Given:
The rational function is:
[tex]f(x)=\dfrac{5-x}{x^2+5x+6}[/tex]
To find:
The points on the graph at the function value [tex]f(x)=3[/tex].
Solution:
We have,
[tex]f(x)=\dfrac{5-x}{x^2+5x+6}[/tex]
Substituting [tex]f(x)=3[/tex], we get
[tex]3=\dfrac{5-x}{x^2+5x+6}[/tex]
[tex]3(x^2+5x+6)=5-x[/tex]
[tex]3x^2+15x+18=5-x[/tex]
Moving all the terms on one side, we get
[tex]3x^2+15x+18-5+x=0[/tex]
[tex]3x^2+16x+13=0[/tex]
Splitting the middle term, we get
[tex]3x^2+3x+13x+13=0[/tex]
[tex]3x(x+1)+13(x+1)=0[/tex]
[tex](3x+13)(x+1)=0[/tex]
Using zero product property, we get
[tex](3x+13)=0\text{ or }(x+1)=0[/tex]
[tex]x=-\dfrac{13}{3}\text{ or }x=-1[/tex]
Therefore, the required values are [tex]-\dfrac{13}{3},-1[/tex].
Assume that the matrices below are partitioned conformably for block multiplication. Compute the product.
[I 0] [W X]
[K I] [Y Z]
Multiplying block matrices works just like multiplication between regular matrices, provided that component matrices have the right sizes.
[tex]\begin{bmatrix}\mathbf I&\mathbf 0\\\mathbf K&\mathbf I\end{bmatrix}\begin{bmatrix}\mathbf W&\mathbf X\\\mathbf Y&\mathbf Z\end{bmatrix} = \begin{bmatrix}\mathbf{IW}+\mathbf{0Y}&\mathbf{IX}+\mathbf{0Z}\\\mathbf{KW}+\mathbf{IY}&\mathbf{KX}+\mathbf{IZ}\end{bmatrix}[/tex]
[tex]\begin{bmatrix}\mathbf I&\mathbf 0\\\mathbf K&\mathbf I\end{bmatrix}\begin{bmatrix}\mathbf W&\mathbf X\\\mathbf Y&\mathbf Z\end{bmatrix} = \begin{bmatrix}\mathbf W+\mathbf 0&\mathbf X+\mathbf 0\\\mathbf{KW}+\mathbf Y&\mathbf{KX}+\mathbf Z\end{bmatrix}[/tex]
[tex]\begin{bmatrix}\mathbf I&\mathbf 0\\\mathbf K&\mathbf I\end{bmatrix}\begin{bmatrix}\mathbf W&\mathbf X\\\mathbf Y&\mathbf Z\end{bmatrix} = \begin{bmatrix}\mathbf W&\mathbf X\\\mathbf{KW}+\mathbf Y&\mathbf{KX}+\mathbf Z\end{bmatrix}[/tex]
(I assume I is the identity matrix and 0 is the zero matrix.)
identify the roots of the equation and the multiplicities of the roots 8(x - 2)³ = 0
Answer:
The root of the equation is 2 with multiplicity 3
Step-by-step explanation:
8(x-2)^3=0
(x-2)^3=0
The root of the equation is 2 with multiplicity 3
a) Everyone on the team talks until the entire team agrees on one decision. O b) Everyone on the team discusses options and then votes. O c) The team passes the decision-making responsibility to an outside person. O di The team leader makes a decision without input from the other members.
Answer:
a) Everyone on the team talks until the entire team agrees on one decision.
Step-by-step explanation:
Option B consists of voting and not everyone would like the outcome. Option C is making an outsider the decision maker, which can't be helpful since he / she won't have as strong opinions as the team itself. Option D is just plain wrong as it defeats the purpose of team work and deciding as one team. So, I believe option A makes the most sense
Enter a formula in cell B10 to return the value of 35000 if the net profit after tax cell B9 is greater than or equal to 470000 or 100 if it is not
Answer:
I hope it help and I guess it is correct
Air-USA has a policy of booking as many as 22 people on an airplane that can only seat 20 people. (Past studies have revealed that only 82% of the booked passengers actually show up for the flight.) a) Find the probability that if Air-USA books 22 people, not enough seats will be available. Round your answer to 4 decimal places. P ( X > 20 )
Answer:
The answer is "0.07404893".
Step-by-step explanation:
Applying the binomial distribution:
[tex]n = 22\\\\p= 82\%=0.82\\\\q = 1-0.82 = 0.18\\\\[/tex]
Calculating the probability for not enough seats:
[tex]=P(X>20)\\\\= P(21) + P(22)\\\\[/tex]
[tex]= \binom{22}{21} (0.82)^{21}(0.18)^1+ \binom{22}{22} (0.82)^{22}(0.18)[/tex]
[tex]=0 .06134598+ 0.01270295\\\\=0.07404893[/tex]
An expression is shown below:
6x2y − 3xy − 24xy2 + 12y2
Part A: Rewrite the expression by factoring out the greatest common factor. (4 points)
Part B: Factor the entire expression completely. Show the steps of your work. (6 points)
Given:
The given expression is:
[tex]6x^2y-3xy-24xy^2+12y^2[/tex]
To find:
Part A: The expression by factoring out the greatest common factor.
Part B: Factor the entire expression completely.
Solution:
Part A:
We have,
[tex]6x^2y-3xy-24xy^2+12y^2[/tex]
Taking out the highest common factor 3y, we get
[tex]=3y(2x^2-x-8xy+4y)[/tex]
Therefore, the required expression is [tex]3y(2x^2-x-8xy+4y)[/tex].
Part B:
From part A, we have,
[tex]3y(2x^2-x-8xy+4y)[/tex]
By grouping method, we get
[tex]=3y(x(2x-1)-4y(2x-1))[/tex]
[tex]=3y(x-4y)(2x-1)[/tex]
Therefore, the required factored form of the given expression is [tex]3y(x-4y)(2x-1)[/tex].
If (4x-5) :(9x-5) = 3:8 find the value of x.
Answer:
x is 5
Step-by-step explanation:
[tex] \frac{4x - 5}{9x - 5} = \frac{3}{8} \\ \\ 8(4x - 5) = 3(9x - 5) \\ 32x - 40 = 27x - 15 \\ 5x = 25 \\ x = \frac{25}{5} \\ \\ x = 5[/tex]
Step-by-step explanation:
as you can see as i solved above. all you need to do was to rationalize the both equations
what percent of 70 is 35
Answer:
50%
Step-by-step explanation:
35 is halve of 70 therefore it is 50%
hope it helps u...........
find the missing length indicated
explainion:
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
Use The (Pythagorean Theorem) to find the length of any side of a right triangle. Form it like its shown in picture above. Follow the instructions that also shown in the picture above.
Which equation can be used to find the length of Line segment A C?
Answer:
I don't see the problem.
Step-by-step explanation:
HURRY plSSSSSSSSSSSSSSSSSSSSSS
What is the measure of the unknown angle?
Image of a straight angle divided into two angles. One angle is eighty degrees and the other is unknown.
Answer:
The unknown is 100
Step-by-step explanation:
A straight line is 180 degrees
We have two angles x, and 80
x+80 = 180
x = 180-80
x= 100
An electrician charges a fee of $40 plus $25 per hour. Let y be the cost in dollars of using the electrician for x hours. Choose the correct equation.
y = 40x - 25
y = 25x + 40
y = 25x - 40
y = 40x + 25
Answer:
y = 25x + 40
Step-by-step explanation:
The electrician charges $25 per hour.
The number of hours is x.
Therefore after x hours the electrician will charge $25x. (multiply the charge by the number of hours $25 * x)
Therefore fee(y) charged by the electrician = $40 + $25x
Hence y = 25x + 40
Karissa purchased a set of LED lights online that normally sells for $72.00 but was marked down to $48.96. What is the discount rate Karissa received? (2 points)
32%
47%
68%
If 5000 is divided by 10 and 10 again what answer will be reached
Hey there!
First, divide 5,000 by 10. You will get 500.
Now, 500 ÷ 10, and you will get your answer, 50.
Hope this helps! Have a great day!
50T Q12 A man wants to buy bags of gravel to cover his driveway. He decides to work out the area of his driveway. 1 bag of gravel covers 14m2 3m Sketch of driveway Not to scale 3m 8m 6m What is the area of his driveway? How many bags of gravel must he buy?
Answer:
hi amki nai patajjdkfkejd
Shaun is planting trees along his driveway, and he has 66 redwoods and 66 pine trees to plant in one row. What is the probability that he randomly plants the trees so that all 66 redwoods are next to each other and all 66 pine trees are next to each other
Answer:
0.0022 = 0.22% probability that he randomly plants the trees so that all 6 redwoods are next to each other and all 6 pine trees are next to each other.
Step-by-step explanation:
The trees are arranged, so the arrangements formula is used to solve this question. Also, a probability is the number of desired outcomes divided by the number of total outcomes.
Arrangements formula:
The number of possible arrangements of n elements is given by:
[tex]A_n = n![/tex]
Desired outcomes:
Two cases:
6 redwoods(6! ways) then the 6 pine trees(6! ways)
6 pine trees(6! ways) then the 6 redwoods(6! ways)
So
[tex]D = 2*6!*6![/tex]
Total outcomes:
12 trees, so:
[tex]D = 12![/tex]
What is the probability that he randomly plants the trees so that all 6 redwoods are next to each other and all 6 pine trees are next to each other?
[tex]p = \frac{D}{T} = \frac{2*6!*6!}{12!} = 0.0022[/tex]
0.0022 = 0.22% probability that he randomly plants the trees so that all 6 redwoods are next to each other and all 6 pine trees are next to each other.
The length of a rectangle is 10 yd less than three times the width, and the area of the rectangle is 77 yd^2. Find the dimensions of the rectangle.
Answer:
W=7 and L=11
Step-by-step explanation:
We have two unknowns so we must create two equations.
First the problem states that length of a rectangle is 10 yd less than three times the width so: L= 3w-10
Next we are given the area so: L X W = 77
Then solve for the variable algebraically. It is just a system of equations.
3W^2 - 10W - 77 = 0
(3W + 11)(W - 7) = 0
W = -11/3 and/or W=7
Discard the negative solution as the width of the rectangle cannot be less then 0.
So W=7
Plug that into the first equation.
3(7)-10= 11 so L=11
which of these figures has rotational symmetry
9514 1404 393
Answer:
A
Step-by-step explanation:
The parallelogram has rotational symmetry of degree 2. It looks the same after rotation by 180°.
_____
Additional comment
When a figure only looks like itself after a full rotation of 360°, it is said to have rotational symmetry of degree 1. All of the figures here will return to their original appearance after one 360° rotation. So, we assume the intent of the question is to identify figures with a rotational symmetry of degree greater than 1.
Question with last attempt is displayed for your review only
Amanda rented a bike from Ted's Bikes.
It costs $9 for the helmet plus $5.25 per hour.
If Amanda paid about $43.13, how many hours did she rent the bike?
Let h = the number of hours she rented the bike. Write the equation you would use to solve this problem.
Answer:
[tex]43.13 = 5.25h + 9[/tex]
Step-by-step explanation:
Let's solve this by making an equation.
$9 for the helmet, and $5.25 per hour.
h will stand for hours, C will stand for Amanda's cost.
[tex]C = 5.25h + 9[/tex]
Now, substitute in what we learned from the problem.
[tex]43.13 = 5.25h + 9[/tex]
This is an equation you can use to solve for the hours.
Find the length of the missing side
Answer:
Step-by-step explanation:
Side=AC=9[tex]\sqrt{2}[/tex]
Side AB= x
Hypotenuse =CB= y
Side AB = 9[tex]\sqrt{2}[/tex]
Hypotenuse CB = 36
A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment.
n=12, p=0.35, x=2
Answer:
0.1088 or 10.88%
Step-by-step explanation:
q = 1 - 0.35 = 0.65
P(X=2) = 12C2 × (0.35)² × (0.65)¹⁰
= 0.1088
what is the least common multiple between 25 and 8
Answer:
200
Step-by-step explanation:
Break down 25 = 5*5
Break down 8 = 2*2*2
They have no common factors
The least common multiple is
5*5*2*2*2 = 25*8 = 200
Answer:
200
Step-by-step explanation:
list the factors of 25: 5,5
factors of 8:2,2,2,
A capark has 34 rows and each row can acommodate 40 cars. If there are 976 cars parked, how many cars can still be parked?
Answer:
384 cars
Step-by-step explanation:
To find the total number of spaces in the carpark, we must multiply the number of rows by how many cars they can accommodate:
34 ⋅ 40 = 1360
As you can see, we have 1360 total spaces. Since there are 976 cars parked, and we want to find out how many spaces are left, we have to subtract the amount of cars parked from the total spaces.
1360 - 976 = 384
Therefore, our answer is 384, specifically, 384 cars.
Answer:
384 cars.
Step-by-step explanation:
40 * 34 - 976
= 1360 - 976
= 384.
Write the equation of the line that passes through the points (- 5, 1) and (2, 0) . Put your answer in fully reduced slope intercept form, unless it is a vertical or horizontal line
Pls help me with this one:(
Answer:
y=-1/7x + 12/7
Step-by-step explanation:
Start by finding the slope
m=(1-0)/(-5-2)
m=-1/7
next plug the slope and the point (-5,1) into point slope formula
y-y1=m(x-x1)
y1=1
x1= -5
m=-1/7
y- 1 = -1/7(x - -5)
y-1=-1/7(x+5)
Distribute -1/7 first
y- 1=-1/7x + 5/7
Add 1 on both sides, but since its a fraction add 7/7
y=-1/7x + (5/7+7/7)
y=-1/7x+12/7
Answer:
Step-by-step explanation:
(-5,1) (2,0)
m=(y-y)/(x-x)
m = (0-1)/2- -5)
m = -1/7
(2,0)
y-0= -1/7 (x-2)
y = -1/7x + 2/7
Solve the system of equations.
6x−y=−14
2x−3y=6
whats the answer please C:
Answer:
Step-by-step explanation:
Determine whether each relation is a function. Give the domain and range for each relation.
{(3, 4), (3, 5), (4, 4), (4, 5)}
Answer:
Not a function
Domain: {3,4}
Range: {4,5}
Step-by-step explanation:
A function is a relation where each input has its own output. In other words if the x value has multiple corresponding y values then the relation is not a function
For the relation given {(3, 4), (3, 5), (4, 4), (4, 5)} the x value 3 and 4 have more than one corresponding y value therefore the relation shown is not a function
Now let's find the domain and range.
Domain is the set of x values in a relation.
The x values of the given relation are 3 and 4 so the domain is {3,4}
The range is the set of y values in a relation
The y value of the given relation include 4 and 5
So the range would be {4,5}
Notes:
The values of x and y should be written from least to greatest when writing them out as domain and range.
They should be written inside of brackets
Do not repeat numbers when writing the domain and range
Help please ….. help
Answer:
Step-by-step explanation:
a) categorical
b) add all of the numbers and divide by how many numbers there were.
c) outliers means any that were far away from the rest of the data
d) not entirely, you can make an estimate based on it, but nat an exact answer.
Identify the slope and y intercept of the line with equation 2y = 5x + 4
Answer:
Slope is 5/2
y-intercept is 2
Step-by-step explanation:
Turn the equation into slope intercept form [ y = mx + b ].
2y = 5x + 4
~Divide everything by 2
y = 5/2x + 2
Remember that in slope intercept form, m = slope and b = y-intercept.
Best of Luck!
Answer:
slope: 2.5
y-intercept: 2
Step-by-step explanation:
First isolate the y variable which changes the equation to y=2.5x+2
The equation of a line is mx + b where m is the slope and b and the
y-intercept. Leading us to conclude that 2.5 is the slope and 2 is the y-intercept.
Select the statement that best justifies the conclusion based on the given information.
If a(b + c) = d, then ab + ac = d.
associative
commutative
distributive
closure
Answer:
distributive
Step-by-step explanation:
a(b + c)=ab + ac
it's distributive one
Charity is planting trees along her driveway, and she has 6 pine trees and 6 willows to plant in one row. What is the probability that she randomly plants the trees so that all 6 pine trees are next to each other and all 6 willows are next to each other
Answer:
0.0022 = 0.22% probability that she randomly plants the trees so that all 6 pine trees are next to each other and all 6 willows are next to each other.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question, the elements are arranged, so we have to use the arrangements formula.
Arrangements formula:
The number of possible arrangements of n elements is:
[tex]A_{n} = n![/tex]
Desired outcomes:
Pine trees(6!) then the willows(6!) or
Willows(6!) then the pine trees(6!). So
[tex]D = 2*6!*6! = 1036800 [/tex]
Total outcomes:
12 trees, so:
[tex]T = 12! = 479001600 [/tex]
What is the probability that she randomly plants the trees so that all 6 pine trees are next to each other and all 6 willows are next to each other?
[tex]p = \frac{D}{T} = \frac{1036800 }{479001600 } = 0.0022[/tex]
0.0022 = 0.22% probability that she randomly plants the trees so that all 6 pine trees are next to each other and all 6 willows are next to each other.
