Answer:
[tex]\displaystyle \lim_{x\to \infty}\frac{3x^2+4.5}{x^2-1.5}=3[/tex]
Step-by-step explanation:
We want to evaluate the limit:
[tex]\displaystyle \lim_{x\to \infty}\frac{3x^2+4.5}{x^2-1.5}[/tex]
To do so, we can divide everything by x². So:
[tex]=\displaystyle \lim_{x\to \infty}\frac{3+4.5/x^2}{1-1.5/x^2}[/tex]
Now, we can apply direct substitution:
[tex]\Rightarrow \displaystyle \frac{3+4.5/(\infty)^2}{1-1.5/(\infty)^2}[/tex]
Any constant value over infinity tends towards 0. Therefore:
[tex]\displaystyle =\frac{3+0}{1+0}=\frac{3}{1}=3[/tex]
Hence:
[tex]\displaystyle \lim_{x\to \infty}\frac{3x^2+4.5}{x^2-1.5}=3[/tex]
Alternatively, we can simply consider the biggest term of the numerator and the denominator. The term with the strongest influence in the numerator is 3x², and in the denominator it is x². So:
[tex]\displaystyle \Rightarrow \lim_{x\to\infty}\frac{3x^2}{x^2}[/tex]
Simplify:
[tex]\displaystyle =\lim_{x\to\infty}3=3[/tex]
The limit of a constant is simply the constant.
We acquire the same answer.
show how you solved the problem
kyle started at 0ft. went down 15 feet and then up 5 ft . what distance did he travel?
Answer:
20 ft? im not 100% sure tho
Step-by-step explanation:
if one of the factor of x2 + x - 20 is (x+5).find the other.
a.x-4
b.x+2
c.x+4
d.x-2
Answer:
a,x-4
hope it helps .....
I NEED ASAP! IF ANY TROLLS OR LINKS ARE COMMENTED I WILL REPORT THEM. GIVING BRAINLIEST TO THE FIRST WHO ANSWERS CORRECTLY PLEASE HURRY!
04.04) Point R is at (2, 1.2) and Point T is at (2, 2.5) on a coordinate grid. The distance between the two points is such as 8.2.) (Input numbers and decimal point only,
The school is trying to paint one side of the curved dividers as show below for the computer lab. The
can of paint is able to cover an area of 25ft?. Will this be enough paint? Select the best answer.
Answer:
Yes, because the area of one side of the divider is approximately 24ft^2
Answer:
yes 24 squared
Step-by-step explanation:
Math Nation
Help!!!!!!!!!!!!!!!!!!!!!
A because the circle is empty and the line is going backwards
X=
4
6
12
Plzzz help
Answer:
x = 12
Step-by-step explanation:
3x = 6² = 36
x = 12
PLEASE HELP!!!!!!! GIVING BRAINLIEST!!!!!!!
Answer:
side CB
Step-by-step explanation:
draw triangles ABC and ACD next to each other
The longer leg of the triangle ABC is CB, which corresponds with the longest leg of ACD, which is side CD
Answer:
corresponded side
CD=CD
AC=AB
AD=AC
can you help me please
Answer:
D
Step-by-step explanation:
11 1/4 divided by 3= 3.75 (3 3/4)
Answer:
d) [tex]3\frac{3}{4}[/tex] pounds
Step-by-step explanation:
Hi there!
What we know:
- Sarah has [tex]11 \frac{1}{4}[/tex] pounds of dog food
- Sarah is dividing this into 3 containers
1) Convert [tex]11 \frac{1}{4}[/tex] into an improper fraction
[tex]11 \frac{1}{4}[/tex]
Multiply the whole number by the denominator
11 × 4 = 44
Add 44 to the numerator
44 + 1 = 45
[tex]\frac{45}{4}[/tex]
2) Divide [tex]\frac{45}{4}[/tex] by 3
[tex]\frac{45}{4} / 3[/tex]
Dividing by a number is the same as multiplying its reciprocal
[tex]= \frac{45}{4} *\frac{1}{3}[/tex]
Multiply the numerators and the denominators
[tex]45*1 = 45\\4*3 = 12[/tex]
[tex]= \frac{45}{12}[/tex]
3) Convert [tex]\frac{45}{12}[/tex] into a mixed number fraction
[tex]\frac{45}{12}[/tex] ⇒ [tex]3\frac{3}{4}[/tex]
Therefore, there will be [tex]3\frac{3}{4}[/tex] pounds of food in each container.
I hope this helps!
There are 185 deer in a state park. The population is increasing at the rate of 16% per year. Enter a
prediction for how long it will take the population to reach 305. If necessary, round your answer to the nearest tenth.
The deer population will reach 305 in approximately _____
years.
Answer:
Approximately 3.4 years more or less
Step-by-step explanation:
If we represent this exponential growth as P=185(1.16)^n where n is the number of years passed and P is the population, then:
P=185(1.16)^n
305=185(1.16)^n
1.65=1.16^n
log₁.₁₆(1.65)=log₁.₁₆(1.16^n)
3.37=n
So the deer population will reach 305 in approximately 3.4 years.
please help i don't know what to do
A slope and x-intercept
B slope and y-intercept
C Slope and a point that is not an intercept
D x-intercept and y-intercept
E y- intercept and a point that is not an intercept
F two points that are not a intercepts
Answer:
5
It is that because I know this
The graph of the function f(x) = sin(x) is shown. What is the domain of the function?
Find the median for the data set. 1, 1, 2, 6, 3, 1, 6, 6, 3
Which of the following is the best estimate of √80?
Answer:
√80=4√5 is your answer look it once
The soup pot is 8.5 inches tall with a radius of 4 inches
The volume of the cylinder in question is 427.26 inches.
The volume of the cylinder is 427.04 inches 2.
soup pot is 8.5 inches tall
radius of 4 inches.
Volume, is defined as the ratio of the mass of object to its density.
Volume of cylinder = 3.14r^2h
Volume of cylinder = 3.14 x 4 x 4 x 8.5
Volume = 427.04 inches 2
Thus, the required volume is 427.04 inches 2
Learn more about Volume here:
https://brainly.com/question/1578538
#SPJ2
arrange the following whole numbers in increasing and decreasing order
Answer:
Increasing Order:
34, 71, 269, 976, 16759, 49753, 796542
Decreasing Order:
796542, 49753, 16759, 976, 269, 71, 34
In a survey of 400 people, 65% sald they owned a dog. How many people own a dog?
Answer:
260 people own a dog.
Step-by-step explanation:
Think of the equation as this:
65% of 400 people own a dog.
Since "of" in a math equation means to multiply, replace of with a multiplication sign.
65% * 400 = 260 people own a dog.
To check you're answer, make the fraction 260/400 into a percent.
260/400 = 65%
Have a nice day!!! ;D
A wasp is a flying insect. In wasps, wing length is coded for by a single gene. Two scientists studying wasps hypothesize that short wings are recessive to long wings. Which of the following observations best supports this hypothesis?
Wasps with long wings are less likely to survive.
Wasps with long wings can produce offspring with short wings.
Wasps have wing lengths ranging from very long to very short.
Wasps with short wings prefer to mate with wasps with long wings.
Answer:Wasps with long wings are less likely to survive.
Step-by-step explanation:Because offsprings can happen is diffrent ways say a bird had a offsring that made it have one leg it wouldent sureive to the standers of a bird with 2 legs same goes for other animals sorry if there is some spelling misakes hope this helped:)
A countertop is in the shape of a trapezoid. The lengths of the bases are 70 1/2 and 65 1/2 inches long. The area of the countertop is 1,224 square inches. Write and solve an equation to find the height of the countertop.
Answer:
18
Step-by-step explanation:
hope this helps
Please help I’ll mark you as brainliest if correct!
Answer:
A
Step-by-step explanation:
it's done by pythagoreans theorem
√25-9=4
y = −2x + 1
4x + 2y = −2
[tex]\sqrt[3]{32}[/tex]
Answer:
2[tex]\sqrt[3]{4}[/tex]
Step-by-step explanation:
[tex]\sqrt[3]{8}[/tex]·[tex]\sqrt[3]{4}[/tex] = [tex]\sqrt[3]{2^3}[/tex] · [tex]\sqrt[3]{4}[/tex] = 2 [tex]\sqrt[3]{4}[/tex]
Which expression has a value of 252?
Step-by-step explanation:
6^3+6^2=216+36=252
25^2=625
hope that helps :)
Answer:
6^3 + 6^2
Step-by-step explanation:
6^3+6^2=216+36=252
25^2=625
625≠252
Hope this helps =]
Andre correctly solved an equation using the steps shown:
What does Andre’s work show us about the type of solution to the equation? How do you know?
PLEASE ANSWER LEGITIMATELY! THANK YOU!
Answer:
This equation has zero solutions.
Step-by-step explanation:
This equation has zero solutions because 2 is not equal to zero.
please help I'm tired asking 11 times
Answer:
We aren't going to do all your homework for you. That's why no one is answering. If you have one specific question, I can help. No one is going to do this whole assignment/homework.
Select the action you would use to solve x - 3 - 12. Then select the property
that justifies that action.
Select all that apply.
A. Action: Add 3 to both sides.
B. Action: Multiply both sides by 3.
C. Action: Subtract 3 from both sides.
D. Property: Addition property of equality
E. Property: Multiplication property of equality
F. Property: Subtraction property of equality
perform the following Elementary row operation on the augmented Matrix
9514 1404 393
Answer:
[tex]\left[\begin{array}{cc|c}-6&3&-4\\0&-3&11\end{array}\right][/tex]
Step-by-step explanation:
The designated sum can replace either row. Consult your curriculum materials for the intent.
Here, we'll replace row 2 with the sum.
3(2, -2, 5) +(-6, 3, -4) = (3(2)-6, 3(-2)+3, 3(5)-4) = (0, -3, 11)
After the row operation replaces the second row, the augmented matrix is ...
[tex]\left[\begin{array}{cc|c}-6&3&-4\\0&-3&11\end{array}\right][/tex]
Answer:
3(2, -2, 5) +(-6, 3, -4) = (3(2)-6, 3(-2)+3, 3(5)-4) = (0, -3, 11)
After the row operation replaces the second row, the augmented matrix is ...
\begin{gathered}\left[\begin{array}{cc|c}-6&3&-4\\0&-3&11\end{array}\right]\end{gathered}[−603−3−411]
ANWER FAST PLS WILL GIVE BRANLIEST
Step-by-step explanation:
the sum of angle jnm and knp should be 90°
so (7x+2)+(10x+3)=17x+5=90
x=5
so angle knp is 53°
lnk is 90-53=37°
jnm is 37°
jnl js 180-37=143°
jnl is 37+90=127°
The two triangles are similar. Determine the values of x, y, and z.
Answer:
y= 20 m
x= 15 m
z= 22 degree
Step-by-step explanation:
15+x=30 m
x=30-15
x= 15 m
z-18=40
z= 40-18
z= 22m
The fifth graders all decided to have a race afterwords Kylie was so thirsty she drank 3 pints of water Valentina was also thirsty so she drank 24 fluid ounces of water who drank more water Kylie or Valentina?
Answer:
Kylie drank more water than Valentina
Step-by-step explanation:
I know that Kylie drank more water than Valentina.
I know this because I took 3 pints and found how many fluid ounces that would equal. 1 pint is equivalent to 16 fluid ounces. So, three pints would be equal to 48 fluid ounces. 16x3=48
Valentina drank 24 fluid ounces.
48 is greater than 24, so Kylie drank more water than Valentina.