sold. In this case, Sami spent $250 and has nine years before renewal, so the annual amortized expense will be:

$250 / 9 = $27.78

Rounding this to the nearest cent

Therefore, by algebra the answer will be $27.78.

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ZW = 5.656

Since XY ≅ XZ ≅ YZ, △XYZ is an equilateral triangle. This means △XYZ is also equiangular.

Find the measures of the following angles in degrees:

m∠WYZ = 60°

m∠YWZ = 60°

m∠YZW = 60°

Find WY:

WY = 8

Find ZW: Give your answer in both simplest radical form and as an approximation correct to two decimal places.

simplest radical form ZW = 4√2

approximation ZW = 5.656854249492381

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Answer:

16 percent decrease

Step-by-step explanation:

The given equation is z = 1 + iβ/β + 2i. We need to determine the value(s) for β such that the equation holds true.

First, we can multiply both sides of the equation by β + 2i to get rid of the denominator:

z(β + 2i) = 1 + iβ

Next, we can distribute the z on the left-hand side of the equation:

zβ + 2iz = 1 + iβ

Now we can rearrange the equation to get all the β terms on one side:

zβ - iβ = 1 - 2iz

We can factor out the β on the left-hand side:

β(z - i) = 1 - 2iz

Finally, we can divide both sides of the equation by z - i to get the value of β:

β = (1 - 2iz)/(z - i)

This is the value of β that satisfies the given equation. None of the given options match this value, so the correct answer is "None of the given options."

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Answer:

-----------------------

As per table we see:

Since the difference of both variables is common, the function is linear.

The matching choice is C.

What is rhombus ?

A rhombus is a special type of parallelogram in which two pairs of opposite sides are congruent. That means all the sides of a rhombus are equal.

What is the Area of a Rhombus?

The area of a rhombus can be defined as the amount of space enclosed by a rhombus in a two-dimensional space. To recall, a rhombus is a type of quadrilateral projected on a two dimensional (2D) plane, having four sides that are equal in length and are congruent.

Using Diagonals                A = ½ × d1 × d2

Using Base and Height        A = b × h

Using Trigonometry        A = b2 × Sin(a)

the correct answer is the option (C) 340 cm^2

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v=4 or v=-1.

The rational expression is undefined when the denominator is equal to 0. Therefore, we need to find the values of v that make the denominator 0.

v^(2)-3v-4=0

We can factor this equation to find the values of v:

(v-4)(v+1)=0

Therefore, the rational expression is undefined when v=4 or v=-1.

In conclusion, the rational expression (v^(2)+11)/(v^(2)-3v-4) is undefined when v=4 or v=-1.

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The proportional equation for p in terms of s which matches the given context is p = 34s.

What is a proportional equation?

A proportional equation is written as y = kx. The equation's variables are the letters y and x. The proportionality constant, which never changes, is symbolised by the letter k.

We are given that a store buys 10 sweaters for $50 and sells them for $390.

Cost of one sweater = $50 / 10 = $5

Sale price of one sweater = $390 / 10 = $39

We know that total profit = Sale price - Cost price.

So, we get

p = 39s - 5s

p = 34s

Hence, the proportional equation for p in terms of s which matches the given context is p = 34s.

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Answer: 14 miles and the donors will both owe $35 for a total of $70

Step-by-step explanation:

The mother is giving $35 and the grandmother is 2.50 per mile and at the end they both end up owing the same amount

grandmothers 2.50 per miles

you walk 14 miles

you multiply 2.50 and 14 to get $35

The mother and the grandmother both owe $35

so take $35x2= 70

Therefore , the solution of the given problem of percentage comes out to be 38 years old is the median age.

In statistics, a "a%" is a figure or statistic that is expressed as a percentage of 100. The words "pct," "pct," but instead "pc" are also not frequently used. However, the sign "%" is frequently used to represent it. The percentage sum is flat; there are no dimensions. Percentages are truly integers because their numerator almost always equals 100. Either the % symbol (%) or the additional term "fraction" must come before a number to denote that it is a percentage.

Here,

The following algorithm must be used to determine the mean age:

=> mean = (all years added together) / (total number of persons)

The representative age for each age group is the age that falls in the middle of the range. With this approach, we can determine the total age as follows:

=>18(9) + 23(28) + 28(33) + 33(90) + 38(122) + 56(48) + 48(24) + 76(20) + 1089(0.25)

=> 162 + 644 + 924 + 2970 + 4636 + 2688 + 1152 + 1520 + 272.25

=>18(9) + 23(28) + 28(33) + 33(90) + 38(122) + 56(48) + 48(24) + 76(20) + 1089(0.25)

According to the information provided, there are 460 people in total.

=> mean = 17745.25 / 460

=> mean = 17745.25 / 460

As a result, the average lifespan is roughly 38.552 years.

The age category in this instance with the highest frequency has a midpoint of 38 and a frequency of 122. As a result, 38 years old is the median age.

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Answer: -sqrt(3)/4

Step-by-step explanation:

To solve this trigonometric expression, we can use the following trigonometric identities:

sin (180 + x) = -sin x

cos (180 + x) = -cos x

Using these identities, we can rewrite the expression as:

sin(200°)cos(80°) - cos(200°)sin(80°)

= sin(180° + 20°)cos(80°) - cos(180° + 20°)sin(80°)

= -sin(20°)cos(80°) + cos(20°)sin(80°)

= (cos(20°) - sin(20°))sin(80°)

= sin(70°)sin(80°)

= (cos(20°) - cos(150°))/2

= (-sqrt(3)/2 - sqrt(3)/2)/2

= -sqrt(3)/4

Therefore, sin(200°)cos(80°) - cos(200°)sin(80°) = -sqrt(3)/4.

The true statement is 'The value 36 represents the initial water level before it began to recede.

First of all, understand the word problem,  

Given that The water level of a river recedes at a constant rate each day it implies the water level is decreasing at a constant rate. The expression 36 - 0.25x represents the water level after 'x' days.

Here we have

The expression 36 - 0.25x represents the water level after 'x' days

Let x = 0 which implies the water level is not begin to recede

Then the Initial water level = 36 - 0.25(0) = 36  

Hence, we can conclude that the initial water level is 36

Therefore,

The true statement is 'The value 36 represents the initial water level before it began to recede.

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The Complete Question is attached below

Answer: 1, -2

Step-by-step explanation:

Answer:

(1,-2)

Step-by-step explanation:

x-4 you move it to the left 4 units and y-3 you move it down 3 units to get (1,-2)

25. The scale factor is 2.5

26. The congruent angles include

∠ E = ∠ J = 65 degrees

∠ F = ∠ K = 90 degrees

∠ G =  L = 90 degrees

∠ H = ∠ M = 115 degrees

25. The scale factor of JKLM and EFGH is calculated using corresponding sides

side EF * scale factor = side JK

8 * scale factor = 20

scale factor = 20 / 8

scale factor = 2.5

26. The congruent angles include

∠ E = ∠ J = 65 degrees

∠ F = ∠ K = 90 degrees

∠ G =  L = 90 degrees

∠ H = ∠ M = 360 - 90 - 90 - 65 = 115 degrees

27.  the ratios of the corresponding side lengths

JK / EF is proportional to KL / FG is proportional to LM / GH is proportional to MJ / EH

28. the values of x, y, and z

x = 2.5 * FG = 2.5 * 11 = 27.5

y = 30 / 2.5 = 12

z = 65 degrees

29. the perimeter of each polygon

the smaller polygon EFGH = 8 + 11 + 3 + 12 = 34

the bigger polygon JKLM = 20 + 27.5 + (3 * 2.5) + 30 = 85

30. the ratio of the perimeters of JKLM to EFGH

= 85 / 34 = 2.5

31. the area of each polygon

the smaller polygon EFGH = 0.5(3 + 8) * 11 = 60.5

the bigger polygon JKLM = 0.5(20 + 7.5) * 27.5 = 378.125

32. the ratio of the areas of JKLM to EFGH​

= 378.125 / 60.5 = 6.25

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It will take about 5.18 years for the car to be worth 8,200.

We can use the given formula to find the value of the car after x years:

[tex]V = 20,000(0.8)^x[/tex]

We want to know how long it will take for the car to be worth 8,200. So we can set V equal to 8,200 and solve for x:

[tex]8,200 = 20,000(0.8)^x[/tex]

Dividing both sides by 20,000 gives:

[tex]0.41 = (0.8)^x[/tex]

Taking the logarithm of both sides with base 0.8, we get:

[tex]log0.8(0.41) = x[/tex]

Using a calculator, we can find:

x ≈ 5.18

Therefore, it will take about 5.18 years for the car to be worth 8,200.

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Check the picture below.