After adding and subtracting the rational expressions , the simplified rational expression is 4x - 4/x² - 5/x³ + 9 .
We first simplify each expression inside the parentheses :
that means :
⇒ (2x + 5/x² -3x) = (2x - 3x + 5/x²) = (-x + 5/x²) ;
⇒ (3x + 5/x³ - 9x) = (-6x + 5/x³) ;
⇒ (x + 1/x² - 9) = (-9 + x + 1/x²) ;
Now we substitute these expressions into original equation/expression :
we get ; (-x + 5/x²) - (-6x + 5/x³) - (-9 + x + 1/x²)
Simplifying further ,
we get ;
⇒ -x + 5/x² + 6x - 5/x³ + 9 - x - 1/x² ;
On Combining the like terms, we get ;
⇒ 4x - 4/x² - 5/x³ + 9
Therefore, the simplified rational expression is 4x - 4/x² - 5/x³ + 9.
Learn more about Rational Expression here
https://brainly.com/question/6460158
#SPJ4
The given question is incomplete , the complete question is
Adding and subtracting rational expressions, Simplify the rational expression (2x + 5/x² -3x) - (3x + 5/x³ - 9x) - (x + 1/x² - 9) .
X-1
2x + 4
6
X
Determine the value of x in the
given diagram
The value of x in the diagram is given as follows:
x = 10.
What are similar triangles?Similar triangles share these two features:
Congruent angles, that is, angles that have the same measure.Proportional side lengths.Considering the similar triangles, the proportional relationship for the side lengths is given as follows:
6/(6 + x) = (x - 1)/(2x + 4).
Applying cross multiplication, the value of x is obtained as follows:
(x - 1)(x + 6) = 6(2x + 4)
x² + 5x - 6 = 12x + 24
x² - 7x - 30 = 0.
Factoring, we obtain the solutions are follows:
(x - 10)(x + 3) = 0.
x - 10 = 0 -> x = 10 -> value of x.x + 3 = 0 -> x = -3 -> extraneous, as a length cannot be negative.More can be learned about similar triangles at brainly.com/question/11920446
#SPJ1
3 ways a relationship is proportianl
the riverton high rockets won their regional basketball tournament and were awarded this trophy. what is the approximate volume of the trophy?
V Prism is V = B × h=9.5*4=38
the volume of a sphere is V = 4/3 π r³=4/3*22/7*9.5=10.47
V=10.47+38=48.476
A measurement of three-dimensional space is volume. It is frequently expressed in numerical form using SI-derived units, as well as different imperial or US-customary units. In contrast to how much space the container actually occupies, the volume of a container is typically thought of as its capacity, or the amount of fluid it could hold. Volume was initially measured using naturally occurring vessels of a comparable shape and then with standardized containers. Arithmetic formulas can be used to quickly calculate the volume of several straightforward three-dimensional shapes. If a formula for the shape's boundary is known, it is possible to use integral calculus to determine the volumes of more complex shapes. objects in the zero, one, and two dimensions have no volume.
Learn more about volume from
brainly.com/question/463363
#SPJ4
PLEEASSE HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
Over the last three evenings, Tammy received a total of phone calls at the call center. The second evening, she received fewer calls than the first evening. The third evening, she received times as many calls as the first evening. How many phone calls did she receive each evening?
Tammy received 19 phone calls on the first evening, 13 phone calls on the second evening, and 76 phone calls on the third evening.
Let's use algebra to solve the problem.
Let x be the number of phone calls Tammy received on the first evening.
According to the problem, she received 6 fewer calls on the second evening than on the first evening. This means that the number of phone calls she received on the second evening is x - 6.
The problem also states that she received 4 times as many calls on the third evening as she did on the first evening. This means that the number of phone calls she received on the third evening is 4x.
We know that Tammy received a total of 108 phone calls over the three evenings. We can use this information to set up an equation:
x + (x - 6) + 4x = 108
Simplifying the equation:
6x - 6 = 108
Adding 6 to both sides:
6x = 114
Dividing both sides by 6:
x = 19
Therefore, Tammy received 19 phone calls on the first evening, 13 phone calls (19 - 6) on the second evening, and 76 phone calls (4 x 19) on the third evening.
To learn more about equations click on,
https://brainly.com/question/21286244
#SPJ4
Complete question is:
Over the last three evenings, Tammy received a total of 108 phone calls at the call center. The second evening, she received 6 fewer calls than the first evening. The third evening, she received 4 times as many calls as the first evening. How many phone calls did she receive each evening?
A ladder 50m long is placed on the ground in such a way that it touches the top of vertical wall 30m high. Find the distance of the foot of the ladder from the bottom of the wall
The distance between the foot of the ladder from the bottom of the wall is 40 meters.
What is the Pythagorean theorem?The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
Here,
The distance between the foot of the ladder from the bottom of the wall can be found by using the Pythagorean theorem.
The ladder is the hypotenuse, with a length of 50m
The distance from the wall to the ground is 30m
The distance from the wall to the foot of the ladder is x
Using the Pythagorean theorem:
x² + 30² = 50²
x² + 900 = 2500
x² = 1600
x = 40
So, the distance between the foot of the ladder from the bottom of the wall is 40 meters.
Learn more about the Pythagorean theorem here:
https://brainly.com/question/14930619
#SPJ9
in a group of 8 students, 5 are first-year students, while 3 are second-year students.in how many unique ways can we form three groups comprising 3, 3, and 2 students? (within group order does not matter)
The total number of ways to form 3 groups comprising of 3, 3 and 2 students is calculated by multiplying the individual numbers of ways, which results in 280.
The formula for calculating the number of unique ways to form three groups comprising of 3, 3, and 2 students is given by:
Number of ways = Number of ways to select 3 first-year students from 5 first-year students x Number of ways to select 3 second-year students from 3 second-year students x Number of ways to select 2 students from 8 students
=[tex]5C3 x 3C3 x 8C2[/tex]
= 10 x 1 x 28
= 280
Therefore, there are 280 unique ways to form three groups comprising 3, 3, and 2 students. This can be seen by considering the total number of possible arrangements of the 8 students into 3 groups of 3, 3 and 2. First, we need to select 3 students from 5 first-year students in 5C3 ways, which is equal to 10. Second, we need to select 3 students from 3 second-year students in 3C3 ways, which is equal to 1. Finally, we need to select 2 students from 8 students in 8C2 ways, which is equal to 28. Therefore, the total number of ways to form 3 groups comprising of 3, 3 and 2 students is calculated by multiplying the individual numbers of ways, which results in 280.
Learn more about total number here:
https://brainly.com/question/14993202
#SPJ4
1.1 write down the loan term of the truck in years
Answer:
if its 50,000k for example it is gonna be Loan term in years is 7 it depends on the price
Step-by-step explanation:
2 of 3
Some people took part in a game. The frequency shows information about their scores.
Score
1-7
8-10
11-15
16-20
21-35
36-50
Estimate the mean.
Give your answer rounded to 2 decimal places.
Frequency
13
1
19
20
19
20
The mean of the given data is 22.39.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Let us form a table by give data
Score Frequency Midpoint(x) fx
1-7 13 4 52
8-10 1 9 9
11-15 19 13 247
16-20 20 18 360
21-35 19 28 532
36-50 20 43 860
Mean=∑fx/N
=52+9+247+360+532+860/13+1+19+20+19+20
=2060/92
Mean=22.39
Hence, the mean of the given data is 22.39.
To learn more on Statistics click:
https://brainly.com/question/29093686
#SPJ9
plssss helppppp
Factor the polynomial.
x³+3x²-x-3
Answer:
(x-1)(x+1)(x+3)
Step-by-step explanation:
[tex]x^3+3x^2-x-3\\=x^2(x+3)-1(x+3)\\=(x^2-1)(x+3)\\=(x-1)(x+1)(x+3)[/tex]
Which equations for the measures of the unknown
angles x and y are correct? Check all that apply.
x = costa
x= sin" E)
x= tan'a
y= sin "(a)
y = cos-'
The correct equations for the measures of the unknown angles x and y are:
x = cos(a), y = sin(a).
The trigonometric functions (sin, cos, tan) are mathematical functions that describe the relationships between the sides and angles of a right triangle. Given an angle a in a right triangle, we can use these functions to find the values of the side ratios for that angle. For example:
sin(a) = opposite side / hypotenuse
cos(a) = adjacent side / hypotenuse
tan(a) = opposite side / adjacent side
In these expressions, "opposite side" refers to the side opposite the angle a, "adjacent side" refers to the side adjacent to the angle a, and "hypotenuse" refers to the longest side in the right triangle (the one opposite the right angle).
The inverse trigonometric functions[tex](sin^-1, cos^-1, tan^-1)[/tex] are the reverse of the trigonometric functions. Given a value of a trigonometric function, the inverse function returns the measure of the angle (in radians) for which that value is the result. For example:
[tex]sin^-1(y) = a (where y = sin(a))cos^-1(x) = a (where x = cos(a))tan^-1(t) = a (where t = tan(a))[/tex]
So, the correct equations for the measures of the unknown angles x and y are:
[tex]x = cos^-1(x)y = sin^-1(y)[/tex]
To learn more about unknown angles please click on below link.
https://brainly.com/question/28040429
#SPJ4
PARALLEL PERPENDICULAR OR NEITHER
Answer: Neither (look at the image for the solution)
Step-by-step explanation:
Answer: parallel
Step-by-step explanation:
look at the lines and u can see two lines so parallel
Money McGuire invests $50.00 in an account that she expects to double each year. How long will it take her investment to reach $3,200.00?
Answer:
6 years
Step-by-step explanation:
You want the length of time it takes for a $50 investment to total $3200 if it doubles in value each year.
Exponential equationThe value of the investment can be described by ...
v = 50·2^t
where t is the number of years.
You want t when v=3200:
3200 = 50·2^t
64 = 2^t
log(64) = t·log(2) . . . . . take logarithms
t = log(64)/log(2) = 6
It will take 6 years for her investment to reach $3200.
__
Additional comment
If you're familiar with powers of 2, you recognize that 64 = 2⁶. Comparing exponents in ...
64 = 2^t
2^6 = 2^t . . . . . use 2^6 for 64
we can see that t=6. The logarithms are used to formalize this comparison.
NEED HELP DUE ON FRIDAY
Use the image in the lesson to answer questions 2, 3, and 4.
2. How does the distance between the focus and directrix affect the shape of the parabola?
3. What seems to need to be true in order for the parabola to open downward (that is, to be shaped like a hill instead of a valley)?
4. The vertex of the parabola is the lowest point on the curve if it opens upward, or the highest if it opens downward. Where is the vertex located in relationship to the focus and directrix?
The parabola's shape is influenced by the separation between its focus and vertex. The parabola becomes wider as the vertex is focused further away (flatter).
What is parabola?A parabola is a plane curve created when a point moves in such a way that the distance it travels from a fixed point to a fixed line. The parabola's directrix serves as the fixed line, while the focus, represented by the letter F, serves as the fixed point. The line through the F and perpendicular to the directrix is the parabola's axis.
2. As illustrated here, the parabola's shape is influenced by the separation between its focus and vertex.
The parabola becomes wider as the vertex is focused further away (flatter).
The parabola becomes thinner as the vertex comes into focus (steeper).
3. If a > 0 in the quadratic equation the parabola opens upward and if a< 0 then the parabola opens downward.
4. The vertex of the parabola is the location where it crosses the axis.
Learn more about parabola here:
https://brainly.com/question/21685473
#SPJ1
A sea horse weighs 42oz. Together, 3 sea monkeys and a sea horse weighs the same as 8 sea monkeys plus 9oz. How much does a sea monkey weigh?
Answer:
a sea monkey weighs 6.6oz
Step-by-step explanation:
The number of calories consumed during a snack varies directly with the number of chocolates eaten. If Jodi eats 2 chocolates, she will consume 72 calories. How many calories will she consume if she eats 5 chocolates.
The required Jodi will consume 180 calories if she eats 5 chocolates.
What is directly Proportional?When two quantities are directly proportional, it indicates that if one increases by a specific percentage, the other also increases by the same percentage. As gas costs increase, the cost of food may as well as well.
According to question:We can use proportionality to solve this problem. Since the number of calories consumed varies directly with the number of chocolates eaten, we can write:
calories consumed / chocolates eaten = constant
Let's call this constant k. We can solve for k using the information given:
72 calories / 2 chocolates = k
k = 36 calories/chocolate
Now we can use this constant to find the number of calories Jodi will consume if she eats 5 chocolates:
calories consumed / chocolates eaten = k
calories consumed / 5 chocolates = 36 calories/chocolate
calories consumed = 5 chocolates * 36 calories/chocolate
calories consumed = 180 calories
Therefore, Jodi will consume 180 calories if she eats 5 chocolates.
To know more about Proportion visit:
brainly.com/question/28979975
#SPJ1
Help me please
Choose all that are correct
A.Random samples from the same population will vary from sample to sample
B.Values of a sample statistic of different random samples of the same size from the same population will be the same
C.As the sample size increases, the sample distribution more closely resembles the population distribution.
D.if a random sample is chosen from a population with a large cluster of points at the maximum, the sample is likely to have at least one element near the maximum.
The solution is, Option a
Stratified random sample
What is random sample?In statistics, a simple random sample is a subset of individuals chosen from a larger set in which a subset of individuals are chosen randomly, all with the same probability. It is a process of selecting a sample in a random way.
here, we have,
Explanation:
(a) In stratified random sampling, a division of the population occurs in such a way that a population is stratified in different small groups or strata with common traits and same proportion both in population and sample. this type of sample so formed is known as stratified random sample.
(b) Simple random Sample:
This sample is formed by the random and unbiased selection of individual that represents the population.
(c) Population:
The entire set of individuals with certain specific characteristics represents a population whereas a sample is drawn out of the population and can be referred to as the subset of the population.
(d) Cluster Sample:
In this, separate sample groups are formed known as clusters, here sampling of random clusters take place.
To learn more on random sample click:
https://brainly.com/question/13934398
#SPJ9
A bank account has an initial balance of $150. Over a one-week period the following occurred.
• $180 was spent on shoes.
• $300 of debt was added to the account as a cash advance.
• $250 of debt was repaid.
• $110 of debt was added because of a bank fee.
• $150 of debt was removed with a cash deposit.
What was the balance of the account at the end of the week?
To find the balance of the account at the end of the week, we need to calculate all the transactions:
Initial balance: $150
Shoes: -$180
Cash advance: +$300
Repaid debt: -$250
Bank fee: +$110
Cash deposit: -$150
So the final balance would be $150 - $180 + $300 - $250 + $110 - $150 = $-70.
This means the balance of the account at the end of the week would be -$70.
A linear equation in one variable can have solution(s).
a. only 1
b. 2
c. 3
d. any number of
a group of 9 people is going to be formed into committees of 4, 3, and 2 people. how many committees can be formed if
There are 20 different combinations of committees that can be formed since no person can serve on more than one committee.
In order to form committees of 4, 3, and 2 people, we must first determine how many combinations are possible. There are 9 people in total, so the first committee must consist of 4 people. That leaves 5 people. The second committee must consist of 3 people, leaving 2 people for the final committee. To calculate the total number of combinations, we must multiply the number of choices for each committee. For the first committee, there are 9C4 combinations, for the second committee there are 5C3 combinations, and for the third committee there are 2C2 combinations. Multiplying these together, we obtain 9C4 x 5C3 x 2C2 = 20 combinations. Therefore, there are 20 different combinations of committees that can be formed since no person can serve on more than one committee.
The complete question: A group of 9 people is going to be formed into committees of 4, 3, and 2 people. How many can be formed if no person can serve on more than one committee?
Learn more about combinations here
https://brainly.com/question/20211959
#SPJ4
Which additional fact would prove that quadrilateral WXYZ is a parallelogram?
here is a quadrilateral WXYZ in which side XY is parallel to side WZ.
A. XY = YZ
B. m∠X + m∠Y = 180°
C. YZ = WX
D. m∠Y ≅ m∠W
The extra information "XY = YZ" would demonstrate that the parallelogram WXYZ is a parallelogram.
The parallelogram theorem is what?Theorem: The area of a triangle is roughly half the area of a parallelogram if they share a base and are situated between the same parallels.
These bisectors meet at a 90-degree angle.
And it indicates that they are parallel.
We discover that there are four congruent triangles, with XY parallel to WZ and WX parallel to YZ even though they are perpendicular to one another.
In addition, contrasting angles are equal.
The properties of the parallelogram are these two latter results.
Therefore, the additional fact "XY = YZ" would demonstrate that the triangular WXYZ is a parallelogram.
To know more about Parallelogram visit:
https://brainly.com/question/29147156
#SPJ1
A tank in the shape of a hemisphere has a radius of 5 feet. If the liquid that fills the tank has a density of 62. 7 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?
The total weight of the liquid in the tank which is hemisphere in shape is 16,415 pounds.
The density and mass are related to each other with the formula -
Density = mass/volume
So, we have the density. We need to calculate the volume of hemisphere which will be accomodating the liquid. Then we will find the mass.
Volume of hemisphere = 2/3πr³, where r represents radius.
Volume = 2/3×π×5³
Performing multiplication, division and taking cube
Volume = 261.8 feet³
Now, mass = density × volume
Mass = 62.7 × 261.8
Performing multiplication
Mass = 16,414.86 pounds
Rounding off
Mass = 16,415 pounds
Thus, the mass of liquid will be 16,415 pounds.
Learn more about hemisphere -
https://brainly.com/question/333717
#SPJ4
Question 7. A boat rental shop rents paddleboats for a fee plus an additional cost per hour. * O
The cost of renting for different numbers of hours is shown in table. Use the table and the
variables to write an equation. Let y = cost and x = hours.
The equation of the given information is y(x) = 5x+10
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between.
Given that cost of renting for different numbers of hours.
The initial cost, regardless of time, is; $10. then the cost will increase at a rate of $5 per hour that the boat is rented.
Therefore, the cost (y) of renting a paddle boat for 'x' hours is:
y(x) = 5x+10
here linear relationship between x and y, where 5 is the slope of the equation, 10 is the y-intercept, the number of hours is the independent variable, and the cost is the dependent variable.
Learn more about equations here;
https://brainly.com/question/25180086
#SPJ9
Solve for x questions in picture
Answer: x = 22
Step-by-step explanation:
Subtract 34 from both sides.
x + 34 - 34 = 56-34 --> x = 22
The rainforest has about 19,000 known species of insects. However, due to deforestation, some
species are becoming extinct. This can be modeled with an exponential function with growth
constant k = -0.05. How many species will be left in......
5 years?
10 years?
100 years?
Answer:
The main cause of deforestation is agriculture (poorly planned infrastructure is emerging as a big threat too) and the main cause of forest degradation is illegal logging. In 2019, the tropics lost close to 30 soccer fields' worth of trees every single minute
solve the system of equations, with a complete solution
Answer: Solutions for x - 4,4,-5 and for y - 3,-3, 0
Step-by-step explanation: I wrote the solutions in order. To solve this question I combined both equations to eliminate the y variable to solve for x. It looked like this : [tex]x^2+x=20[/tex]. I brought the 20 to the other side and got [tex]x^2+x-20=0[/tex]. Then I factored and got [tex](x+5)(x-4)[/tex] which means x = -5 and x = 4. Finally I plugged in these values into the equation to find the possible y values.
1. The sum of two rational numbers is 5
6
. If one of the numbers is 7
36
,
find the other number.
Answer:
So, the rational number is [tex]\frac{52}{12}[/tex] .
Step-by-step explanation:
Let x be the other number.
We know ,
[tex]\frac{7}{36}[/tex] + x = [tex]\frac{5}{6}[/tex]
To find x, we need to convert both to have a common denominator.
So, if we multiply [tex]\frac{7}{36}[/tex] by [tex]\frac{10}{36}[/tex] ,
[tex]\frac{10}{1}[/tex] × [tex]\frac{7}{36}[/tex] + x = [tex]\frac{56}{10}[/tex]
After multiplication the fraction [tex]\frac{7}{36}[/tex] becomes [tex]\frac{70}{360}[/tex] .
[tex]\frac{70}{360}[/tex]+ x = [tex]\frac{56}{10}[/tex]
Now we have common denominator of 360in both fraction,
Now,
we can simplify the equation ,
[tex]\frac{70}{360}[/tex] + x = [tex]\frac{56}{10}[/tex]
70 + 360x = 56 × 36
2520 + 360x = 2016
504 + 360x = 2016
360x = 1512
x = [tex]\frac{1512}{360}[/tex]
=[tex]\frac{52}{12}[/tex]
So, the rational number is [tex]\frac{52}{12}[/tex] .
HELP will give BRAINLYST
John and Mary are building towers out of lego bricks. John used fewer than 18 bricks for his
tower. Mary used twice as many bricks as John. What is the greatest number of bricks Mary
could have used?
Answer:
34 bricks is the greatest amount Mary could have used
Step-by-step explanation:
Arjun's piggy bank contains two kinds of coins and two kind of bills. There are twice as many $1 bills as $5 bills. The number of quarters is 1 more than three times the number of $5 bills. And the number of dimes is 7 less than the number of quarters. How many of each type of bill and coin if the total is $39.90
The total number of each type of bill and coin are
$5 bills x 5,
$1 bills x 10,
quarters x 16,
dimes x 9.
What is Equation ?Equations are mathematical expressions with two algebraic expressions flanking the equals (=) sign on either side. It shows the relationship of equality between the expression written on the left side with the expression written on the right side.
Now in the given question,
$5 bills = x, total = 5x
$1 bills = 2x, total = x
Quarters = 3x + 1, total = 0.25(3x + 1)
Dimes = 3x + 1 - 7= 3x - 6, total = 0.1(3x - 6)
Equation below as the sum, solve for x:
5x + 2x + 0.25(3x + 1) + 0.1(3x - 6) = 39.9
7x + 0.75x + 0.25 + 0.3x - 0.6 = 39.9
8.05x - 0.35 = 39.9
8.05x = 40.25
x = 40.25/8.05
x = 5
Number of each bill and coin:
$5 bills = 5
$1 bills = 2*5 = 10
Quarters = 3*5 + 1 = 16
Dimes = 3*5 - 6 = 9
To know more about equations, visit:
https://brainly.com/question/29657988
#SPJ1
