3.4.5* At the end of the section, we let r=1/x-1 in x/x-1+2/3=2/x-1 to get x r+2/3=2 r
While at first we may seem stuck because we have two variables instead of one, we can still use this substitution to solve the problem!
(a) Solve the equation r=1/x-1 for x in terms of r. In other words, manipulate the equation until you have x equal to an expression with r' s in it, but no x's.
(b) Substitute this expression for x in the equation x r+2/3=2 r. Do you have a linear equation now? Solve that equation for r. Use your value of r to find x.

The interval of the domain where the function is decreasing are (0, 1) and (3, 4)

From the question, we have the graph that represents the given parameters that can be used in our computation

To determine the decreasing interval on the graph, we look for the points where

The intervals that represent the above highlights are

This can be represented as (0, 1) and (3, 4)

Hence, the intervals are (0, 1) and (3, 4)

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Answer:

11

Step-by-step explanation:

The range is the set of outputs, or the second element in each ordered pair.

The sum of these values is [tex]5+2+1+3=11[/tex].

The value of a is 71°, and the value of b is 109°.

A parallel lines is defined as those type of line that are equidistant to each other which are on the same plane and they doesn't meet each other till infinity.

When two parallel lines are being intersected by another line called the transverse line, the following relationship is bound to occur such as;

From model 4, the pair of alternate exterior angles are equal in measure. That is 71° = angle opposite b°.

That is 180 - 71 = 109°

Also in model 4, the pair of alternate interior angles are equal in measure. a = 71°.

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The measure of missing angle is 145°.

When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°. The linear pair postulate or linear pair theorem in mathematics states the same thing mathematically. The sum of the measurements of two angles that make up a linear pair is 180°.

Given

Missing angle = x°

Opposite angle = 100°

Exterior angle = 35°

x and exterior angle are linear pair

Sum of linear pair is 180

x + 35 = 180

x = 180 - 35

x = 145

The measure of missing angle is 145°.

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Answer:

[tex]\textsf{12.} \quad y = 6x - 5[/tex]

[tex]\textsf{17.} \quad y=-\dfrac{1}{4}x-2[/tex]

Step-by-step explanation:

Find the slope of the line by substituting two points from the given table into the slope formula.

Define the points:

[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{13-7}{3-2}=\dfrac{6}{1}=6[/tex]

Substitute the found slope and point (2, 7) into the point-slope formula to create an equation of the line:

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-7=6(x-2)[/tex]

[tex]\implies y-7=6x-12[/tex]

[tex]\implies y=6x-5[/tex]

Given:

Therefore, two points on the line are:

The y-intercept is the y-value when x = 0.

Therefore, the y-intercept of the line is -2.

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]

Substitute the y-intercept and the point (4, 3) into the slope-intercept formula and solve for m to find the slope:

[tex]\implies y=mx+b[/tex]

[tex]\implies -3=m(4)-2[/tex]

[tex]\implies -1=4m[/tex]

[tex]\implies m=-\dfrac{1}{4}[/tex]

Therefore, the equation of the line is:

[tex]y=-\dfrac{1}{4}x-2[/tex]

An integer is a whole number  x=-11.

The symbol "Z" stands for an integer.

Z= {……-8,-7,-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8,……}

Let the numbers be x, x + 2, x + 4, x + 6...

5(x+x+4)=8(x+2+x+6)+22

5(2x+4)=8(2x+8)+22

10x+20=16x+64+22

The integers are -11,-9,-7,-5,

10x-16x=64+22-20 -6x=66/-6

x=-11.

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Answer: about 61290 employees total

Step-by-step explanation:

18.6% is equal to 11400 employees in one country

18.6% of X = 11400

x=11400/0.186

x=61290

Note that the answer is rounded

The relation between base length and height is: f(x) = 48/x

What is parallelogram?

A parallelogram is a straightforward quadrilateral in Euclidean geometry that has two pairs of parallel sides. A parallelogram has opposite sides that are facing one another and opposite angles that are of equal size.

By the values given in the table, for base length and height of the parallelograms, you can notice that base length increases 1 units, so you have 1, 2, 3, 4, 5.

For height you can notice that while base length increase 1 unit, height decreases by a factor of 1/x, just as follow:

1 - 48

2 - 24

3 - 16

4 - 12

5 - 8

The relation between base length and height is:

f(x) = 48/x

where f(x) is the height and x is the base length. In fact, you have:

f(1) = 48/1 = 48

f(2) = 48/2 = 24

f(3) = 48/3 = 16

f(4) = 48/4 = 12

Hence, the relation between base length and height is: f(x) = 48/x.

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Answer:

2.213

2×1+2(1÷10)+1(1÷100)+3(1÷1000)

2×1+2×0.1+0.01+3×0.001

2+0.2+0.01+0.003

2.213 #

hope this will help ig

Answer:

2.213

Step-by-step explanation:

2×1+2(1÷10)+1(1÷100)+3(1÷1000)

2×1+2×0.1+0.01+3×0.001

2+0.2+0.01+0.003

2.213

For an average intake of 2200 calories per day, the number of acres of land is approximately 2.

If we are given all a function so in that case, we just need to substitute values given in question and solve for unknown variable that is to be determined.

C(x) is a variable that tells the number of calories consumed daily by a person

x is the number of acres that person own.

C(x) = 270㏑(x+1) +1900

In the given question number of acres ask a person to have who consumed 2200 calories in a day.

Therefore,

C(x)=2200

2200=270㏑(x+1) +1900

2200-1900=270㏑(x+1)

300=270㏑(x+1)

300/270 = ㏑(x+1)

10/9 = ㏑ (x+1)

x+1 = [tex]e^{\frac{10}{9} }[/tex]

x+1 = 3.037

x= 3.037-1

x=2.037

x=2(round off)

Therefore, 2 acres of land a person can consume 2200 calories in a day.

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The statement that is true about line segment P'S' is (c) Segment P'S' s 4 units long and lies on a different segment.

How to determine the true statement?

The complete question is in the attached image

From the image, we have:

PS = 8 units

This means that:

P'S' = 1/2 * PS

So, we have:

P'S' = 1/2 * 8

Evaluate

P'S' = 4

Also, the segment PS and P'S' do not lie on the same segment

Hence, the true statement is (c)

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The number of times both spins will be even numbers in 200 spins is (b) 50

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

Sections on the spinner = 1, 2, 3, 4, 5, and 6

Also, from the question;

We have the following statement

The theoretical probability of both spins being even numbers is 9 over 36.

This means that

P(Both even) = 9/36

Lastly, we have

Times of experiment = 200

So, we have

Outcomes of both even = P(Both even) * Times of experiment

Substitute the known values in the above equation, so, we have the following representation

Outcomes of both odd =9/36 * 200

Evaluate

Outcomes of both odd = 50

Hence, the outcomes is (b) 50

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95% confidence that machine calibrated properly is (48.536, 51.424).

We have given that,

n = 25

mean of x = 49.98 mm

S = 0.14 mm

μ = 50.00 mm

and CI = 95%

from t-table we know that,

t at 95% and n - 1 = 25 - 1 = 24 is 2.064

Therefore 95% of CI means that

(x - 2.064 × S√n, x + 2.064 × S√n)

(49.98 - 2.064 × 0.14√25, 49.98 + 2.064 × 0.14√25)

(49.98 - 2.064 × 0.7, 49.98 + 2.064 × 0.7)

(49.98 - 1.444 , 49.98 + 1.444)

(48.536, 51.424)

Therefore 95% confidence that machine calibrated properly is

(48.536, 51.424).

The 95% confidence interval is a range of values that you can be 95% confident contains the true mean of the population.

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Option A satisfy the equation after simplification that is y(y-1) / 3(y+1) when the equation that is 36y / (y²- 2y+1) ÷ 12y² / (y²-1)

Given that,

We have to simplify the equation that is

36y / (y²- 2y+1) ÷ 12y² / (y²-1)

We know that,

We have to divide the equations,

36y / (y²- 2y+1) ÷ 12y² / (y²-1)

We can write in multiplication form that is

36y / (y²- 2y+1) × (y²-1) / 12y²

Now we can divide the 36y by 12 y² we get 3/y

3(y²-1)/ y(y²- 2y+1)

We can write the y²-1 as (y-1)(y+1) and by formula y²-2y+1 as (y-1)²

3(y-1) (y+1)/ y (y-1)²

Now we can divide

3(y+1)/ y(y-1)

So we can see in the options

Therefore, Option A satisfy the equation after simplification that is y(y-1) / 3(y+1) when the equation that is 36y / (y²- 2y+1) ÷ 12y² / (y²-1)

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As we know that, while finding any angles on a line, the full angle is 360°.

Now we have three angles in the image and their sum will be 360°, and the angles are :

Now, 68° + 90° + y = 360°

=> 158° + y = 360°

=> y = 360° - 158°

=> y = 202°

Hence, y = 202° is the answer.

Answer:

a. 0.00,323

b. 745,000

Step-by-step explanation:

a) move the decimal 3 places to the left

b) move the decimal 5 places to the right.

Answer: B

Step-by-step explanation: B. So that people would keep buying new things

Goods are often planned to become obsolete in order to encourage people to continue buying new things. This can be done by intentionally designing products with a limited lifespan or by using materials that are prone to wear and tear. Companies may also release new versions of products or discontinue support for older models in order to encourage consumers to upgrade to the latest version. By making their products become obsolete, companies can create a sense of urgency for consumers to keep buying new things and maintain their sales.

Using listing method the elements in the set are +2 and -2.

What is listing method ?

The listing approach involves writing the members of the set as a list, with commas separating the items and curly brackets enclosing the list. The rule or condition that may be used to determine if an object can belong to the set is specified when using the rule method for sets.

The members of a set are listed using this technique, with commas used to separate them and curly braces used to enclose the list. The four distinct seasons, for instance, can all be written as "Summer, Autumn, Spring, and Winter." The list's elements can be in any order, so don't worry.

We are given the set [tex]\left\{x \mid x^2=4\right\}[/tex]

all such x such that the perfect square is 4. Now, we have

[tex]$x^2=4 \Rightarrow x=\pm 2$[/tex]

Therefore, the elements in the set are +2 and -2.

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The sum is 9/28

What is sum ?

The outcome of adding numbers or quantities mathematically is a summation, often known as a sum. A summation always has an even number of terms in it. There may be just two terms, or there may be 100, 1000, or even a million.

The end result of addition is a sum. For instance, the sum 10, written, is obtained by adding 1, 2, 3, and 4. (1) The sum of the numbers is known as the sum of the addends, or summands occasionally.

1/4 + 1/28 + 1/70 + 1/30 + ............ 1/700

Multiply and divide by 3 in whole series

⇒ 1/3 X [3/4 + 3/28 + 3/70 + 3/130 + ......... 3/700]

⇒1/3 X [1-1/4+1/4-1/7+1/7-1/10+1/10-1/13+..........1/25-1/28]

⇒1/3 x [1 - 1/28]

⇒1/3 * 27/28

⇒ 9 / 28

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Answer:

1/32  

Step-by-step explanation:

There are  2^5   outcomes from flipping 5 times = 32

  only ONE is   T  T  T  T  T         1 OUT OF 32 =  1/32

The Medals are as follows:

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

A + B + C = 119

Country B won 9 more than Country C so:

B = C + 9

Also, Country A won 39 more than the other two combined so:

A = B + C + 39

  = (C + 9) + C + 39

  = 2C + 48

Now we substitute into the equation:

A + B + C = 129

(2C + 48) + (C + 9) + C = 129

4C + 57 = 129

4C = 72

C = 18

So, if B = C + 9  then B = 27

and, A = 2C + 48 = 36+ 48 = 84

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Answer:

-6

Step-by-step explanation:

12-8x= -5x-5x

Combine like terms

12-8x= -10x

Add 8x to both sides

12-8x= -10x

  +8x.  +8x

12= -2x

Divide both sides by -2

12= -2x

/-2.   ;-2

-6=x

Hopes this helps please mark brainliest

The triangles are similar triangles. Then the value of the variable 'x' will be 6.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

Similar triangles are shown below.

We know that the ratio of the corresponding sides of similar triangles remains constant. Then the equation is given as,

(6x - 1) / 15 = 14 / 6

Simplify the equation, then we have

(6x - 1) / 15 = 14 / 6

(6x - 1) / 5 = 7

6x - 1 = 35

6x = 36

x = 6

The triangles are comparable triangles. Then, at that point, the worth of the variable 'x' will be 6.

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Answer:

(x-3)^2=17

Step-by-step explanation:

i took dis test b4

Answer:

[tex]\textsf{B)} \quad y-9=2(x-2)[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}[/tex]

Given points:

Substitute the given points into the slope formula to find the slope of the line:

[tex]\implies m=\dfrac{9-(-1)}{2-(-3)}=\dfrac{10}{5}=2[/tex]

[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]

Substitute the found slope and point (-3, -1) into the point-slope formula:

[tex]\implies y-(-1)=2(x-(-3))[/tex]

[tex]\implies y+1=2(x+3)[/tex]

Substitute the found slope and point (2, 9) into the point-slope formula:

[tex]\implies y-9=2(x-2)[/tex]

Therefore, the correct answer option is:

[tex]\textsf{B)} \quad y-9=2(x-2)[/tex]

Answer: $385,993.09

Step-by-step explanation:

Initial Amount: 6500

Rate: 0.0911 comp. monthly

Time: 45 years

Answer: 385,993.09

The interval notation of domain and range is (-∞, ∞).

Interval notation:

In algebra, interval notation refers the way to describe continuous sets of real numbers by the numbers that bound them.

Given,

Here we need to write the interval notation of domain and range.

In order to find the interval notation, first we have to know the definition of domain and range.

In math domain refers the domain of a function is the set of values that we are allowed to plug into our function. Basically, this set is the x values in a function such as f(x).

And where as the range of a function is the set of values that the function assumes. And it is the values that the function shoots out after we plug an x value in.

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The value of p(12) is $996

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

"Find p(24)" also means "Find the amount of money Owen pays for lawn service after 12 months" as we're given 12 for t. As such, rewrite the given function as p(12) = 108 + 74(12)

p(12) = 108 + 74(12)

p(12) = 108 + 888

p(12) = $996

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The required number of employees does it have in total is 68877.

A percentage is a part of an entire communicated as a number somewhere in the range of 0 and 100 as opposed to as a small portion. Something is all 100%, a big part of it is 50%, none of something is zero percent. To decide a rate, you partition the piece of the entire by the actual entire and duplicate by 100.

Let total population of the company be X

So,

19.6% of x = 13500

x(19.6/100) = 13500

X = 13500×100/19.6 = 68877 employees

Thus, required number of employees is 68877.

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