Answer:
The quotient of the rational function is [tex]3 -\frac{1}{x+2}[/tex].
Step-by-step explanation:
We proceed to solve the expression by solely algebraic means below:
1) [tex]\frac{3\cdot x + 5}{x+2}[/tex] Given
2) [tex]\frac{(3\cdot x + 5) + 0}{x + 2}[/tex] Modulative property
3) [tex]\frac{(3\cdot x +5) + [1+(-1)]}{x+2}[/tex] Existence of additive inverse/Associative property
4) [tex]\frac{(3\cdot x + 6)+(-1)}{x+2}[/tex] Definition of addition/Commutative and associative properties
5) [tex]\frac{3\cdot (x+2)}{x+2} + \left(-\frac{1}{x+2} \right)[/tex] [tex]\frac{a+b}{c} = \frac{a}{c} + \frac{b}{c}[/tex]/ [tex]\frac{-a}{b} = \frac{a}{-b} = -\frac{a}{b}[/tex]/Distributive property
6) [tex]3 -\frac{1}{x+2}[/tex] Definition of division/Existence of multiplicative inverse/Modulative property/Definition of subtraction/Result
The quotient of the rational function is [tex]3 -\frac{1}{x+2}[/tex].
how to write 6 in a expanded form?
Answer: 6 × 1
To write a number in expanded form, add the places by it's number.
Ex: 231 → 200 + 30 + 1 = 231
In the problem, 6 is what we're expanding.
Since 6 is only just 1 digit, it is possible to expand a 1 digit number. All you'll need to do it multiply the digit by 1.
6 → 6 × 1 = 6
Therefore, 6 × 1 is the expanded form of 6.
The Great Knightrola Small Monster Association has four chartered positions: President, Vice President, Treasurer, and Secretary; it also has 12 officers chosen at large. All of these seats must be filled by members of GKSMA, of which there are 50. No member may hold more than 1 position. How many different ways are there to fill the positions
Answer:
Number of different ways of filling the position is 8961115245946500
Step-by-step explanation:
There are total of 4 positions which can be arranged in 4! Ways
Like wise there are 12 positions. Hence the number of arrangements for these 12 positions would be 12!
Overall there are 12+4 = 16 positions in which 50 people needs to be arranged
Number of different ways of filling the position is
50P16 /(12! *4!)
= 8961115245946500
The number of different ways of filling the position is, 8961115245946500
There are total of 4 positions can be arranged in 4! Ways
Similarly there are 12 positions.
Therefore, the number of arrangements for these 12 positions is 12!
When we use the permutation?If there is an arrangement of the data then we use the permutation
Therefore we can say that there are 12+4 = 16 positions in which 50 people needs to be arranged.
The number of different ways of filling the position is,
[tex]50P16 /(12! *4!)[/tex]
By using the calculater you can find,
= 8961115245946500
To learn more about the permutation visit:
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Can someone help me ill give you 25 points!!! no wrong answers or ill have brainly take all your points and band you forever Uhm yeah so......... plz help
Answer: Mean = 2.36 Median = 4 Range = 0
Step-by-step explanation:
Mean - the sum of the data values divided by the number of data values
Median - the middle number in an ordered set of data
Range - the difference between the greatest and least numbers in a data set
Phil has 5 times as many toy race cars as Richard has. Phil has 425 toy race cars. How many race cars does Richard have? *
Answer:
85
Step-by-step explanation:
425 divided by 8= 85
Answer:
He as 85 race cars.
Step-by-step explanation:
Just divide 425 by 5 and you have your answer.
A container in the shape of a cylinder has a volume of 60 cubic meters. Its base has an area of 15 square units. What is the height of the container?
options
3m
2m
4m
5m
The answer would be 4m
how do you determine a function if a relation is a function
Answer:
Hello! A function is easily identified when an x value does not have more than 1 y value. a y value can have as many x values to infinity, but x can only have one y.
Example...
x y
3 5
4 5
1 2
The diameter of a semicircle is 10 meters. What is the perimeter of the semicircle, in meters? Round your answer to the nearest tenth.
Answer:
25.7 m
Step-by-step explanation:
The formula for the circumference of a circle is C = 2(pi)(r), where r is the radius, which in turn is half the diameter. Thus, the formula for the circumference is C = (d)(pi). The perimeter of a semicircle is half that, or
C = (pi)(r), which here is (3.14)(5 m) = 15.7 m. Finally, the total perimeter is the sum of this 15.7 m and the 10 m diameter of the circle:
P = 15.7 m + 10 m = 25.7 m
Find x. This is not drawn to scale.
H
150°
GX 54°
J
E
Are
F
Answer:
48°
Step-by-step explanation:
We solve the above question using circle theorem.
Finding x
The formula is given as
x = 1/2 (150° - 54°)
x = 1/2 (96)°
x = 48°
find x
answer choices
6
7
9
10
8
The answer should be 10
Here is an equation and all the steps Clare and Lin took to solve it. Are both of their solutions correct? Explain your reasoning.
Answer:
Both solutions are correct
Step-by-step explanation:
Given
Expression:
[tex]14x - 2x +3 = 3(5x + 9)[/tex]
See attachment for Clare and Lins' solution
Required
Determine if they are correct or not
[tex]14x - 2x +3 = 3(5x + 9)[/tex]
Open bracket
[tex]14x - 2x + 3 = 15x + 27[/tex]
Collect like terms
[tex]14x - 2x -15x = -3 + 27[/tex]
[tex]-3x = 24[/tex]
Divide by -3
[tex]x = \frac{24}{-3}[/tex]
[tex]x = -8[/tex]
Both solutions are correct
what are the answers to a, b, c, d?
Answer:
Step-by-step explanation:
The sum of the first nine terms in a sequence is 49,205. Each term is 3 times the previous term. What is the third term?
Answer:
a₃ = 32 805Step-by-step explanation:
Each term is 3 times the previous term:
r = 3
The sum of the first nine terms in a sequence is 49,205:
[tex]S_n=a_1\cdot\dfrac{1-q^n}{1-q}\\\\\\49205=a_1\cdot\dfrac{1-3^9}{1-3}\\\\49205=a_1\cdot\dfrac{1-19683}{-2}\\\\49205=a_1\cdot9841\\\\a_1=5[/tex]
What is the third term?
[tex]a_n=a_1\cdot q^{n-1}\\\\a_3=5\cdot3^8=32805[/tex]
Find the midpoint of the segment with the following endpoints.
(9,6) and (5,2)
Answer:
[tex]M(7 ; 4)[/tex]
Step-by-step explanation:
midpoint -M
[tex]M(\frac{x_{1}+x_{2}}{2} ; \frac{y_{1}+y_{2}}{2} )[/tex]
[tex]M(\frac{9+5}{2} ; \frac{6+2}{2} )[/tex]
[tex]M(7 ; 4)[/tex]
Answer:
(7, 4 )
Step-by-step explanation:
Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )
Here (x₁, y₁ ) = (9, 6) and (x₂, y₂ ) = (5, 2) , then
midpoint = ( [tex]\frac{9+5}{2}[/tex] , [tex]\frac{6+2}{2}[/tex] ) = ([tex]\frac{14}{2}[/tex] , [tex]\frac{8}{2}[/tex] ) = (7, 4 )
Clara visits the aquarium while on vacation. The aquarium is 2 1/2 from her hotel. She walks 1/4 mile to the bus stop, take the bus for 1 3/4 miles, and walks the rest of the way to the aquarium.
Answer:
1/2
Step-by-step explanation:
The rectangular prism has a volume of 936 cubic inches. Write and solve an equation to find the missing dimension of the prism.
Answer: Solution in photo
Please help me with the question please ASAP I’ll mark u as a brnlist
*2 questions
Answer:
First answer is 76.50 and the second one is scale factor of 1/2
Step-by-step explanation: Mark brainlist or im deleting my answer :)
Answer:
scale factor = [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
The scale factor is the ratio of corresponding sides, image to original, that is
scale factor = [tex]\frac{WX}{AB}[/tex] = [tex]\frac{12}{8}[/tex] = [tex]\frac{3}{2}[/tex]
------------------------------------------
1 pizza costs $12.75 and feeds 4
To feed 24 students he needs 24 ÷ 4 = 6 pizzas , then
6 cost = 6 × $12.75 = $76.50
Answer this question
y is less than or equal to three more than the product of x and negative two thirds put it on standard form
Helpppppppp pleaseeeeee I will give brainliest if you knowww pleaseeee helpppppppp
Answer:
I think the answer is 1/2 but dont take my word
An element with a mass of 700 grams decays by 6.1% per minute. To the nearest
tenth of a minute, how long will it be until there are 220 grams of the element
remaining?
Answer:
11.2 minutes
Step-by-step explanation:
If the element decreases by 6.1, every minute, it means that the mass lost every minute = 0.061 x 700g = 42.7g
The mass remaining after a minute = 657.30g
The equation that can be used to solve this question is :
700 - 42.7m = 220
m = minutes
Collect like terms
700 - 220 = 42.7m
480 = 42.7m
divide both sides of the equation by 42.7
m = 11.241218 minutes
the tenth is the first number after the decimal place. To convert to the nearest tenth, look at the number after the tenth (the hundredth). If the number is greater or equal to 5, add 1 to the tenth figure. If this is not the case, add zero
Here, the hundredth is less than 5, so zero would be added to 2. the answer is 11.2 minutes
Answer:
18.4
Step-by-step explanation:
I answered the question
Jacob distributed a survey to his fellow students asking them how many hours they'd spent playing sports in the past day. He also asked them to rate their mood on a scale from 0 to 10, with 10 being the happiest. A line was fit to the data to model the relationship.
Which of these linear equations best describes the given model?
Choose 1 answer:
5x+1.5
1.5x+5
−1.5x+5
Based on this equation, estimate the mood rating for a student that spent 2.52, point, 5 hours playing sports.
Round your answer to the nearest hundredth.
Answer:8.75
Step-by-step explanation:
Answer: it’s B
Step-by-step explanation:
Gabe can travel 40 miles on his motorbike in the same time it takes Dena to travel 15 miles on her bicycle. If Dena rides her bicycle 20 mph slower than Gabe rides his motorbike, find
Dena's rate.
Answer:
answer is 12 miles vause he can travel faster
Step-by-step explanation:
Question 7: The red line has an equation of y = -1/2 x + 2. The blue line is perpendicular to the red line. Write the equation for the blue line. EXPLAIN PLS
Answer:y=2+2x
Step-by-step explanation:
Perpendicular means the slope is the opposite reciprocal of the red line’s. Opposite reciprocal means that if the red line has a negative slope the blue line will have a positive one, and you flip the fraction of the red line from 1/2 to 2. The y intercept is at 2 so that’s why there is a +2
A car can go 35 1/2 miles in 1 1/2 miles gallons. How many gallons does a car need to go 639 miles?
Need work please!!
Answer: 27 gallons
Step-by-step explanation:
Since the car can go 35½ miles in 1½ miles gallons, we need to first calculate the number of miles that the car can go in 1 gallon. This will be:
= 35½ / 1½
= 71/2 / 3/2
= 71/2 × 2/3
= 23⅔ miles per gallon.
Therefore, the amount of gallons that the car need to go 639 miles will be:
= 639 / 23⅔
= 639 ÷ 71/3
= 639 × 3/71
= 27
The car will need 27 gallons.
You have 35 plants. You want to split them equally between 4 sections of your garden. You use as many as you can in each section. How many plants do you have left?
answer:
3 plants are left !
step-by-step explanation:
hi there!
first lets use our times table to see which number gets use closest to 35 when it is multiplied by 4
4, 8, 12, 16, 20, 24, 28, 32,
4 * 8
= 32
then you can just subtract 35 by 32 to get you final answer of
35 - 32
= 3 plants are left over
( i hope i did the problem right since the wording of it was kinda hard to understand it )
________________________________________________________
| | | | |
| 1 | 2 | 3 | 4 |
| | | | |
________________________________________________________
| | | | |
| 5 | 6 | 7 | 8 |
| | | | |
________________________________________________________
| | | | |
| 9 | 10 | 11 | 12 |
| | | | |
________________________________________________________
| | | | |
| 13 | 14 | 15 | 16 |
| | | | |
________________________________________________________
| | | | |
| 17 | 18 | 19 | 20 |
| | | | |
________________________________________________________
| | | | |
| 21 | 22 | 23 | 24 |
| | | | |
________________________________________________________
| | | | |
| 25 | 26 | 27 | 28 |
| | | | |
________________________________________________________
| | | | |
| 29 | 30 | 31 | 32 |
| | | | |
________________________________________________________
i made a table with each number being the plant! just in case your a visual learner like me!
but i hope this help you and if i made anything confusing or if i made a mistake please let me know! but other then that i hope you have a good rest of your day :)
There are 3 plants left.
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
Total number of plants = 35
And, You want to split them equally between 4 sections of your garden.
Now,
To find the left plants after splitting into 4 sections, we can divide and find the remainder as;
The number of left plants = 35 ÷ 4
4 ) 35 ( 8
- 32
-------
3
Clearly, The remainder = 3
Thus, There are 3 plants left.
Learn more about the divide visit:
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If the data point is at (3, 10.5) and the prediction equation is y = -6.1x + 12.5, what is the value of the residual for this data point?
Given:
The data point is (3,10.5).
The prediction equation is [tex]y=-6.1x+12.5[/tex].
To find:
The value of the residual for this data point.
Step-by-step explanation:
The data point is (3,10.5). So, the actual value is 10.5 at [tex]x=3[/tex].
Prediction equation is
[tex]y=-6.1x+12.5[/tex]
Putting [tex]x=3[/tex], we get
[tex]y=-6.1(3)+12.5[/tex]
[tex]y=-18.3+12.5[/tex]
[tex]y=-5.8[/tex]
The formula for residual is:
Residual = Actual value - Expected value
[tex]Residual=10.5-(-5.8)[/tex]
[tex]Residual=10.5+5.8[/tex]
[tex]Residual=16.3[/tex]
Therefore, the residual for the given data point is 16.3.
PLEASE HELPPPPP
WILL GIVE BRAINLIEST
Answer:
Step-by-step explanation:
From the given table,
A. The unit rate for each car is,
Car A = [tex]\frac{416}{13}[/tex]
= 32 miles per gallon
Car B = [tex]\frac{544}{16}[/tex]
= 34 miles per gallon
Car C = [tex]\frac{665}{19}[/tex]
= 35 miles per gallon
Car D = [tex]\frac{775}{25}[/tex]
= 31 miles per gallon
B. From the derived values in A, the car that uses the least amount of gas is Car C.
C. Total distance covered = 496 miles x 4
= 1984 miles
The gallons of gas the Car A would need for the journey can be determined by;
Car A requires 1 gallon for 32 miles
So that for 1984 miles = [tex]\frac{1984}{32}[/tex]
= 62 gallons
Car A would need 62 gallons of gas to make the trip.
D. Amount spent on gas for Car A = $2.12 x 62
= $131.44
E. speed = [tex]\frac{distance}{time}[/tex]
⇒ time = [tex]\frac{distance}{speed}[/tex]
Given the for Car A, speed = 68 miles per hour.
time = [tex]\frac{1984}{68}[/tex]
= 29.1765
time = 29 hours
It would take approximately 29 hours for Car A to cover the total distance of 1984 miles.
Mark is going to an awards dinner and wants to dress appropriately. He has one blue dress shirt, one white dress shirt, one black dress shirt, one pair of black slacks, one pair of grey slacks, and one red tie. All six of Mark's possible outfits are listed below.
Ir we take outfits 1, 2, 5, and 6 as a subset of the sample space, which of the statements below describe this subset?
Choose all answers that apply:
(Choice A)
The subset consists of all the outfits that do not have a white shirt.
(Choice B)
The subset consists of all the outfits that have either a blue shirt or a black shirt.
(Choice C)
The subset consists of all the outfits that have a black shirt.
(Choice D)
The subset consists of all the outfits that have a white shirt.
Solution:
Outfit Shirt Slacks Tie
Outfit 1 Blue Black Red
Outfit 2 Blue Grey Red
Outfit 3 White Black Red
Outfit 4 White Grey Red
Outfit 5 Black Black Red
Outfit 6 Black Grey Red
We take the outfits 1, 2 , 5 and 6 as a subset of the sample space.
So these 1, 2, 5 and 6 consists either a blue shirt or a black shirt.
The subset consists of all the outfits that do not have a white shirt.
So the correct options are :
1. (Choice A)
The subset consists of all the outfits that do not have a white shirt.
2. (Choice C)
The subset consists of all the outfits that have a black shirt.
The following are the temperatures in °C for the first 8 days of January:
-2.5, 0, 4, 4.5, -0.5, -1, 5, 3
What is the median temperature for those 8 days?
Give your answer as a decimal.
help i need it ASAP!!!
Answer:
1.5 °C
Step-by-step explanation:
-2.5, -1, -0.5, 0, 3, 4, 4.5, 5
median is the middle number in the list of numbers
Gina and Rhonda work for different real estate agencies. Gina earns a monthly salary of $5,000 plus a 6% commission on her sales. Rhonda earns a monthly salary of $6,500 plus a 4% commission on her sales. How much must each sell to earn the same amount in a month?
Answer: Gina and Rhonda work for different real estate agencies. Gina earns a monthly salary of $5,000 plus a 6% commission on her sales. Rhonda earns a monthly salary of $6,500 plus a 4% commission on her sales. How much must each sell to earn the same amount in a month?
Step-by-step explanation:
$5,000 + 6% + $6,500 + 4% = 11500.1 or 11500
Shana is doing a craft project
using yarn and sticks. She
has 3 green yam pieces and
7 blue yam pieces. She has 3
times as many sticks as yarn
pieces. Write an expression.
Plz help
Answer:
3(5 + 7)
Step-by-step explanation:
Shana is carrying our a craft project
She is making use of yarns and stuck
She has three green yarn pieces and seven blue yarn pieces
She has three times as many yarn pieces
Therefore the expression can be represented as follows
3(5 + 7)
