Answers
Answer:
[tex] \frac{0.75x - 3}{x - 1} [/tex]
Step-by-step explanation:
Equation of a rational function is
[tex] \frac{p(x}{q(x)} [/tex]
where q(x) isn't zero.
There is a vertical asymptote at
[tex]x = 1[/tex]
So this mean that our denomiator must have a zero that occur at x=1.
That zero is
[tex]x - 1[/tex]
So our denomiator is
[tex] \frac{p(x)}{x - 1} [/tex]
Since our horinzontal asymptote is a non zero value, the numerator must be a linear equation as well.
So our rational function is
[tex] \frac{ax + b}{x - 1} [/tex]
We know the graph pass through (0,3)
So if we apply that logic,
[tex] \frac{a(0) + b}{0 - 1} = 3[/tex]
[tex] \frac{b}{ - 1} = 3[/tex]
[tex]b = - 3[/tex]
And it passes through (4,0)
[tex] \frac{a(4) + b}{3} = 0[/tex]
[tex]4a + b = 0[/tex]
[tex]4a + ( - 3) = 0[/tex]
[tex]4a = 3[/tex]
[tex]a = \frac{3}{4} [/tex]
So our rational equation is
[tex] \frac{0.75x - 3}{x - 1} [/tex]
Related Questions
Future value of 10% savings from earnings of1470 earning 3.5% annual interest compounded monthly for 25 years
Answers
hmmm so let's see first how much is 10% of the earnings of 1470.
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{10\% of 1470}}{\left( \cfrac{10}{100} \right)1470}\implies 147[/tex]
so then
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$147\\ r=rate\to 3.5\%\to \frac{3.5}{100}\dotfill &0.035\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &25 \end{cases}[/tex]
[tex]A=147\left(1+\frac{0.035}{12}\right)^{12\cdot 25}\implies A=147\left( \frac{2407}{2400} \right)^{300}\implies \boxed{A\approx 352.19}[/tex]
[tex]\begin{equation}\text { Question: If } \int_{\frac{-1}{\sqrt{2}}}^{\frac{1}{\sqrt{2}}}\left(\left(\frac{x-1}{x+1}\right)^{2}+\left(\frac{x+1}{x-1}\right)^{2}-2\right)^{\frac{1}{2}} d x\end{equation}[/tex]
Options:
(a) ln16
(b) 2ln16
(c) 3ln16
(d) 4ln16
Answers
We want to evaluate
[tex]\displaystyle \int_{-\frac1{\sqrt2}}^{\frac1{\sqrt2}} \sqrt{\left(\frac{x-1}{x+1}\right)^2 + \left(\frac{x+1}{x-1}\right)^2 - 2} \, dx[/tex]
First we note that the integrand is even (replacing x with -x doesn't fundamentally alter the function being integrated), so this is equal to
[tex]\displaystyle 2 \int_0^{\frac1{\sqrt2}} \sqrt{\left(\frac{x-1}{x+1}\right)^2 + \left(\frac{x+1}{x-1}\right)^2 - 2} \, dx[/tex]
The radicand reduces significantly to
[tex]\displaystyle \left(\frac{x-1}{x+1}\right)^2 + \left(\frac{x+1}{x-1}\right)^2 - 2 = \frac{16x^2}{(1-x^2)^2}[/tex]
so that taking the square root, we simplify the integral to
[tex]\displaystyle 8 \int_0^{\frac1{\sqrt2}} \frac x{1-x^2} \, dx[/tex]
which is trivially computed with a substitution of [tex]y = 1 - x^2[/tex] and [tex]dy=-2x\,dx[/tex]:
[tex]\displaystyle -4 \int_1^{\frac12} \frac{dy}y = 4 \int_{\frac12}^1 \frac{dy}y = -4 \ln\left(\frac12\right) = \ln(2^4) = \boxed{\ln(16)}[/tex]
Jeremiah is starting a t-shirt making business. He needs to spend $1050 to buy the equipment to print on t-shirts. On each t-shirt he sells, he makes a $4 profit. How many t-shirts must Jeremiah sell to break even?
Answers
Which of the
following graphs
satisfies these
inequalities?
x- y< 2.
x + 2y > 8
y<4
A
B
2
f
Answers
B
is the answer. Good luck!!
i don't understand the calculation of learning rate , how it came 75%
Answers
Answer:
Increase the learning rate after each mini-batch by multiplying it by a small constant.
An angle measures 26.8° less than the measure of its complementary angle. What is the measure of each angle?
Answers
Given :
An angle which measures 26.8° less than the measure of its complementary angle.⠀
To Find :
The measure of each angle.⠀
Solution :
Let's assume the one of the complementary angle as "x" and the other angle as (x – 26.8)° .⠀
Now,
⠀
According to the Question :
⠀
[tex]{\longrightarrow \qquad \sf{ x + {(x - 26.8)}^{ \circ} = {90}^{ \circ} }}[/tex]
⠀
[tex]{\longrightarrow \qquad \sf{ x + {x - 26.8}^{ \circ} = {90}^{ \circ} }}[/tex]
⠀
[tex]{\longrightarrow \qquad \sf{ 2 {x - 26.8}^{ \circ} = {90}^{ \circ} }}[/tex]
⠀
[tex]{\longrightarrow \qquad \sf{ 2 x = {90}^{ \circ} + 26.8^{ \circ}}}[/tex]
⠀
[tex]{\longrightarrow \qquad \sf{ 2 x = 116.8^{ \circ}}}[/tex]
⠀
[tex]{\longrightarrow \qquad \sf{ x = \dfrac{116.8^{ \circ}}{2}}}[/tex]
⠀
[tex]{\longrightarrow \qquad \frak{\pmb{ x =58.4^{ \circ}}}}[/tex]
⠀
Therefore,
One angle = 58.4°Other angle = 58.4° – 26.8° = 31.6°⠀
Hence,
The measure of the each angles are 58.4° and 31.6° .Answer:
The measurement of each angle is 58.4° and 31.6°
Step-by-step explanation:
Given :-
Value of an angle is 26.8° less than its complementary angleTo Find :-
Measurement of each angleSolution:-
let one angle be x and other be x - 26.8°
we know that, Sum of complementary angle is 90°
X + X - 26.8° = 90°
2x = 90° + 26.8°
x = 58.4
So , one angle is 58.4° and other one is 58.4 - 26.8 which is 31.6
How many cars are needed to transport 82 children if each car can take 6 children
Answers
Which of the following is the correct factorization of the polynomial below?
x^3 - 12
A. (x + 3)(x - 4)
B. (x - 3)(x + 4)
C. (x + 3)(x^2 - 4x + 4)
D. The polynomial is irreducible.
Answers
Been struggling with math lately. I would appreciate it if anyone out there can help me out!
Answers
Answer:
21°
Step-by-step explanation:
Dilation is a similarity transformation. It does not change angles. It changes lengths proportionally.
∠A'B'C' ≅ ∠ABC = 21°
Builtrite bonds have the following: 5 1/2% coupon, 10 years until maturity, $1000 par and are currently selling at $1044. If you purchase this bond, what would be your AYTM?
Answers
The annual yield to maturity (AYTM) of the Builtrite bonds is at 5.5% for 10 years with a $1,000 par value and the current price of $1,044 is A. 4.9%.
What is the annual yield to maturity (AYTM)?The annual yield to maturity (AYTM) is the total return expected from a bond if the bond is held till maturity.
The AYTM rate is the rate at which all future expected cash flows are discounted to find out the current value or the price of the bond.
We can use the following Yield to Maturity formula to calculate the AYTM.
Yield to Maturity = [Annual Interest + {(FV-Price)/Maturity}] / [(FV+Price)/2]
Data and Calculations:Annual Interest = Annual Interest Payout by the Bond = $55 ($1,000 x 5.5%)
FV = Face Value of the Bond = $1,000
Price = Current Market Price of the Bond = $1,044
Maturity = Time to Maturity = 10 years
= {$55 + ($1,000 - $1,044)/10} / {($1,000 + $1,044)/2}
= $55 + -4.4 / 1,022
= 50.6/1,022
= 4.95%
We can also use an online finance calculator to check the calculated value above as follows:
N (# of periods) = 10
I/Y (Interest per year) = 4.95%
PMT (Periodic Payment) = $55 ($1,000 x 5.5%)
FV (Future Value) = $1,000
Results:
PV = $1,044
Sum of all periodic payments = $550 ($55 x 10)
Total Interest $503.44
Answer Options:A. 4.9%
B. 5.1%
C. 5.3%
D. 5.5%
Thus, the annual yield to maturity (AYTM) of the Builtrite bonds is at 5.5% for 10 years with a $1,000 par value and the current price of $1,044 is A. 4.9%.
Learn more about the yield to maturity at https://brainly.com/question/26657407
Is there a relationship between the distance and the sum? Is there a relationship between the distance and the difference? A 5-column table with 3 rows. Column 1 is labeled a with entries 1, 4, negative 6. Column 2 is labeled b with entries 2, negative 1, negative 3. Column 3 is labeled a + b with entries 3, 3, negative 9. Column 4 is labeled a minus b with entries negative 1, 5, negative 3. Column 5 is labeled Distance with entries 1 unit, 5 units, 3 units. Which describes the relationship between the distance and the difference? The distance is always the opposite of the difference. The distance is exactly the difference. The distance is the absolute value of the difference. The distance is not related to difference.
Answers
Answer:
C) The distance is the absolute value of the differenceStep-by-step explanation:
We are interested in the last two columns.
If we compare them we see that each value of the distance column is the absolute value of corresponding value of difference:
a - b = 1, 5, - 3distance = 1, 5, 3Corect choice is C
Answer:
The distance is the absolute value of the difference.
Step-by-step explanation:
Given table:
[tex]\begin{array}{|c|c|c|c|c|}\cline{1-5} a & b & a+b & a-b & \sf distance\\\cline{1-5} 1 & 2 & 3 & -1 & 1 \sf \: unit\\\cline{1-5} 4 & -1 & 3 & 5 & 5 \sf \: units\\\cline{1-5} -6 & -3 & -9 & -3 & 3 \sf \: units\\\cline{1-5}\end{array}[/tex]
The difference is column 4.
The distance is column 5.
The absolute value of a number is its positive numerical value. It is denoted by a vertical line either side of the real number.
For example, |5| means 'the absolute value of 5', and |-5| means 'the absolute value of -5'.
Taking the absolute values of the differences:
⇒ |-1| = 1
⇒ |5| = 5
⇒ |-3| = 3
Therefore, the distance is the absolute value of the difference.
Can someone tell me what I did wrong here
Answers
Answer:
no roots.
Step-by-step explanation:
1) [tex]\sqrt{8x+16}=2-8; \ - \ correct;[/tex]
2) [tex]\sqrt{8x+16}=-6; \ - \ correct;[/tex]
note, the value after operation 'square root' cannot be negative ('-6' is on the right side!), then
3) it means, the given equation has no real roots.
can someone please help me with this question???? its an exam study guide and i dont understand it
Josef owns four par value $1,000 bonds from Dowc Beverage Co. Each bond has a market value of 104.561 and gives 9.2% interest. Josef also owns 170 shares of stock in Dowc Beverage Co. Stock in Dowc Beverage Co. has a share price of 26.25 and pays a dividend of $2.38. If the broker Josef employed to purchase these stocks and bonds charges a commission of $72 for each ten shares of stock bought or sold and a commission of 4% of the market value of each bond bought or sold, which aspect of Josef’s investment in Dowc Beverage Co. has a greater percent yield, and how much greater is it?
a.
The stocks have a yield 2.15 percentage points higher than that of the bonds.
b.
The stocks have a yield 0.27 percentage points higher than that of the bonds.
c.
The bonds have a yield 1.35 percentage points higher than that of the stocks.
d.
The bonds have a yield 2.08 percentage points higher than that of the stocks.
Answers
Answer:
If the broker Josef employed to purchase these stocks and bonds charges a commission of $72 for each ten shares of stock bought or sold and a commission of 4% of the market value of each bond bought or sold, then the bonds have a yield 1.35 percentage points higher than that of the stocks.
Step-by-step explanation:
Find the surface area of the pyramid. DO THIS AS QUICK AS POSSIBLE
Answers
Explanation:
How many surface has a pyramid?
5 Faces
It has 5 Faces. The 4 Side Faces are Triangles. The Base is a Square.
Use a fraction or mixed number to represent the time on a number line. Let 0 represent noon.
8:30 A.M.
Answers
The time 8:30AM is 3 and half hours before noon.
The fraction that represents 8:30AM is -3 1/2
How to represent the time as fraction?The time is given as:
Time = 8:30 A.M
Given that Noon is represented by 0.
It means that time before noon would be represented with negative value
8:30AM is 3 and half hours before noon.
So, we have:
8:30AM = -3 1/2
Hence, the fraction that represents 8:30AM is -3 1/2
Read more about fractions at:
https://brainly.com/question/1622425
The expression below is a sum of cubes.
125x^3 + 144
A. True
B. False
Answers
Answer:
False
Step-by-step explanation:
Hey there!
If this is a sum of cubes, this means that both numbers have whole numbers as the cube root of that number
The cube root of 125 is 5
But the cube root for 144 is a decimal meaning this is not a sum of cubes
Lainey is sliding down a water slide that is 423 feet long at a rate of 47 feet per second. How long will it take Lainey to travel from the top to the bottom of the slide?
Answers
Answer:
It will take Lainey 9 seconds to travel from top to bottom
Further explanation:
The formula of speed will be used to calculate the time to reach from top to bottom of the slide.
Given
\begin{gathered}Distance=d=423\ feet\\Speed=s=47\ feet\ per\ second\end{gathered}
Distance=d=423 feet
Speed=s=47 feet per second
The formula for speed is:
s=\frac{d}{t}s=
t
d
Putting the values of distance and speed in the formula:
\begin{gathered}47=\frac{423}{t}\\t=\frac{423}{47}\\t=9\ seconds\end{gathered}
47=
t
423
t=
47
423
t=9 seconds
It will take Lainey 9 seconds to travel from top to bottom
Keywords: Speed, distance
Learn more about speed
Simplify the expression.
(m^-1 m^5/m^-2)^-3
a)- 3m^4/m^2
b)-m^216
c)m^18
d)1/m^18
Answers
Answer:
option d
Step-by-step explanation:
[tex]\sf \boxed{a^m*a^n = a^{m+n}\\\\}[/tex]
[tex]\sf \left(\frac{m^{-1}m^{5}}{m^{-2}} \right)^{-3} =\left(\dfrac{m^{-1+5}}{m^{-2}}\right)^{-3}[/tex]
[tex]\sf = \left(\dfrac{m^4}{m^{-2}}\right)^{-3}\\\\[/tex]
[tex]\boxed{\dfrac{a^{m}}{a^{n}}=a^{m+n}}[/tex]
[tex]\sf = \left(m^{4-[-2]}\right)^{-3}\\\\ =\left(m^{4+2}\right)^{-3}\\\\ = \left(m^6\right)^{-3}\\\\[/tex]
[tex]\boxed{(a^{m})^n=a^{m*n}}[/tex]
[tex]\sf= m^{6*(-3)}\\\\ = m^{-18}[/tex]
[tex]\boxed{a^{-m}=\dfrac{1}{a^m}}[/tex]
[tex]\sf=\dfrac{1}{m^{18}}[/tex]
Adam deposited $50,000 in a savings account with simple interest. Three years later, he had earned $6,000 in interest. What was the interest rate
Answers
Last Friday Trevon had $29. Over the weekend he received some money for cleaning the attic. He now has $41. Write an algebraic equation to represent how much money he received
Answers
Answer:
x + 29 = 41
Step-by-step explanation:
Trevon received some money, but we don't know how much, so we will represent that with x.
The money he received will be add the amount he had last friday, $29.
The equation will equal his current amount, $41.
!! 100 PTS+BRAINLIEST 4 CORRECT ANSWER+EXPLANATION!!
use the photo provided
thanks
Answers
Answer:
19.0 cm (3 sf)
Step-by-step explanation:
Formula
[tex]\sf arc \ length=2\pi r \left(\dfrac{\theta}{360}}\right)[/tex]
(where r is the radius)
Arc length of white sector
Radius of white sector = 8 - 4.5 = 3.5 cm
[tex]\sf \implies arc \ length=2\pi \cdot 3.5 \left(\dfrac{50}{360}}\right)=\dfrac{35}{36} \pi \ cm[/tex]
Arc length of grey sector
Radius = 8 cm
[tex]\sf \implies arc \ length=2\pi \cdot 8 \left(\dfrac{50}{360}}\right)=\dfrac{20}{9} \pi \ cm[/tex]
Perimeter of shaded part
Perimeter = arc length (white) + arc length (grey) + 2 x 4.5
[tex]\sf =\dfrac{35}{36} \pi + \dfrac{20}{9} \pi +9[/tex]
[tex]\sf =19.0356432...[/tex]
[tex]\sf =19.0 \ cm \ (3 \ sf)[/tex]
I need help on this question
Answers
~Denki Kaminari here~
Answer:
5t\sqrt(6su) (THE SECOND ONE)
Step-by-step explanation:
simplify the radical by breaking it up into known factors, assuming positive real numbers.
hope this helps :D
X+10 please help
I really need help with inequality’s I will give 100 points for this answer no bull
Answers
Answer:
x+10=-3x+38
Step-by-step explanation:
subtract 10 from both sides Subtract the numbers then add 3x on both sides
Simplify the expression.
(m^-1 m^5/m^-2)^-3
a)- 3m^4/m^2
b)-m^216
c)m^18
d)1/m^18
Answers
Explanation:
(m^-2/m-1m5)^3
m^-6/m^-3m^15
1/m^6 / m^15/m^3
1/m^6 / m^12
1/m^6 (1/m^12)
1/m^18
let me know if you want clarification
Answer:
[tex]D)\frac{1}{m^{18} }[/tex]
Step-by-step explanation:
Multiply [tex]m^{-1}[/tex] by [tex]m^{5}[/tex] by adding the exponents.
Use the power rule [tex]a^{m} a^{n} =a^{m+n}[/tex] to combine exponents.
[tex](\frac{m^{-1+5} }{m^{-2} } )^{-3} \\[/tex]
Add -1 and 5.
[tex](\frac{m^{4} }{m^{-2} } )^{-3}[/tex]
Move [tex]m^{-2}[/tex] to the numerator using the negative exponent rule [tex]\frac{1}{b^{-n} } =b^{n}[/tex].
[tex](m^{4} m^{2} )[/tex]
Multiply [tex]m^{4}[/tex] by [tex]m^{2}[/tex] by adding the exponents.
Use the power rule [tex]a^{m} a^{n} =a^{m+n}[/tex] to combine exponents.
[tex](m^{4+2} )^{-3}[/tex]
Add 4 and 2.
[tex](m^{6} )^{-3}[/tex]
Multiply the exponents in [tex](m^6)^{-3}[/tex]
Apply the rule and multiply exponents, [tex](a^m)^n=a^{mn}[/tex].
[tex]m^{6*-3}[/tex]
Multiply 6 by -3.
[tex]m^{-18}[/tex]
Rewrite the expression using the negative exponent rule [tex]b^{-n} =\frac{1}{b^{n} }[/tex].
[tex]\frac{1}{m^{18} }[/tex]
Si un átomo tiene un número atómico de 18 y 22 neutrones, ¿cuál es su masa atómica?
DOY CORONA
Answers
su masa atómica es de 4 creo
Jed rode his scooter to school at 20 miles per hour and then jogged back at 8 miles per hour. If the round trip took him 7 hours, how many miles was it to school?
Answers
Answer:
196 Miles
Step-by-step explanation:
Jed Rode=20 miles per hour
jog back 8 miles per hour
28×7 = 196
Answer: 196 miles
Step-by-step explanation: 7(20+8) You have to distribute the 7 to each number(20 & 8). Then add the answers you get from the 7x20 and 7x8.
7x20=140
7x8= 56
56+140=196
Find the area of the parallelogram. of 6 m 10 m
Answers
Answer:
60m
Step-by-step explanation:
The formula for the area of a parallelogram is base x height.
b x h
6m x 10m = 60m
pls help me on this i dont get it i wasnt trached this aswell
Answers
Answer:
answer below.
Step-by-step explanation:
1. 1/5----0.2
2. 1/3---0.3 repeating
3. 1/2---0.5
4. 7/10---0.7
5. 3/4---0.75
What is P(factor of 64)? Write your answer as a percentage.
Answers
Answer:
the ansewr is eight percent
Which fraction represents the decimal 0.8888...?
StartFraction 80 Over 99 EndFraction
StartFraction 1,111 Over 1,250 EndFraction
Eight-ninths
Nine-eighths
Answers
Answer:
1111/1250
Step-by-step explanation:
Hey there!
To find what fraction represents the decimal shown, you can take each answer choice, and divide the two numbers
We can do this because a fraction is a simple way of dividing two rational numbers
Our answer is 1111/1250
In order to check if this is correct, we can just divide 1111 and 1250
When you divide this, you get 0.8888...
So the fraction that represents 0.888... is 1111/1250
A fraction that represents the decimal 0.8888 is: 1111/1250
What is fraction?In Mathematics, fractions are represented as a numerical value, can be defined as the parts of a whole. A fraction can be a portion or section of any quantity out of a whole, where, the whole can be any number, a specific value, or a thing.
Given is decimal number 0.8888... we need to convert it into a fraction,
Since the number has 4 decimal places, then the first thing to do is multiply and divide the number by 10000.
We have then:
0.8888* (10000/10000) = 8888/10000
Simplifying we have:
8888/10000 = 4444/5000
4444/5000 = 2222/2500
2222/2500 = 1111/1250
Hence, the fraction that represents the decimal 0.8888 is: 1111/1250
Learn more about fraction, click;
https://brainly.com/question/10354322
#SPJ7
