I’m not sure how to solve this, really need help, would appreciate if you showed work so i could learn how to solve it too thank you
Answers
Answer:
There are two solutions:
[tex]\boxed{v = \dfrac{4}{3} \text { and }v = \dfrac{3}{2}}\\\\or\\\\\boxed{v = 1.3333.... \text{ and }v= 1.5}\\[/tex]
Step-by-step explanation:
The given equation is :
[tex]\dfrac{2}{v-2}=-6\:+\:\dfrac {1}{v-1}\\\\[/tex]
Find the LCM of the denominators:
LCM = [tex]\left(v-2\right)\left(v-1\right)[/tex]
Multiply by LCM:
[tex]\dfrac{2}{v-2}\left(v-2\right)\left(v-1\right)=-6\left(v-2\right)\left(v-1\right)+\dfrac{1}{v-1}\left(v-2\right)\left(v-1\right)[/tex]
Simplify
[tex]\dfrac{2}{v-2}\left(v-2\right)\left(v-1\right):\quad 2\left(v-1\right)[/tex]
[tex]\dfrac{1}{v-1}\left(v-2\right)\left(v-1\right):\quad v-2[/tex]
So the equality becomes
[tex]2\left(v-1\right)=-6\left(v-2\right)\left(v-1\right)+v-2[/tex]
Expand the brackets:
[tex]2\left(v-1\right):\quad 2v-2[/tex]
[tex]\text {Right side becomes: }\\-6\left(v-2\right)\left(v-1\right)+v-2\\Expand \; \left(v-2\right)\left(v-1\right):\quad v^2-3v+2\\\\\text {Right side becomes}\\-6\left(v^2-3v+2\right) + v -2\\= -6v^2+6\cdot \:3v-6\cdot \:2 + v - 2\\\\\\= -6v^2+18v-12+v-2\\\\\text{Simplify}\\= -6v^2+19v-14\\\\\text{Left side}2(v-1= 2v-2\\\\\text{Finally we get}\\2v - 2 = 6v^2+19v-14\\\\[/tex]
Switch sides:
[tex]-6v^2+19v-14=2v-2[/tex]
Move 2 from right to left(sign changes)
[tex]-6v^2+19v-14 + 2 =2v\\\rightarrow -6v^2+19v-12=2v\\\\[/tex]
Move 2v to left side(sign changes)
[tex]-6v^2+19v-12-2v = 0\\\\\rightarrow -6v^2+17v-12=0\\\\[/tex]
This is a quadratic equation which can be solved with a quadratic equation calculator. I used a calculator to solve this:
The solutions are:
[tex]v = \dfrac{4}{3} \text { and }v = \dfrac{3}{2}\\\\\\\text{In decimal these would be}\\\\v = 1.3333.... \text{ and v}= 1.5\\[/tex]
Related Questions
If a cubic polynomial has zeros of 3, -2, 0, write the polynomial in standard form.
Answers
The polynomial in standard form is x³ + 2x² - 3x² - 6x = 0.
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
The cubic polynomial has zeros of 3, -2, and 0.
This means,
x = 3
x - 3 = 0 _____(1)
x = -2
x + 2 = 0 ______(2)
x = 0 ______(3)
Now,
The zeroes can be written as,
x (x - 3) (x + 2) = 0
x (x² + 2x - 3x - 6) = 0
x³ + 2x² - 3x² - 6x = 0
Thus,
x³ + 2x² - 3x² - 6x = 0 is the standard form of the polynomial equation.
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NEED HELP ASAP!!
Given the graph of the function f(x) which graph shows the function g(x) if g(x) = f(x) + 2?
Answers
The graph of function g(x) is given by the following option:
First graph.
(right below the text).
What is a translation?A translation happens when either a figure or a function are moved horizontally or vertically.
The four translation rules for functions are given as follows:
Left a units: f(x + a).Right a units: f(x - a).Up a units: f(x) + a.Down a units: f(x) - a.The definition of function g(x) for this problem is given as follows:
g(x) = f(x) + 2.
Meaning that it underwent a translation of 2 units up, hence the first graph is correct, as the values of x remain constant, just the values of y are increased by two for each point on the graph.
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K
The perimeter of a rectangular sports court is 148 feet. After a game, a player's coach estimates that the athlete has run
a total of 353 feet, which is equivalent to four times the court's length plus seven times its width. What are the
dimensions of the sports court?
The length is
feet.
Answers
Answer: Let's call the length of the rectangular court "L" and the width "W". Then, the perimeter of the court is 2 * (L + W) = 148 feet, so 2 * L + 2 * W = 148 feet.
And, according to the coach's estimate, the athlete ran a total of 4 * L + 7 * W = 353 feet.
We can use these two equations to find the dimensions of the court. Solving the first equation for W:
W = (148 - 2 * L) / 2.
Substituting this expression for W into the second equation:
4 * L + 7 * (148 - 2 * L) / 2 = 353
Expanding and simplifying the right side of the equation:
4 * L + 74 - 7 * L = 353
-3 * L = -279
L = 93 feet.
Finally, using the expression for W from the first equation:
W = (148 - 2 * L) / 2 = (148 - 2 * 93) / 2 = 32 feet.
So the dimensions of the sports court are 93 feet by 32 feet.
Step-by-step explanation:
Sunrise, a bed-and-breakfast hotel, charges a one-time deposit of $25 plus $95 per night. Another bed-and-breakfast hotel called Bright Eyes charges a flat rate of $110 per night. Amanda wants to book a hotel for 5 nights. Which hotel costs less to stay for 5 nights? How much less?
Answers
Answer:
Sunrise: 95x5+25 = 500
Bright Eyes: 110x5= 550
Sunrise Will be 50$ Cheaper
oops sorry did my math wrong
Answer: Sunrise Hotel is cheaper by $50
Step-by-step explanation:
First, you do $95 x 5 nights = $475, and then add $25 and get $500 per night (Sunrise).
Then multiply $110 and 5 nights and get $550 per night (Bright Eyes).
Lastly, subtract $550 and $500 and get $50.
To begin a bacteria study, a petri dish had
2700
bacteria cells. Each hour since, the number of cells has increased by
17%
.
Let
t
be the number of hours since the start of the study. Let
y
be the number of bacteria cells.
Write an exponential function showing the relationship between
y
and
t
Answers
The exponential equation is y = 2700 ( 1 + 0.17 )ⁿ , where n = t , the number of hours since the start of the study
What is exponential growth factor?The exponential growth or decay formula is given by
x ( t ) = x₀ × ( 1 + r )ⁿ
x ( t ) is the value at time t
x₀ is the initial value at time t = 0.
r is the growth rate when r>0 or decay rate when r<0, in percent
t is the time in discrete intervals and selected time units
Given data ,
Let the exponential equation be represented as y
Now , the number of bacteria cells = y
The number of hours since the start of the study = n = t
The initial number of bacteria = 2,700 cells
The percentage of increase in the cells = 17 %
So , The exponential growth formula is given by
x ( t ) = x₀ × ( 1 + r )ⁿ
Substituting the values in the equation , we get
y = 2700 ( 1 + 0.17 )ⁿ
On simplifying the equation , we get
y = 2700 ( 1.17 )ⁿ
where n = t , the number of hours since the start of the study
Hence , the equation is y = 2700 ( 1.17 )ⁿ
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9 create factor trees of the following 8 20 27 36 72
Answers
Factor Trees are diagrams that show the prime factorization of a number by breaking it down into smaller factors until only prime numbers are left.
Here are the factor trees for the numbers you provided:
The Factor Trees8:
8
/
2 4
/
2 2
20:
20
/
2 10
/
2 5
27:
27
/
3 9
/
3 3
36:
36
/
2 18
/
2 9
/
3 3
72:
72
/
2 36
/
2 18
/
2 9
/
3 3.
To solve this, I used the process of prime factorization. Prime factorization is the process of finding the prime numbers that multiply together to form a given number.
The steps I followed to solve this problem are:
Starting with the first number, I divided it by 2 until I couldn't divide it anymore.If the result of the division is not a prime number, I divided it again by the smallest possible prime number.I repeated this process until all the factors of the number were prime numbers.I repeated this process for all the numbers provided.I then organized the prime factors in a tree-like structure, with the original number at the top and the prime factors branching off into their own factors, until all the factors were prime numbers.Read more about factor trees here:
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A car covers a distance of 189km in 4.5 hours, what is the average speed
Answers
Step-by-step explanation:
The average speed is 42 km/hr.
To calculate the average speed, you divide the total distance by the time it took to travel that distance:
189 km / 4.5 hours = 42 km/hr
[tex]\texttt{speed}=\dfrac{d}{t}[/tex]
distance = 189 km
time = 4.5 hours
[tex]\texttt{speed}=\dfrac{189}{4.5}[/tex]
[tex]\fbox{speed = 42 km/hr}[/tex]
In a class full of men and women
2
9
of the class are women. What is the ratio of men to women in its simplest form?
Answers
Explanation: if 2/9 of the class is female, that means that 7/9 of the class is male.
So now, our ratio is7/9:2/9
Notice that both numbers have the common denominator, so we can multiply both sides to eliminate the 9 from the denominator, like so:
7:2
However, we can divide 7 by 2, to get a decimal value:
3.5:1
I hope this helps!
Equivalent to 28 to the second power-3
Answers
Answer:
13 since the second power (-3) is doubled.
The temperature fell from 0Degrees Fahrenheit to 6 and three-fifthsDegrees Fahrenheit below 0Degrees Fahrenheit in 2 and one-fifth hours. What was the temperature change per hour?
A. -3
B. -4 2/5
C. 3
D. 4 2/5
Answers
Calculate the area of a rectangular room that is 72 feet wide and 39 feet long.
Answers
Answer: 2808 ft.
Step-by-step explanation:
72(39) = 2808
Answer:
Area for a rectangle is Length * Width or A=l*w
Length= 72ft
width= 39ft
72*39= 2808
The area of the rectangular room is 2808
Step-by-step explanation:
Hope this helps!! :))) Mark me brainliest! :))
Check each value and decide if it is a factor of 50 or not: 15, 2, 5, 3, 20, 50, 25, 10
Answers
Answer:
3 and 20 are NOT factors of 50.
15, 2, 5, 50, 25, and 10 are factors of 50.
Step-by-step explanation:
Hope it helps! =D
CAN SOMEONE HELP WITH THIS QUESTION?✨
Answers
The differentiation of the f(x) = g(x)/h(x), using the quotient rule, indicates that the value of f'(2) = 20/81
What is the quotient rule?The Quotient Rule for finding the derivative of a ratio of two functions, [tex]f(x) = \frac{g(x)}{h(x)}[/tex] that are differentiable is presented as follows;
[tex]f'(x) = \frac{h(x) \cdot g'(x) - g(x) \cdot h'(x)}{h(x)^2}[/tex]
The equation of the lines are found as follows;
The points on the line g(x) are; (1, 2), and (3, 6)
Therefore, we get;
Slope of the line = (6 - 2)/(3 - 1) = 2
Equation of the line is; y - 2 = 2·(x - 1) = 2·x - 2
y - 2 = 2·x - 2
y = 2·x - 2 + 2 = 2·x
The equation of the line is presented as follows;
g(x) = 2·x
Points on the graph of the function h(x) when x = 2 are; (2.5, 5), and (0, 2.5)
Slope of the graph of h(x) when x = 2 is; (2.5 - 5)/(0 - 2.5) = 1
The equation of the line is therefore; y - 5 = 1·(x - 2.5) = x - 2.5
y - 5 = x - 2.5
y = x - 2.5 + 5 = x + 2.5
h(x) = x + 2.5
f(x) = g(x)/h(x)
The value of f'(x) using the quotient rule, is therefore;
f'(x) = (h(x)·g'(x) - g(x)·h'(x))/(h(x))²
g'(x) = 2
h'(x) = 1
Therefore;
f'(x) = ((x + 2.5)×2 - 2·x × 1)/(x + 2.5)² = (2·x + 5 - 2·x)/((x + 2.5)²)
(2·x + 5 - 2·x)/((x + 2.5)²) = 5/(x + 2.5)²
f'(2) = 5/(2 + 2.5)² = 20/81
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The water level is a number that indicates whether the level is above or below normal using positive or negative values. After a heavy storm, the water level of a river is −3.7 feet. This level is 1/2 times 2.5 feet more than the previous water level.
What was the previous water level?
A. -18.5
B. -9.9
C. -4.9
D. -4.3
Note: I think it is -4.9. If you have the actual right answer please leave it down below. Thanks.
Answers
Answer:
I also believe it is -4.9 but I may be mistaken
Step-by-step explanation:
7. In the first picture of two intersecting lines, what is the m ∠2? How do you know?
8. In the second picture of parallel lines cut by a transversal, which angle is supplementary to ∠8? How do you know?
9. The third picture shows parallel lines cut by a transversal. What is the m ∠2? How do you know?
10. Use the fourth picture of parallel lines cut by a transversal. What is the value of x?
Answers
7. m<2 = 138° based on the definition of vertical angles.
8. m<3 is supplementary to angle 8
9. The measure of angle 2 = 50°
10. The value of x = 20
What is a Supplementary Angle?A supplementary angle is a pair of angles whose sum is equal to 180 degrees. In other words, two angles are supplementary if they add up to a straight angle.
For example, if one angle measures 70 degrees, its supplement would be 180 - 70 = 110 degrees.
7. m<2 = 138° (reason: vertical angles are equal).
8. m<3 is supplementary to angle 8 because angle 3 and 5 are supplementary, and angle 5 is congruent to angle 8.
9. 5x + 55 = 2x + 100 (corresponding angles are equal)
Find x:
5x - 2x = -55 + 100
3x = 45
x = 15
m<2 = 180 - (5x + 55) (linear pair is equal to 180 degrees)
Plug in the value of x
m<2 = 180 - (5(15) + 55)
m<2 = 180 - 130
m<2 = 50°
10. 45 + 5x + 35 = 180 (supplementary angles)
5x + 80 = 180
5x = 180 - 80
5x = 100
x = 20
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if 2x-17=13. then x=?
Answers
Answer:
x=15
Step-by-step explanation:
2x-17=13
2x=30
x=15
Hope this helped! :)
Answer:
15
Step-by-step explanation:
2x - 17 = 13
Add 17 to both sides:
2x = 30
Divide both sides by 2:
[x = 15]
53) Jim drove 180 miles in 5 hours. If he can keep the same pace, how long will it take him to drive 900 miles?
Answers
The total number of hours for Jim to drive 900 miles is given by the proportion A = 25 hours
What is Proportion?The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The proportional equation is given as y ∝ x
And , y = kx where k is the proportionality constant
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given data ,
Let the number of hours for Jim to drive 900 miles be A
Now , the number of hours = 5 hours
The total distance traveled by Jim in 5 hours = 180 miles
Now , the distance traveled by Jim = 900 miles
And , the proportion will be
A / 900 = 5 / 180
Multiply both sides of the equation by 900 , we get
A = ( 5 x 900 ) / 180
On simplifying the equation , we get
A = 5 x 5
A = 25 hours
Hence , the number of hours is 25 hours
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Consider the line y=7x-3.
Find the equation of the line that is parallel to this line and passes through the point (-4,-6).
Find the equation of the line that is perpendicular to this line and passes through the point (-4, -6).
Answers
The equation of the line that is parallel to this line and passes through the point (-4,-6) is y = 7x + 22
The equation of the line that is perpendicular to this line and passes through the point (-4,-6) is y = -(1/7)x - 46/7
What is an equation?An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.
The slope intercept form of a line is:
y = mx + b
where m is the slope and b is the y intercept
Two lines are parallel if they have the same slope and are perpendicular if the product of their slope is -1.
Given the line:
y = 7x - 3
The slope is 7. The line parallel to this line would also have a slope of 7, while the line perpendicular have a slope of -1/7
The equation of the line that is parallel to this line and passes through the point (-4,-6) is:
y - (-6) = 7(x - (-4))
y = 7x + 22
The equation of the line that is perpendicular to this line and passes through the point (-4,-6) is:
y - (-6) = (-1/7)(x - (-4))
y = -(1/7)x - 46/7
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mr. hollens give away $800 per month. He has determind that this is 16% if his buget. About how much is his overall budget
Answers
Answer:
5000
Step-by-step explanation:
800/16% = 5000
I think that is the answer
represent the shaded area in the drawing as a mixed number and also as an improper fraction
I got 1 3/4 & 3/5 but it is incorrect
Answers
Answer:
Mixed number: 1 3/8
Improper fraction: 11/8
Step-by-step explanation:
The first circle is 1 whole 1 = 8/8
The second circle is 3/8 *
8/8 + 3/8 = 11/8
----------------------
If you want to write a mixed number as improper fraction just multiply the whole number by the denominator and add the numerator's fraction.
1 3/8 Mixed number
1x8=8
8+3=11
11/8 Improper fraction
-----------------------
* the second circle is not divided into 4 parts. It is divided into 8 equal parts. Each part is 1/8. There are three shaded parts which means 3/8.
----------------------
I hope this helps!
The mean of the waiting times in an emergency room is 80.2 minutes with a standard deviation of 10.5 minutes for people who are admitted for additional treatment. The mean waiting time for patients who are discharged after receiving treatment is 120.6 minutes with a standard deviation of 18.3 minutes. Which times are more variable?
Answers
The variance for waiting times for patients who are discharged after receiving treatment is more, so waiting times for patients who are discharged after receiving treatment is more variable.
What is variance?In probability and statistics, variance is the actual value of the squared variation of a stochastic process from its mean value. Informally, variance calculates the degree to which a random group of numbers deviates from the mean value.
Another essential tool, the measurement of variance is equal to the square of the standard deviation.
Since the variance for waiting times for patients who are discharged after receiving treatment is more, so waiting times for patients who are discharged after receiving treatment is more variable.
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PLEASE HELP ME ASAP!! THATS ALL I NEED
Randy needs to buy school supplies. He needs a headset that costs $30.00. He also needs notebooks that cost $3.00 each.
Part 1
Complete the table to determine his total cost for a given number of notebooks.
Format your response using 2 decimal places and NO symbols. Example: 25.00
Answers
The total cost for a given number of notebooks is 30 + 3x
How to determine the total cost for a given number of notebooksFrom the question, we have the following parameters that can be used in our computation:
Headset = $30.00
Notebook = $3.00
The total cost for x number of notebooks can be calculated as follows:
$30.00 + (3.00 * x)
So, we have
Total Cost = 30 + 3x
The response in two decimal places is Total cost = 30.00 + x * 3.00
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What is the slope-intercept form of this equation?
3x + 9y = 18
please help :)
Answers
Answer:
Below
Step-by-step explanation:
Solve the given equation for y
3x+9y = 18
9y = -3x + 18 divide by 9
y = - 1/3 x + 2 done
Find Sn for the arithmetic series where a1= 3 , an= 36, n= 12
Find sn for the arithmetic series where a1= 3, d= 2, n= 100
Answers
The value of the sum of the series is are 234 and 10200
How to determine the sum of the seriesIn an arithmetic series, the sum of the first "n" terms (Sn) is given by the formula:
Sn = n/2 * (a1 + an)
Where "a1" is the first term and "an" is the nth term.
For the first series, we have
In this series, a1=3 , an=36 , n=12
Plugging these values into the formula, we get:
Sn = 12/2 * (3 + 36)
Sn = 234
For the second series, we have
In this series, a1=3 , d = 2 , n=100
So, we have
an = a + (n - 1)d = 3 + 99 * 2 = 201
Plugging these values into the formula, we get:
Sn = 100/2 * (3 + 201)
Sn = 10200
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A cylinder has a height of 10cm.
The diameter of the cylinder is
4/5
its height.
Calculate the volume of the cylinder in terms of π.
Answers
The radius is the center of circle to its edge or half of a diameter so half of 4/5 is 0.4 since 0.8 / 2 = 0.4.
To find the volume we need to do the equation π r² h.
So, π x 0.4^2 x 10 = 5.02654825.
Round 5.02654825 to the nearest hundredth and it is 5.03.
Volume is 5.03.
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One inequality in a system is y ≥ 2x + 3. Write another
possible inequality in the system so that (-2, 6) is a solution of the
system.
ystem of
Answers
Answer:
Step-by-step explanation
y≥ 2x + 3 is -6,2
Tanya drove 312 hours and used 13 tank of gas.
For how long could Tanya drive using 12 tank of gas?
Enter your answer as a mixed number in simplest form in the box.
hours please
Answers
Assuming you meant 3/12, 1/3 and 1/2. The answer would be 5[tex]\frac{1}{4\\}[/tex].
Answer:
[tex]288\frac{0}{13}[/tex]
Solution :We can use the proportional method in this question
This case is a direct proportion
What is Direct Proportion?Direct proportion is a type of proportionality relationship. For direct proportion, as one value increases, so does the other value and conversely, as one value decreases, so does the other value. The symbol ∝ represents a proportional relationship.
We put the variable as x that represents the hour
We put it into a fractional form
[tex]\frac{312}{13} = \frac{x}{12}[/tex]
Cross Multiplying
[tex]312X12 = 13x[/tex]
[tex]3744 = 13x[/tex]
[tex]\frac{3744}{13} = x[/tex]
[tex]288\frac{0}{13} = x[/tex]
what the number 125% of 280
Answers
Answer:350
Step-by-step explanation: 280/4=70
280+70=350
Answer:
350
Step-by-step explanation:
The percentage is converted to decimal place and then multiplied by 280
[tex]280(\frac{125}{100} )=280(1.25)=350[/tex]
Hope this helps.
A cuboid has the total surface area 1168 cm². If it's length and breadth are 16 cm and 14 cm respectively, what it's height?
Answers
A cuboid has 6 faces and the formula for its total surface area is:
2lw + 2lh + 2wh, where l is the length, w is the breadth, and h is the height.
Given the total surface area of 1168 cm² and the length and breadth being 16 cm and 14 cm, respectively:
2(16)(14) + 2(16)h + 2(14)h = 1168
Expanding the expression:
448 + 32h + 28h = 1168
Combining like terms:
60h = 720
Dividing both sides by 60:
h = 12 cm
So the height of the cuboid is 12 cm.
Use formula to find the area of the figure
Answers
The area of the figure in this problem is given as follows:
A. 30 in².
How to obtain the area of the figure?The area of a triangle is given by half the multiplication of the base length by the height of the triangle.
Applying the Pythagorean Theorem, we can obtain the missing side length, as follows:
4² + x² = 6²
x² = 36 - 16
x² = 20
x = square root of 20
x = 4.47.
For a right triangle, one side is considered the height of the other, hence the sides are:
4 in.4.47 + 8 = 12.47 in.Hence the area of the triangle is then obtained as follows:
Area = 0.5 x 4 x 12.47
Area = 25 in².
Which is closest to 30 in².
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