Answers
Hello there today we will solve your problem, we will need to factorize btw...
[tex]{\huge{\boxed{\mathfrak{Equation}}}[/tex]
[tex]{\big{\boxed{\frac{x^2-5x+4}{x^2-4x}}}}[/tex]
First we will factor [tex]x^2-5x+4[/tex], which gives us [tex]\left(x-1\right)\left(x-4\right)[/tex]
[tex]\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\left(x-1\right)\left(x-4\right)}{x^2-4x}\\[/tex]
factorize [tex]x^2-4x[/tex] giving us [tex]x\left(x-4\right)[/tex]
[tex]\frac{\left(x-1\right)\left(x-4\right)}{x\left(x-4\right)}[/tex]
cancel the common factor [tex]x-4[/tex]
and we get [tex]\frac{x-1}{x}[/tex]
Related Questions
Write the equation of the line that passes through (0,5) and is perpendicular to the line x = 3.
Answers
Answer:
(0,5)x3=(15,5)
Step-by-step explanation:
nth term of 5,8,13,20,29
Answers
Answer:
nth term = 4 + n^2
Step-by-step explanation:
Sorry if the answer is long but I'm hoping my explanation can help.
In order to understand the issue, we should try to find the pattern between the terms given.
The terms given were 5, 8, 13, 20 and 29.
Between the first term and second term, the difference is 3.
Between the second and third term, the difference is 5.
The pattern goes on and we find out that the difference between the (n-1)th term and the nth term is
2n - 1.
Hence, we can determine the pattern of the numbers is
nth term = (n-1) term + 2n - 1
We can use this to find term 0 (before term 1) by plugging in the values for term 1
5 = 0th term + 2 (1) - 1
5 = 0th term + 1
Hence the 0th term = 4
If we expand on the summation,
We can find the nth term
nth term = 4 + 2 (1) - 1 + 2(2) - 1 + ... + 2(n-1) - 1 + 2n - 1
As we can see, the number 1 has been subtracted n times (excluding the -1 in 2(n-1)). Hence, we can split combine all of the subtracted ones into -n.
We can rewrite it as
nth term = 4 + 2 (1) + 2(2) + ... + 2(n-1) + 2n - n
Now, we will move 4 and n to one side.
nth term = 4 - n + 2 (1) + 2(2) + ... + 2(n-1) + 2n
We can factorize 2 out from every term to the right of -n. This would give out
nth term = 4 - n + 2 (1 + 2 + ... + (n-1) + n)
The term (1 + 2 + ... + (n-1) + n) can actually be rewritten by using the triangular formula.
The triangular formula is stated such that
Tn = (n*(n+1))/2
This heavily simplifies the equation into
nth term = 4 - n + 2 [(n*(n+1))/2]
This equation becomes
nth term = 4 - n + n^2 + n.
Now, we can finally simplify into the final equation
nth term = 4 + n^2
i need help assap
Consider the function g(x) shown below over a domain of [1,∞).
g(x) = 2(x – 1)2 – 3
Part A
Determine g–1(x).
Part B
Identify the domain and range of g(x) and g–1(x). Represent the domains and ranges in inequality, interval, and set notation. Describe the relationship between the domains and ranges of g(x) and g–1(x).
Part C
Graph g(x) and g–1(x). Describe the relationship between the graphs of g(x) and g–1(x).
Answers
In Lucy's coin collection, 15% of the coins are quarters.
If there are 12 quarters, find the total number of coins in Lucy's coin collection.
Answers
The total number of coins in Lucy's coin collection is equal to 80 coins.
Let the total number of coins be C.Given the following data:
Percentage of quarters = 15%Total number of quarters = 12 quartersTo the total number of coins in Lucy's coin collection:
Since the percentage of the quarters in Lucy's coin collection is equal to fifteen percent (15%) of the total number of coins. Thus, we would multiply the total number of coins by 15% and equate it to 12 quarters.
Total number of coins:
[tex]\frac{15}{100} \times C = 12\\\\15C=12 \times 100\\\\15C =1200\\\\C=\frac{1200}{15}[/tex]
C = 80 coins.
Read more on word problem here: https://brainly.com/question/24604067
Answer:
80 coins
Step-by-step explanation:
Let the total number of coins be C.
Given the following data:
Percentage of quarters = 15%
Total number of quarters = 12 quarters
To the total number of coins in Lucy's coin collection:
Since the percentage of the quarters in Lucy's coin collection is equal to fifteen percent (15%) of the total number of coins. Thus, we would multiply the total number of coins by 15% and equate it to 12 quarters.
Total number of coins:
C = 80 coins.
So the total number of coins in Lucy's coin collection is 80 coins.
(03.02 MC)
The vertices of AGHI are G (2, 4), H (4,8), and I (8,4). The vertices of AJKL are ) (1.), K (2, 3), and L (4,1). Which conclusion is true about the triangles?
whats the answer
Answers
Answer:
The coordinates of J are missing. Plus, I don't see options for the conclusions. I made an imaginary point J, which you could correct to form the proper triangle.
Step-by-step explanation:
See the attachment. Plot all the vertices, including a corrected point J and draw the resulting triangle. It might be that AJKL is a slightly smaller, shifted version of AGHI. Enter the correct coordinates and then compare.
2. What is the equation of a line that has a slope of 3 and passes through the point(-1,4)?
y + 4 = 3(x - 1)
y - 1 = 3(x + 4)
y + 1 = 3(x – 4)
y – 4 = 3(x + 1)
Answers
Answer:
last one
Step-by-step explanation:
point slope form:
[tex](y - y1 )= m(x - x1)[/tex]
just plug in the numbers and you will get the answer:
[tex](y - 4) = 3(x + 1)[/tex]
Find the zeros of this polynomial:
p(x)= (x²+4x+3)(x²-4)
Answers
====================================================
Explanation:
Set each factor equal to zero and solve for x. I'm using the zero product property which says A*B = 0 leads to either A = 0 or B = 0.
Let's apply that idea to the first factor.
x^2+4x+3 = 0
(x+1)(x+3) = 0
x+1 = 0 or x+3 = 0
x = -1 or x = -3 are two roots
-------------
Do the same for the other factor as well.
x^2 - 4 = 0
(x-2)(x+2) = 0 .... difference of squares rule
x-2 = 0 or x+2 = 0
x = 2 or x = -2 are another two roots
--------------
In total, the four roots are:
x = -3x = -2x = -1x = 2Side note: The term "root" is the same as the zeros of a polynomial. Visually, this corresponds to the x intercepts. Plugging any of those four items into p(x) will lead to p(x) = 0.
start a conversation with me and you get 100 points :D
Answers
Answer:
lol hi :D
Step-by-step explanation:
Answer:
Hey what's up?
Step-by-step explanation:
How's life
4 divided by 3220 pls help me due in 2 hours
Answers
Answer:
1/805
Step-by-step explanation:
4/3220 = 1/805 = 0.00124223....
Please help on both. I’m not sure of my answrs before I submit. Thank u :)
Answers
Which equation best fits the graphed data?
6+
4+
2+
+X
-6
-4
- 2
2
6
N
-2+
.
.
-4
-6+
Answers
Answer:
D
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
if x + y = 180 and y = 45, then x + 45 = 180 an example of substitution?
Answers
This is an example of substitution because you have substituted the 'y' variable to find the 'x' variable.
Hoped this helped.
[tex]BrainiacUser1357[/tex]
Make x the subject of the formula x/a 2 + 3 b = 2 c
Answers
Answer: x=-3ab/2+ac
Step-by-step explanation:
Multiply to remove the fraction, then set equal to 0 and solve.
PLS ANSWER THE FOLLOWING QUESTION
*AND I WILL MARK U AS BRAINLIST*
Answers
Answer:
729
Step-by-step explanation:
Multiply and cross cancel
Work out the area of the shaded shape.
5m
9m
11m
8m
The diagram is not drawn to scale.
Answers
5x11=55
8-5=3
11-9=2
2x3=6
6+55=61
and since it is the area it is squared
hope this helps
A function f(x) is graphed on the coordinate plane.
What is the function rule in slope-intercept form?
Enter your answer in the box below.
f(x) = ____
Answers
Answer:
mx+b
Step-by-step explanation:
One way to express linear function rules is called slope-intercept form. Sometimes, f(x)=mx+b is used. In either case, m and b describe the general characteristics of the line. m indicates the slope, and b indicates the y-intercept.
The required function of the line would be y = 2x + 1 which is shown in the given graph.
What is the function rule in slope-intercept form?The slope-intercept form is one rule to represent linear function rules. f(x)=mx+b is sometimes used. In any scenario, m and b describe the line's overall features. The slope is denoted by m, while the y-intercept is denoted by b.
According to the given figure,
We clearly see that the coordinates of the y-intercept would be (0, 1).
The value of the x-coordinate is 1 when y-coordinate is 3.
Here the line passes through points (0, 1) and (1, 3).
Let the required linear function would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x₂ -x]
x₁ = 0, y₁ = 1
x₂ = 1, y₂ = 3
⇒ y - y₂ = (y₂ - y₁)/(x₂ -x₁ )[x -x₂]
⇒ y - 3 = (3 - 1)/(1 - 0 )[x -1]
⇒ y - 3 = (2)[x -1]
⇒ y - 3 = 2x - 2
⇒ y = 2x - 2 + 3
⇒ y = 2x + 1
Therefore, the required function of the line would be y = 2x + 1 which is shown in the given graph.
Learn more about the Linear function here:
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#SPJ5
where is paint d on the number line
Answers
Answer:
-1.1
Step-by-step explanation:
=4x+5y=-10
20x - 25y = 50
Answers
B =
Round your answer to the nearest hundredth.
Answers
Answer:
Angle B = 48.19
#Rounded off to the nearest hundredth after the decimal point
Step-by-step explanation:
As Seen in the diagram is a right angled triangle and by using the infamous laws of Trigonometry, we can use the Trigonometric ratios in an indirect sense to find our answer...
Now to solve this question we need to first see what values are given to us! So the values given to us are
Hypotenuse= 3
Adjacent= 2
C= 90° (since it is the angle opposite to the hypotenuse and if observed with every right angled triangle, it will always be the case)
B=?
A=?
Questions objective= find B
I shall provide a labelled version of right angled triangle which shall aid where is the adjacent, opposite or the Hypotenuse below
Now coming back to the question,
The Opposite side of the angle we are trying to find is the adjacent and there are many Trigonometric ratios but for the sake of the question, we will need to use the one affiliated with Cosine
the way we shall interpret it is quite simple
Cos ∅°= [tex]\frac{Adjacent}{Hypotenuse}[/tex]
Now by interpreting the values from the diagram
Cos A°= [tex]\frac{2}{3}[/tex]
Now to find the actual value of a number that has an operation that disrupts the actual value, we only need to use the inverse of the operation on it to find the actual value
so by this statement we need to put an inverse of Cos
∴ A°= [tex]Cos^{-1}[/tex]([tex]\frac{2}{3}[/tex])
A°= 48.1896851
Now we need to subtract the value of 180° - (Angle A + Angle C)
by doing so we will get the value of 41.82 (rounded off to the nearest hundredth)
hence B= 41.82 °
We can add up all the values and it will be approximately be equal to 180 (keep in mind that some of these values of triangle are irrational due to which they never end)
Please do double-check it as I could've made a mistake too
Till then a Thank You, aa 5 Stars or even better, A BRAINIEST will make my day
Take care of yourself and I guess the answers complete :)
Calculate 3 tonnes 335kg - 905kg and give the answer in tonnes
Answers
Answer:
2430kg
Step-by-step explanation:
3 tonnes is 3000kg so 3 tonnes 335kg is 3335kg. Take 3335 - 905 you get 2430
Name the ray in TWO different ways.
M N P
Answers
PM
Assuming your n is on a side
-34 = -8 + 9(b + 4)
What is the value of the variable?
Answers
First switch sides
-8+9(b+4) =-34
Then add 8 to both sides
-8+9(b+4) +8 =-34+8
Then simplify
9(b+4) =-26
Divide both sides by 9
9(b+4) over 9 = -26 over 9
Simplify
B+4 =-26 over 9
Subtract 4 from both sides
B+4-4=-26/9 (over 9) -4
Simplify and get -62/9 (over 9)
Hope this helps :)
Student Council sponsors weekly dances at their school on Friday nights. The admission price for each person is $4 for Student Council members. Members pay an annual fee of $50 for membership dues.
A. Write a function that can be used to determine c, the total cost, for a member to attend n, number of dances a year.
B. How much will a member pay if they attend 15 dances during the school year.
1. Summarize the given situation in your own words. (What do you notice?)
2. Explain: What is the essential information you can use to find the solution?
3. Find the Solutions to parts A and B above. Show your thinking in the space below.
Answers
The total cost during a school year to attend a given number of daces is a
linear function of the number of dances attended.
The correct responses are;
Part A; The function for the total cost is; c = 50 + 4·nPart B; The total cost for attending 15 dances is; c = $1101. The initial cost is $50 and the rate is $42. The annual fee, the admission price, and the number of dances attended3. The solution are: Part A; c = 50 + 4·n, Part B; c = $110Reasons:
The given parameter are;
Admission price per person = $4
The annual fees members pay = $50
A. The function that can be used to determine c is a linear function, with a y-intercept (initial value) of 50 and a rate (slope) of 4
The total cost to attend n dances a year, c = 50 + 4·n
B. If a member attends 15 dances a year, we have;
n = 15
Therefore;
The total cost, c = 50 + 4 × 15 = 110
The total cost for 15 dances a year, c = $110
1. As the number of dances attended increase, the total cost increase, and the cost when no dance is attended by a member during the year is $50.
2. The essential information that can be used to find the solution are;
The admission price for each person.The annual fee for membership dues.The number of dances a member attends in a year.3. Part A; c = 50 + 4·n
Part B; c = $110
Learn more about linear functions here:
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A culture of bacteria has an initial population of 74000 bacteria and doubles every 3 hours. Using the formula
P
t
=
P
0
⋅
2
t
d
P
t
=P
0
⋅2
d
t
, where
P
t
P
t
is the population after t hours,
P
0
P
0
is the initial population, t is the time in hours and d is the doubling time, what is the population of bacteria in the culture after 13 hours, to the nearest whole number?
Answers
Using an exponential function, it is found that the population of bacteria in the culture after 13 hours is of 1,491,747.
An exponential function, with a doubling time of d, after t hours, is given by:
[tex]A(t) = A(0)(2)^{\frac{t}{d}}[/tex]
In which A(0) is the initial amount.In this problem:
The doubling time is of 3 hours, hence [tex]d = 3[/tex].The initial population is of 74000 bacteria, hence [tex]A(0) = 74000[/tex].Then:
[tex]A(t) = A(0)(2)^{\frac{t}{d}}[/tex]
[tex]A(t) = 74000(2)^{\frac{t}{3}}[/tex]
After 13 hours:
[tex]A(13) = 74000(2)^{\frac{13}{3}} = 1491747[/tex]
The population of bacteria in the culture after 13 hours is of 1,491,747.
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through:(-3,-1), slope=4/3
Answers
A circular fish pond is shown below. What
is the circumference of the pond? The radius is 18.5cm
Answers
Answer:
about 116.18
Step-by-step explanation:
Circumference is 2PI*radius
So it should equal 37*3.14 which equals about 116.18
Please help me with my math homework what is the answer!!!
Answers
Answer:
Step-by-step explanation:
The letters are easy enough.
y^3 determines that 3 ys are needed. y^2 is taken in by the cubed.
x^4 determines that 4 xs are needed. x^3 is part of x^4 and you don't need any more xs
12 and 42 are the parts that will cause the problem. Factor them both into prime factors
12: 2 * 2 * 3
42: 2 * 3 * 7
You need two 2s.
You need one 3
You need one 7
LCD = 2 *2*3 * 7 = 84
Jim is riding his bicycle. He rides for 22.5 kilometers at a speed of 9 kilometers per hour. For how many hours does he ride?
Answers
Answer:
It is 2.5 hours.
Step-by-step explanation:
Assume that you are going to open a checking account. You are examining different banks and banking accounts to choose a bank account for your needs. Which of the following statements should not be one of your reasons for examining different banks?
a. Being more informed leads to being better prepared to make financial decisions
b. Bank E offers you a chocolate bar for filling out an application for checking and credit at the same time.
c. Banks could have charges that you do not know about until reading carefully.
d. You will become more aware of how well the banks meet your particular needs.
Answers
Answer:the answer is b
Step-by-step explanation:
i took the test
Which system of equations is equivalent to the following system? 2x 4y = 14 4x y = 20 2x 4y = 14 â’16x â’ 4y = â’80 2x 4y = 14 â’4x y = â’20 4x 8y = â’28 4x y = 20 â’2x â’ 4y = 14 4x y = 20.
Answers
The equivalent equations of [tex]2x+ 4y = 14[/tex] and [tex]4x + y = 20[/tex]
are [tex]2x+ 4y = 14[/tex] and[tex]-16x -4y = -80[/tex]
The system of equations is given as:
[tex]2x+ 4y = 14[/tex]
[tex]4x + y = 20[/tex]
Multiply both sides of the equations by -4.
So, we have:
[tex]-4 \times (4x + y) = -4 \times 20[/tex]
Distribute the expression
[tex]-4 \times 4x -4 \times y = -4 \times 20[/tex]
Evaluate all products
[tex]-16x -4y = -80[/tex]
So, we have the following system of equations
[tex]2x+ 4y = 14[/tex]
[tex]-16x -4y = -80[/tex]
Hence, the equivalent equations are [tex]2x+ 4y = 14[/tex] and[tex]-16x -4y = -80[/tex]
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