Answers
Answer:
d. √(1/(x+1))
Step-by-step explanation:
Just as operations can be performed on numbers and variables, so can operations be performed on functions. Here, you're asked to simplify the ratio of two functions.
[tex]\displaystyle\left(\frac{g}{f}\right)(x)=\frac{g(x)}{f(x)}=\frac{\sqrt{x-1}}{\sqrt{x^2-1}}=\sqrt{\frac{x-1}{x^2-1}}[/tex]
At this point, you're supposed to know the factoring of the difference of squares:
[tex]\displaystyle=\sqrt{\frac{x-1}{(x-1)(x+1)}}=\boxed{\sqrt{\frac{1}{x+1}}}[/tex]
Related Questions
Lena buys candy that costs $7 per pound. She will buy less than 12 pounds of candy. What are the possible amounts she will spend on candy
Answers
Answer:
Lena can buy candy in infinite no of ways with the possible amounts:-
1 pound of candy = $7
1.1 pound of candy = $7.7
2 pounds of candy = $14
3 pounds of candy = $21
4 pounds of candy = $28
5 pounds of candy = $35
6 pounds of candy = $42
7 pounds of candy = $49
8 pounds of candy = $56
9 pounds of candy = $63
10 pounds of candy = $70
11 pounds of candy = $77
11.9 pounds of candy = $83.3
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.
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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.
the original price of a jacket was $74.00 .A store manager marked the price down by
25 1/2% . By how much was the price reduced?
Answers
74 = 100%
1.35 = 1% --> 100% : 74 = 1.35
34.46 = 25.5%
the new price is 39.54
A, E and B lie on a straight line segment.
C, D and B lie on a straight line segment.
BD = 3m, CD = 15m and AB = 21m.
Work out the length of BE.
Give your answer as a decimal.
Answers
The length of line BE on the given line segment is 3.5 m.
The given parameters:
Length BD = 3 mLength CD = 15 mLength AB = 21 mThe sketch of the given line segments is presented in the diagram uploaded.
The length of BE is determined by applying similar triangle theorem as follows;
[tex]\frac{CB}{AB} = \frac{BD}{EB} \\\\\frac{15 + 3}{21} = \frac{3}{EB} \\\\18EB = 63 \\\\EB = \frac{63}{18} \\\\EB = 3.5 \ m[/tex]
Thus, the length of line BE on the given line segment is 3.5 m.
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Solve the following equation algebraically: 3 x squared = 12 a. Plus-or-minus 3 b. Plus-or-minus 2 c. Plus-or-minus 3.5 d. Plus-or-minus 1.5
Answers
Answer:
b) ±2
Step-by-step explanation:
3x² = 12
divide each side by 3 to get:
x² = 4
x = ±2
The value of the equation 3x² = 12 is x = ±2.
Option B is the correct answer.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x = 6 is an equation.
We have,
3x² = 12
Divide 3 on both sides.
x² = 4
x = ±√4
x = ±2
Thus,
The value of x is ±2.
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What is the inverse of [tex]f(x)=\frac{2}{x-1} +6?[/tex]
[tex]f^{-1} (x)=\frac{2}{x-1} +6[/tex]
[tex]f^{-1} (x)=\frac{2}{x} +7[/tex]
[tex]f^{-1} (x)=\frac{2}{y-6} +1[/tex]
[tex]f^{-1} (x)=\frac{2}{x-6} +1[/tex]
Answers
Answer:
[tex] {f}^{ - 1} (x) = \frac{2}{x - 6} + 1[/tex]
Step-by-step explanation:
we will subistitute f(x) by y and solve the equation in order to get the value of x,
then we subistitute x by y and y by x and y=f^-1(x)
What are the roots of the function
2x^2-8x=0
Answers
Answer:
[tex]x=0[/tex] and [tex]x=4[/tex]
Step-by-step explanation:
The roots of a function (also known as "x-intercepts" or "zeroes") are defined where y=0. Therefore, we will solve the quadratic:
[tex]2x^2-8x=0[/tex]
[tex]2x(x-4)=0[/tex]
[tex]x=0[/tex] and [tex]x=4[/tex]
Sheila has 11
1
2
pounds of potato salad. She wants to divide the potato salad into containers, each of which holds 1
1
4
pounds. How many containers does she need? Complete the explanation.
Containers are counted in
mixed
numbers, so she will need containers.
Answers
Answer:
She will need 10 containers
Step-by-step explanation:
Using long division and converting both solutions to decimals we can use the equation 11.50 divided by 1.25. This will equal 9.20, we then know that she would need 9 containers but we would still have a remainder of .20 so in total to fit everything she would need 10.
I hope this helps have a great day :)
I need this points for algebra help please
Answers
Answer:
ur mom
Step-by-step explanation:
lol
Evaluate the numerical expression 24
Enter your answer in the grid below.
Answers
Answer:
what grid below
Step-by-step explanation:
Answer:
what grid below
Step-by-step explanation:
what is the standard deviation of 77, 45, 72, 56, 98, 60, 70, 89, 50, 80, 95, 70, 34, 77, 65, 70, 70, 82, 86, 86.
What percentage of the scores are within one standard deviation of the mean (±1)? Please include the range of values for this deviation and the exact values from the data set that are included in this range.
What percentage of the scores are within two standard deviations of the mean (±2)? Please include the range of values for this deviation and the exact values from the data set that are included in this range.
Does this data fit the model of a normal distribution? Why or why not?
Answers
Standard deviation of the numbers is 16.154.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
The given observations are
77,45,72,56,98,60,70,89,50,80,95,70,34,77,65,70,70,82,86,86
Average or mean of the data is
x=Sum of n values/ Total number of values
x=1432/20=71.6
The Standard deviation of the data is
[tex]\sigma=\sqrt{\frac{\sum(x-mean)^{2}}{n} }[/tex]
=√5218.8/20
=√260.94
=16.154
Hence, standard deviation of the numbers is 16.154.
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where does the normal line to the ellipse x2−xy y2=3 at the point (−1,1) intersect the ellipse for the second time?
Answers
Answer:
where does the normal line to the ellipse x2−xy y2=3 at the point (−1,1) intersect the ellipse for the second time?
Step-by-step explanation:
they Juan Carlos y los sigo pliss yyi de bvz
PLEASE HELP FAST!!!
3
11
2
Which ordered pair is a solution to the system of linear equations 3 x- y- fo and x+By-to-
10?
O
12
o 5.3
21
o 35
21
3:5
Answers
30x-45y=11...(1)
12x+5y=9...(12)
Multiply the second equation by 9, to eliminate y
30x-45y=11
+ 108x+45y=81
———————-
138x=92
x=92/138 (reduce fraction with 46)
x=2/3
Substitute x=2/3 into equation 2
12(2/3x)+5y=9
y=1/5
Therefore, the solution to the system is C. (2/3, 1,5)
I think of a number, increase it by four and double the answer. The
result is 20 more than the number. Find this number.
Answers
Answer:
(x+4)2=x+20
2x+8=x+20
2x-x=20-8
x=12
The number I thought of is 12.
How to convert statements into numerical expressions ?To convert statements into numerical expression break the statement into chunks write the terms with mathematical operations.Interpret twice, thrice, half of this etc logically.Practice a lot.
According to the given question I think of a number,Let the number be x.
I increase it by four and double (x+4)×2 = 2(x+4).
The result is 20 more than the number which is (x+20).
∴ 2(x+4) = (x+20)
2x + 8 = x + 20.
2x - x = 20 - 8.
x = 12.
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which steps transform the graph of y=x^2 to y=-(x-3)^2+2
Answers
Answer:
reflection over the x-axis
shifted 3 right
shifted 2 up
Step-by-step explanation:
This function is quadratic. Quadratic graphs are written as y=a(x-h)^2+k. Where a is a non-zero number that affects the vertical appearance of the graph, h is the horizontal placement, and k is the vertical placement.
When a is negative then, the graph has been reflected over the x-axis. This makes it look like it has been turned upside down. The variable h affects how the x-values are shifted. In this equation, h looks negative but it is actually positive because if you look at the formula, h is being subtracted. Positive h values move the graph right. So, the graph is shifted 3 units to the right. Finally, k does the same thing as h but on the vertical (y) axis. So, +2 makes the graph shift 2 units up.
if the compound interest on a sum for 2 years at 4% p.a. is ₹408, then the simple interest on the same sum at the same rate and for the same period is (I) ₹400 (ii) ₹398 (iii) ₹200 (iv) ₹204
Answers
Given that:
CI = ₹408
years = 2 years
Rate of interest = 4%
A = P{1+(R/100)}^
A-P = p{1+(R/100)}^n - P
I = P[1+(R/100)}^n - 1]
408 = P[{1+(4/100)²} - 1]
= P[{1+(1/25)²} - 1]
= P[(26/25)² - 1]
= P[(676/625) - 1]
= P[(676-625)/625]
408 = P(51/625)
P = 408*(625/51)
= 8*625 = 5000
Sum = 5000
Simple Interest (I) = (P*R)/100
= 5000*2*(4/100)
= 50*2*4 = 400
From the given above options, option (a) ₹400 is your correct answer.
please help, thank you!
Answers
Answer:
x = 6
Step-by-step explanation:
45°+45°+m∆2 = 180°
m∆2 = 90°
; m∆2 = 16x-6
90 = 16x-6
96 = 16x
96/16 = x
6 = x
Please Help!!!!!! Tom says that he needs 6 rolls to obtain each possible outcome on a 6-sided die. On the fourth roll, he rolls his second "3”. Tom says that the die is loaded and that each outcome is not equally likely. Is Tom correct here? If you think Tom is incorrect, how many rolls should Tom make until he sees each number occurring about 1/6 of the time?
Answers
Answer:
I think he is correct.
Step-by-step explanation:
I think he is correct because when you roll a die, it is 10 to 1 for the die to get the number you want.
Tom says that the dices outcome is NOT equally likely. When actually the outcome is equally likely.
On dice no two number repeat twice. So in this case every time he rolls the die he has the same chance of getting 3 than he does any other number.
So Tom is incorrect.
And for how many times it will take Tom for all the numbers to occur is all by luck and chance.
But each number is equally likely to come.
0.2343217 Is it rational or irrational
Answers
What is the Area of semicircle?
Answers
Step-by-step explanation:
Area of Semi Circle
The area of a semicircle is half of the area of the circle. As the area of a circle is πr2. So, the area of a semicircle is 1/2(πr2 ), where r is the radius.
Finley is making a pancake recipe
that calls for 3 cups of flour. He uses
13 cups of white flour and the rest will
be wheat flour. How many cups of
wheat flour will Finley need?
Answers
arkadaşım bilemiyorum
In the past month, Raina rented 6 video games and 1 DVD. The rental price for each video game was $2.25 . The rental price for the DVD was $3.80 . What is the total amount that Raina spent on video game and DVD rentals in the past month?
Answers
Answer:
$17.30
Step-by-step explanation:
6 (video games) multiplied by $2.25 equals $13.50
or
(2.25 + 2.25 + 2.25 + 2.25 + 2.25 + 2.25) = 13.50
and
1 (DVD) is $3.80
$13.50 + $3.80 = $17.30
$17.30
Please I really really do need help like now please and thank you
Answers
6+8+12+10+6+4+10=56
Mike earned x dollars the first week of his new job. He earned 5% more the second week than the first week. Which expression represents the total amount of money Mike earned for both weeks?
1.50x
1.50 x
1.05x
1.05 x
2.00x
2.00 x
2.05x
Answers
Answer:
1.05x I think
simplify and factor if necessary
Answers
Answer:
[tex]\frac{1}{x}[/tex]
Step-by-step explanation:
[tex]\frac{3x - 12}{3x^{2} - 12x}[/tex]
[tex]\frac{3x - 12}{x(3x-12)}[/tex] Factor out x.
[tex]\frac{1}{x}[/tex] Simplify.
Davina travelled 500 miles in 7 days. What is the average
distance travelled each day?
Answers
71 is the answer
71 miles
Step by step explanation:
500:7 and u will have the average distance travelled each day
Find the HCF of x 2 y 3 and x 3 y
Answers
Answer:
the answer is to the question is x2×y×3
What is the value of the expression when h = 5? h + 7
Answers
Answer:
12
Step-by-step explanation:
if h=5
then h+7 = 5+7 = 12
[tex]\huge\bf\underline{\underline{\pink{A}\orange{N}\blue{S}\green{W}\red{E}\purple{R:-}}}[/tex]
[tex]\implies\sf{h + 7} \\ \\ \implies\sf{5 + 7} \\ \\ \implies\sf{12}[/tex]
. What is 6 8ths x 5? Draw a model of your choice to help you solve.
WILL GIVE BRAINIST
Answers
Answer:
The complete and simplified answer to the question what is 6/8 of 5 is:
3 3/4
Step-by-step explanation:
You probably know that the number above the fraction line is called the numerator and the number below it is called the denominator. To work out the fraction of any number, we first need to convert that whole number into a fraction as well.
Here's a little tip for you. Any number can be converted to fraction if you use 1 as the denominator: 5/1
So now that we've converted 5 into a fraction, to work out the answer, we put the fraction 6/8 side by side with our new fraction, 5/1 so that we can multiply those two fractions.
That's right, all you need to do is convert the whole number to a fraction and then multiply the numerators and denominators. Let's take a look:
6 x 5/ 8 x 1 = 30 /8
In this case, our new fraction can actually be simplified down further. To do that, we need to find the greatest common factor of both numbers.
You can use our handy GCF calculator to work this out yourself if you want to. We already did that, and the GCF of 30 and 8 is 2.
We can now divide both the new numerator and the denominator by 2 to simplify this fraction down to its lowest terms.
30/2 = 15
8/2 = 4
When we put that together, we can see that our complete answer is:
15/ 4
If you now simplifiy the COMPLETE anwser is:
3 3/4
Help please help please
Answers
Answer:
just use algebraic expression