Answer:
Problem: [tex]\frac{x-8}{x+11} \cdot \frac{x+8}{x-11}[/tex]
Answer: [tex]\frac{x^2-64}{x^2-121}[/tex]
Step-by-step explanation:
[tex]\frac{x-8}{x+11} \cdot \frac{x+8}{x-11}[/tex]
Writing as one fraction:
[tex]\frac{(x-8)(x+8)}{(x+11)(x-11)}[/tex]
Now before we continue, notice both of your bottom and top are in the form of (a-b)(a+b) or (a+b)(a-b) which is the same format.
That is, we are multiplying conjugates on top and bottom.
When multiplying conjugates, all you have to do it first and last.
For example:
[tex](a-b)(a+b)=a^2-b^2[/tex].
So your problem becomes this after the multiplication of conjugates:
[tex]\frac{x^2-64}{x^2-121}[/tex]
Answer:
[tex] \frac { ( x - 8 ) ( x + 8 ) } { ( x + 1 1 ) ( x - 1 1 ) } [/tex]
Step-by-step explanation:
We are to find the product of the rational expression below:
[tex] \frac { x - 8 } { x + 1 1 } \times \frac { x + 8 } { x - 1 1 } [/tex]
We are to multiply these terms by taking the LCM to get:
[tex] \frac { ( x - 8 ) ( x + 8 ) } { ( x + 1 1 ) ( x - 1 1 ) } [/tex]
Since the signs of all the terms are different so we cannot add them up.
If Doris paid $24.30 for 8.1 pounds of Swiss cheese, what was the price of 1
pound of Swiss cheese? Do not include $ in your answer.
Which of the following rational functions is graphed below?
Answer:
the answer to your question is A.
Answer:
Option A. is correct
Step-by-step explanation:
A rational fraction is an algebraic fraction such that both the numerator and denominator are polynomials.
Here, a graph is given .
We need to find which of the given rational functions is graphed in image.
On x-axis, 1 unit = 2 units
Clearly, we can see the graph is not defined at point x = - 4 and at x = 1.
Corresponding to x = - 4, factor is (x+4) .
Corresponding to x = 1, factor is (x-1) .
So, this graph is of the rational fraction [tex]F(x)=\frac{1}{(x-1)(x+4)}[/tex]
Hence, Option A. is correct
solve and write solution in interval notation 4(x+1)+3>x-5
Answer:
[tex]\large\boxed{x\in\left(-\dfrac{13}{3},\ \infty\right)}[/tex]
Step-by-step explanation:
[tex]4(x+1)+4>x-5\qquad\text{use the distributive property}\\\\4x+4+4>x-5\\\\4x+8>x-5\qquad\text{subtract 8 from both sides}\\\\4x>x-13\qquad\text{subtract}\ x\ \text{from both sides}\\\\3x>-13\qquad\text{divide both sides by 3}\\\\x>-\dfrac{13}{3}\to x\in\left(-\dfrac{13}{3},\ \infty\right)[/tex]
rectangle ABCD is reflected over the x-axis. What rule shows the input and output of the reflection, and what is the new coordinate of A'?
A. (x, y) -> (y, -x) A' is at (1, 5)
B. (x, y) -> (-y, x) A' is at (-1, -5)
C. (x, y) -> (-x, y) A' is at (5, 1)
D. (x, y) -> (x, -y) A' is at (-5, -1)
Answer:
Option D; (x, y) -> (x, -y); A' is at (-5, -1)
.
Step-by-step explanation:
Reflection is one of the linear transformations which reflect any object along the line of reflection. The size of the shape remains the same but the orientation changes.
Reflection along the x-axis means that the sign of y-coordinate changes but the sign of the x-coordinate remains same.
From figure we identified the coordinates of point A:
A (-5,1)
So, A' will be (x,-y)
=> A' = (x,-y) = (-5,-1)
So, Option D (x, y) -> (x, -y); A' is at (-5, -1) is correct.
In circle P, which pair of arcs are adjacent arcs?
Answer: BA and AE are adjacent angles
Answer:
Arc AB and AE are adjacent arc.
Step-by-step explanation:
Given; A circle P with diameter AD and BE.
To find : which pair of arcs are adjacent arcs.
Solution : We have given A circle P with diameter AD and BE.
Arc length is the distance between two points along a section of a curve.
Here curve AB and AE are two arc which are adjacent to each other.
Therefore, Arc AB and AE are adjacent arc.
determine the equations of the vertical and horizontal asymptotes, if any, for g(x)=x^3/(x-2)(x+1)
for a rational, we find the vertical asymptotes where its denominator is 0, thus
(x-2)(x+1) = 0, gives us two vertical asymptotes when that happens, x = 2 and x = -1.
if we expand the denominator, we'll end up with a quadratic equation, namely a 2nd degree equation, whilst the numerator is of 3rd degree. Whenever the numerator has a higher degree than the denominator, the rational has no horizontal asymptotes, however when the numerator is exactly 1 degree higher like in this case, it has an oblique asymptote instead.
Answer:
A
x=2,x=-1
Step-by-step explanation:
What is the measure of angle ABC?
let f(x)=x^7-4e^x
A) f'(-1)
b)f''(-1)
Answer:
Step-by-step explanation:
Let f(x) = x^7 - 4e^x .
Then f '(x) = 7x^6 - 4e^x, and
f "(x) = 42x^5 - 4e^x, and so:
f '(-1) = 7(-1)^6 - 4e^(-1) = 7 + 4/e
and
f "(x) = 42(-1)^5 - 4e^(-1) = -42 + 4/e
In a U. S . Poll 8 out of 12 citizens said they were happy with the job Obama is doing. If 126 people were surveyed...
How many people were happy with Obama?
8 out of 12 people were happy.
8/12 reduces to 2/3 of the people were happy.
Multiply the total people surveyed by 2/3:
126 x 2/3 = (126 x 2) /3 = 252/3 = 84
84 people were happy.
Find the following rates. Round your answer to the nearest hundredth. a. ? % of 75 = 5 b. ? % of 28 = 140 c. ? % of 100 = 40 d. ? % of 200 = 15
Answer:
a) 6.67% b) 500% c) 40% d) 7.5%
Step-by-step explanation:
a. ? % of 75 = 5
Let ? be y.
Of means multiply so we will replace it with a multiplication sign.
y% x 75 = 5
y% = 5/75
y% = 1/15 x 100
y = 6.67 %
b) ?% of 28 = 140
Let ? be y.
Of means multiply so we will replace it with a multiplication sign.
y% x 28 = 140
y% = 140/28
y% = 5
y = 5 x 100
y = 500%
c) ?% of 100 = 40
Let ? be y.
Of means multiply so we will replace it with a multiplication sign.
y% x 100 = 40
y% = 40/100
y% = 2/5
y = 2/5 x 100
y = 40%
d) ?% of 200 = 15
Let ? be y.
Of means multiply so we will replace it with a multiplication sign.
y% x 200 = 15
y% = 15/200
y% = 3/40
y = 3/40 x 100
y = 7.5 %
!!
To find what percent one number is of another, divide the 'part' by the 'whole' and multiply by 100. Answers provided were calculated according to this method and rounded to the nearest hundredth when necessary.
To find what percent of a number another number is, you use the formula part over whole times 100. Let's apply this to the questions at hand.
? % of 75 = 5: To find the percent, you divide 5 by 75 and then multiply by 100. So, the calculation is (5 / 75) * 100 = 6.67%.? % of 28 = 140: This case is a bit different because 140 is greater than 28, which indicates it's more than 100%. The calculation is (140 / 28) * 100 = 500%.? % of 100 = 40: Here 40 is part of 100, so the percent is straightforward, (40 / 100) * 100 = 40%.? % of 200 = 15: Again, divide the part by the whole number and multiply by 100. The calculation is (15 / 200) * 100 = 7.5%.Always remember to round your answer to the nearest hundredth, as per the instruction.
Mrs. Cleary's class is selling candy bars to
raise money for a field trip. The students
in the class set a goal of how much
money they would like to raise.
The following formula describes this
scenario:
where
g = goal for money raised
p = profit made from each candy bar sold
n = number of candy bars sold. The class wants to raise a total of $600. If they sell 600 candy bars , how much profit will they receive from each candy bar ?
Answer:
1
Step-by-step explanation:
Assuming g(n)=pn, and plugging in
g=600 and n=600:
600=p(600)
600/600=p
1=p
profit per candy bar is $1
What is the product of 2p + q and -3q - 6p + 1
Answer:
[tex]\large\boxed{(2p+q)(-3q-6p+1)=-3q^2-12p^2-12pq+2p+q}[/tex]
Step-by-step explanation:
Use the distributive property: a(b + c) = ab + ac
[tex](2p+q)(-3q-6p+1)=(2p+q)(-3q)+(2p+q)(-6p)+(2p+q)(1)\\\\=(2p)(-3q)+(q)(-3q)+(2p)(-6p)+(q)(-6p)+2p+q\\\\=-6pq-3q^2-12p^2-6pq+2p+q\qquad\text{combine like terms}\\\\=-3q^2-12p^2+(-6pq-6pq)+2p+q=-3q^2-12p^2-12pq+2p+q[/tex]
Find a numerical value of one trigonometric function of x for cos^2x+2sinx-2=0
Answer:
[tex]\sin x=1[/tex]
Step-by-step explanation:
The given function is
[tex]\cos^2x+2\sin x-2=0[/tex]
We use the identity: [tex]\sin^2x+\cos^2x=1[/tex] [tex]\implies \cos^2x=1-\sin^2x[/tex]
This implies that:
[tex]1-\sin^2x+2\sin x-2=0[/tex]
[tex]-\sin^2x+2\sin x-1=0[/tex]
[tex]\sin^2x-2\sin x+1=0[/tex]
[tex](\sin x-1)^2=0[/tex]
[tex]\sin x-1=0[/tex]
[tex]\sin x=1[/tex]
Hence the numerical value of one trigonometric function(the sine function) is 1
Answer:
Step-by-step explanation:
From
\cos^2x+2\sin x-2=0
Using the identity, we have: \sin^2x+\cos^2x=1 \implying \cos^2x=1-\sin^2x
Opperating:
1-\sin^2x+2\sin x-2=0
-\sin^2x+2\sin x-1=0
\sin^2x-2\sin x+1=0
(\sin x-1)^2=0
\sin x-1=0
\sin x=1
A numerical value for x would be for example x=90 degrees or pi/2 (radians)
And this answer is valid for every angle x=90+360n (n=0,1,2,3,etc) or x=pi/2+2pi*n (n=0,1,2,3,etc)
If F(x)=4-x squared/4-x,find F(-2)
Answer:
0 if the function is [tex]F(x)=\frac{4-x^2}{4-x}[/tex]. Please tell me if this is not the right function.
Step-by-step explanation:
I'm assuming the function is [tex]F(x)=\frac{4-x^2}{4-x}[/tex]. Please tell me if it is not the right assumption.
F(-2) means to use the expression called F and replace x with -2.
Like this:
[tex]F(-2)=\frac{4-(-2)^2}{4-(-2)}=\frac{4-4}{4+2}=\frac{0}{6}=0[/tex]
So the value of F(-2) is 0.
F(-2)=0.
Which expression shows the result of applying the distributive property to 9(2+5m) ?
a) 2 + 45m
b) 11 + 14m
c) 18 + 45m
d) 18 + 5m
Answer:
c) 18 + 45m
Step-by-step explanation:
9(2+5m)
We multiply the 9 by each term inside the parentheses
9*2 + 9*5m
18+45m
9(2+5m)
Multiply the bracket with 9
9(2)+9(5m)
18+45m
Answer : 18+45m-c)
27x = 9x − 4
x = 8
x = 4
x = −4
x = −8
The solution to the equation 27x = 9x - 4 is x = -2/9, which is not listed in the provided options. None of the options (8, 4, -4, -8) are correct, and the correct solution can be verified by substituting back into the original equation.
The correct option is (d).
When solving the equation 27x = 9x − 4, we aim to find the value of x that satisfies the equation. To do this, we can follow a step-by-step approach:
First, we subtract 9x from both sides of the equation to get 18x = -4.Next, we divide both sides of the equation by 18 to isolate x, which results in x = -4/18.Simplifying the fraction gives us the solution x = -2/9.We must then verify if any of the provided options (8, 4, -4, -8) match our solution. As none of these values is equal to -2/9, none of the options provided is correct.
To check our solution, we can substitute x back into the original equation and verify that it leads to an identity, confirming that we have found the correct solution. Here, our verification step would show that 27(-2/9) is indeed equal to 9(-2/9) - 4, verifying the solution is correct.
complete question given below:
27x = 9x − 4
a.x = 1/8
b.x = 4
c.x = −4/3
d.x = −2/9
The average rate of change from x = -2 to x = 6 for the function shown in the graph is______?
Answer: -1/2
Step-by-step explanation:
Answer:
-1/2 (2nd option)
Step-by-step explanation:
Just did it on Edg 2021
What is the sum of the geometric sequence 1,-6,36 if there are 6 terms
Answer:
The sum of the six terms is 9331
Step-by-step explanation:
* Lets explain what is the geometric sequence
- There is a constant ratio between each two consecutive numbers
- Ex:
# 5 , 10 , 20 , 40 , 80 , ………………………. (×2)
# 5000 , 1000 , 200 , 40 , …………………………(÷5)
* General term (nth term) of a Geometric sequence:
# U1 = a , U2 = ar , U3 = ar² , U4 = ar³ , U5 = ar^4
# [tex]U_{n}=ar^{n-1}[/tex], where a is the first term , r is the constant
ratio between each two consecutive terms, n is the position
of the term
- The sum of n terms of the geometric sequence is:
[tex]S_{n}=\frac{a(1-r^{n})}{1-r}[/tex] , where n is the number of the terms
a is the first term and r is the common ratio
* Lets solve the problem
∵ The geometric sequence is 1 , -6 , 36 , .........
∵ The common ratio r = U2/U1
∵ U1 = 1 and U2 = -6
∴ r = -6/1 = -6
∵ The first term is 1
∴ a = 1
∵ There are 6 terms in the sequence
∴ n = 6
∴ The sum = [tex]\frac{1[1 - (-6)^{6}]}{1-6}=\frac{1[1-46656]}{-5}=\frac{-46655}{-5}=9331[/tex]
* The sum of the six terms is 9331
Solve the following system by graphing and identify the point of intersection.
Image shows the answer choices and question:) Thank you
Answer:
The solution is the point (-4,-2)
Step-by-step explanation:
we have
-0.1x-0.8y=2 -----> equation A
0.6x-0.5y=-1.4 ----> equation B
Solve by graphing
Remember that the solution of the system of equations by graphing is the intersection point both lines
using a graphing tool
The intersection point is (-4,-2)
see the attached figure
therefore
The solution is the point (-4,-2)
If the side length of a square pyramid is tripled and the slant height is divided by 5, what would be the formula to find the modified surface area?
Final answer:
The modified surface area of a square pyramid, with the side length tripled and slant height divided by 5, is calculated as 9s^2 + 6sl/5, where 's' is the original side length and 'l' is the original slant height.
Explanation:
To find the modified surface area of the square pyramid when the side length is tripled and the slant height is divided by 5, we need to recall the formula for the surface area of a square pyramid. The original surface area formula for a square pyramid is given by the sum of the area of the base plus the area of the four triangular faces, which can be represented as:
Surface Area = base area + 4 × (1/2 × slant height × side length)
For the modified pyramid, if the original side length is 's' and the slant height is 'l', tripling the side length would make it '3s' and dividing the slant height by 5 would make it 'l/5'. Using these new values, the formula for the modified surface area becomes:
Modified Surface Area = (3s)^2 + 4 × (1/2 × (l/5) × 3s)
Simplifying, we get:
Modified Surface Area = 9s^2 + 6s(l/5)
This accounts for the nine-fold increase in the base area (since area is proportional to the side length squared) and the change in the area of the triangular faces.
Which equation shows the quadratic formula used correctly to solve 5x2 + 3x – 4 = 0 for x?
Answer:
[-3 ±√(89)]/10
Step-by-step explanation:
Points to remember
Quadratic formula for finding the solution of a quadratic equation ax² + bx + c = 0 is given by,
x = [-b ± √(b² - 4ac)]/2a
It is given a quadratic equation,
5x² + 3x - 4
To find the solution using formula
Here a = 5, b = 3 and c = -4
x = [-b ± √(b² - 4ac)]/2a
= [-3 ± √((-3)² - 4*5*(-4))]/2*5
= [-3 ±√(9 +80)]/10
= [-3 ±√(89)]/10
On a road in the city of Madison, the maximum speed is 45 miles per hour and the minimum speed is 35 miles per hour. Let x represents the speed. You can write two inequalities to represent the speed restrictions. The inequalities and can be combined and can be written without using and.
a. Explain how compound inequalities can be use to describe the speed restrictions on roads.
b. Include a compound inequality describing a possible age restriction for driving on roads. Describe what this represents. (Minimum driving age is 16 years, and most drivers stop renewing their licenses by age 100.)
Answer:
a. 35≤x≤45 where x represents speed
b. 16≤y≤100 where y represents age
Step-by-step explanation:
a. Explain how compound inequalities can be use to describe the speed restrictions on roads.
x represents the speed, then
the maximum speed is 45 miles
x≤45
the minimum speed is 35 miles
x≥35
Both inequalities represent the speed restrictions
The compound inequality will be:
35≤x≤45
b. Include a compound inequality describing a possible age restriction for driving on roads. Describe what this represents. (Minimum driving age is 16 years, and most drivers stop renewing their licenses by age 100.)
Let y be the age
then
Minimum driving age is 16 years
y≥16
most drivers stop renewing their licenses by age 100.)
y≤100
The compound inequality will be:
16≤y≤100 ..
Answer:
a. 35 ≤ x ≤ 45
b. 16 ≤ x ≤ 100.
Step-by-step explanation:
On a road in the city of Madison, the maximum speed is 45 miles per hour and minimum speed is 35 miles per hour.
If x represents the speed then
x ≥ 35
and x ≤ 45 are the inequalities to represent the speed restrictions.
(a) combined inequality will be 35 ≤ x ≤ 45
which shows the combined speed limits on the road.
(b) Let the driving age of a driver is x years.
So by the statement x ≥ 16 and x ≤ 100
When we combine these inequalities 16 ≤ x ≤ 100.
what answer would this be? Question is attached
Answer:
0.65m
Step-by-step explanation:
Given the function as
[tex]P(h)=P_0*e^{-0.00012h}[/tex]
Lets take the air pressure at the surface of the Earth to be x
[tex]P_0=x[/tex]
Then 65% of this will be the air pressure P(h)
[tex]P(h)=\frac{65}{100} *x=0.65x[/tex]
The function will be
[tex]0.65x(h)=x*e^{-0.00012h}[/tex]
Divide both sides by x
[tex]0.65=e^{-0.00012h}\\ \\\\e=2.71828182846\\\\\\0.65=2.7182818284^{-0.00012h} \\\\\\0.65=0.99989h\\\\\\\frac{0.65}{0.99989} =\frac{0.99989h}{0.99989} \\\\\\h=0.65m[/tex]
Option: A is the correct answer.
A. 3589.9 m
Step-by-step explanation:The function which determines the pressure h height above the surface of earth is:
[tex]P(h)=P_0\cdot e^{-0.00012h}[/tex]
where [tex]P_0[/tex] is the pressure at the surface of the earth.
We are asked to find the height when the pressure above the surface of earth is equal to 65% of the pressure at the surface of earth.
i.e.
[tex]P_0\cdot e^{-0.00012h}=0.65\cdot P_0\\\\i.e.\\\\e^{-0.00012h}=0.65\\\\i.e.\\\\e^{0.00012h}=\dfrac{1}{0.65}\\\\i.e.\\\\\ln(e^{0.00012h}}=\ln(\dfrac{1}{0.65})\\\\i.e.\\\\0.00012h=\ln(\dfrac{1}{0.65})\\\\i.e.\\\\h=3589.8576\ m[/tex]
which is approximately equal to:
[tex]h=3589.9\ m[/tex]
a manufator makes two different sizes of spherical ball bEARINGS for use in motors. If the radius of the larger ball bearing is twice the radius of the smaller one, then the volume of the larger ball bearing is how many times the volume of the smaller one? EXPLAIN!
A) 2
B) 4
C) 6
D) 8
Answer:
Option D is the answer.
Step-by-step explanation:
Volume of sphere is given as:
[tex]\frac{4}{3}\pi r^{3}[/tex]
Case 1:
Lets say the radius is 3 cm.
Volume = [tex]\frac{4}{3}\times3.14\times3\times3\times3[/tex]
= 113.04 cubic cm
Case 2:
Lets say the radius is twice 3 cm that is 6 cm.
Volume = [tex]\frac{4}{3}\times3.14\times6\times6\times6[/tex]
= 904.32 cubic cm.
The volume of the larger ball is [tex]\frac{904.32}{113.04}[/tex] = 8 times the smaller one.
So, the answer is option D : 8 times.
Anyeny bought 3/4 pound of raspberries for $6. What is the cost of 1&1/4 pounds of raspberries?
Sorry usually able to answer this type of question but summers got me forgetting everything.
At your local farmers market , it costs $10 to rent to rent a stand , and $7 for every hour you stay there . If you paid a total of $38 , how many hours did you stay at the farmers market?
Subtract the rental fee, then divide the left over amount by the cost per hour.
38-10 = 28
28 / 7 = 4
The answer is 4 hours.
Please answer this correctly
Answer:
The answer should become clearer once we convert everything to a common denominator:
14/15,12/15,10/15,8/15
We can now see we have an arithmetic sequence with common difference 2/5. The next term is thus
6/15=2/5
2/5 is the answer
Answer:
2/5
Step-by-step explanation:
because I someone didn't let me solve it the way I normally do;
you need to convert all of them to a common denominator;
making them [tex]\frac{14}{15}[/tex], [tex]\frac{12}{15}[/tex], [tex]\frac{10}{15}[/tex], [tex]\frac{8}{15}[/tex]
making the next one [tex]\frac{6}{15}[/tex] or [tex]\frac{2}{5}[/tex]
As the loan amortizes and nears the end, the majority of the payment is used to pay the ___
Answer: principle APEX
Step-by-step explanation:
As the loan amortizes and nears the end, the majority of the payment is used to pay the principal is the correct answer.
What is a loan?A loan is a commitment that you (the borrower) will receive money from a lender, and you will pay back the total borrowed, with added interest, over a defined time period. A loan may be secured by collateral such as a mortgage or it may be unsecured such as a credit card.
For the given situation,
At the beginning of the loan's term, the majority of the payments are given to interest and just a small part to the loan's principal.
Near the end of the loan's term, the majority of each payment given to principal, and only a small portion is allocated to interest.
Hence we can conclude that as the loan amortizes and nears the end, the majority of the payment is used to pay the principal is the correct answer.
Learn more about loan here
https://brainly.com/question/15259527
#SPJ2
helppp???????????????
Answer:
BStep-by-step explanation:
No, the graph fails the vertical line test.
If a vertical line intersects a curve more than once then the curve does not represent a function. If all vertical lines intersect a curve at most once then the curve represents a function.
Spaceship Earth, a spherical attraction at Walt Disney World’s Epcot Center, has a diameter of 50 meters. Find the surface area of the structure. JUSTIFY
Answer:
≈ 7854 m²
Step-by-step explanation:
The surface area (A) of a sphere is calculated as
A = 4π r² ← r is the radius
here diameter = 50, hence r = 25, so
A= 4π × 25²
= 4π × 625 = 2500π ≈ 7854 m²
Answer:
The surface area of the structure ≅ 7854 meter²
Step-by-step explanation:
* Lets revise the surface area of the sphere
- The surface area of a sphere is the same as the lateral surface area
of a cylinder having the same radius as the sphere and a height
equal the length of the diameter of the sphere.
- The lateral surface area of the cylinder is 2πrh
- The height of the cylinder = 2r , then the surface area of the sphere is
2πr(2r) = 4πr²
* Now lets solve the problem
∵ The sphere has diameter = 50 meters
∵ The diameter is twice the radius
∴ 2r = 50 meters ⇒ divide both sides by 2
∴ r = 25 meters
∵ The surface area of the sphere = 4πr²
∴ The surface area of the sphere = 4π(25)² = 7853.98
∴ The surface area of the sphere ≅ 7854 meters²