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
Answers
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
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answer:
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Which problem can be solved with 56 + 7 = 8?
Chloe has 56 pennies. Her brother has 7 times as
many pennies as she has, How many pennies does
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Chloe has 56 pennies. She finds 7 more pennies.
How many pennies does she have now?
Chloe has 56 pennies. She puts the pennies into
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Answer:
she puts the pennies into equal stacks
Step-by-step explanation:
I think you meant 56 DIVIDED by 7=8, not 56 PLUS 7=8
Answer:
C.Chloe has 56 pennies. She puts the pennies intoequal stacks of 7. How many stacks does she make?
Step-by-step explanation:
FIRST CORRECT ANSWER GETS BRAINLIEST!!!!!!!! Suppose you were digging at a rate of 10 feet per day. Assume you are ar sea level when you begin digging. If there are 365 days in a year, write an equation to represent the depth of the hole where d= depth in feet and t= time in years
Answers
Answer:
simple
Step-by-step explanation:
365 x 10 = 3650 feet
took you 1 year
and adding on sea level 1,312 feet
3650 + 1,312 = 4962 in 1 year
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Please help this is due in 5 minutes. Choose one of the answer to respond to
Answers
Answer:
Option 2
Step-by-step explanation:
I agree with this statement. Biodiversity indicates the health of the ecosystem. Maintaining biodiversity can provide clean air, water, pollination of plants, pest control, food, and keep everything in balance. It can also reduce the impact of natural disasters! One example is a flood.
Answer:
Option 1
Step-by-step explanation:
I do agree with this statement because without matter, we wouldn't have anything. Matter is weight and anything physical.
Six years ago Matt was four times as old as Brown, and in 3 years the sum of their
ages will be 43 years. Find their present ages.
Answers
Answer:
Matt=26
Brown=11
Step-by-step explanation:
Just trust me!!!
The present age of Matt given the information in the question is 26.
The present age of Brown given the information in the question is 8.
What are the linear equations that represent the question?4y - 6 = x equation 1
x + y + 6 = 43 equation 2
Where:
x = Matt's agey = Brown's ageWhat is Brown's age?Subsistute for x in equation 2
4y - 6 + y + 3 = 43
Combine similar terms
5y = 40
y = 8
What is Matt's age?
Subsitute for y in equation 1
4(8) - 6 = x
32 - 6 = 26
To learn more about simultaneous equations, please check: https://brainly.com/question/25875552
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Answers
9514 1404 393
Answer:
1 m³
Step-by-step explanation:
The ratio of volumes is the cube of the ratio of corresponding linear dimensions.
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Answers
Answer:
150 pairs
Step-by-step explanation:
so total money spent Is equal to 5000
profit is equal to 3000
profit on each pair is equal to 20
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Answer:
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Which function shows the function f(x) = 3^x being
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A. f(x) = 3^x – 5
B. f(x) = 3^(x+5)
C. f(x) = 3^(x - 5)
D. f(x) = 3^x + 5
Answers
Answer:
B.
Step-by-step explanation:
When you want to move a function on a graph from left to right, you "move" the x, and when moving the x; it's the opposite. So, C would move the function 5 units to the right because it is subtracting.
The correct option will be f(x) = 3^(x - 5)
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Given that, the function f(x) = 3ˣ, being translated 5 units to the left.
Since, the function is being translated in left, therefore, we subtract 5 from x,
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For more references on translation, click;
https://brainly.com/question/12463306
#SPJ2
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Answers
Answer:
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Step-by-step explanation:
just divide 2156 by 11 :p i hope im right lol.
Answer:
196 hours
Step-by-step explanation:
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Answers
Answer:
3.5%
Step-by-step explanation:
Interest = 10100 - 8000 or 2100
I = Prt
2100 = 8000(9/12)r
2100 = 600r
2100/600 = r
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Answers
Answer:
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answer:
the lateral area=perimeter of triangle ×height=
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There are two spinners containing only white and green slices. Spinner A has 4 white slices and 1 green slice. All the slices are the same size. Spinner B has 3 white slices and 9 green slices. All the slices are the same size. Each spinner is spun. List these events from least likely to most likely. Event : Spinner B lands on a green slice. Event : Spinner A lands on a white or green slice. Event : Spinner A lands on a white slice. Event : Spinner B lands on a yellow slice.
Answers
Answer:
Step-by-step explanation:
Ok, lets list the important things
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this means that the order is:
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2. option 3
3. option 1
4. option 2
because it is least likely to most likely.
hope this helped you out and if you need any questions feel free to ask
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-cheesetoasty
The sales tax for an item was $27.20 and it cost $340 before tax.
What is the sales tax rate?
Write your answer as a percentage.
Answers
Answer:
8%
Step-by-step explanation:
27.20/340=0.08
=8%
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Answers
Answer:
choice 1) 0, -4/5
Step-by-step explanation:
1/(t² + t) = 1/t - 5
multiply both sides of the equation by (t² + t):
1 = (t² + t)/t - 5t² - 5t
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t = 0
-5t = 4
divide both sides by -5:
t = -4/5
Solve: 1/3(−6q+4)=−1/12(4q+4)
Answers
Answer:
Combine multiplied terms into a single fraction
13(−6+4)=−112(4+4)
13(−6q+4)=−112(4q+4)\frac{1}{3}(-6q+4)=\frac{-1}{12}(4q+4)31(−6q+4)=12−1(4q+4)
1(−6+4)3=−112(4+4)
1(−6q+4)3=−112(4q+4)\frac{1(-6q+4)}{3}=\frac{-1}{12}(4q+4)31(−6q+4)=12−1(4q+4)
2
Multiply by 1
3
Combine multiplied terms into a single fraction
4
Distribute
5
Multiply all terms by the same value to eliminate fraction denominators
6
Cancel multiplied terms that are in the denominator
7
Distribute
8
Subtract
16
161616
from both sides of the equation
9
Simplify
10
Add
4
4q4q4q
to both sides of the equation
11
Simplify
12
Divide both sides of the equation by the same term
13
Simplify
Show less
Solution
=1
Step-by-step explanation:
Answer:
q=1
Step 1: Simplify both sides of the equation.
Step 2: Add 1/3q to both sides.
Step 3: Subtract 4/3 from both sides.
Step 4: Multiply both sides by 3/(-5).
Question 7 of 8
Calculate the amount of interest earned on a $7,500 investment made for 2 years at
5.5% p.a..
Answers
Answer:
$825
Step-by-step explanation:
Formula we use:
I = Prt
Given:
P = 7500
r = 5.5% or 0.055
t = 2
Work:
I = Prt
I = 7500(0.055)(2)
I = 412.5(2)
I = 825
Mathematical Literacy , What does a basic fee mean?
Answers
Answer:
Basic Fee means the compensation provided to Construction Manager for providing Basic Services. ＋ New List. Basic Fee means the compensation provided to Pre-Construction Contractor for providing Basic Services.Step-by-step explanation:
someone please help. this is the rest of my points. and it's worth 50% of my grade
Answers
Answer:
a=52
b=128
r=s=100
Step-by-step explanation:
true or false: sin 50* = sin 130*
Answers
Answer:
True
Step-by-step explanation:
sin(130)
sin(180-50)
By difference rule for sine
sin(180)cos(50)-sin(50)cos(180)
0*cos(50)-sin(50)*-1
0+sin(50)
sin(50)
The answer is true.
i need help now please
Answers
Answer:
12
Step-by-step explanation:
A = ½(b1 + b2)h
A = (3 + 5)(3)/2
A = 12
Dividend and divisior with quotient 32000 using powers of 10
Answers
Answer:
320,000/10=32000
Step-by-step explanation:
3. Maxine has assets worth $145,000 and liabilities totaling $75,000. What is Maxine's net worth?
A $155,000
B-$15,000
C $70,000
D-$85,000
Answers
Explanation:
Assets - Liabilities = Net worth
$145,000 - $75,000 = $70,000
145,000- 75,000=70000
Kala received a $70 gift card for a coffee store. She used it in buying some coffee that cost $8.58 per pound. After buying the coffee, she had 18.52 left on her card. How many pounds of coffee did she buy?
Answers
The volume of the polyhedron is ______ yd3.
Answers
Answer:
122,850 yd³
Step-by-step explanation:
The polyhedron is a right triangle prism
Area of the right triangle prism = ½*a*c*h
a = 91 yd
c = 60 yd
h = 45 yd
Volume = ½*91*60*45
= 122,850 yd³
If you walk around a circular path TWICE, and the circle has a diameter of 100 m, how far did you walk in TOTAL?
Answers
Answer:
628.32 m
Step-by-step explanation:
C = πd
C = π*(100m)
C = 314.16 m
Total Distance = 2*C
2*C = 628.32 m
Leave a like and brainist if this helped
What is the first step to solve this equation:
11 - 3x = 44
Add 3 to both sides
Add 11 to both sides
Subtract 11 from both sides
Divide 3 on both sides.
Answers
please help i will give brainliest.
Answers
Answer:
754 ft²Step-by-step explanation:
Given
d = 24 fth = 4 ftRequired amount of vinyl:
πdh + πd²/4 =3.14*24*4 + 3.14*24²/4 = 754 ft² (rounded)