Answers
[tex] \lim\limits_{x\to11}\dfrac{\sqrt{x+5}-4}{x-11}=\lim\limits_{x\to11}\dfrac{(\sqrt{x+5}-4)(\sqrt{x+5}+4)}{(x-11)(\sqrt{x+5}+4)}\\\\=\lim\limits_{x\to11}\dfrac{(\sqrt{x+5})^2-4^2}{(x-11)(\sqrt{x+5}+4)}=\lim\limits_{x\to11}\dfrac{x+5-16}{(x-11)(\sqrt{x+5}+4)}\\\\=\lim\limits_{x\to11}\dfrac{x-11}{(x-11)(\sqrt{x+5}+4)}=\lim\limits_{x\to11}\dfrac{1}{\sqrt{x+5}+4}=\dfrac{1}{\sqrt{11+5}+4}\\\\=\dfrac{1}{\sqrt{16}+4}=\dfrac{1}{4+4}=\dfrac{1}{8}\\\\Answer:\ d.\ \dfrac{1}{8} [/tex]
Related Questions
if the circumference of the base=126 cm and h=10 cm, find the volume
Answers
A cylinder has a circular base with a diameter of 12ft. The height of cylinder is 4 ft. What is the volume of the cylinder rounded to the nearest whole number? Use 3.14 for pi.
Answers
Volume = (3.14)(12÷2)²(4) = 452 ft³ (nearest whole number)
Answer: 452 ft³
Write each mixed numbers as a product of a whole number and a unit fraction
1 1/2
1 3/5
3 3/4
Answers
2. 1/5 x 8
3. 1/4 x 15
Keisha has one penny, one nickel, and one dime in her pocket. She randomly takes on coin out of her pocket. Without putting it back, she randomly takes out another coin. If Keisha lists all the possible outcomes of picking the two coins one at a time, how many outcomes are there?
Answers
In a large apartment building, 35 of the apartments have a balcony and 55 do not. An apartment us randomly selected as part of a survey. What is the probably it has a balcony?
Answers
11/18 probability
90 apartments total
35/90=
11/18
Answer:
Thanks
Step-by-step explanation:
This person is correct peeps :DD
Evaluate the expression. If necessary, round to the nearest hundredth. lne
Answers
For example: log has a base of 10, log10 = 1
ln stands for Natural Log. The Base of the natural log is e. So we can also write the given expression as:
[tex]ln(e)= log_{e}(e) [/tex]
When the base of log is equal to the value for which you are finding the log, the answer is always equal to 1.
So the answer to this question is 1.
3/7÷1/2 how do you graph this
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Not sure what you mean by graphing it though. Like on a number line? There is no x or y in your equation.
please please someone help me and show me how you got the answer super super thanks in advance
Answers
18/100
=0.18
Convert it to a percent by moving the decimal point two places to the right.
So 40/100
=.40
Move the decimal point over two and add the percent sign.
40%
In the diagram,CD is tangent to the circle, AB = 6 in, and BD = 10 in. Find AD.
Answers
we know that
AB=6 in-----> this is the radius of circle
BC=AB-----> 6 in
AC=12 in-------> is the diameter of circle
BD=10 in
in the right triangle BCD
Applying the Pythagoras theorem
BD²=BC²+CD² --------> CD²=BD²-BC²-----> CD²=10²-6²----> CD²=66
CD=√66 in
in the right triangle ACD
AD²=AC²+CD²-----> AD²=12²+(√66)²----> AD²=144+66----> AD²=210
AD=√210 in-----> AD=14.49 in
the answer is
AD is 14.49 in
a furnace is rated 4000 BTU per hour. How many foot pounds of energy are released in one hour?
- 5.1 foot pounds
- 2,456,000 foot pounds
- 0.2 foot pounds
- 3,112,000 foot pounds
Answers
Now we just need to multiply 4000 BTU by our conversion factor:
[tex]4000BTU*\frac{778foot-pound}{1BTU}=3112000foot-pound[/tex]
We can conclude that the furnace released 3,112,000 foot pounds of energy in one hour.
The area of a square can be found using the equation A = s², where A is the area and s is the measure of one side of the square.
Match the equation for how to solve for the side length of a square to its description.
Drag the equation into the box to match the description.
Answers
hope it helps
Answer: middle
Step-by-step explanation:
the first computer is usually regarded as one called ROACH completed in 1945. Email was invited in 1971. how many years after the computer was email invented
Answers
the first computer is usually regarded as one called ROACH completed in 1945. Email was invited in 1971. how many years after the computer was email invented
in this vase we will use soustraction
1971-1945=26
email was invented 26 years after computers
hopes this helped you well
may i please have the brainliest
have a wonderful day or night
Final answer:
Email was invented 26 years after the completion of the first recognized computer in 1945.
Explanation:
The first computer is often attributed to the work carried out during World War II, with machines like ENIAC, completed in 1945, incorporating vacuum tubes and filling entire rooms. However, the question references a machine called ROACH, which seems to be a typo or a misunderstanding; we usually refer to ENIAC as one of the first computers. Email, on the other hand, was invented in 1971 by Ray Tomlinson. Calculating the difference between the years when the first computer was completed and when email was invented gives us the number of years it took for email to be developed after the advent of the computer.
To find this, we subtract the year the first computer was completed, 1945, from the year email was invented, 1971:
1971 (the year email was invited) - 1945 (the year the computer was completed) = 26 years.Email was invented 26 years after the completion of the first computer.
Solve the system of equations algebraically.
3x-3y=6
6x-7y=5
a. (8,8)
b. (9,7)
c. many solutions
d. no solution
Answers
The system of equations has a solution at (9, 7), which is an option (b).
What are Systems of equations?Simultaneous equations, a system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.
There are four methods for solving systems of equations: graphing, substitution, elimination, and matrices.
The given equations are:
3x-3y=6
6x-7y=5
Multiply the first equation by 2 to get rid of the coefficient of x in the second equation:
6x - 6y = 12
6x - 7y = 5
Subtract the first equation from the second equation to eliminate x:
0x - y = -7
y = 7
Substitute y = 7 into one of the original equations and solve for x:
3x - 3y = 6
3x - 3(7) = 6
3x - 21 = 6
3x = 27
x = 9
Therefore, the solution to the system of equations is (9, 7), which corresponds to option (b).
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The following data shows the low temperature in Vancouver, in degrees Celsius, for two weeks in January one year. 8.90, 8.35, 8.50, 8.65, 8.55, 8.20, 8.50, 8.32, 8.50, 8.60, 8.60, 8.30, 8.10, 8.65 Which box plot best represents this data?
Answers
8.10, 8.20, 8.30, 8.32, 8.34, 8.50, 8.50, 8.50, 8.55, 8.60, 8.60, 8.65, 8.65, 8.90
Lower extreme: 8.10
Upper extreme: 8.90
Median: 8.50
1st/lower quartile: 8.32
3rd/upper quartile: 8.60
Please see the attached picture for the boxplot.
A square garden has an area of 64 square feet. What is the length of the garden?
Answers
Area = Length²
Length² = 64
Length = √64
Length = 8 feet
Answer: 8 feet
The length of the garden will be 8 feet.
It should be noted that the area of a square is gotten by multiplying its lengths together. For example, the area of a square with length of 2cm will be: = 2 × 2 = 4cm²
Therefore, since the square garden has an area of 64 square feet, the length of the garden will be:
= ✓64
= 8 feet
Therefore, the length is 8 feet.
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need urgent help Which sets of numbers are closed under addition?
Choose all answers that are correct.
A.
whole numbers
B.
natural numbers
C.
negative integers
D.
integers
Answers
Whole numbers are closed under addition and multiplication
Integers are closed under addition, subtraction, and multiplication
natural numbers are positive whole integers so they are also closed under addition
The answers are A, B and D
Hope this helps!
1)What is the solution to the equation below?
2) How did you get your answer?
x+3 = 8
Answers
Short answer: #1; 5 #2; Explained below
So, we know the answer is 5, so how did I get that? Well, to find that, you have to subtract the two known numbers, 8 and 3. What is 8 - 3? 5. ((8 - 3 = 5))
Hope this helped you! ♥
0.8 x 3.15 it’s multiplying rational numbers
Answers
Let me know if you want me to show my work
Simplify the expression.
2^2 • 2^3
A.
4^5
B.
4^6
C.
2^6
D.
2^5
Answers
[tex] 2^{2} 2^{3} = 2^{2*3} = 2^{6} [/tex]
The answer you're looking for is ( D ) because in exponents, the rule is..
║If the bases are the same, add the exponents║
2 ^2 * 2 ^3 = ? (Bases are the same, add the exponents)
Answer: D = 2^5
║Hope that helps :)║
Please find perimeter and area. also show work plz. It's really easy. I will mark as brainliest.
Answers
The perimeter of an enclosure is the length around the enclosure, or the sum of all the outer sides added up (red+blue lines in picture).
1) We are told that the two vertical sides of the enclosure (shown in blue) are each 20ft, making it 20 + 20 = 40ft total. All we need to find is the sum of the lengths of the four sides of the triangles (shown in red).
2) We are given the height of the triangle, 16ft, and the length of the base of the triangle, 20ft. To find the length of the edge we're looking for, we need to find the hypotenuse of the right triangle shaded in green. One of the legs of the triangle is 10ft (half of the base of the larger triangle) and the other leg is 16ft (same as height of the larger triangle).
Use the pythagorean theorem, which says [tex] a^{2} + b^{2} = c^{2} [/tex].
a and b are the length of your legs, 10ft and 16ft, and c is the length of the hypotenuse, or the side we're looking for. Plug your numbers in and find c:
[tex]10^{2} + 16^{2} = c^{2} \\ c^{2} = 356\\ c = 18.868 ft[/tex]
3) Now you know each red side is 18.868 ft. There are 4 red sides, so 4 x 18.868ft = 75.472ft. Add this number to the length of your two blue sides to get the perimeter:
75.472ft + 40ft = 115.472ft.
--------------
Area: [tex]720ft^2[/tex]
The area of the enclosure is shaded in yellow. To find the area of the enclosure, you want to find the sum of the areas of all the shapes. Break the enclosure down into one square (in the middle) with two triangles on the top and bottom, find the area of those three shapes, and add those areas together.
1) The equation for the area of the square is [tex]A=s^2[/tex], where s = length of the side.
You're told that the length, s = 20ft. Plug that in and solve for the area of the square:
[tex]A=s^2\\ A=20^2\\ A = 400 ft^2[/tex]
2) The equation for the area of a triangle is [tex]A = \frac{1}{2} bh[/tex], where b = length of base and h = height of triangle.
You're told that the length of the base, b = 20ft and the height of the triangle, h = 16ft. Plug these values in and solve for area of one of the triangles:
[tex]A = \frac{1}{2} bh\\ A = \frac{1}{2} (20)(16)\\ A = 160 ft^2[/tex]
3) Since you have two identical triangles, multiply the area of one triangle by two to get the total area of the two triangles:
[tex]160 ft^2 \times 2 = 320 ft^2[/tex]
4) Add up the areas of the square and the two triangles to get the total area of the enclosure:
[tex]400 ft ^2 + 320 ft^2 = 720ft^2[/tex]
Leo has 100 coins in his piggy bank. All coins are either nickels, or dimes, or quarters. There are as many nickels as dimes and quarters together. How much money are nickels in Leo's piggy bank worth? will mark brainliest!!! PLEASE HELP
Answers
Total money nickles are worth of = $2.5
Let number of nickles coins be 'x'
Let number of dime coins be 'y'
Let number of quarter coins be 'z'
we have,
x + y + z = 100 and x = y +z
on solving the two equations, we get x = 50
1 nickle = 5 cents
50 nickles = 250 cents = $2.5
Kathy is baking cakes each cake requires 1/12 of a teaspoon of vanilla and she has 9/12 of a teaspoon how many cakes can she bake?
Answers
use the given graph to determine the period of the function. 1 & 2 plz
Answers
We have then:
Part 1:
The period of the function is:
T = 3
Part 2:
The period of the function is:
T = 4
Answer:
The period of functions 1 and 2 respectively are:
T = 3
T = 4
which numbers are rational numbers 2, -4.0, 8.1, 3/4, 0, -8
Answers
Writing a Real-World Inequality Anise wants to have longer hair than her sister. Her sister’s hair is 2.25 feet long. How long does Anise’s hair have to be?
Answers
Answer:
B the second graph
Step-by-step explanation:
Have trust in me and give brainiest
which of the following is equal to the rational expression.......
Answers
The expression equal to the rational expression is 3/(x + 6)
Calculating the value of the rational expression
from the question, we have the following parameters that can be used in our computation:
3(x + 2)/(x + 6)(x + 2)
Divide the fraction by x + 2
So, we have
3(x + 2)/(x + 6)(x + 2) = 3/(x + 6)
Hence, the value of the rational expression is 3/(x + 6)
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A box containing 3 small bags of flour weighs 950 grams. Each bag of flour weighs 300 grams. How much does the empty box weigh
Answers
3x300=900
950-900=50
50 is the total weight that is left fi you were to take the 3 bags out of the box
The table below shows the values of y for different values of x:
x y
0
0
1
5
2
10
3
15
Which equation shows the relationship between x and y?
x = 5y
y = 5 + x
x = 5 + y
y = 5x
Answers
0 0
1 5
2 10
3 15
The answer is y = 5x
we can check this by plugging in the numbers from the table:
5 = 1(5)
5 = 5
This makes this answer correct because it makes the equation true.
Answer:
D. [tex]y=5x[/tex]
Step-by-step explanation:
We have been given a table of values. We are asked to find the equation that shows the relationship between x and y.
x y
0 0
1 5
2 10
3 15
Upon looking at our given table, we can see that with each increase in x value, the value of x increases by 5. This means that slope of our given line is 5.
We can also see that initial value or y-intercept is 0.
Upon substituting our given values in slope intercept form of equation, we will get:
[tex]y=5x+0[/tex]
[tex]y=5x[/tex]
Therefore, our required equation is [tex]y=5x[/tex] and option D is the correct choice.
Parker was able to pay for 44% of his college tuition with his scholarship.
The remaining $10,054.52 he paid for with a student loan.
What was the total cost of Parker's college tuition?
Round your answer to the nearest dollar.
Tuition cost = $_
Answers
Let x be the total amount of his tuition. He paid for 44% of it, or 0.44, with his scholarship. This leaves 100%-44% = 56% = 0.56 of it to be taken care of with loans. We know he took out 10054.52 in loans:
0.56x = 10054.52
Divide both sides by 0.56:
0.56x/0.56 = 10054.52/0.56
x = 17954.50 ≈ 17955
The total cost of Parker's college tuition, rounded to the nearest dollar, is $17,952.
Explanation:If Parker was able to pay for 44% of his total college tuition with his scholarship, this means that the $10,054.52, which he paid using his student loan, represents the remaining 56% of his tuition cost. Therefore, to find the total cost of tuition, we need to divide the amount he paid with a loan by 0.56. Performing this calculation gives us:
$10,054.52 / 0.56 = $17,952.00
Therefore, the total cost of Parker's tuition rounded to the nearest dollar is $17,952.
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What property is used to transform the equation x-2y=14 into -3x+6y=-42
Answers
To get from equation 1 to equation 2, everything in equation 1 was multiplied by -3.