Can someone please answer these questions to help me understand? Please and thank you! Will mark as brainliest!!
Answers
QUESTION 1
If a function is continuous at [tex]x=a[/tex], then [tex]\lim_{x \to a}f(x)=f(a)[/tex]
Let us find the limit first,
[tex]\lim_{x \to 4} \frac{x-4}{x+5}[/tex]
As [tex]x \rightarrow 4[/tex], [tex]x-4 \rightarrow 0[/tex],[tex]x+5 \rightarrow 9[/tex] and [tex]f(x) \rightarrow \frac{0}{9}=0[/tex]
[tex]\therefore \lim_{x \to 4} \frac{x-4}{x+5}=0[/tex]
Let us now find the functional value at [tex]x=4[/tex]
[tex]f(4)=\frac{4-4}{4+5} =\frac{0}{9}=0[/tex]
Since
[tex]\lim_{x \to 4} f(x)=\frac{x-4}{x+5}=f(4)[/tex], the function is continuous at [tex]a=4[/tex].
QUESTION 2
The correct answer is table 2. See attachment.
In this table the values of x approaches zero from both sides.
This can help us determine if the one sided limits are approaching the same value.
As we are getting closer and closer to zero from both sides, the function is approaching 2.
The values are also very close to zero unlike those in table 4.
The correct answer is B
QUESTION 3
We want to evaluate;
[tex]\lim_{x \to 1} \frac{x^3+5x^2+3x-9}{x-1}[/tex]
using the properties of limits.
A direct evaluation gives [tex]\frac{1^3+5(1)^2+3(1)-9}{1-1}=\frac{0}{0}[/tex].
This indeterminate form suggests that, we simplify the function first.
We factor to obtain,
[tex]\lim_{x \to 1} \frac{(x-1)(x+3)^2}{x-1}[/tex]
We cancel common factors to get,
[tex]\lim_{x \to 1} (x+3)^2[/tex]
[tex]=(1+3)^2=16[/tex]
The correct answer is D
QUESTION 4
We can see from the table that as x approaches [tex]-2[/tex] from both sides, the function approaches [tex]-4[/tex]
Hence the limit is [tex]-4[/tex].
See attachment
The correct answer is option A
Related Questions
*Help ASAP Please! Studying for finals and I'm stuck on this question!*
5. Find the measure, to the nearest tenth, of the diagonal of a rectangle with dimensions 14 cm by 6 cm.
A) 16.3 cm
B) 12.6 cm
C) 15.2 cm
D) 4.5 cm
Answers
Answer: C
Step-by-step explanation:
A rectangle has 90° angles. So, the diagonal cuts the rectangle into two right triangles where the length (base) and the width (side) are the legs of the right triangle and the diagonal is the hypotenuse. Thus, the Pythagorean Theorem can be used: (leg a)² + (leg b)² = (hypotenuse)²
14² + 6² = hypotenuse²
196 + 36 = hypotenuse²
232 = hypotenuse²
√232 = √hypotenuse²
15.23 = hypotenuse
In the figure below, if BE is the perpendicular bisector of AD , what is the value of x?
Answers
Answer:
x = 10Step-by-step explanation:
Since BE is perpendicular bisector AE=EDSubstituting we have:3x + 5 = x + 25 solving for x x = 10Find the measure of x and y in the isosceles triangle shown below:
x=22, y=136
x=22, y=48
x=44, y=65
x=20, y=65
Answers
Answer:
x=22, y=48
Step-by-step explanation:
If this is an isosceles triangle, then <G is equal to <J
<g = <j
x+44 = 3x
Subtract x from each side
x+44-x = 3x-x
44= 2x
Divide each side by 2
44/2 = 2x/2
22= x
The three angles of a triangle add to 180 degrees
<G + <J + <H = 180
x+44 + 3x + y = 180
22+44 +66 + y = 180
Combine like terms
132+ y =180
Subtract 132 from each side
132-132+y = 180-132
y = 48
A cube has a volume of 1/8. If the cube holds 24 of these sugar cubes, what is the total volume of the box?
Answers
[tex] \frac{1}{8} \div 24 = 3[/tex]
Answer:
the answer is 3 in.3
Step-by-step explanation:
Jon is looking into a $4250 vacation package that is offered for 25% off. There is a 9% resort fee added on to the total. How much will the vacation cost Jon?
Answers
Answer:
3187.59
Step-by-step explanation:
Add 4250 - 25% + 9% and u should have this exact answer
- The one guy who has a F in math
Triangle STU is dilated to form new triangle VWX. If angle S is congruent to angle V, what other information will prove that the two triangles are similar? Side ST is congruent to side VW. Angle T is congruent to angle V. Side US is congruent to side XV. Angle U is congruent to angle X.
Answers
Answer:
(D)
Step-by-step explanation:
Two triangles are similar if it satisfies the following properties:
1) Corresponding angles are congruent.
2) Corresponding sides are all in same proportion.
Here, ΔSTU and ΔVWX are given, where ∠S is congruent to ∠V.
To prove these two triangles similar, we need one more corresponding angle to be congruent.
And from all the options, (d) Angle U is congruent to angle X. will help in proving ΔSTU and ΔVWX similar triangles.
Therefore, (d) is correct.
Answer:
d)Angle U is congruent to angle X.
Step-by-step explanation:
can someone help me please and thank you
Answers
Find the ratio of the two similar sides that both dimensions are given.
The smaller triangle aide that is 4 units is the similar side of the larger triangle given as 8 units.
8 / 4 =2, this means the larger triangle is 2 times the size of the smaller triangle, which also means the smaller triangle is 1/2 the size of the larger triangle.
X on the smaller triangle is 1/2 11 units which equals 5.5 units.
Y is 2 times 3, which equals 6 units.
x = 5.5
y = 6
How many ways can the letters be arranged?
TJKL
A) 10 ways
B) 16 ways
C) 18 ways
D) 24 ways
Answers
The answer is D.
4 x 3 x 2 x 1 = 24 ways
This can be quickly worked out on your calculator using the ' ! ' button after inputting the number of letters/numbers.
You can always check as well, by simply working out every single way.
TJKL - different letters
for the first place you have 4 letters to choose from
for the second place you have 3 letters to choose from
for the third place you have 2 letters to choose from
for the last place you have only one letter
Therefore your answer is:
[tex]\boxed{4}\cdot\boxed{3}\cdot\boxed{2}\cdot\boxed{1}=24\to\boxed{D)}[/tex]
Penelope is 4 times old as Jose. Jose is 3 years older than Eliot. If the sum of the ages of all three is 57, how old is Jose?
Answers
Answer:
10
Step-by-step explanation:
jose is x,so the penelope is 4x, eliot is x-3,
so :
x+4x+x-3=57,
then:
6x=60, x=10
The commission Gary earns is proportional to the cost of the shoes he sellis. Gary earns $15 in commission for every S150 worth of shoes that he sells. Which equation gives the total commission, C Gary will earn based on the cost, s, of the shoes he sels?
Answers
Answer:
15x + 150
Step-by-step explanation:
Find the fifth roots of 243(cos 260° + i sin 260°).
Answers
Answer:
z1=3 cos (52 + i sin 52)
z2 =3 cos (124 + i sin 124)
z3 = 3 cos (196 + i sin 196)
z4 =3 cos (268 + i sin 268)
z5= 3 cos (340 + i sin 340)
Step-by-step explanation:
To find the fifth roots of 243 (cos 260° + i sin 260°).
z ^ 1/5 = r^1/5 ( cis ( theta + 360 *k)/5) where k=0,1,2,3,4
So the first root of 243 (cos 260° + i sin 260°)
is z1 = 243^1/5 ( cis ( 260 + 360 *0)/5)
3 cis ( 260/5)
= 3 cis (52)
= 3 cos (52 + i sin 52)
The second root of 243 (cos 260° + i sin 260°)
is z2 = 243^1/5 ( cis ( 260 + 360 *1)/5)
3 cis ( 620/5)
= 3 cis (124)
= 3 cos (124 + i sin 124)
The third root of 243 (cos 260° + i sin 260°)
is z3 = 243^1/5 ( cis ( 260 + 360 *2)/5)
3 cis ( 980/5)
= 3 cis (196)
= 3 cos (196 + i sin 196)
The fourth root of 243 (cos 260° + i sin 260°)
is z4 = 243^1/5 ( cis ( 260 + 360 *3)/5)
3 cis ( 1340/5)
= 3 cis (268)
= 3 cos (268 + i sin 268)
The fifth root of 243 (cos 260° + i sin 260°)
is z5 = 243^1/5 ( cis ( 260 + 360 *4)/5)
3 cis ( 1700/5)
= 3 cis (340)
= 3 cos (340 + i sin 340)
Justin is a software salesman. His base salary is 1900
, and he makes an additional 50
for every copy of English is Fun he sells.
Let P
represent his total pay (in dollars), and let N
represent the number of copies of English is Fun he sells. Write an equation relating P
to N
. Then use this equation to find his total pay if he sells 27
copies of English is Fun.
Answers
Answer:
3250 is your total; p = 50n + 1900 is your equation.
Step-by-step explanation:
"p" represents total pay; "n" represents the number of copies he sells.
Base salary is 1900, and each copy sold gives him an extra 50
p = 50n + 1900 is your equation.
If he sells 27 copies. Plug in 27 for n
p = 50n + 1900
p = 50(27) + 1900
Simplify. Remember to follow PEMDAS. First, multiply, then add.
p = 50(27) + 1900
p = 1350 + 1900
p = 3250
~
If Nelson invests $5,000 for 4 years and earns $600, what is the simple interest rate?
Answers
Simple interest rate = 3%.
Since the given invested amount = $5000, number of years of investment = 4 years, interest earned = $600. 600 = 5000 × R × 4, 600 = 20000R, Dividing both sides by 20000, we get 0.003 which is 3%.
Answer:
3
Step-by-step explanation:
What are examples of self-reliant and how are you self-reliant?
I need to hear from other peers, thank you:)
Answers
Most children have parents. Children are self reliant on parents until age eighteen or even later, because they rely on their parents to cook, maintain the house, pay for their food, etc.
I am self reliant sometimes on my friends because I rely on them to give me the answers for math class or to teach me.
PLEASE NEED HELP!
:"3
Answers
Answer:
Option 2
Step-by-step explanation:
When completing a proof, the statements and reasons should be directly connected. Since the reason listed next to the missing statement is Def of Complimentary Angles, the statement must be about angles adding to 90 degrees. The definition of Complimentary Angles is that two angles add to 90. This means option 2 is the answer.
What is the approximate volume of the oblique cone?Use the pi equals 3.14 and round to the nearest tenth?
Answers
Answer:
You didn't give enough information for an actual answer, but here's the formula: (x-a)^2 + (y-b)^2 = ((z-c)R)^2 where (a,b,c) is the vertex. Good Luck. Hope this was helpful.
A student bought a truck with a down payment of 4000 and monthly payments of $250 for four years. What was the total cost of the truck
Answers
Down Payment plus the price per month, multiplied by the years. The total cost should be $16000.
Is b perpendicular to a? Justify your answer.
Answers
Set up the equation: 2x+37+3x+y=180 ⇒ 4x+y=143
2x+y+3y-21=180 ⇒2x+4y=201.
Solving for x and y, you get that y=37, thus making x=26.5
Now, for b to be perpendicular to a, 2x+37 must equal 90.
2*26.5+37=90, so b is perpendicular to a.
Whether 'b' is perpendicular to 'a' is determined by their dot product. If the dot product of 'b' and 'a' is zero, then 'b' is perpendicular to 'a'. However, without knowing the specific components of these vectors, a precise computation can't be made.
Explanation:In mathematics, particularly in vector algebra, vectors are said to be perpendicular or orthogonal if their dot product is zero. This is because the dot product of two vectors encapsulates the angle between them, defined as A·B = |A||B|cos(θ), where θ is the angle. If θ is 90 degrees (indicating the vectors are perpendicular), cos(θ) becomes 0, thus the dot product should be zero.
Therefore, to determine whether 'b' is perpendicular to 'a', we need to compute their dot product. If their dot product equals zero, then we can conclusively say that 'b' is perpendicular to 'a'. Beyond this, you'd need to provide the components of vectors 'a' and 'b' for a specific computation.
Learn more about Perpendicular Vectors here:https://brainly.com/question/35891441
#SPJ11
Use the factor Theorem to determine whether h(x)=x-1 is a factor of f(x)=14x^99-65x^56+51.
A. Yes
B. No
Answers
Factor theorem: if x-k is a factor of p(x), then p(k) = 0. The same can be said in reverse: if p(k) = 0, then x-k is a factor of p(x).
In this case, x-1 = x-k so k = 1. We'll plug this into f(x) below
f(x) = 14x^99 - 65x^56 + 51
f(1) = 14(1)^99 - 65(1)^56 + 51 ... replace every x with 1
f(1) = 14(1) - 65(1) + 51
f(1) = 14 - 65 + 51
f(1) = -51 + 51
f(1) = 0
The result is 0, so h(x) = (x-1) is a factor of f(x) = 14x^99-65x^56+51
-------------------
Answer: Choice A) yes
Write 4/9, 5/9, and 6/9 as decimals. What pattern do you see? Use the pattern to predict the decimal form of 7/9 and 8/9
Answers
I'm not quite sure what an outlier is :/
Answers
Answer:
An outlier is the piece of data that isnt quite the same or near the others.
Step-by-step explanation:
so the outlier would be 28 due to the fact that it is not quite close to the other part of the data
Answer:
28
Step-by-step explanation:
An outlier is something that's way off compared to the rest of the group, basically. Like a person who stands out, but in this case it's a number.
The numbers listed here are all near 40 except 28. So 28 is the outlier, or the 'odd one out.'
How many soccer players that are getting paid around the world are there???
Answer for 15 points! PLZ be correct info!!!
Answers
Could someone help I can’t get this one
Answers
Statement Reason
1. AB = CD, AD = CB 1. Given
2. AC = AC 2. Reflexive Property
3. ΔADC ≅ ΔCBA 3. SSS
4. ∠1 = ∠4 4. CPCTC
5. DC || AB 5. Alternate Interior Angles Converse Thm
Jenna bought a bike for $200. The value of the bike decreases by 5% each year. Write an equation to model the situation.
Answers
This is an exponential function. Since each year the value of the bike decreases by 5%, each year, the value of the bike is 100%-5%=95% of it's original value. So after x years, the value of the bike would be 200(0.95)^x.
Answer:
(200 - (200 x 5 / 100))^Y
Step-by-step explanation:
As the initial value of the bike is $200, that would be a fixed number in our equation. Each year, this will lose 5% of its value, therefore, it would be another fixed value in it. Then, we have to exponentiate it by the number of years that have passed since the initial value (Y). As a result, the equation to model the situation would be this one:
(200 - (200 x 5 / 100))^Y
What is the domain restriction of this expression?
(m-7)/(4m-20)
Answer:
m ≠ ____.
Answers
Answer:
m ≠5
Step-by-step explanation:
We cannot divide by zero, so the denominator cannot equal zero. That is the only restriction on the domain.
4m-20 ≠ 0
Add 20 to each side
4m-20+20 ≠20
4m ≠20
Divide each side by 4
4m/4 ≠20/4
m ≠5
Answer:
m ≠ 5
——
Step-by-step explanation:
Make the equation equal to zero.
4m - 20 = 0
Solve for the restriction.
4m - 20 = 0
Add 20 to both sides.
4m = 20
Divide both sides by 4.
m = 5
Answer:
m ≠ 5
On mars,your weigh is about 1/3 of your weigh on earth. If a fifth grader weighs 96 pounds on earth,about how much would they weigh on mars
Answers
Answer:
32
Step-by-step explanation:
You just have to find out whats 1/3 of 96
just divided 96 by 3 to get 32
the trip to omaha to salt lake city interstate 80 is about 1516 kilometers. at 90 km perhour the trip would take about
Answers
I think?
Someone please help.
ABC has vertices A(0,6) B(4,6) C(1,3). Sketch a graph of ABC and use it to find the orthocenter of ABC. Then list the steps you took to find the orthocenter including any necessary points or slopes you had to derive.
Answers
Answer:
Step-by-step explanation:
It's solved by grafic method
Lynne used 3 over 8 cup of flour and over 3 cup of sugar in a recipe.What number is a common denominator for 3 over 8 and 1 over 3
Answers
Answer: The common denominator for 3/8 and 1/3 is 24
Step-by-step explanation:
3/8 and 1/3 can be multiplied by each other in the numerator and denominator: 3/8(3/3) = 9/24 and 1/3(8/8) = 8/24
Give the equation of the line in slope-intercept form that has the slope of 5 and goes through the point (0, -3).
Answers
Answer:
y=-3x+5
-3 is y ntercept