[tex]\text{The domain}\\\\x\neq0\ \wedge\ x\neq-2\ \wedge\ x\neq2[/tex]
[tex]\dfrac{5}{x^2-4}+\dfrac{2}{x}=\dfrac{2}{x-2}\qquad\text{subtract}\ \dfrac{2}{x-2}\ \text{from obth sides}\\\\\dfrac{5}{x^2-2^2}+\dfrac{2}{x}-\dfrac{2}{x-2}=0\\\\\dfrac{5}{(x-2)(x+2)}+\dfrac{2}{x}-\dfrac{2}{x-2}=0\\\\\dfrac{5x}{x(x-2)(x+2)}+\dfrac{2(x-2)(x+2)}{x(x-2)(x+2)}-\dfrac{2x(x+2)}{x(x-2)(x+2)}=0\\\\\dfrac{5x+2(x^2-4)-2x(x+2)}{x(x-2)(x+2)}=0\\\\\dfrac{5x+2x^2-8-2x^2-4x}{x(x-2)(x+2)}=0\\\\\dfrac{x-8}{x(x-2)(x+2)}=0\iff x-8=0\to\boxed{x=8}\in D[/tex]
A recursive rule for a geometric sequence is a1=3;an=1/2an−1.
What is the explicit rule for this sequence?
Enter your answer in the box.
A recursive rule for a geometric sequence:
[tex]a_1\\\\a_n=r\cdot a_{n-1}[/tex]
---------------------------------------------------
[tex]a_1=3\\\\a_n=\dfrac{1}{2}a_{n-1}\to \boxed{r=\dfrac{1}{2}}[/tex]
--------------------------------------------------
Exciplit rule:
[tex]a_n=a_1r^{n-1}[/tex]
Substitute:
[tex]a_n=3\left(\dfrac{1}{2}\right)^{n-1}=3\cdot\left(\dfrac{1}{2}\right)^n\cdot\left(\dfrac{1}{2}\right)^{-1}=3\cdot\left(\dfrac{1}{2}\right)^n\cdot2\\\\\boxed{a_n=6\cdot\left(\dfrac{1}{2}\right)^n}[/tex]
Answer:
The answer is: a_n = 6*(1/2)^n
Jasmine works at the public library after school. she makes $7.00 per hour. she cannot work more than 15 hours per week. if y = 7x represents jasmine's earning, what are the values in the domain?
a.x ≤ 15
b.0 ≤ x ≤ 15
c.1 ≤ x ≤ 15
d.all real numbers
Answer: ITS B
Step-by-step explanation:
Use the substitution method to solve the system of equations
Answer:
We put the value of "y" into the second equation:
x * 5 = -15
x = -15 / 5
x = -3
Step-by-step explanation:
George bought 30 packs of football cards.There were 14 cards in each pack.How many cards did George buy
Answer:
there would be 420 cards in total
Step-by-step explanation:
3 log 2x=4 Please solve
[tex]3 log 2x=4\ /:3\\log2x=\frac{4}{3}\\10^{\frac{4}{3}}=2x\ /:2\\x=\frac{10\sqrt[3]{10} }{2}\\x=5\sqrt[3]{10}[/tex]
Saul in third in line. Enid is last in line. There are 3 children between them. What position is Enid in line?
Final answer:
Starting with Saul in the 3rd position and counting the 3 children between him and Enid, Enid is determined to be in the 7th position in the line.
Explanation:
To find the position of Enid in line, we start with Saul who is third in line. If there are 3 children between Saul and Enid, and Enid is last, we need to count the positions:
Saul is 3rd in line.
1st child after Saul is in the 4th position.
2nd child after Saul is in the 5th position.
3rd child after Saul is in the 6th position.
Enid is after the 3rd child, placing her in the 7th position.
Therefore, Enid is in the 7th position in line.
If a matrix does NOT have an inverse, what do know about the determinant?
A) The determinant does not exist.
B) The determinant is O.
C) The determinant is 1.
D) The determinant is -1.
Midsegment of Triangles
Find x
Answer: x = 3
Step-by-step explanation:
If 3x is the midsegment of the triangle, then it is half the length of the base, which implies that the length of the base equals twice the length of the midsegment:
base = 2 * midsegment
18 = 2 (3x)
18 = 6x
÷6 ÷6
3 = x
Which is a root of [tex]f(x)=0[/tex] with a multiplicity of 2?
Answer:
3
Step-by-step explanation:
The zero at the point x=3 is a result of a factor of even degree, because the function does not change sign as the value of (x -3) changes sign. Since a cubic only has 3 factors, the even degree must be 2. That is, (x -3)² is a factor of f(x) and the root at x=3 has multiplicity 2.
How can you tell by looking at the coordinates of the two triangles that δ a'b'c' is a 180° rotation of δ abc?
a.the coordinates cannot prove a 180° rotation.
b.the y-coordinates of the points on δa'b'c' have opposite signs from the corresponding points on δabc.
c.the x-coordinates of the points on δa'b'c' have opposite signs from the corresponding points on δabc. eliminate
d.both the x and y coordinates of the points on δa'b'c' have opposite signs from the corresponding points on δabc?
Answer:
Option d is correct.
Both the x and y coordinates of the point on δa'b'c' have opposite signs from the corresponding points on δabc.
Step-by-step explanation:
The rule of 180 degree rotation about the origin is:
[tex](x, y) \rightarrow (-x , -y)[/tex]
Since a Rotation of a point through 180°, about the origin when a point a(h, k) is rotated about the origin through 180° in anticlockwise or clockwise direction.
then, By the rule of 180 degree rotation;
[tex]a(h, k) \rightarrow a'(-h , -k)[/tex]
so, it takes the new position i.e, [tex]a'(-h , -k)[/tex]
Therefore, both the x and y coordinates of the point on δa'b'c' have opposite signs from the corresponding points on δabc.
A school replaced 20% of its computers with new ones what is the total number of computers in the school if 55 computers were replaced
Answer:
There were 275 computers
Step-by-step explanation:
Computers replaced = total computers * percent replaced
What do we know?
The percent replaced is 20 = .2
55 computers were replaced.
Substitute this in
55 = total computers * .2
Divide each side by .2
55/.2 = total computers *.2 /.2
275 = total computers
There were 275 computers
x 1 2 3 4
y 5 10 15 20
What's the constant?
Answer:
x ---> 1
y ---> 5
Step-by-step explanation:
We are given paired values for two variables x and y and we are to determine the constant number by which each term is increased such that they are in a proportional relationship.
For x, we have the following paired values:
[tex]x: 1, 2, 3, 4[/tex]
So here the difference between each consecutive term is 1 so the constant is 1.
And for y, we have:
[tex]y: 5, 10, 15, 20[/tex]
In this case, the difference between each consecutive term is 5 so the constant is 5.
HHHHHUUUUUUUURRRRRRRYYYYY!!!!!!!
The quotient of a number and 18 is 109.8.
which statements are correct?
It can be solved by using the division property of equality.
It can be solved by using the multiplication property of equality.
The equation should be x/18=109.8
The equation should be 18x=109.8
The answer is 6.1.
The answer is 1,976.4.
Answer:
2. It can be solved by using the multiplication property of equality.
3. The equation should be: [tex]\frac{x}{18}=109.8[/tex]
6. The answer is 1,976.4.
Step-by-step explanation:
Let x be the number.
We have been given that the quotient of a number and 18 is 109.8.
Since we know that in a division problem the number which is being divided called dividend and by which number we divide is called divisor.
[tex]\text{Dividend}\div \text{Divisor }=\text{ Quotient}[/tex]
We can represent our given information as:
[tex]\frac{x}{18}=109.8[/tex]
By using multiplication property of equality we will get,
[tex]18*\frac{x}{18}=18*109.8[/tex]
[tex]x=18*109.8[/tex]
[tex]x=1976.4[/tex]
Upon looking at our given choices we can see that 2nd, 3rd and 6th statements are correct choices.
can someone help me with this question?
Answer: [tex]\bold{(A)\ \dfrac{\text{51 miles}}{\text{1 hour}}}[/tex]
Step-by-step explanation:
Consider the formula "distance (d) = rate (r) x time(t)" and solve for r.
d = r · t
÷ t ÷ t
[tex]\dfrac{d}{t}=r[/tex]
Now plug in the given d and t values from the table to solve for r:
[tex]r=\dfrac{\text{204 miles}}{\text{4 hours}}[/tex]
[tex]=\dfrac{\text{51 miles}}{\text{1 hour}}[/tex] simplified the fraction
You can check this by plugging in the other 3 values from the table:
[tex]r=\dfrac{\text{306 miles}}{\text{6 hours}}[/tex]
[tex]=\dfrac{\text{51 miles}}{\text{1 hour}}[/tex]
[tex]r=\dfrac{\text{408 miles}}{\text{8 hours}}[/tex]
[tex]=\dfrac{\text{51 miles}}{\text{1 hour}}[/tex]
[tex]r=\dfrac{\text{510 miles}}{\text{10 hours}}[/tex]
[tex]=\dfrac{\text{51 miles}}{\text{1 hour}}[/tex]
Phyllis Doran worked at Symmes Medical Center for 7 1/2 hours on Monday and from 8:00 a.M. Until 1:00 p.M. On Tuesday What is the total number of hours she worked
Answer:
Step-by-step explanation:
B is the midpoint of AC and D is the midpoint of CE solve for X given BD equals 3X +5 and ae equals 4X +20?
Answer:
x = 5
Step-by-step explanation:
Refer the attached image.
B is midpoint of AC
D is midpoint of CE
So,
[tex]AB=BC=CD=DE[/tex]
[tex]BD=BC+CD= AB+DE=\frac{1}{2}(AE)[/tex]
[tex](3x+5)=\frac{1}{2} (4x+20)[/tex]
Solving for 'x' we get,
[tex]3x+5=2x+10[/tex]
[tex]3x-2x=10-5[/tex]
[tex]x=5[/tex]
So the value of 'x' is 5.
Our Einstein has baked a cake and cut it into 8 slices. If he hands out 3 slices to his guests, what fraction of the cake is left?
Answer:
[tex]\frac{5}{8}[/tex]
Step-by-step explanation:
We have been given that our Einstein has baked a cake and cut it into 8 slices. So each slice will be equal [tex]\frac{1}{8}[/tex].
He hands out 3 slices to his guests. Let us find out part of the cake given to guests.
[tex]\text{The part of the cake given to guests}=\frac{1}{8}+\frac{1}{8}+\frac{1}{8}[/tex]
[tex]\text{The part of the cake given to guests}=\frac{1+1+1}{8}[/tex]
[tex]\text{The part of the cake given to guests}=\frac{3}{8}[/tex]
To find the fraction of left cake we will subtract [tex]\frac{3}{8}[/tex] from 1 as Einstein has 1 whole cake.
[tex]\text{fraction of cake is left}=1-\frac{3}{8}[/tex]
[tex]\text{fraction of cake is left}=\frac{8}{8}-\frac{3}{8}[/tex]
[tex]\text{fraction of cake is left}=\frac{8-3}{8}[/tex]
[tex]\text{fraction of cake is left}=\frac{5}{8}[/tex]
Therefore, [tex]\frac{5}{8}[/tex] of the cake is left.
Answer:
As per the given statement: Our Einstein has baked a cake and cut it into 8 slices.
⇒ Total slice of cake Einstein has baked = 8
Also, it is given that if he hands out 3 slices to his guests.
⇒ Number of slice he hands out to his guests = 3
Remaining slice of a cake Einstein left with = 8 -3 = 5.
We have to find the fraction of the cake is left.
Fraction states that a fraction is a number that represents a part of a whole. Also, It consists of a numerator and a denominator, where numerator represents the number of equal parts of a whole, while the denominator is the total number of parts.
Fraction of the cake is left = [tex]\frac{\text{Slices of cake left}}{\text{Total number of slices of a cake}}[/tex]
Substitute the given values we get;
[tex]\text{Fraction of the cake is left} =\frac{5}{8}[/tex]
therefore, the fraction of the cake is left is, [tex]\frac{5}{8}[/tex]
Stephanie bought 3 pizzas for a total of $9.00. Which expression shows p, the cost of each pizza?
Answer:
the answer is 3
Step-by-step explanation:
3 pizzas equal $9.00 so in order to know how much each pizza was, we will have to do division:
9 divided by 3
9/3
3
Soe found a sweatshirt that she wanted at JC Penny when she went shopping the other day it was on sale for 30% off. What was the original cost of the sweat shirt if the sale price was $21
Answer:
$30
Step-by-step explanation:
x*0.70=21
21/0.70= 30
There were 50 students in the chess club. The membership went up by 10%. How many more students joined the club?
The membership went up by 10%.
There are now 55 total students in the club.
The formula for calculating the percentage change is
[tex]p=\frac{N-O}{O}.100[/tex]
where p is the percent change, N is the New Value and O is the Old Value.
In this problem we are given the Old Value (50) and the percent change (10). We can substitute this into the formula and solve for N:
[tex]10=\frac{N-50}{50} .100\\10=2(N-50)\\5=N-50\\N=55[/tex]
There are now 55 total students in the club.
For more information:
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What percentage is the fraction `2/(10)` equal to?
Answer:
20%
Step-by-step explanation:
Percentage means out of 100
We need to get 2/10 to be out of 100
Multiply by 10/10
2/10*10/10
= 20/100
This is 20%
One number is five more than another and their sum Is there less than three times the smaller find the numbers
Answer:
The numbers are 8 and 13
Step-by-step explanation:
In order to find this, we set the smaller number as x. Then we can set the larger one as x + 5, since it is 5 more than the smaller.
Given these two, we can then set them equal to 3x - 3, since the answer is three less than three times the larger.
x + x + 5 = 3x - 3
2x + 5 = 3x - 3
5 = x - 3
8 = x
Now to find the larger number, put into the larger number equation.
x + 5
(8) + 5
13
The numbers are 8 and 13.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The algebraic expression is,
''One number is five more than another and their sum Is there less than three times the smaller''.
Now,
Let the smaller number = x
Then, The another number = x + 5
Write the expression as;
x + x + 5 = 3x - 3
2x + 5 = 3x - 3
2x - 3x = - 3 - 5
- x = - 8
x = 8
And, The another number = x + 5
= 8 + 5
= 13
Thus, The numbers are 8 and 13.
Learn more about the mathematical expression visit:
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Omar is an avid video game player and movie watcher. He has a choice of belonging to a video club with a monthly fee of $12 and $1-a-day rental fee for any movie or game, or he can be a nonmemeber and pay $2.50-a-day rental fee for any movie or game. Find the number of movies or video games Omar must rent for one day for the cost to be equal between membership and nonmembership.
Answer:
8 movies or video games.
Step-by-step explanation:
Let x be the number of movies or video games on rent.
We have been given that Omar has a choice of belonging to a video club with a monthly fee of $12 and $1-a-day rental fee for any movie or game. We can represent the charges for x movies or video games for a member of club as: [tex]x+12[/tex].
Omar can be a non-member and pay $2.50-a-day rental fee for any movie or game. We can represent the charges of a non-member for x movies or video games as: [tex]2.5x[/tex].
To find the number of movies for one day for the cost to be equal we will equate our both expressions.
[tex]x+12=2.5x[/tex]
[tex]x+12-x=2.5x-x[/tex]
[tex]12=1.5x[/tex]
[tex]x=\frac{12}{1.5}[/tex]
[tex]x=8[/tex]
Therefore, Omar must rent 8 movies or video games for one day for the cost to be equal between membership and non-membership.
By renting 8 movies or video games charges for membership will be: 8+12=20.
By renting 8 movies or video games charges for a non-membership be: 2.5*8=20.
Hence charges of renting 8 movies or video games are same for both membership or non-membership.
Omar needs to rent 8 movies or video games in one month for the costs of a membership and nonmembership to be the same. The membership includes a monthly fee of $12, and rentals cost $1 per day. Non-membership rentals cost $2.50 per day.
Omar wants to determine how many movies or video games he must rent for the cost of membership and non-membership to be equal. To find this, we will set up an equation comparing the two costs.
Membership Plan:
Monthly fee: $12Rental fee: $1 per movie/game per dayNon-membership Plan:
Rental fee: $2.50 per movie/game per day
Let's denote the number of movies or games rented by x.
For the membership plan, the total cost is: $12 + $1x
For the non-membership plan, the total cost is:$2.50x
We set the two costs equal to find x: $12 + $1x = $2.50x
Subtract $1x from both sides: $12 = $1.50x
Divide both sides by $1.50: x = 8
Omar must rent 8 movies or video games in one month for the costs of membership and non-membership to be equal.
Hey y'all please help me with this geometry problem,would really appreciate it :)
180-(x+50)+180-4x+180-(2x+40)+180-3x=360
720-x-50-4x-2x-40-3x=360
630 - 10x=360
-10x=360-630
-10x=-270 /:(-10)
x=27
Answer this question please! 25 points and brainliest!
Answer: c
Step-by-step explanation:
the number with one dot < on the left side means its the smaller number
Answer:
c x< 9
Step-by-step explanation:
A number less than 9
x must be less than 9
No equals sign because it is less than
The inequality faces the larger number
x < 9
helps please i need it
Subtract 7a^4-4a^2b^2+67a 4 −4a 2 b 2 +6 from 3a^4+2ab^2+113a 4 +2ab 2 +11.
Final answer:
To subtract the polynomials, we subtract the coefficients of like terms: the a⁴ terms give -4a⁴, there are no changes to the ab² term since it's not present in both polynomials, and for the a terms, we get 46a. So, the result is -4a⁴ + 2ab² + 46a.
Explanation:
The question asks us to perform polynomial subtraction. Specifically, the question requires subtracting 7a⁴ - 4a²b² + 67a from 3a⁴ + 2ab² + 113a. To do this, we subtract the coefficients of like terms, which are terms with the same variable raised to the same power.
Let's subtract step-by-step:
Subtract the a⁴ terms: 3a⁴ - 7a⁴ = -4a⁴Subtract the ab² terms: We do not have a term with ab² in the second polynomial, so we simply bring down the 2ab² term.Subtract the a terms: 113a - 67a = 46aPutting it all together, the result of our subtraction is -4a⁴ + 2ab² + 46a.
BRAINLIEST AND 60 POINTS
A dartboard is divide into sections numbered 1-20. Leon throws a dart at the board 30 times. 8 times the dart lands on the number 2. What is the experimental probability that the dart lands on number 2?
Answer:
4/15
Step-by-step explanation:
Experimental probability is the actual times the event occurs divided by the number of trials
Actual times : 8
Number of trials: 30
Experimental probability of a 2: 8/30 = 4/15
A football signs a contract that pays him $16 million over 4 years. What is his average pay per year?
Answer:
the footballer's average pay would be $4 million/annum.
Fatema bought 35 feet of window trim at a hardware store. The trim cost $1.75 per foot, including sales tax. If Fatema paid with a $100.00 bill, how much change should she have received?
Answer:$38.75
Step-by-step explanation:
35(number of feet) * $1.75(cost per foot) = $61.25(total cost)
$100(bill used) - $61.25(total cost) = $38.75(amount given in change)
Answer:
$38.75
Step-by-step explanation:
We have given that : The trim cost per foot =$1.75
for 35 feet of window trim cost = 35×1.75 = $61.25
Now, Fatima paid $100.00 bill
Amount she received = Amount she pay - cost of trim she buy
= $100 - $61.25
=$38.75