Answer:
[tex]\lim_{x \to 5}f(x)=-5\\\lim_{x \to 1^-} f(x)=3\\\lim_{x \to 1^+} f(x)=3\\\lim_{x \to 1} f(x)=4\\[/tex]
Step-by-step explanation:
[tex]\lim_{x \to 5}f(x)[/tex]
This means "the limit of f(x) as x approaches 5"
In this case, f(x) is a basic linear function while x > 1, so a limit is not necessary but it can still be used as it is here. For this one, you can just calculate f(5), and that is:
[tex]f(x)=5-2x[/tex]
[tex]f(5)=5-2(5)=5-10=-5[/tex]
[tex]\lim_{x \to 5}f(x)=-5[/tex]
===================
[tex]\lim_{x \to 1^-} f(x)[/tex]
This one is a little different. It means "the limit of f(x) as x approaches 1 from the negative (left) direction"
The negative direction of course means x will be less than 1, so we'll use this function:
[tex]f(x)=4-x[/tex]
It's easier if you graph it, but you can also do it like this:
[tex]f(0)=4+0=4\\f(0.5)=4-0.5=3.5\\f(0.75)=4-0.75=3.25\\f(0.9)=4-0.9=3.1\\f(0.99)=4-0.99=3.01[/tex]
There's a clear pattern there. You can see that f(1) should be 3, but this function only applies while x is less than 1 so it can never reach 3. It will get infinitely close, and that can be shown with the limit:
[tex]\lim_{x \to 1^-} f(x)=3[/tex]
===================
[tex]\lim_{x \to 1^+} f(x)[/tex]
This one works the same way, but from the positive (right) direction.
[tex]f(2)=5-4=1\\f(1.5)=5-3=2\\f(1.25)=5-2.5=2.5\\f(1.1)=5-2.2=2.8\\f(1.01)=5-2.02=2.98\\f(1.001)=5-2.002=2.998[/tex]
It will also get infinitely close to 3 when x = 1, but won't ever reach it because this function only applies when x is greater than 1.
[tex]\lim_{x \to 1^+} f(x)=3[/tex]
===================
[tex]\lim_{x \to 1} f(x)[/tex]
Here, the function for x=1 is just:
[tex]f(x)=4[/tex]
It's given already, so the limit is just:
[tex]\lim_{x \to 1} f(x)=4[/tex]
Which of the following is a solution to the given equation?
y=-3x - 7
A)
(-2,-1)
B)
(-1,-10)
C
(4,-5)
D
(3,-2)
Answer: A
Step-by-step explanation:
By replacing in the given equation:
y=-3x-7
y=-3(-2)-7
y=6-7
y=-1
But for choices B, C and D the given x values don't fit with the images.
9:12=15:______
I need the answer pls!
Answer:
15:20
Step-by-step explanation:
We can simplify the ratio to 3:4
after doing that we can multiply both sides by 5 giving us
15:20 as our answer
Or you can cross multiply
9 : 12 = 15 : x
Now we have 9x = 180
divide both sides by 9 and we get
x=20
which would work giving us the ratio of 9 : 12 = 15 : 20
HELP I NEED THIS!! I'LL MARK BRAINLIEST
lines AB and CD are straight lines. find x and y
simplify 5 − 2(2.5 − 6.7)^2
Answer:
-30.28
Step-by-step explanation:
What is the smallest whole number that is a multiple of 5, 9, and 12?
Answer:180
Step-by-step explanation:
you start by finding the prime factorization of the number
5=1*5
9=3*3
12=2*2*3
the shortest way to find the factors is to find is most of them like example, at max, there are 2 two's, 2 three's and 1 five then you multiply them all together
4*9*5=180 and that's the answer
Answer:
180
Step-by-step explanation:
Simplify the following and write your answer in simplest radical form: Multiply the polynomials
25a² + 10ab² + b²
X.................5a + b²
________________
Answer:
Step-by-step explanation:
125a³ + 50a²b² + 5ab² + 25a²b² + 10ab⁴ + b⁴
125a³ + 75a²b² + 5ab² + 10ab⁴ + b⁴
Which equation could be represented by the number line?
[tex]Hiya![/tex]
Sokka is here to help!!
I believe it is D..
Hopefully, this helps you!
[tex]Sokka[/tex]
Answer:
I think it is C.
Step-by-step explanation:
It has a starting point. It also has an arrow that is going toward the negatives. It also has a gap of 9 units. So therefore, C is our answer.
Charlie saves $2 for every $9 he earns. Melody saves $4 for
every $12'she earns. Is Charlie's ratio of money saved to money
earned equivalent to Melody's ratio of money saved to money
earned?
no they are not equivalent
Step-by-step explanation:
due that when you subtract 12 from 4 =8
but when you subtract 9-2=7 and that when Charlie will be losing a dollar and that Melody will have a dollar more
The integers set included in the interval -45 x <3 is {-4,-3,-2,-1,0,1,2,3}.
True or False
Answer:
False
Step-by-step explanation:
-45x < 3
-x < 3/45
-x < 1/15 Multiply by -1 because x is negative and remember to
change all parts to its opposite.
Therefore x > -1/15
Mr. Peate is building a rectangular fence around his house. The fence will be 32 feet long and 29 feet wide. What will be the perimeter of the fence? The perimeter will be ?
Answer:
112
Step-by-step explanation:
32*2+29*2=112
Quiz
2² =
4² =
use the method, no calculation
Step-by-step explanation:
2²
= 2 × 2
= 4
▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎
4²
= 4 × 4
= 16
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I Hope This HelpMr. Darson bought 6 boxes of nails from a shop. Each box had an equal number of nails. He gave 8 nails to each of his 38 students. He then had 26 nails left. Find the number of nails in each box.
Answer:55 nail boxes
Step-by-step explanation: first we have to find out the total amount of nails in all the boxes so for this we do 38*8=304
when he gave all the nails to all his students he has 26 extra nails left. so we add this amount to the original which gives us 330 total nails.
to find out the number of nails in eadh box we divide 330/6=55
3
Which number line shows a number equivalent to
1 Sume
Choose 1 answer:
ctions
++
wat tract
>
2
0
1
A
U
HHH
iz 1
X 8 min
>
2
0
1
N
ctions
FE
4HHHH
0
>
2
1
iz 2
6 3 mor
Answer: B
Step-by-step explanation:
2/3 means 1.5
answer me......
...................
......
........
...........
Answer:
Step-by-step explanation:
Okay! What times 9 is 90? 10!
what times 8 is 72? 9!
what times 7 is 56? 8
what times 6 is 42? 7!
what times 5 is 30? 6!
what times 4 is 20? 5!
what times 3 is 12? 4!
Do you see the pattern?
9=90
8=72
7=56
6=42
5=30
4=20
3=12
2=6
1=2
HOPE THIS HELPPEDD :3
the number of decimal places after which the decimal expansion of 23 upon 2²*5 will terminate will
Answer:
Given:
⇒ \frac{23}{2^2(5)}
2
2
(5)
23
To Find:
Expansion of the given number = ?
Solution:
⇒ \frac{23}{2^2(5)}
2
2
(5)
23
By opening the squares, we get
⇒ \frac{23}{2\times 2\times 5}
2×2×5
23
⇒ \frac{23}{4\times 5}
4×5
23
⇒ \frac{23}{20}
20
23
⇒ 1.151.15
what is the domain of the relation below?
Answer:
The domain of a relation is the set of all first coordinates (x-coordinates) of the ordered pairs. The range of a relation is the set of all second coordinates (y-coordinates) of the ordered pairs.Step-by-step explanation:
Answer:
A - {-1, 0, 1, 3}
Step-by-step explanation:
the domain is how far the relation stretches across the x axis. the points here are -1, 0, 1, and 3, so that is the domain
hello! i am doing a practice test for school & i need some help.
Answer:
C IS YOUR ANSWER ,,,,,,,,,,,,,,TICK THAT ANSWER
What is the probability that a point chosen at random in the rectangle is also in the blue triangle?
A triangle inside of a rectangle. The triangle is shaded and has a base of 5 inches and height of 4 inches. The rectangle is not shaded and has a height of 4 inches and length of 5 inches.
One-half
Four-fifths
1
2Simplify:
Answer:
1/2
Step-by-step explanation:
I did the quiz on Edge 2021 and got it right with 100%.
Please give me brainliest!
3/2 x -1/9
-5/4 divided by 1 3/7
Show your work please
Answer:
3/2 x -1/9= -1/6
-5/4 divided by 1 3/7=-7/8
Step-by-step explanation:
(x-4)2 = 36
Which of the following expressions represents the solutions to the given equation?
0-4+ V(36)
O4 + V(36)
16+ (36)
Donna bought a notebook for $3.50 and then spent half of her money for a textbook. Next she bought sheet music for $4.00 and then spent half of the remaining money on a calculator. She had $8.00 left. How much money did she start with?
Answer:
$43.50
Step-by-step explanation:
(Work out backward to find the answer)
Remaining money => $8
=> 8 x 2 = 16
=> 16 + 4 = 20
=> 20 x 2 = 40
=> 40 + 3.50 = 43.50
= $ 43.50
Hence, she had $ 43.50 at the beginning.
1) The temperature in Chicago is 42°F and the temperature in
Dayton is 19° cooler. What is the temperature in Dayton?
A. 25°F B. 61°F C. 23°F D. 58°F
The following statement is from the contract Peter signed with his Homeowner's Association (HOA).
"Overnight parking on community streets is prohibited. For the purpose of this contract, 'overnight' will be defined as the hours between 11:00 p.m. and 4:00 a.m. The HOA will monitor overnight parking not less than once every calendar week with nightly patrols by community security.
"In the event a car is found parked on community streets overnight and that ownership of the offending car can accurately be verified as a community homeowner, the homeowner will receive one (1) written warning asking him or her to correct the situation. A second and third infraction by the same homeowner, whether or not it is with the same car, will result in a monetary fine as permitted by CC&R guidelines and HOA bylaws. Further infractions (past 3) will result in monetary fines in addition to the towing of the car at the homeowner's expense."
Because of the extremely low ground effects and body profile on his racing car, Peter is unable to drive his car off of the street and onto the driveway. He has parked on the street overnight for the past five weeks. He has received one written warning and one monetary fine from the HOA. What consequences should Peter expect after this week's security check?
a.
His car will be towed.
b.
He will receive another monetary fine.
c.
He will receive a monetary fine and his car will be towed.
d.
A "boot" will be place on his car to prevent him from driving it.
Use the similar triangles below to find the height of the tree
Answer:
D. 44 feetStep-by-step explanation:
The ratio of corresponding sides is same for similar triangles:
H/5.5 = 24/3H = 5.5*8H = 44 feetCorrect choice is D
Joy needs 8 feet of fabric for a project she is working on, but the store only sells the fabric in meters. One meter of fabric costs $1.15. How much will the fabric cost?
[1 ft = 0.305m]
$9.20
$2.12
$2.81
$30.16
Answer:
$2.81
Step-by-step explanation:
8 feet = 2.44 meters
2.44 · $1.15 = $2.81
I hope that this helps!!!
Answer:
c. 2.81
Step-by-step explanation:
How do I get a percentage of a number
Answer:
Convert the problem to an equation using the percentage formula: P% * X = Y.
P is 10%, X is 150, so the equation is 10% * 150 = Y.
Convert 10% to a decimal by removing the percent sign and dividing by 100: 10/100 = 0.10.
what is the relevance of the background of the study in your research paper?
Answer:
The relevance of the background is to give more insight into a topic you are researching. It can provide clarifying information to your reader.
Hope this helped and have a great day,
Ginny
Step-by-step explanation:
How do the slopes of A B ↔ and the parallel line through point C compare?
Answer:
The slopes of AB↔ and the parallel line through point C are equal.
Step-by-step explanation:
Edmentum
Answer:
The slopes of the parallel AB lines through point C are equal.
Step-by-step explanation:
show that √20 = 2√5
hence , 2√5 = √20
solve for x someone pls help
Answer:
50+90+3x+1=180.....................