a. to make f(x) continuous at x = 11, we need to define f(11) = 1/22. b. there is a solution for the equation f(x) = 0 on the interval [1, 2].
a) f(11)=5
To make the function f(x) continuous at x = 11, we need to remove the infinite discontinuity at x = 11. We can do this by factoring out (x-11) from the numerator and simplifying the expression. After factoring out (x-11), we get (sqrt(x) + 5 + 4)/(x - 11) = (sqrt(x) + 9)/(x - 11). We can see that this expression is undefined at x = 11, so we need to determine the limit of the expression as x approaches 11. We can use L'Hopital's rule to find that the limit is 1/22. Therefore, to make f(x) continuous at x = 11, we need to define f(11) = 1/22.
b) No. because f(1)<0 and f(2)<0.
The intermediate value theorem states that if f(x) is continuous on the closed interval [a, b] and if k is any number between f(a) and f(b), then there exists at least one number c in the open interval (a, b) such that f(c) = k. In this case, f(x) = 2x^3 - sqrt(6x + 2) is continuous on the closed interval [1, 2]. We can see that f(1) is negative and f(2) is also negative. Therefore, by the intermediate value theorem, we cannot conclude that there is a solution for the equation f(x) = 0 on the interval [1, 2].
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2^2/5+ 3^1/10
HELP ASAP
Answer:
[tex]\sqrt[5]{4}[/tex] + [tex]\sqrt[10]{3}[/tex]
Step-by-step explanation:
We sure can write 2^2/5+ 3^1/10 as [tex]2^{\frac{2}{5} } + 3^{\frac{1}{10} }[/tex]
// use the [tex]a^{\frac{m}{n} } =\sqrt[n]{a^{m} }[/tex] to transform the expression
Convert [tex]2^{\frac{2}{5} }[/tex] to [tex]\sqrt[5]{2^{2} }[/tex] = [tex]\sqrt[5]{4}[/tex] (here a = 2, n = 5, m = 2)
Then convert [tex]3^{\frac{1}{10} }[/tex] to [tex]\sqrt[10]{3^{1} }[/tex] = [tex]\sqrt[10]{3}[/tex] (here a = 3, n = 10, m = 1)
Now we get [tex]2^{\frac{2}{5} } + 3^{\frac{1}{10} }[/tex] = [tex]\sqrt[5]{4}[/tex] + [tex]\sqrt[10]{3}[/tex] . This is the simplified form, which is the answer.
In a survey conducted on 200 people, it was found that 105 of them prefer coffee, 50 prefer
tea and the remaining prefer both. Find the fraction of people who prefer both tea and coffee.
Given:
Total number of people = 200
People who prefer coffee = 105
People who prefer tea = 50
The remaining prefer both.
To find:
The fraction of people who prefer both tea and coffee.
Solution:
The number of remaining people who prefer both tea and coffee is
Remaining people = Total number of people - People who prefer coffee - People who prefer tea
Remaining people = 200 - 105 - 50
= 45
Now, the fraction of people who prefer both tea and coffee is
[tex]\text{Required fraction}=\dfrac{\text{Remaining people}}{\text{Total number of people}}[/tex]
[tex]\text{Required fraction}=\dfrac{45}{200}[/tex]
[tex]\text{Required fraction}=\dfrac{9}{40}[/tex]
Therefore, [tex]\dfrac{9}{40}[/tex] of people prefer both tea and coffee.
April wrote two equations to represent this system of equations. She wrote: y = 5x +
I and y = 14x - 10. Do you agree or disagree with April?
Answer:
Disagree
Step-by-step explanation:
The lines are parallel, which means they have different y-intercepts but the same slope.
April's two equations have different slopes (5 and 14), so they do not properly represent two parallel lines.
I need help on this assignment, I need to find the angles of the blank spaces. Anything is appreciated!
Answer:
3: 97
10: 97
9: 83
5: 97
7: 83
16: 97
Im 100% on these answers bc Ive already taken this class :)
Answer:
Step-by-step explanation:
9) m∠3 = m∠2 {Vertically opposite angles}
m∠3 = 97
m∠10 = m∠2 {Corresponding angle}
m∠10 = 97
m∠9 +m∠10 = 180 {Linear pair}
m∠9 + 97 = 180
m∠9 = 180 - 97
m∠9 = 83
m∠6 = 83
m∠5 + m∠6 = 180 {linear pair}
m∠5 + 83 = 180
m∠5 = 180 - 83
m∠5 = 97
m∠7 = m∠6
m∠7 = 83
m∠8 = m∠5 {Vertically opposite angles}
m∠8 = 97
m∠16 = m∠8 {Corresponding angle}
m∠16 = 97
Someone please let me know the answer
Answer:
The answer is 30°
Step-by-step explanation:
[tex]when \: \: \sqrt{3} \sin( \alpha ) - \cos( \alpha ) = 0 \\ \sqrt{3} \sin( \alpha ) = \cos( \alpha ) \\ multiply \: by \: \frac{1}{ \sqrt{3} \cos( \alpha ) } \\ then \\ \frac{ \sin( \alpha ) }{ \cos( \alpha ) } = \frac{1}{ \sqrt{3} } \\ \tan( \alpha ) = \frac{1}{ \sqrt{3} } \\ then \: \alpha = 30[/tex]
a student has a savings account with $475 in in it. She deposits $125 of her paycheck into the account every week. Her goal is to save 7,000 for college. How long will it take her to reach her goal of $7000?
Answer:
52.2 weeks
Step-by-step explanation:
7000 - 475 = 6,525
6525 ÷ 125 = 52.2
Answer:
It will take her 53 weeks to get her goal of 7,000$
Step-by-step explanation:
I subtracted 475 from 7,000 to see how much she needed to save for. I got 6525. I multiplied 125 times 52 and got 6500. To get to her goal she needs 25 more dollars so, she'll have to work another week to get to that goal.
:)
A bag contains 5 red marbles, 6 blue marble, 3 green marbles, 4 black marbles, 2 yellow marbles. A marble will be drawn from a bag and replaced 200 times. What is a resonanle predition for each times a yellow or green marble will be drawn
Answer:
50 times
Step-by-step explanation:
Red = 5 ; blue = 6 ; green = 3 ; black = 4 ; yellow = 2
Total number of marbles :
(5 + 6 + 3 + 4 + 2) = 20
Probability of drawing a yellow or green marble :
P(yellow) + p(green)
(2 / 20) + (3 / 20)
5 / 20
Hence, Number of times from 200 draws :
(5 / 20) * 200
= 50
Please answer the pictures provided
Answer:
-6-3
Step-by-step explanation:
Joan measures the mass of a solid metal object. It has a mass of 102.0 g. She also measures the volume of that object and the object has a volume of q 027 mL a)
What is the density of the metal object?
What metal could it be made Of?
Step-by-step explanation:
P=m/v
P=102,0 ÷027
P=3,77 that is the density
It is made of copper
Which of these ordered pairs is a solution to the inequality y - 2x < -3? ( (2,4) (-2, 3) (3, 4) (1,-1)
Answer:
(3, 4)
Step-by-step explanation:
What is the square root?
True or False: An decrease in a particle's thermal energy will decrease its speed. *
Answer:
true
Step-by-step explanation:
Answer:
True
Step-by-step explanation:
The total cost of flooring a room at Rs .9.50 per square meter is Rs 760, If the length of the room is 10 m, find its breadth.
Answer:
8 metre
Step-by-step explanation:
cost of flooring per square metre = Rs .9.50
total cost of flooring= Rs760
Area of room= 760/9.50
= 80 m^2
Area of the given room= Lenght × Breadth
length of the room is = 10 m
80= 10 × Breadth
Breadth= 80/10= 8 m
Hence, breadth of the room is 8metre
help quick due in 10 mins
Answer:
95
Step-by-step explanation:
We have the expression q over 19 = 5 and are asked to solve for q.
We have a dillemma here, q is in a fraction, to solve, all we need to do is get rid of this fraction. Since 19 is the denominator, we can multiply it by both sides :
[tex]\frac{q}{19} = 5[/tex]
19 * 5
95
Therefore :
q = 95
find the area of the shape using Pythagoras Theorem please
Answer:
122.09 (the answer may change depending on how many decimals you need if you need more or less just follow the steps using however many decimals)
Step-by-step explanation:
to get the other triangle side do 18-11= 7
then use the Pythagoras theorem to solve for the other side so 7^2+b^2=11^2
49+b^2= 121
121-49= b^2
72=b^2
b= 8.48(simplified)
then use that side to get the area of the rectangle:
8.42×11=92.62
then get area of the triangle:
1/2(8.42×7)=29.47
add the 2 areas to get total area:
92.62+29.47=122.09
A large rectangular box has a volume of 15.75 cubic feet. The box is 2.5 feet long and 1.5 feet wide. What is the height of the box?
Answer:
2.5 x 1.5= 3.75
15.75/3.75=4.2
Answer- 4.2
Step-by-step explanation:
Which transformation would take Figure A to Figure B
Answer:
6 squares to right and 6 squares down
Step-by-step explanation:
Go with the coordinate (-1, 5) on shape A
Hope it helps :)
Move 6 squares to right and 6 squares down.
The initial coordinate that is the x value is -5 and the transformation figure has x value 5.
So move figure A 6 squares to the right . And then move 6 squares to the down we get the transformation figure B.
Therefore, by moving 6 squares to right and 6 squares to down we get the transformation figure B.
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Consider the quadratic function: f (x) = 5x2 + 20x + 20. What are the zeros of the function using completing the square?
Step-by-step explanation:
step 1. f(x) = 5x^2 + 20x + 20
step 2. f(x) = 5(x^2 + 4x + 4)
step 3. f(x) = 5(x + 2)^2
step 4. 0 = 5(x + 2)^2
step 5. zeros: -2
Which is a correct classification for the triangle?
O obtuse triangle
O right triangle
O acute triangle
O equiangular triangle
Answer:
obtuse triangle is the correct classification for the triangleThe correct classification of the triangle should be considered as the obtuse triangle.
What is the obtuse triangle?In the obtuse triangle here one of the angle should be considered as the obtuse angle.
In the case when the sum of the squares of the two shorter sides of a triangle should be smaller than the square of the longest side so it considered as the obtuse triangle.
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Which of the values in the set {2, 3, 4, 5} is a solution to the equation 2x + 4 = 10? (4 points) a 2 b 3 c 4 d 5
Answer:
B: 3
Step-by-step explanation:
2x
x=3 3times2= 6
6+4 =10
Hope this helps
True or False Exponential Growth occurs when the same number is added to
the consecutive output values.
Answer:
False
Step-by-step explanation:
Because you're not supposed to add to the output values, you need to multiply the output values.
please help for brainlist ASAP and explain or no brainlist
Answer:
A
Step-by-step explanation:
because as you see the odd number is 1 its A
Answer:it’s 1/3 because it would be 1/2 to get two even number or odd so it’s 1/3
Step-by-step explanation:there’s 3 even numbers on one dice and it’s 1/2 a chance to get even and same for odds so with two dices it’s 1/3 because it’s 1/3 to get both evens and 1/3 to get both odds so it’s 1/3
Please help me to solve this!
Answer:
7 days im not sure
Step-by-step explanation:
can you trying giving us the answer that comes with the question if they have them
What is the value of the expression 52 + 22?
Answer:
55 + 22 = n
= 77
n = 77
Hope this helps! :D
Step-by-step explanation:
f(-4) = 3x^2-2x pls help i dont know this question
Step-by-step explanation:
f ( - 4) = 3 ( - 4) ² - 2( - 4)
=. 3 ( 16) + 8
=. 48 + 8 = 56
plz mark my answer as brainlist plzzzz.
hope this will be helpful to you.
When h(1)=-2, and h(n)=h*(n-1)+n, what is h(2)=
Answer:
h(2)=0
Step-by-step explanation:
That’s what I got when I got it wrong and I asked for the answer and I promise it’s 0
Answer:
its 0
Step-by-step explanation:
what’s the answer, help please !
You have two cans of paint, Can A and Can B. Can A contains 80% red paint and 20% blue. Can B contains half blue and half red. How much blue paint should be added to 3 liters of Can A to make it the same as Can B?
Answer:
0.9 liters.
Step-by-step explanation:
The difference between 20% of 3 and 50% of 3 is 30%. 30% of 3 liters is 0.9 liters so this is what you add to can A.
please help me i need to get this done
Answer:
15 students are wearing sneakers.
Step-by-step explanation:
There are 33 students in total, which will compare to 11 (5+6).
33 ÷ 11 = 3
The scale factor is 3.
Sneakers: 3 x 5 = 15 students
Bella has a cell phone plan in which she pays for each call minute and text message she sends. The total number of minutes used and text messages sent last month was 561. If call minutes cost 8 cents each and text messages cost 5 cents each and her bill was $34.26. how many minutes did she use?
Answer:
⇒Let the no. of call minute be = x
⇒& no. of text messages be = y
⇒As total number of minutes used and text messages sent last month was 561
So x + y = 561.................................(1)
⇒Now as call minutes cost 8 cents each and text messages cost 5 cents each and her bill was $34.26
So 8x + 5y = 3426............................(2)
On solving equation 1 & 2 we have
we got x = 354 cent
& y = 207 cent
Answer:
Step-by-step explanation:
x (354,307)