Answer:
20
Step-by-step explanation:
cause
Find the following limit. Limit of StartFraction StartRoot x + 2 EndRoot minus 3 Over x minus 7 EndFraction as x approaches 7 Which statements describe finding the limit shown? Check all that apply. Multiply by StartFraction StartRoot x + 2 EndRoot + 3 Over StartRoot x + 2 EndRoot + 3 EndFraction. Get x – 1 in the numerator. Get (x -7)(StartRoot x + 2 EndRoot minus 3) in the denominator. Divide out a common factor of x – 7. Calculate the limit as StartFraction 1 Over 6 EndFraction.
ANSWERS: A,D,E
Answer:
a,d,e
Step-by-step explanation:
In this question, we apply limit concepts to get the desired limit, finding that the correct options are: A, D and E, leading to the result of the limit being [tex]\frac{1}{6}[/tex].
Limit:
The limit given is:
[tex]\lim_{x \rightarrow 7} \frac{\sqrt{x+2}-3}{x-7}[/tex]
If we apply the usual thing, of just replacing x by 7, the denominator will be 0, so this is not possible.
When we have a term with roots, we rationalize it, multiplying both the denominator and the denominator by the conjugate.
Multiplication by the conjugate:
The term with the root is:
[tex]\sqrt{x+2} - 3[/tex]
It's conjugate is:
[tex]\sqrt{x+2}+3[/tex]
Multiplying numerator and denominator by the conjugate, meaning option A is correct:
[tex]\lim_{x \rightarrow 7} \frac{\sqrt{x+2}-3}{x-7} \times \frac{\sqrt{x+2}+3}{\sqrt{x+2}+3}[/tex]
We do this because at the numerator we can apply:
[tex](a+b)(a-b) = a^2 - b^2[/tex]
Thus
[tex]\lim_{x \rightarrow 7} \frac{\sqrt{x+2}-3}{x-7} \times \frac{\sqrt{x+2}+3}{\sqrt{x+2}+3} = \lim_{x \rightarrow 7} \frac{(\sqrt{x+2})^2 - 3^2}{(x-7)(\sqrt{x+2}+3)} = \lim_{x \rightarrow 7}\frac{x+2-9}{(x-7)(\sqrt{x+2}+3)} = \lim_{x \rightarrow 7}\frac{x-7}{(x-7)(\sqrt{x+2}+3)}[/tex]
Thus, we can simplify the factors of x - 7, meaning that option D is correct, and we get:
[tex]\lim_{x \rightarrow 7} \frac{1}{\sqrt{x+2}+3}[/tex]
Now, we just calculate the limit:
[tex]\lim_{x \rightarrow 7} \frac{1}{\sqrt{x+2}+3} = \frac{1}{\sqrt{7+2}+3} = \frac{1}{3+3} = \frac{1}{6}[/tex]
Thus, option E is also correct.
Using a limit calculator, as given by the image below, we have that 1/6 is the correct answer.
For more on limits, you can check https://brainly.com/question/12207599
What type of angles are A and B?
Answer:
supplementary angles
Step-by-step explanation:
Answer:
supplementary
they are also adjacent
they also form a 'straight angle'
they can also be termed as a 'linear pair'
Step-by-step explanation:
1.2 + 3.45 + 6.789 = ?????
Step-by-step explanation:
[tex]1.2 + 3.45 + 6.789 \\ = 4.65 + 6.789 \\ = 11.439[/tex]
Answer:
11.4
Step-by-step explanation:
1.2 + 3.45 + 6.789 = 11.43926 ≈ 11.4
-TheUnknownScientist
Find the conjugate and product of the following surds
1) i3 + i5
2) i3 + 9
3) - i2 + 1
4) - 3 + iy
Answer:
(1) Conjugate = -i8
(2) Conjugate = -i3+9
(3) Conjugate = i2+1
(4) Conjugate = -3-iy
Step-by-step explanation:
From the question,
Conjugate of a surd is formed by changing the sign between a rational number and a surd in an expression.
The conjugate of a surd is obtained by changing the sign of the surd in the expression.
Given
(1) i3+i5 = i8
Conjugate is -i8
(2) i3+9
Conjugate is -i3+9
(3) -i2+1
Conjugate is i2+1
(4) -3+iy
Conjugate is -3-iy
The sum of the interior angle measures of a convex polygon is 540° . How many sides does it have?
Answer:
5 sides
Step-by-step explanation:
A polygon includes the shape pentagon which has 5 sides.
If n are number of sides of a convex polygon, sum of its interior angles is 540 degrees.
As in given case sum of interior angles is 540°, we have
( n − 2 ) × 180 ° = 540°
When we solve this equation, we get 5 sides.
We can check this by plugging 5 into n, so the equation is
(5 - 2) x 180° = 540, this becomes...
3 x 180 = 540; this is correct so you answer is 5 sides.
PLEASE PLEASE HELP ME THIS IS DUE VERY SOON I NEED YOUR HELP!
Answer:
1. (3,-2)
2. (-1, -3)
3. (-4, 5)
4. (2, 5)
Step-by-step explanation:
Please answer the question in the picture Thxx
Answer:
A) 3, 4, and 5
D) 9, 12, and 15
Step-by-step explanation:
A) 3, 4, and 5
D) 9, 12, and 15
If you square and add the first two, you get the third one squared. That doesn’t work for B and C.
Camp counselors kept track of the number of granola bars they served each day.
What is the median of the data set?
Answer:
the median is 43
Step-by-step explanation:
Divide.
4,617 ÷ 23
Enter your answer as a mixed number in simplest form by filling in the boxes.
$$
Answer:
200.7391304348
Rounded: 200.74
Answer: 200.74
Step-by-step explanation:
A hairstylist schedules hour to trim a customer's hair and hour to style the customer's hair. The hairstylist plans to
work 3 hours each day for 5 days each week. How many appointments can the hairstylist schedule each week if each
customer must be trimmed and styled?
appointments
Answer:
5 customers
Step-by-step explanation:
If she takes 1 hour to trim and 1 hour to style, she will take 2 hours per customer.
She plans to work 3 hours a day. So, she can only fit 1 customer in per day because if she scheduled 2 she would need at least 4 hours.
If she can only have 1 customer per day over a 5 day week she will only be able to schedule 5 customers per week.
Benson owns four dogs. When he walks to his neighborhood pet store to get pet supplies, he randomly chooses one of his dogs to take with him. Describe a simulation you could use to help Benson with his selection.
Answer:
Benson could use a deck of cards.
Diamonds for the first dog.
Clubs for the second dog.
Hearts for the third dog.
Spades for the fourth dog.
Calcula el área y perímetro de un rectángulo que tiene como base (x+y) y altura (x-1).
Answer:
A = x^2 - x + xy - y
P = 4x + 2y - 2
Step-by-step explanation:
[tex]a = (x + y)(x - 1) \\ a = {x}^{2} - x + xy - y \\ \\ p = 2((x + y) + (x - 1)) \\ p = 2(2x + y + - 1) \\ p = 4x + 2y - 2[/tex]
I hope that is useful for you :)
2 1/6 feet equal how many inches in fraction form
Answer each question below 26. A pair of shoes that normally costs $85 is now on sale for 45% off. What is the sale price of the shoes?
27. After Christmas, I was able to buy lights for 60% off. How much did I pay for lights that normally cost $12?
28. This past weekend, I went to Bed, Bath & Beyond to purchase a new frying pan. I was able to use a 20% off
coupon on one item. The frying pan was originally $40. What is the sale price of the frying pan?
29. When eating at a restaurant, it is recommended that you leave a 15% tip. If my bill was $24, how much
should I leave as a tip?
Answer:
26. $46.75
27. $4.80
28. $32.00
29. $3.60
A person invested $220 in an account growing at a rate allowing the money to double every 13 years how much money would be in the account after 27 years?
Answer:
the answer should be 456.92
Answer:
928
Step-by-step explanation:
help me dont put links while answering question
Answer:
It's A, 3.82
Step-by-step explanation:
the decimal table goes up to left
A 99 ft length of wire is to be cut into 2 pieces, so that the longer piece is eight feet longer than six times the shorter piece. Fond the length of each piece.
9514 1404 393
Answer:
13 ft86 ftStep-by-step explanation:
Let s represent the length of the short piece. Then the long piece is 6s+8, and the total length is ...
s +(6s+8) = 99
7s = 91 . . . . . . . . subtract 8, collect terms
s = 13 . . . . . . . . . divide by 7
99 -13 = 86 = 6(13)+8 . . . length of long piece
The short piece is 13 feet long; the long piece is 86 feet long.
What number gives a result of −1 when 9 is subtracted from the quotient of the number and 4?
Step-by-step explanation:
x/4 - 9 = -1
×/4 = -1 + 9
x/4 = 8
4 (x/4) = 4 (8)
x = 32
Answer:
32
Step-by-step explanation:
(Quotient of a and b = a/b)
Let the number = x
Quotient of the number and four: x/4
9 subtracted from the quotient of the number and four: x/4 - 9
-1 is the result of 9 subtracted from the quotient of the number and four: x/4 - 9 = -1
x/4 -9 = -1
x/4 = 8
x = 32
Find an equation of the line satisfying the following conditions: Point (3,2);m= -5/6
Answer:
A
Step-by-step explanation:
y -2 = -5/6(x -3)
y-2 = -5/6x + 15/6
y = -5/6x + 27/6
y = -5/6x + 9/2
Which choice is equivalent to the fraction below?
7/12
A. divided 12
B. 7•12
C. 7-12
D. 12 divided 7
Answer:
b
Step-by-step explanation:
:)
. Select all the properties of a rectangle.
A. Has right angles
B. Has at least one obtuse angle
C. Has parallel lines
D. Has perpendicular lines
E. Has at least one acute angle
Answer:
A, C, D
Step-by-step explanation:
3. A newspaper reporter wants to know how popular the hobby of bird watching is in the city. He asked people at the local bird refuge if they watched birds as a hobby. Which of the following best explains whether the reporter's data is valid or not?
A. The data is valid for the entire city because the bird refuge is located in the city.
B. The data is not valid for the entire city because people can have more than one hobby.
C. The data is not valid for the entire city because bird watchers
are more likely to visit a bird refuge.
D. The data is valid for the entire city because a bird refuge is a good place to find people who like to watch birds.
Answer:
try c
Step-by-step explanation:
i dont know
Pls help extra points
An online retailer collects 7% sales tax. If the sub total of the purchase is $76,00, then how much is collected for sales tax
Answer:
$5.32
Step-by-step explanation:
76 x .07 = 5.32
solve and check please help
Answer:
7) 24 8) 75 9) .9
Step-by-step explanation:
You multiply the denominatior with the whole number.
Answer:
x = 24 b = 75 s = 0.9
Step-by-step explanation:
7. Multiply both sides by 2 and you get x = 24
8. Multiply both sides by 5 and you get b = 75
9. Multiply both sides by 0.3 and you get s = 0.9
The volume of the polyhedron rounded to the nearest tenth is ______ cm3.
Answer:
62.9
Step-by-step explanation:
volume of a cylinder = nr^2h
22/7 x 5 x 2^2 = 62.90 cm^3
If anybody can help it be really appreciated
Answer: PD
Step-by-step explanation:
Given
PA=PB
and PC=PD
We know, If two chords AC and BD intersect internally or externally at point P then
[tex]PA\times PC=PB\times PD[/tex]
Therefore, the missing term is PD
In a certain test, the number of successful candidates was three times than that of unsuccessful candidate, if there had been 16 fewer candidates and if 6 more would have been unsuccessful, the number would have been as 2 to 1. Find the number of candidates.
Answer:
The number of candidates is 136.
Step-by-step explanation:
Explain one way to find the area of the polygon at the right. Then find the area in square units.
Answer:
27 Units^2
Step-by-step explanation:
Split it up into sections, attached below are 3 different sections.
Section 1:
5*3=15
Section 2:
2*4=8
Section 3:
4*2/2 = 4
Add all the sections together:
15+8+4 = 27 Units^2
Please Mark Brainliest if this helped
Please Mark Brainliest if this helped
What is the solution to this equation? 9^x– 1 = 2 Α. 1/2 B. 1 C. 2 D. -1/2
Answer:
for 9^(x)-1=2 the answer is 1/2 or .5
The solution to this equation 9ˣ - 1 = 2 is 1/2.
The correct option is A.
What is an equation?Two algebraic expressions having same value and symbol '=' in between are called as an equation.
Given:
An equation:
9ˣ - 1 = 2
Simplifying,
9ˣ = 3
3²ˣ = 3
Comparing, we get,
2x = 1
x = 1/2
Therefore, the solution is x = 1/2.
To learn more about the equation;
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