The equivalent rational expression of the given expression, 9/5u² - 40u - 45, is 9/(5u + 5)(u - 9)
The equivalent rational expression of the given expression, 2u/5u² + 30u + 25 , is 2u/(5u + 5)(u + 5)
Writing equivalent expressionsFrom the question, we are to rewrite the given expressions as equivalent rational expressions.
The given expressions are:
9/5u² - 40u - 45 and 2u/5u² + 30u + 25
Writing an equivalent expression for 9/5u² - 40u - 45
Factorize the denominator
5u² - 40u - 45
5u² - 45u + 5u - 45
5u(u - 9) + 5(u - 9)
(5u + 5)(u - 9)
Thus,
The equivalent expression is 9/(5u + 5)(u - 9)
Writing an equivalent expression for 2u/5u² +30u + 25
Factorize the denominator
5u² +30u + 25
5u² +25u + 5u + 25
5u(u + 5) + 5(u + 5)
(5u + 5)(u + 5)
Thus,
The equivalent expression is 2u/(5u + 5)(u + 5)
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I need help on this Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
Answer:
{3, 4, 6, 7, 8}
Step-by-step explanation:
For sets U = {1, 2, 3, 4, 5, 6, 7, 8}, A = {1, 2, 5, 6}, and C = {1, 2, 3, 4, 5}, you want the set {A∩C}'.
A∩CThe set A∩C contains the elements that are common to both sets. Those are {1, 2, 5}.
{A∩C}'The set of interest contains the elements of U that are not in A∩C. Those are ...
{3, 4, 6, 7, 8}
__
Additional comment
DeMorgan's theorem tells us the desired set is equivalent to A'∪C', or {3, 4, 7, 8}∪{6, 7, 8}. That, too, is ...
(3, 4, 6, 7, 8}
The board of a major credit card company requires that the mean wait time for customers when they call customer service is at most 3.50 minutes. To make sure that the mean wait time is not exceeding the requirement, an assistant manager tracks the wait times of 41 randomly selected calls. The mean wait time was calculated to be 3.94 minutes. Assuming the population standard deviation is 1.30 minutes, is there sufficient evidence to say that the mean wait time for customers is longer than 3.50 minutes with a 95% level of confidence?
Step 2 of 3 : Compute the value of the test statistic. Round your answer to two decimal places.
The value of the test statistic is given as follows:
z = 2.17.
There is sufficient evidence to say that the mean wait time for customers is longer than 3.50 minutes.
How to obtain the value of the test statistic?The value of the test statistic is obtained using the z-distribution, as the population standard deviation is known in the context of this problem.
The equation that gives the test statistic is given as follows:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which the parameters of the equation are listed as follows:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value claimed at the test of the hypothesis.[tex]\sigma[/tex] is the standard deviation of the population.n is the sample size.In the context of this problem, the values of these parameters are given as follows:
[tex]\overline{x} = 3.94, \mu = 3.50, \sigma = 1.30, n = 41[/tex]
(all values are taken from the text).
Then the numeric value of the test statistic is obtained as follows:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{3.94 - 3.50}{\frac{1.30}{\sqrt{41}}}[/tex]
z = 2.17.
There is sufficient evidence to say that the mean wait time for customers is longer than 3.50 minutes, as the critical value for the right-tailed test with 95% confidence is of z = 1.645, and the test statistic is greater than this.
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What is the graph of the system of inequality?
Graph of the system of inequality is a solid line and a portion of area is shaded which satisfy the condition of the inequality.
What is inequality?
When left hand side is not exactly equal to the right hand side of an equation then it is known as inequality. For system of inequality, there are four types of inequalities <, >, [tex]\le[/tex], and [tex]\ge[/tex].
Using following steps anyone can graph the inequality:
1. Get y alone on one side of a linear inequality in two variables (like x and y) before graphing it. Then, take into account the associated equation that was created by switching the inequality sign for an equality sign. This equation has a line as its graph.
2. The graph is a dashed line if the inequality is strict ( < or >). The graph is a solid line if the inequality is not strict ([tex]\le[/tex] or [tex]\ge[/tex] ).
3. The last step is to choose a point that is not on either line (typically (0, 0) is the simplest) and determine whether or not these coordinates fulfil the inequality. If so, shade the portion of the half-plane that contains that point. If not, shade the opposite half-plane.
Hence, the graph of the system of inequality is a solid line and a portion of area is shaded which satisfy the condition of the inequality.
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A certain triangle has a 30° angle and a 60° angle. Which must be a true
statement about the triangle?
OA. The longest side is 3 times as long as the shortest side.
OB. The second-longest side is twice as long as the shortest side.
OCTwo sides of the triangle have the same length.
Sons
D. The longest side is twice as long as the shortest side.
Answer:
D. The longest side is twice as long as the shortest side.
Step-by-step explanation:
Given one angle is 30° and another is 60°, the third must be 90°, making a Special 30-60-90 triangle. In a 30-60-90 triangle, the hypotenuse (longest side) is twice (two times) as long as the shortest side.
what are the 12 kinds of polygons
The 12 kinds of polygons are:
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
Hendecagon
Dodecagon
Tridecagon
Tetradecagon
Polygons:
A polygon is a closed shape figure that has a minimum of three sides and three vertices.
Poly → many
gon → angle
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After a 20% discount, you purchase a television for $240. What was the television's
price before the reduction? (Define a variable, create an equation, solve using algebra,
and answer in a sentence.)
===========================================
Work Shown:
x = price of the TV before the discount
20% of x = 0.20x = discount, aka amount saved
x - 0.20x = 0.80x = price after discount
0.80x = 240
x = 240/0.80
x = 300
The TV was $300 before the discount.
-------------
Check:
20% of 300 = 0.20*300 = 60 dollars is the amount saved
300-60 = 240 is the price after the discount, which matches the given info. The answer is confirmed.
Volunteers are folding pamphlets. The time it takes to fold the pamphlets varies directly with the number of pamphlets and inversely as the number of volunteers working. If it takes 4 volunteers 2 hours to fold 400 pamphlets, how long would it take 5 volunteers to fold 600 pamphlets?
Answer:
2 hours and 24 minutes
Step-by-step explanation:
If each worker does 100 each hour than 5 workers do 500 in 2 hourse leaving 100 left so then you 2 hours aka 120 minutes divided by 5 = 24 so it all adds to be 2 hours 24 minutes
1 Select the correct answer. Each statement describes a transformation of the graph of . Which statement correctly describes the graph of y = f(x − 7) + 3? A. It is the graph of f translated 3 units up and 7 units to the left. B. It is the graph of f translated 7 units down and 3 units to the right. C. It is the graph of f translated 7 units up and 3 units to the right. D. It is the graph of f translated 3 units up and 7 units to the right.
Using translation concepts, it is found that the correct option is:
D. It is the graph of translated 3 units up and 7 units to the right.
The parent function is:
[tex]f(x)=y=1nx[/tex]
Shifting a function a units to the right is equivalent to finding f(x - a), thus:
[tex]f(x-7)=1n(x-7)[/tex]
Shifting a function a units up is equivalent to finding f(x) + a, thus:
[tex]f(x-7)+3=1n(x-7)+3[/tex]
Which means that the function was shifted 7 units to the right and 3 up, thus, option D is correct.
The sum of two numbers is 66. Two times the lesser number is 15 more than the greater number. What are the numbers
If x is a lesser number, the equation is
Answer:
See below!
Step-by-step explanation:
Let the two numbers be x and y
Condition # 1:x + y = 66 ----------------(1)
Condition # 2:2x = y + 15
2x - y = 15 ---------------(2)
Add both equations
x + y + 2x - y = 66 + 15
x + 2x = 66 + 15
3x = 81
Divide both sides by 3
x = 27Put x = 27 in Eq. 1
27 + y = 66
Subtract 27 to both sides
y = 66 - 27
y = 39[tex]\rule[225]{225}{2}[/tex]
II. Write each improper fraction as a mixed number and each mixed number as a improper fraction 23/5 20/12 3 3/4 4 7/15 18/8 45/18 8 3/10 1 11/12
Answer: 23/5 = 4 3/5
20/12 = 1 8/12 = 1 2/3
3 3/4 = 15/5
4 7/15 = 67/15
18/8 = 2 2/8 = 2 1/4
45/18 = 2 9/18 = 2 1/2
8 3/10 = 83/10
1 11/12 = 33/12
Step-by-step explanation:
What is the equation of the line of symmetry for the parabola represented by the equation y=−2(x−7^)2+11?
Enter your answer as the correct equation, like this: x = 42
Answer:
x = 7
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]
Given equation:
[tex]y=-2(x-7)^2+11[/tex]
The given equation is in vertex form.
The axis of symmetry of a parabola with a vertical axis of symmetry is:
x = hwhere h is the x-value of the vertex.
As the vertex of the given equation is (7, 11), the axis of symmetry is:
x = 7help me i dont get this at all
Answer: 18
D
Step-by-step explanation:
The constant of proportionality is y/x, not x/y, which is what your friend found.
X= 1
y=18
18/1=18
5 2/3 divided by 2 1/8 Perform the indicated operation.
Answer: 2 and 2/3
Step-by-step explanation: To divide these mixed numbers, I would first rewrite them as improper fractions.
You should be familiar with how do this and if you aren't, send me a comment below and I can give you a quick review.
So 5 and 2/3 becomes 17/3 and 2 and 1/8 becomes 17/8.
This gives us 17/3 ÷ 17/8.
When we divide fractions, we just change the division sign
to multiplication and take the reciprocal (flip) the second fraction.
So we have 17/3 · 8/17.
before multiplying, we can cross-cancel the 17's by dividing by their greatest common factor of 17 to get 1.
So we have 1/3 · 8/1 which is 8/3.
Now since 3 goes into 8 twice, our we have 2 as our whole fraction.
Since there is 2/3 left over, we have a fraction of 2/3.
So our final answer is 2 and 2/3.
Look at the pattern.
72, 67, 62, 57
Which of these is the rule for the pattern?
a
b
d
subtract 5
add 5
subtract 9
add 9
Answer:
Subtract 5
Step-by-step explanation:
72 , 67, 62, 57,..
Each term is obtained by subtracting 5 from the previous term.
72 - 5 = 67
67 - 5 = 62
62 - 5 = 57
WHAT WILL YOU WEAR?
You are getting ready for Thanksgiving dinner and trying to find the perfect outfit. You want to wear your new sweater from Infinity21. The manufacturer advertises that this sweater is most comfortable to wear when the temperature satisfies |t-56| ≤6 degree: Fahrenheit. The weaather report says it will be 53°F on Thanksgiving Day at mealtime.
Can you wear your new sweater comfortably?
By solving a linear inequation, it can be concluded that
The sweater can be worn comfortably
What is a linear inequation?
Inequation shows the comparision between two algebraic expressions by connecting the two algebraic expressions by > . < , ≤, ≥
A one degree inequation is known as linear inequation.
Here, the given linear inequation is
[tex]|t - 56| \leq 6\\t - 56 \geq -6 \ or \ t - 56 \leq 6\\t \geq 56 - 6 \ or \ t \leq 56+6\\t \geq 50 \ or \ t \leq 62\\50 \leq t \leq 62[/tex]
As 53° F lies between 50 and 62, the sweater can be worn comfortably
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Annika is comparing two companies based on the costs for renting a bike for the . Company A charges a $20 rental fee plus $4.50 the bike is rented. Company B charges a 9 rental fee plus $6.50 per hour the bike is rented.
Answer:
depends on how long u need it for
Step-by-step explanation:
convert 1/2 into a decimal
Answer:0.5
Step-by-step explanation:
here you go
What is the rule of proof?
The rules of proof is that every statement should be justified and never assume things when proofing in contradiction
The basic rules of proofs are as followings:
Each assertion should be legitimate.A support can allude to earlier lines of the verification, the speculation as well as recently demonstrated explanations from the book.Cases are frequently expected to finish a proof which has proclamations with an "or" in them.A logical inconsistency is reached when an assertion goes against any of the speculations, an earlier line of the confirmation, or any well established truth .A proof by logical inconsistency is possibly finished when a logical inconsistency has been arrived at for each situation.On the off chance that you can't find a defense and you are certain it is valid, you might wish to compose a separate verification as an after thought to demonstrate that support and afterward apply it to your unique circumstanceDuring a proof you might present new factors by saying "Let x be..."To know more about Proof here
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Luke and Cade have started running. Luke runs 15 more than three times the number of miles Cade runs. Together they run a total of 63 miles. Write an equation to determine the number of miles Luke and Cade ran.
*
1 point
3x + 15 = 63
x + 15 + 3x = 63
x - 15 + 3x = 63
3x - 15 = 63
The Linear equation that represents the above situation is given by
x + 3x + 15 = 63
Linear Equation:A linear Equation is a Mathematical expression that is used to calculate an unknown number of values or any unknown quantity. Here we use variables to represent the unknown numbers.
Here given that
Luke and Cade have started running
Luke runs 15 more miles than thrice of that of number of miles Cade runs
Since we don't know the number of miles run by Cade
Let us assume that Cade runs x miles
=> Number of miles run by Cade = x miles
From the given data,
The number of miles run by Luke will be = 3x + 15
=> Number of miles run by Luke and Cade = x + 3x + 15
Given that the total mile run by Luke and Cade = 63 miles
=> x + 3x + 15 = 63
Therefore,
The Linear equation that represents the above situation is given by
x + 3x + 15 = 63
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if I can vaccinate 10 people in 2 hours. how many people will I get vaccinated in 5 hours?
y=the number of people being vaccinated
x= the number of hours
Answer:
25 people
Step-by-step explanation:
10 people will be vaccinated for 2hrs
10 = 2
y people will be vaccinated for 5hrs
y = 5
(To find y we need to cross multiply)
10 = 2
y = 5
2y= 50
y=50/2
y=25
:- 25 people will be vaccinated in 5hrs.
Lets check if our answer is correct let us make 5 hrs our unknown x
10 = 2
25 = x
(cross multiply)
25×2=10x
50=10x
x=5hrs
so our answer is correct.
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You read 6 chapters. Each chapter has 8 pages. Your brother reads the same number of pages. His chapters have 12 pages. How many chapters does your brother read?
The sixth chapter's Brother 0.66 pages were read.
How to calculated the chapters in 12 pages?According to the order of operations, you should perform multiplication and division first, going from left to right, before adding and subtracting.
Add and subtract from left to right while continuing to multiply and divide. the next step is to add and subtract from left to right.
Assumed the question is how many pages are in each chapter.
Let it be x:
6x + 8 = 12
6x = 4
x = 4 /6
x = 0.66.
The sixth chapter's Brother 0.66 pages were read.
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What are the 7 types of triangles?
The 7 names of triangles:
Scalene, Isosceles, Equilateral, Equiangular triangle, Acute triangle,
Right triangle, Obtuse triangle
What are triangles?
Three vertices make up a triangle, a three-sided polygon. The triangle's angles are formed by a point where the three sides are joined end to end. The triangle's three angles add up to a total of 180 degrees.
Equiangular triangle: All angles are equal.
Acute triangle . . . all three angles are less than 90°
Right triangle . . . one angle is 90°
Obtuse triangle . . . one angle is greater than 90°
Equilateral triangle . . . all three sides are the same length
Isosceles triangle . . . two sides are the same length
Scalene triangle . . . all three sides are different lengths
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if somthing costid 64 dolers and thay sold it for 90% of the originol price how much wold it be
?
Answer:
6.40
Step-by-step explanation:
For this we will divide,
look below for a explanation
Purchase Price:
$64
Discount:
(64 x 90)/100 = $57.60
Final Price:
64 - 57.60 = $6.40
If −2≤f(x)≤5 on [−1,3] then find upper and lower bounds for ∫−13f(x)dx
Answer:
Answer is attached as a photo. I will be honest I am not familiar with a calculus problem being set up that way. I am guessing that is what they are looking for...
Step-by-step explanation:
The upper bound of the given function is 20 while the lower bound of the given function is -8.
What is a function?A certain kind of relationship called a function binds inputs to essentially one output.
In other words, the function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +6 like that.
As per the given function,
-2 ≤ f(x) ≤ 5
At the upper bond, f(x) = 5
[tex]\int\limits^{3}_{-1} {f(x)} \, dx[/tex] = [tex]\int\limits^{3}_{-1} {5} \, dx[/tex]
⇒ 5(3 + 1) = 20
At the lower bond f(x) = -2
[tex]\int\limits^{3}_{-1} {f(x)} \, dx=\int\limits^{3}_{-1} {-2} \, dx[/tex]
⇒ -2(3 + 1) = -8
Hence "The upper bound of the given function is 20 while the lower bound of the given function is -8".
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0 x ≤-21
0 x ≤21
0 x ≤-15
0 x ≤15
21. 2z>-28 (I point)
O z>-56
O z>-14
O z<-14
O z<14
Answer: [tex]z > -14[/tex]
Step-by-step explanation:
Divide both sides by 2.
Lydia and Claudia have the same number of charms in their collections. Lydia started with 6 charms and bought 3 more packs. Claudia started with 9 charms and bought 2 more packs. If each pack had x charms, which equation be used to find x?
A. x=(2+3)-(6+9)
B. x=6+3+9+2
C. 6x+3=9x+2
D. 3x-2x=6+9
E. 3x+6=2x+9
The equation that can be used to find x is
3x + 6 = 2x + 9
Option E is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Lydia started with 6 charms and bought 3 more packs.
Claudia started with 9 charms and bought 2 more packs.
If each pack had x charms.
This can be written as,
Lydia:
Number of charms = 6 + 3x
Claudia:
Number of charms = 9 + 2x
Now,
Lydia and Claudia have the same number of charms in their collections.
This can be written as,
6 + 3x = 9 + 2x
3x + 6 = 2x + 9
Thus,
The equation that can be used to find x is
3x + 6 = 2x + 9
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A recipe for flapjacks uses only syrup, butter and oats, in the ratio 1: 2: 3
a) Trevor makes some flapjacks using this recipe and uses 200g of syrup.
(i) What quantity of butter should he use? _________g
(ii) What quantity of oats should he use? _________g
b) Using this recipe, 150g of syrup are needed to make 8 flapjacks. Find the quantity of oats needed to make 16 of these flapjacks.
Answer: _____g
By using Unitary method, it can be calculated that
a) Quantity of butter Trevor uses = 200 [tex]\times[/tex] 2 = 400 g
Quantity of oats Trevor uses = 200 [tex]\times[/tex] 3 = 600 g
b) 900 g of oats is required to make 16 flapjacks
What is Unitary method?
Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity
Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.
Here Unitary method will be required
a) Let Trevor use x g Syrup, 2x g butter and 3x g oats
Trevor uses 200 g syrup
So x = 200
i) Quantity of butter Trevor uses = 200 [tex]\times[/tex] 2 = 400 g
ii) Quantity of oats Trevor uses = 200 [tex]\times[/tex] 3 = 600 g
b) To make 8 flapjacks 150 g of syrup is used
To make 1 flapjack [tex]\frac{150}{8}[/tex] g of syrup is used
To make 16 flapjacks [tex]\frac{150}{8} \times 16[/tex] g of syrup is used
To make 16 flapjacks 300g of syrup is used
To make 16 flapjacks 300 [tex]\times[/tex] 3 g of oats is used
To make 16 flapjacks 900 g of oats is used
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Graph -7x+5y=35−7x+5y=35minus, 7, x, plus, 5, y, equals, 35.
Answer:
835786543225644323567
-18-18 Swap sides variables are on the 1eft and
changes sign direction. Please help me graph answer x2>-18 thanks
The graph of the expression x² > -18 does not exist
How to determine the graph of the expression?From the question, we have the following inequality expression that can be used in our computation:
x2 > -18
This expression can be rewritten properly
So, we have the following representation
x² > -18
Next, we take the square roots of both sides of the expression
This gives
√x² > √-18
Evaluate the exponents
So, we have
x > 3√-2
The radical is a complex number
This means that the inequality expression cannot be graphed (because of the presence of the complex expression)
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Chelsey puts twelve colored pieces of chocolate candy in a bag. Three pieces are green, four pieces are yellow, two pieces are purple, and three pieces are red. She draws one piece of candy from the bag at a time and eats it.
problem A: What is the probability that Chelsey will draw out three pieces of candy in this order: red, green, yellow?
Problem B: What is the probability that Chelsey will draw out three pieces of candy in this order: green, yellow, red?
problem C: What is the probability that Chelsey will draw out three pieces of candy in this order: yellow, red, green?
problem D: Make a conclusion about how the order in which she draws out the red, green, and yellow pieces affects the probability.
The probability for each event are
[A] - 36/1320
[B] - 36/1320
[C] - 36/1320
[D] - The probability doesn’t change in any order.
What is a expression? What is a mathematical equation? What is Probability?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. The formula to calculate the probability of occurrence of an event 'A' can be written as -P(A) = n(A)/n(S)
where -
n(A) = Number of outcomes favorable to event A.
n(S) = Total number of outcomes
We have Chelsey who puts twelve colored pieces of chocolate candy in a bag. Three pieces are green, four pieces are yellow, two pieces are purple, and three pieces are red. She draws one piece of candy from the bag at a time and eats it.
[A] -
{3/12} x {3/11} x {4/10} =
36/1320
[B] -
{3/12} x {4/11} x {3/10}
36/1320
{C} -
{4/12} x {3/11} x {3/10}
36/1320
D) The probability doesn’t change in any order.
Therefore, the probability for each event are -
[A] - 36/1320
[B] - 36/1320
[C] - 36/1320
[D] - The probability doesn’t change in any order.
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