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.
Answers
a) Making x the subject of the formula in terms of r is; x = (r + 1)/r
b) Solving for r and x gives; r = 5/3 and x = 8/5
How to change the subject of the formula?a) We are given that;
r = 1/(x - 1)
We are asked to make x the subject of the formula in terms of r. Thus;
Multiply both sides by (x - 1) to get;
rx - r = 1
r + 1 = xr
x = (r + 1)/r
b) We are given that;
xr + ²/₃ = 2r
Put (r + 1)/r for x to get;
r(r + 1)/r + ²/₃ = 2r
r + 1 + ²/₃ = 2r
1 + ²/₃ = r
r = 5/3
Put 5/3 for r into the x equation to get;
x = ((5/3) + 1)/(5/3)
x = (8/3)/(5/3)
x = 8/5
Read more about subject of formula at; https://brainly.com/question/10643782
#SPJ1
Related Questions
The data set of the diameters of the metal cylinders manufactured an automatic machine has sample size of n = 25, mean of x = 49.98 mm and std. of S = 0.14 mm. Expected diameter of metal cylinder is mu = 50.00 mm. Can we be 95% confident that machine calibrated properly? {Solution Tips: Yes; if 95% confidence interval includes expected diameter of metal cylinder.}
Answers
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.
To know more about confidence interval here
https://brainly.com/question/13073612
#SPJ4
Please help, this is geometry and I need to find the measure of the missing angle
Answers
The measure of missing angle is 145°.
Define linear pair theorem.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°.
To learn more about linear pair theorem, visit:
https://brainly.com/question/5598970
#SPJ1
In a recent international sport competition, the top three
countries--Country A, Country B, and Country C-won a total of
129 medals. Country B won 9 more medals than Country C.
Country A won 39 more medals than the total amount won by the
other two. How many medals did each of the top three countries
win?
Answers
The Medals are as follows:
A = 84 medalsB = 27 medalsC = 18 medalsWhat is Algebra?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
Learn more about Algebra here:
https://brainly.com/question/24875240
#SPJ1
Find the value of x.
Answers
The triangles are similar triangles. Then the value of the variable 'x' will be 6.
What is the triangle?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.
More about the triangle link is given below.
https://brainly.com/question/25813512
#SPJ1
Which equation is equivalent to the given equation?
x² - 6x = 8
Answers
Answer:
(x-3)^2=17
Step-by-step explanation:
i took dis test b4
Write answer using listing method
Answers
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.
To learn more about listing method visit:https://brainly.com/question/14934644
#SPJ1
An international company has 11,400 employees in one country if this represents 18.6% how many employees does it have in total?
Answers
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
How do you solve 12-8x=-5x-5x??
Please help me!!
Answers
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
help meeeeeeeeeee pleaseee
Answers
For an average intake of 2200 calories per day, the number of acres of land is approximately 2.
How to solve equations?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.
To know more about solving function: https://brainly.com/question/29626703
#SPJ1
What is the equation in point-slope form of the line that passes through the points (-3, -1) and (2, 9)?
y-1 = 2(x+3)
y-9=2(x-2)
y+9=2(x-2)
y-1= 2(x-3)
Answers
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:
(-3, -1)(2, 9)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]
6) Tyger and Newton have a long jump
competition. Tyger jumps 20% further than
Newton. If Newton jumps 475 cm, how far
does Tyger jump?
★need help solving this problem
Answers
475 times 1.20 equals 570
ANS: Tyger jumps 570 cm
what is 2×1+2×
1/
10
+1×
1/
100
+3×
1/
1000
Answers
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
The four models each show two parallel lines cut by a transversal and some angle measures formed by the
intersection of the lines.
What are the values of angle measures a and b in model 4?
Move the correct answer to each box. Each answer may be used more than once. Not all answers will be used.
19° 71° 90° 109° 180° 119°
The value of a is _____, and the value of b is _____.
Answers
The value of a is 71°, and the value of b is 109°.
What is a parallel line?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;
Corresponding angles, Alternate Interior Angles, Alternate Interior Angles, Alternate Exterior Angles and Consecutive Interior Angles.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°.
Learn more about parallel lines here:
https://brainly.com/question/24607467
#SPJ1
Quadra, PQRS is dilated by scale factor of 1/2 with point or as the center of dilation resulting in the image PQRS which statement is true about line Ps
Answers
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)
Read more about line segment at:
https://brainly.com/question/25727583
#SPJ1
PLS HELP THANK YOU SO MUCH
Answers
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 :
68° 90° yNow, 68° + 90° + y = 360°
=> 158° + y = 360°
=> y = 360° - 158°
=> y = 202°
Hence, y = 202° is the answer.
Find the sum
5. 1/4+ 1/28+ 1/70+ ,.....
Answers
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
To learn more about sum from the given link
https://brainly.com/question/25734188
#SPJ4
Why were goods planned to become obsolete?
A. So that the company would become known for quality goods
B. So that people would keep buying new things
C. So that companies could protect their brand
D. So that people could save as much money as possible
Answers
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.
Given the function p(t) in the graph below, identify the intervals over which the function appears to be decreasing.
Answers
The interval of the domain where the function is decreasing are (0, 1) and (3, 4)
How to determine the increasing interval?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
As the values on the x-axis increaseThe values on the y-axis decreaseThe intervals that represent the above highlights are
From x = 0 to x = 1From x = 3 to x = 4This can be represented as (0, 1) and (3, 4)
Hence, the intervals are (0, 1) and (3, 4)
Read more about function interval at
https://brainly.com/question/1503051
#SPJ1
Bobby and Garnetta thought of four consecutive odd intergers such as five times the sum of the first and the third was 22 greater than the product of 8 and the sum of the second and the fourth. Find the numbers.
Answers
An integer is a whole number x=-11.
What are Integers?The Latin term "Integer," which implies whole or intact, is the source of the English word "integer." A particular category of numbers called integers includes zero, positive numbers, and negative numbers.SymbolThe symbol "Z" stands for an integer.
Z= {……-8,-7,-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8,……}
Example :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.
To Learn more About Integers, refer To:
https://brainly.com/question/929808
#SPJ1
30 POINTS // A spinner is divided into six equal parts numbered 1, 2, 3, 4, 5, and 6. In a repeated experiment, Ryan spun the spinner twice. The theoretical probability of both spins being even numbers is 9 over 36.
If the experiment is repeated 200 times, predict the number of times both spins will be even numbers.
36
50
100
200
Answers
The number of times both spins will be even numbers in 200 spins is (b) 50
How to predict the number of times both spins will be even numbers.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
Read more about probability at
brainly.com/question/251701
#SPJ1
{ (0,5), (9,2), (7,1), (6,3)}, What is the sum of all the elements in the range?
Answers
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].
any help on this question
Answers
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)
To learn more about equation visit: https://brainly.com/question/29657983
#SPJ1
Rewrite the following scientific notation numbers into standard form. (Be sure to use commas)
a. 3.23x10 -3
b. 7.45x10 5 =
Answers
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.
A retirement account is opened with an initial deposit of $6,500 and earns 9.11% interest compounded monthly. What will the account be worth in 45 years?
Answers
Answer: $385,993.09
Step-by-step explanation:
Initial Amount: 6500
Rate: 0.0911 comp. monthly
Time: 45 years
Answer: 385,993.09
i only need 12 and 17, first good response i will give brainliest please i’m desperate
Answers
Answer:
[tex]\textsf{12.} \quad y = 6x - 5[/tex]
[tex]\textsf{17.} \quad y=-\dfrac{1}{4}x-2[/tex]
Step-by-step explanation:
Question 12Find the slope of the line by substituting two points from the given table into the slope formula.
Define the points:
Let (x₁, y₁) = (2, 7)Let (x₂, y₂) = (3, 13)[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{13-7}{3-2}=\dfrac{6}{1}=6[/tex]
Substitute the found slope and point (2, 7) into the point-slope formula to create an equation of the line:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-7=6(x-2)[/tex]
[tex]\implies y-7=6x-12[/tex]
[tex]\implies y=6x-5[/tex]
Question 17Given:
f(4) = 3f(0) = -2Therefore, two points on the line are:
(4, -3)(0, -2)The y-intercept is the y-value when x = 0.
Therefore, the y-intercept of the line is -2.
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$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]
Owen paid a landscaping company $108 for an initial lawn treatment,
then $74 per month thereafter.
The function p(t) = 108 + 74t represents the total amount of money he will
have paid after t months.
Find p(12).
Answers
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
To learn more about the equation from the given link
https://brainly.com/question/28218072
#SPJ1
An international company has 13,500 employees in one country. If this represents 19.6% of the company's employees, how many employees does it have in total?
Round your answer to the nearest whole number.
Answers
The required number of employees does it have in total is 68877.
What is percentage?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.
According to question: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.
To know more about percentage visit:
brainly.com/question/29306119
#SPJ1
What is the probability of obtaining five tails in a row when flipping a coin?
Answers
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
10. The table represents the relationship between the base length and the height of some parallelograms, Both measurements are in inches. What is the relationship between the base length and height of these parallelograms?
Answers
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.
To know more about parallelogram, click on the link
https://brainly.com/question/970600
#SPJ1
Fill in the blanks. (Enter the domain in interval notation.) Function Alternative Notation Domain Range 2. -12 points LarPCakcCC3 4.7002 Fill in the blanks. (Enter the range in interval notation.) Function Alternative Notation Domain Range y cos-1x -1 s x s 1 3. -3 points LarPCakcc3 4.7.003 Fill in the blanks. (Enter the domain and the range in interval notation.) Function Alternative Notation Domain Range y-arctan x y-
Answers
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.
To know more about Interval notation here.
https://brainly.com/question/29531272
#SPJ4