The value of k in the equation f(x) = (9x^2 + 37x + 41) / (3x + 5) with an oblique asymptote at y = 3x + k is k = 41.
To find the value of k in the equation f(x) = (9x^2 + 37x + 41) / (3x + 5), where f(x) has an oblique asymptote at y = 3x + k, we need to determine the relationship between the numerator and denominator as x approaches infinity.
To do this, we can perform polynomial division. Divide the numerator (9x^2 + 37x + 41) by the denominator (3x + 5). The result should give us the oblique asymptote equation y = 3x + k.
Performing polynomial division:
3x + 5 ) 9x^2 + 37x + 41
- (9x^2 + 15x)
----------------------
22x + 41
The result of the division is 22x + 41.
Therefore, the oblique asymptote equation y = 3x + k becomes y = 22x + 41.
Comparing this equation to y = 3x + k, we can see that the value of k is 41.
So, the value of k in the equation f(x) = (9x^2 + 37x + 41) / (3x + 5) with an oblique asymptote at y = 3x + k is k = 41.
Which of the following statements is true about the greatest integer function? A. The function is defined as the greatest integer greater than or equal to x. B. The greatest integer function is classified as a piecewise function. C. The range of the greatest integer function is the set of natural numbers. D. The domain of the greatest integer function is all whole numbers. 2. What's the common difference of the sequence –5, –2, 1, 4, 7, . . . ?
Final answer:
The true statement about the greatest integer function is that it is a piecewise function. The common difference of the given sequence is 3.
Explanation:
Let's break down each part of the question to provide a clear and accurate response.
Part 1: Greatest Integer Function
The statement that is true about the greatest integer function is B. The greatest integer function is classified as a piecewise function. The greatest integer function, denoted as [x], returns the greatest integer less than or equal to x. This function is indeed piecewise because it is defined in multiple pieces - for each interval of real numbers between integers, it takes a constant value equal to the lower endpoint of that interval.
Part 2: Common Difference of Sequences
To find the common difference of the sequence – 5, – 2, 1, 4, 7, …, you subtract any term from the term that follows it. For instance, – 2 - (– 5) = 3. Therefore, the common difference is 3.
Jack made $200 for working 40 hours. Saida made $242 for 44 hours of work. Are the pay rates proportional?
Answer:
No.
Step-by-step explanation:
If they are proportional, they equal each other.
We can use a proportion.
200/40 = 242/44
Simplify.
5 = 5.5
So they are not proportional.
What is the distance between –14 and –5 on a number line?
Final answer:
The distance between – 14 and – 5 on a number line is 9 units, calculated by finding the absolute value of the difference between the two numbers.
Explanation:
The distance between two points on a number line is the absolute value of the difference between those two numbers. To find the distance between – 14 and – 5, subtract the smaller number (– 14) from the larger number (– 5) and then take the absolute value:
Distance = |(– 5) – (– 14)|
Distance = |9|
Distance = 9
Therefore, the distance on the number line between – 14 and – 5 is 9 units.
For which equation would x = 3 be a solution?
x + 7 = 4
x - 2 = 1
5 + x = 9
8 - x = 11
What is the solution to the equation 7.5 - x = 2.8?
x = 4.7
x = 5.3
x = 5.7
x = 10.3
x = 3 is a solution for the equation x - 2 = 1. The solution for 7.5 - x = 2.8 is x = 4.7. Both solutions were verified by substituting back into the original equations.
Let's first determine for which equations x = 3 is a solution:
x + 7 = 4
Substitute x = 3: 3 + 7 = 10, which is not equal to 4. Hence, x = 3 is not a solution to this equation.
x - 2 = 1
Substitute x = 3: 3 - 2 = 1, which is correct. Therefore, x = 3 is a solution to this equation.
5 + x = 9
Substitute x = 3: 5 + 3 = 8, which is not equal to 9. Thus, x = 3 is not a solution to this equation.
8 - x = 11
Substitute x = 3: 8 - 3 = 5, which is not equal to 11. Therefore, x = 3 is not a solution to this equation.
The correct option is- b
Now, we solve the equation 7.5 - x = 2.8:
1. Start by isolating x:
7.5 - x = 2.8
2. Subtract 7.5 from both sides of the equation:
-x = 2.8 - 7.5
-x = -4.7
3. Multiply both sides by -1 to solve for x:
x = 4.7
The correct option is- a
Hence, the solution to the equation is x = 4.7.
Therefore x = 3 is a solution for the equation x - 2 = 1. The solution for 7.5 - x = 2.8 is x = 4.7.
A map is drawn using the scale 2 cm:100 mi. On the map, Town B is 3.5 centimeters from Town A, and Town C is 2 centimeters past Town B. How many miles apart are Town A and Town C?
Answer:
[tex]275\ mi[/tex]
Step-by-step explanation:
we know that
The distance on the map from Town A and Town C is equal to
3.5 cm+2 cm=5.5 cm
The scale map is equal to
[tex]\frac{2}{100}\frac{cm}{mi}[/tex]
Simplify
[tex]\frac{1}{50}\frac{cm}{mi}[/tex]
That means-----> 1 cm on a map is 50 mi on the actual
so
by proportion
[tex]\frac{1}{50}\frac{cm}{mi} =\frac{5.5}{x}\\ \\x=50*5.5\\ \\x=275\ mi[/tex]
Which matrix is equal to... (picture added)
Answer:
D [tex]\left[\begin{array}{ccc}-6&-6.5&1.7\\-2&-8.5&19.3\end{array}\right][/tex]
Step-by-step explanation:
Two matrices are equal when they
have the same sizes (so options A and B are false)have equal corresponding elements (so option C is false, because -6≠6, -6.5≠6.5, 1.7≠-1.7 and so on)If in option D the second row is 2 -8.5 19.3 , then these matrix is equal to the given.
Answer:
Its D on edge
Step-by-step explanation:
ILL GIVE BRANLIEST!!!
What value of g makes the equation true? (X+7)(x-4)=x^2+gc-28
Answer:
The left side is not equal to the right side, which means that the given statement is false.
False
Step-by-step explanation:
Answer: g= 3x/c
Not sure if this helps
A piece wise function is graphed below. Fill in all of the blanks to give an algebraic description of the function
Answer:
P - 4
Step-by-step explanation:
there are 12 collectors donating a total of 48 paintings.
48/12=4
each collector will donate 4 paintings.
Sergio has (p) paintings now, so after he donates 4 paintings, he will have p-4 paintings in his art collection.
Sergio will have p-4 paintings in his art collection after his donation
What is the classification for this polynomial 4uv2w2
Answer:
The polynomial 4uv²w² is a monomial, since its a single term.
Degree of polynomial: it is sum of exponent of its variables.
power of u = 1, power of v = 2, power of w = 2
Degree of polynomial: 5
What is the value of x?
Answer:
x = 30 degrees
Jackie is selling smoothies at a school fair. She starts the day with $15 in her cash box to provide change to her customers. If each smoothie costs $3.75, which graph represents the balance of the cash box, y, after Jackie sells x smoothies?
the answer would be D
Answer with Step-by-step explanation:
Jackie is selling smoothies at a school fair. She starts the day with $15 in her cash box to provide change to her customers.
Each smoothie costs $3.75, then cost of x smoothies is: $3.75x
Then, y=3.75x+15
When x=0 y=15
when x=4 y=3.75×4+15
i.e. y=30
The only graph which satisfies y=0 at x=0 and y=30 at x=4 is D.
Hence, the correct graph is:
D.
Based on the graph how many real nunber solutions does x^3+6x^2+8=0 have ?
Answer:
ONE
Step-by-step explanation:
ONE real number solution. The graph intersects the x-axis in only one place.
Find the slope intercept form of the equation for the line that goes through (3, 5) and is parallel to y=5x - 1.
Answer:
y=5x-10
Step-by-step explanation:
slope intercept form is y=mx+b
since we know it is parallel to y=5x-1, we know that it has the same slope of 5.
So, we plug it in:
y=mx+b
y=5
x=3
(taken from point (3,5))
m=5
(taken from parallel line)
5=(5)(3)+b
5=15+b
b=-10
The equation would be y=5x-10
Julia decides to ride her bicycle around the track five times each day
Which best describes how far Julia will ride her bicycle around the track each day?
Plz help me
Answer:
B - Between 1 mle and 1.5 miles
Step-by-step explanation:
One lap around the track is .25 of a mile
Multipy times 5 and you get 1.25 miles
Answer:
b
Step-by-step explanation:
because thatch between anything
A piece of machinery valued at $250,000 depreciates at 12% per year by the fixed rate method. After how many years will the value have depreciated to 100,000
Answer:
6.7 years (approx)
Step-by-step explanation:
A bookshop has a sale.
A book normally costing $39.95 is priced at $23.97.
By what percentage has the price been reduced?
please show working out
Answer:
The price been reduced by a percentage of 40%
Step-by-step explanation:
we know that
$39.95 -----> represent the 100%
so
The difference of prices is equal to ($39.95-$23.97)=$15.98
Using proportion
Find the percentage of the difference
100/39.95=x/15.98
x=100*15.98/39.95
x=40%
Answer:
40% is the percentage decreased.
Hope it helped!
Thanks.
Which function results after applying the sequence of transformations to
f(x) = x^5?
• stretch vertically by 3
• translate up 1 unit
• translate left 2 units
Answer:
The resulting function after the sequence of transformations is [tex]f(x)=3(x+2)^5+1[/tex]
Step-by-step explanation:
Given a function f(x)
the function a*f(x) will be a vertical stretch of factor a, given a > 1 the function f(x) + b will be the translated function vertically up b unitsthe function f(x+c) will be horizontally translated function of the original by c units leftRemembering these points, we can apply the rules to [tex]x^5[/tex].
Strech vertically by 3 would be [tex]3x^5[/tex]translate up 1 unit would be [tex]3x^{5}+1[/tex]translate left 2 units would make it [tex]3(x+2)^5+1[/tex]Hence the new function would be [tex]3(x+2)^5+1[/tex]
Answer:
f(x) = 3(x+2)⁵+1
Step-by-step explanation:
Ap3x
what is 2/5 of 255???
Answer:
102
Step-by-step explanation:
Answer:
102.
Step-by-step explanation:
First, divide 255 by 5 (255÷5=51).
Then multiply the result of 255÷5 by 2 (51×2)
And 51×2=102
Solve the equation 24= 6(-x - 3)
Answer:
X= -7
I LOVE LOVE LOVE LOVE EQUATIONS.
Step-by-step explanation:
ALRIGHT!
1. 6*(-x)= -6x
2. 6*(-3)= -18
3. Now right in normal 24= -6x-18
4. Now keep the variables on one side and the numbers on the other and simplify it. And when keeping the variables on one side and the numbers on the other what ever you switch you must change it's expression. So if it's + you make it - and if it - you make it +. so 6x=-18-24= 6x=-42
5. Now simplify it. as a fraction. 6x = -42 = divide 6 on both sides now X= -7 6 6
Simplify.
2
(8w)
Write your answer without parentheses.
Answer: I believe the answer would be 64w2.
Step-by-step explanation: 8 squared is 8 x 8, which equals 64, and then w squared is just w2, since we don't know what it is. Put them together, and the answer is 64w2.
Hi There!
--------------------------------------
Answer:
64w²
Step-by-step explanation:
= (8w)²
= 8w × 8w
= 64w²
--------------------------------------
Hope This Helps :)
From 11:50 a.m. to 12:40 p.m. is
If you’re wondering the minutes in between it would be 50 minutes from 11:50am to 12:40pm
Factor the trinomial x^2- 5x- 36 Which of the following is one of the factors?
Answer:
Final factor is (x-9)(x+4)
Step-by-step explanation:
Given expression is [tex]x^2- 5x- 36[/tex].
Now we need to factor that expression
[tex]x^2- 5x- 36[/tex]
Find two numbers whose product is -36 and sum is -5.
Two such numbers oare -9 and +4. So we get:
[tex]=x^2- 9x+4x- 36[/tex]
[tex]=x(x-9)+4(x-9)[/tex]
[tex]=(x-9)(x+4)[/tex]
Hence final factor is (x-9)(x+4)
Answer:
(x-9) (x+4)
Step-by-step explanation:
x^2- 5x- 36
What two numbers multiply to -36 and add to -5
-9*4 = -36
-9+4 = -5
(x-9) (x+4)
Answer the question in the picture.
Answer:
247 people per square mile
Step-by-step explanation:
Population density is people per area
We need to find the area
We are given the radius
We will assume a circular area since we are given radius
A = pi r^2
A = 3.14 * 5^2
A = 3.14 *25
A = 78.5 miles ^2
19400 people
---------------------
78.5 miles ^2
247.133758 people per square mile
Rounding to the nearest person
247 people per square mile
The ratio of roses to daisies is 8 roses to 6 daisies.
If there are 16 roses, how many daisies are there?
12 Roses since your multiplying by 2
Answer:12
Step-by-step explanation: there are 8 roses and 6 daisies, if 8 turns into 16, that’s multiplied by 2, so you multiply 6 by 2 and get 12,
8 * 6
_ * _
16*X, cross multiply
when is a sequence geometric
I also think its A cause you find the next term when your multiply the constant (common ratio) so it makes sense for it to be A
Answer:
when each term is multipled by the same number to get the next numberStep-by-step explanation:
[tex]\text{A geometric sequence:}\\\\a_1,\ a_2,\ a_3,\ a_4,\ ....\\\\\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=\dfrac{a_4}{a_3}=...=\dfrac{a_n}{a_{n-1}}=r=constant\\\\r-\text{common ratio}\\\\a_2=a_1r\\a_3=a_2r\\a_4=a_3r\\\vdots\\a_n=a_{n-1}r\\\\\text{next term is created from the previous one by multiplying it}\\\text{by the same number}[/tex]
The ____ identity is 1.
a) additive
b) multiplicative
c) distributive
I think it’s B) multiplicative
Lines XU and WY intersect at point A.
Based on the diagram, determine, determine whether the statement is True or False.
The angle vertical to YAU measures 50°
(A.) True
(B.) False
The answer is A. True
Find the similarity ratio of the larger triangle to the smaller one.
Answer:
A
Step-by-step explanation:
The base of the larger triangle is twice as large as the smaller one: 6 v 3 --> 6 : 3 --> 2 : 1.
AN
Jamal has 10 sets of collectible coins. Each set has 5 coins. How many collectible coins does Jamal have?
5
10
50
100
Answer:50
Step-by-step explanation:each of the 10 sets have 5 coins basically (10*5) = 50
50
10sets*5coins=50total coins
The total cost of a dress,including tax, was $121.37. If 6% tax was added to the sale price, what was the sale price before taxes?
Answer:
We have
sale price + 6% x sale price = $121.37;
Then
(106/100) x sale price = $121.37;
sale price = $121.37 x 100 / 106;
sale price = $12137 / 106;
sale price = $114.50;
Step-by-step explanation:
To find the sale price of a dress before a 6% tax added up to a total of $121.37, divide the total by 1.06. The original sale price was $114.50.
The student is asking how to calculate the sale price of a dress before tax when the total cost, including a 6% tax, was $121.37. To find the sale price before taxes, you need to divide the total cost by 1 plus the tax rate expressed as a decimal.
First, convert the percentage to a decimal, which gives us 0.06 for a 6% tax. Then, add 1 to the tax rate (1 + 0.06 = 1.06) and divide the total cost by this sum to get the original price:
Sale price = Total cost / (1 + Tax rate)
Sale price = $121.37 / 1.06
Sale price = $114.50 (rounded to the nearest penny)
Therefore, the original sale price of the dress was $114.50.