Which statement make correctly uses limits determine a vertical asymptote of G(x)=-7(x-5)^2(x+6)/(x-5)(x+5)
Answers
Answer:
There is a vertical Asymptote at x = 5 because [tex]\lim_{x \to 5^{-} } G(x) = \infty\\lim_{x \to 5^{+} } G(x) = -\infty[/tex]
There is a vertical Asymptote at x = -5 because [tex]\lim_{x \to -5^{-} } G(x) = \infty\\\lim_{x \to -5^{+} } G(x) = -\infty[/tex]
Step-by-step explanation:
The exact question is as follows :
Given - G(x) = -7(x-5)^2(x+6)/(x-5)(x+5)
To find - Which statement make correctly uses limits determine a vertical Asymptote of G(x)
Solution -
Vertical Asymptotes are vertical lines which correspond to the zeroes of the denominator of a rational function.
Here the given function is the rational function
Denominator of G(x) = (x - 5)(x + 5)
So,
Put denominator = 0, we get
(x - 5)(x + 5) = 0
⇒x = 5, -5
∴ we get
G(x) has vertical Asymptotes at x = 5 and x = -5
Now,
At x= 5
[tex]\lim_{x \to 5^{-} } G(x) = \infty\\\lim_{x \to 5^{+} } G(x) = -\infty[/tex]
And
At x = -5
[tex]\lim_{x \to -5^{-} } G(x) = \infty\\\lim_{x \to -5^{+} } G(x) = -\infty[/tex]
∴ we get
There is a vertical Asymptote at x = 5 because [tex]\lim_{x \to 5^{-} } G(x) = \infty\\lim_{x \to 5^{+} } G(x) = -\infty[/tex]
There is a vertical Asymptote at x = -5 because [tex]\lim_{x \to -5^{-} } G(x) = \infty\\\lim_{x \to -5^{+} } G(x) = -\infty[/tex]
Answer:
Step-by-step explanation: A
Related Questions
. A pitcher’s mound on a women’s softball field is 43 feet from home plate and the distance between the bases is 60 feet. How far is the pitcher’s mound from first base?
Answers
Answer:
42.43 ft
Step-by-step explanation:
Please find attached an image of the softball pitch
h² = p² + f² -2x p×f×cos45
h² = 43² + 60² - 2x (43)(60) x 0.7071
h² = 1849 + 3600 - 3648.636
h² = 1800.364
h = √1800.364
h = 42.43 feet
A 13-foot ladder is leaning against a building, forming a right triangle. The height where the ladder touches the building is 7 feet more than the distance of the base of the ladder from the building. At what height does the ladder hit the building
Answers
Answer:
Step-by-step explanation:
The length of the ladder is the length of the hypotenuse of the right triangle formed. Since the height up the building is based on the distance the ladder is from the base of the building, and that distance is x, then the height up the building is x + 7. So what we have is a right triangle with one leg measuring x, the other leg measuring x + 7, and the hypotenuse measuring 13. Set up using Pythagorean's Theorem:
[tex]13^2=(x+7)^2+x^2[/tex] and do some simplifying. The left side is easy since 13-squared is 169; the right side not so much. We first have to expand that set of parenthesis by multiplying x + 7 by itself twice to get a second degree polynomial:
[tex](x+7)(x+7)=x^2+14x+49[/tex] and now we have:
[tex]169=x^2+14x+49+x^2[/tex] which simplifies down a bit to
[tex]169=2x^2+14x+49[/tex]
The only way to solve this for x, the height up the side of the building, is to factor. In order to do that, everything has to be on one side of the equals sign, setting the whole messy thing equal to 0:
[tex]2x^2+14x+49-169=0[/tex] and
[tex]2x^2+14x-120=0[/tex]. Begin by factoring out a 2:
[tex]2(x^2+7x-60)=0[/tex] and then factor the remaining quadratic using whatever method you are currently using in class to solve for x. Doing this will give that
x = -12 and 5. Since a side length will never be negative, we determine that x = 5 which is the distance between the bases of the buildings, and the height up the building where the ladder hits it is 12.
hii! i’ll give brainliest pls help
Answers
Answer:
b is correct
Step-by-step explanation:
Select the correct answer.
What is the solution of 3x + y = 9 and 3x - 5y = 15?
OA.
= y = -1
OB.
r = g.y = 1
O c.
x = -1,4 = 12
OD. I = ly =
Reset
Next
Answers
Answer:
c
Step-by-step explanation:
i calculated and x was -1 and y was 10/3
need this for final
Write the following statement as an algebraic expression: Five less than the product of 4 and a number.
Group of answer choices
5(4 - x)
5(x - 4)
4x - 5
5 - 4x
Answers
Answer:
D
Step-by-step explanation:
it means 5 minus 4x where x is the coefficient of x. Good luck.
(x ^ 3 + 3x ^ 2 - 4x + 5)/(x ^ 2 - 2)
Answers
Answer:
4x(3x^2 + 1)(x – 5) glad to help!!!!
Everyone learns differently. Some people like to use models and tools to help them learn math concepts. Many people like to use a combination of these strategies. What tools and strategies do you use to help yourself learn new ideas in math?
Answers
Answer:
Kindly check explanation
Step-by-step explanation:
Learning could be explained as a process of acquiring knowledge about a certain subject, trade or other aspects of life. In terms of learning about certain school subjects, a student needs to discover him or herself in other to make acquiring knowledge easy and less tedious for him or her. Now, there are designated tools more than evwr which could aid learning. A very important recommendation which could aid acquiring matematicka knowledge is the use of models to gain an insight to the fundamentals of a mathematical problem and thus seeing how it works. After this one can then break down the mathematical procedure embedded or used it aid the model manually in other to grasp the full concept of the principle.
A small bank vault is being designed in the shape of a rectangular prism. The vault’s sides and top should all be 3 feet thick. The outer length of the vault should be twice the outer width. The outer height should be the same as the outer width. What should the outer dimensions of the vault be if is to have 972 cubic feet of space?
(^ incase the words got cut off in the pic)
Answers
This represents the exterior length, width and height in that order.
============================================================
Work Shown:
The steps you have written so far are 100% correct.
From there, you multiply the interior width, length and height to get the interior volume 972. Solve for x
So,
(length)*(width)*(height) = volume
(2x-6)(x-6)(x-3) = 972
(2x-6)(x^2-9x+18) = 972
2x(x^2-9x+18)-6(x^2-9x+18) = 972
2x^3-18x^2+36x-6x^2+54x-108 = 972
2x^3-24x^2+90x-108 = 972
2x^3-24x^2+90x-108-972 = 0
2x^3-24x^2+90x-1080 = 0
2(x^3-12x^2+45x-540) = 0
x^3-12x^2+45x-540 = 0
From here, we can use the factor by grouping method
x^3-12x^2+45x-540 = 0
(x^3-12x^2)+(45x-540) = 0
x^2(x-12)+45(x-12) = 0
(x^2+45)(x-12) = 0
Setting each factor equal to 0 leads to....
x^2+45 = 0 doesn't have any real valued solutions for x, since sqrt(-45) is a complex number. We'll ignore this case and move on.x-12 = 0 solves to x = 12So x = 12 is the only solution here.
If x = 12, then we have these exterior dimensions:
length = 2x = 2*12 = 24 ftwidth = x = 12 ftheight = x = 12 ftThe outer dimensions are 24 ft by 12 ft by 12 ft
From that, the inner dimensions would be:
L = 24-6 = 18 ft
W = 12-6 = 6 ft
H = 12-3 = 9 ft.
Then note how L*W*H = 18*6*9 = 972 ft^3 to help confirm the answer.
a batch of granola uses 2 cups of honey to make 24 servings. how much honey is needed to make 42 servings
Answers
Answer:
hi hlo wat is ur help tell me quick
what should be the price of each toaster if the company wants to make a profit of 42$ per toaster?
Answers
Answer:
$42?
Step-by-step explanation:
Is your answer I hope this helps
Pls help me a quick financial maths problem
Answers
Answer:
$74 492.30
Step-by-step explanation:
P= 50 000
r= 8/100 = 0.08
n= 12
t= 5
P(1 + r/n) ^ (nt)
[tex] = 50000(1 + { \frac{0.08}{12} )}^{(12 \times 5)} [/tex]
=74492.285
Find the value of y when x=3.
y=10-3x
y=
Answers
y= 10-3x
y= 10-3(3)
y= 10-9
Therefore, y = 1
Answer:
the value of y is y= 1
Step-by-step explanation:
3×3=9
y=10-9
y= 1
how many solutions does 3 (y-2) = 3y - 6 have
Answers
Answer:
Infinitely many solutions
Step-by-step explanation:
Simplify this
3 (y-2) = 3y-6
3 (y) + 3 ( -2) = 3y-6
3y-6=3y-6
Because these two equations are equal to each other, it is infinitely many solutions.
If this helps please mark as brainliest
Of the 585 people that live in Benton, 187 live within two miles of the post office. Use mental math to find how many people live farther than two miles from the post office.
Answers
It clearly states to use mental math not brainly, sorry bro can't do anything for you
what value of x will solve the equation 3/4x + 10 = 4
Answers
Answer:
-8
Step-by-step explanation:
Answer:
x = -8
Step-by-step explanation:
[tex]\frac{3}{4}x+10=4[/tex]
[tex]\frac{3}{4} x-10[/tex] [tex]-10[/tex] Subtract 10 from both sides
[tex]\frac{3}{4}x=[/tex] [tex]-6[/tex]
[tex]\frac{3}{4}(-8)[/tex] [tex]=-6[/tex] Substitute x for [tex](-8)[/tex] then Multiply [tex](-8)[/tex] by [tex]\frac{3}{4}[/tex]
[tex]-\frac{24}{4}[/tex] [tex]=-6[/tex] Simplify [tex]-\frac{24}{4}[/tex]
[tex]-6=-6[/tex]
Write an equation if the line that passes through (0,-2) and (2,2)
Answers
Answer:
[tex]y=2x-2[/tex]
Step-by-step explanation:
Hi there!
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)
1) Determine the slope (m)
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] where the two points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the given points (0,-2) and (2,2)
[tex]=\frac{2-(-2)}{2-0}\\=\frac{2+2}{2}\\=\frac{4}{2}\\=2[/tex]
Therefore, the slope of the line is 2. Plug this into [tex]y=mx+b[/tex] as m:
[tex]y=2x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=2x+b[/tex]
Plug in one of the given points and solve for b
[tex]2=2(2)+b\\2=4+b[/tex]
Subtract 4 from both sides to isolate b
[tex]2-4=4+b-4\\-2=b[/tex]
Therefore, the y-intercept of the line is -2. Plug this back into [tex]y=2x+b[/tex]
[tex]y=2x-2[/tex]
I hope this helps!
Please help I am really confused with this
Answers
The answer should be A. 4 Meters
PLSSSS HELPP MEEEEE BRAINLIEST REWARDD
Answers
Answer:
40.) the third one
42.)the last one
Step-by-step explanation:
2. The quotient of two polynomials is always a polynomials
What is the measure of angle 2 in degrees?
Answers
Answer:
The measure of angle 2 is... 60 degrees.
Angle 1 - 93 degrees
Angle 2 - 60 degrees
Angle 3 - 27 degrees
A study was conducted by a certain firm to determine who curses at their computer. The results indicated that 30% of people age 18-34 years have cursed at their computer. What are the odds against a randomly selected 18- to 34-year old having cursed at his or her computer. LOADING... Click the icon to view an explanation of odds. The odds, in the most simplified form, are nothing to nothing against a randomly selected 18- to 34-year old having cursed at his or her computer. (Type whole numbers.)
Answers
Answer:
The odds, in the most simplified form, are 7 to 3 against a randomly selected 18- to 34-year-old having cursed at his or her computer.
Step-by-step explanation:
Given
[tex]p = 30\%[/tex] ---- proportion that cursed their computer
Required
Odds against the selected
Using the complement formula, the proportion that the selected has not cursed at their computer is:
[tex]p' = 1 - p[/tex]
[tex]p' = 1 - 30\%[/tex]
[tex]p' = 70\%[/tex]
So, the odds against the selected is:
[tex]Odds = p' : p[/tex]
[tex]Odds = 70\% : 30\%[/tex]
Divide by 10%
[tex]Odds = 7: 3[/tex]
According to the graph what is the solution to this system of equations?
O 5.-7)
O €7.5)
O 5.7)
O 7.5)
Answers
Answer:
you showed no graph dude
This is the graph btw.
Select the graph of Y = sec X Please help!!!!
Answers
Answer:
A
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
Help! Need this done quickly! picture is upside down so please flip your screen! sorry!
Answers
Answer:
x=6
Step-by-step explanation:
Hi there!
1) Determine the perimeter of the square
We're given that the perimeters of the square and the rectangle are equal. Therefore, after finding the perimeter of the square, we will also know the perimeter of the rectangle.
Find the side length of the square using the area formula:
[tex]A=l^2[/tex] where l is the side length
Plug in the given area 121 in.²
[tex]121=l^2[/tex]
Take the square root of both sides
[tex]\sqrt{121} = \sqrt{l^2} \\11=l[/tex]
Therefore, the side length of the square is 11 inches. Plug this into the perimeter formula:
[tex]P=4l[/tex] where l is the side length
[tex]P=4(11)\\P=44[/tex]
Therefore, the perimeter of the square is 44 inches. The perimeter of the rectangle is also 44 inches.
2) Determine the value of x
Use the formula for the perimeter of a rectangle:
[tex]P=2(l+w)[/tex] where l is the length and w is the width
Plug in 3x and x-2 as the length and width
[tex]P=2(3x+(x-2))\\P=2(3x+x-2)\\P=2(4x-2)[/tex]
Plug in the perimeter 44 in.
[tex]44=2(4x-2)[/tex]
Expand the parentheses
[tex]44=8x-4[/tex]
Add 4 to both sides to isolate 8x
[tex]44+4=8x-4+4\\48=8x[/tex]
Divide both sides by 8 to isolate x
[tex]\frac{48}{8}=\frac{8x}{8} \\6=x[/tex]
Therefore, the value of x is 6.
I hope this helps!
Simplify:
B^4 . B^3
^ = means I’m squaring it.
Answers
Step-by-step explanation:
B⁴×B³B^(4+3)B⁷stay safe healthy and happy...
PLEASE I NEED HELP I DONT UNDERSTAND HOW TO DO ILL GIVW MORE IF RIGHT
Answers
Answer: 207 degrees
Step-by-step explanation:
Since a circle is 360 degrees,
103+50+35+27 = 215, 360-215=145
Add ED and BC to 145 to get - 207
[42
2
X Х
3
5 1 3 6
+1916 51
2,3
6
Answers
jxjxjxnxnxnnxnnxncncncxxnx
Skzkkxkxkfnzxnxnncnvnvnnv XMMMXMidjjcnfnndnmcmcmcmcmcmxmdnndjd
Yes invests $1500 that compounds interest monthly with a 4.5% rate. How much money will he have after the 12 years?
Answers
Answer:
FV= $2,571.41
Step-by-step explanation:
Giving the following information:
Initial investment (PV)= $1,500
Interest rate (i)= 0.045/12= 0.00375
Number of periods (n)= 12*12= 144 months
To calculate the future value, we need to use the following formula:
FV= PV*(1 + i)^n
FV= 1,500*(1.00375^144)
FV= $2,571.41
The circular rug is placed on a square floor. The rug touches all four walls. How much of the floor space is not covered by the rug? Round your answer to the nearest hundredth.
Answers
Answer:
Step-by-step explanation:
To solve this, we first need the area of the square, then subtract from it the area of the circle. Since our instructions tell us to round to the nearest hundredth, we will use 3.1415 for pi. First the square:
A = s * s so
A = 15 * 15 and
A = 225; next the circle:
A = 3.1415 * 7.5*7.5 (the area of a circle is pi times the radius squared. The radius is half of the diameter which is 15, so r = 7.5) so
A = 176.709
Subtracting the area of the circle from the area of the square:
225 - 176.709 = 48.29 ft squared.
Pls, help with this math question
Answers
Step-by-step explanation:
OCB=CBO(base angle of isosceles triangle are equal)
now,
OCB+CBO+BOC=180°(sum of angles of triangles)
BOC=180-62
BOC=118°
again,
x=BOC/2{inscribed angle is half of central angle standing on Same base}
x=118/2
x=59°
stay safe healthy and happy...five hundred dollars and eighty two cents as a decimal
Answers
Answer:
500.82
Step-by-step explanation:
Answer: 500.82 mhm mhm yup