Answers
Answer:
[tex]\Large \boxed{\sf \bf \ \ \dfrac{x^2-x-6}{x^2-3x+2} \ \ }[/tex]
Step-by-step explanation:
Hello, first of all, we will check if we can factorise the polynomials.
[tex]\boxed{x^2+6x+8}\\\\\text{The sum of the zeroes is -6=(-4)+(-2) and the product 8=(-4)*(-2), so}\\\\x^2+6x+8=x^2+2x+4x+8=x(x+2)+4(x+2)=(x+2)(x+4)[/tex]
[tex]\boxed{x^2+3x-10}\\\\\text{The sum of the zeroes is -3=(-5)+(+2) and the product -10=(-5)*(+2), so}\\\\x^2+3x-10=x^2+5x-2x-10=x(x+5)-2(x+5)=(x+5)(x-2)[/tex]
[tex]\boxed{x^2+2x-15}\\\\\text{The sum of the zeroes is -2=(-5)+(+3) and the product -15=(-5)*(+3), so}\\\\x^2+2x-15=x^2-3x+5x-15=x(x-3)+5(x-3)=(x+5)(x-3)[/tex]
[tex]\boxed{x^2+3x-4}\\\\\text{The sum of the zeroes is -3=(-4)+(+1) and the product -4=(-4)*(+1), so}\\\\x^2+3x-4=x^2-x+4x-4=x(x-1)+4(x-1)=(x+4)(x-1)[/tex]
Now, let's compute the product.
[tex]\dfrac{x^2+6x+8}{x^2+3x-10}\cdot \dfrac{x^2+2x-15}{x^2+3x-4}\\\\\\=\dfrac{(x+2)(x+4)}{(x+5)(x-2)}\cdot \dfrac{(x+5)(x-3)}{(x+4)(x-1)}\\\\\\\text{We can simplify}\\\\=\dfrac{(x+2)}{(x-2)}\cdot \dfrac{(x-3)}{(x-1)}\\\\\\=\large \boxed{\dfrac{x^2-x-6}{x^2-3x+2}}[/tex]
So the correct answer is the first one.
Thank you.
Related Questions
Find the limit, if it exists. (If an answer does not exist, enter DNE.) lim (x, y) → (0, 0) x4 − 34y2 x2 + 17y2
Answers
Answer:
DNEStep-by-step explanation:
Given the limit of the function [tex]\lim_{(x,y) \to (0,0)} \frac{x^4-34y^2}{x^2+17y^2}[/tex], to find the limit, the following steps must be taken.
Step 1: Substitute the limit at x = 0 and y = 0 into the function
[tex]= \lim_{(x,y) \to (0,0)} \frac{x^4-34y^2}{x^2+17y^2}\\= \frac{0^4-34(0)^2}{0^2+17(0)^2}\\= \frac{0}{0} (indeterminate)[/tex]
Step 2: Substitute y = mx int o the function and simplify
[tex]= \lim_{(x,mx) \to (0,0)} \frac{x^4-34(mx)^2}{x^2+17(mx)^2}\\\\= \lim_{(x,mx) \to (0,0)} \frac{x^4-34m^2x^2}{x^2+17m^2x^2}\\\\\\= \lim_{(x,mx) \to (0,0)} \frac{x^2(x^2-34m^2)}{x^2(1+17m^2)}\\\\\\= \lim_{(x,mx) \to (0,0)} \frac{x^2-34m^2}{1+17m^2}\\[/tex]
[tex]= \frac{0^2-34m^2}{1+17m^2}\\\\= \frac{34m^2}{1+17m^2}\\\\[/tex]
Since there are still variable 'm' in the resulting function, this shows that the limit of the function does not exist, Hence, the function DNE
How many petals are on the graph? Find the trigonometric form of a given function.
Answers
Answer:
Attachment 1 : Option A,
Attachment 2 : Option C
Step-by-step explanation:
( 1 ) Here we know that " n " is 6. Now remember if n is odd, the number of petals on the graph will be n. However if n is even, the number of petals on the graph will be 2n.
6 is even, and hence the number of petals will be 2(6) = 12 petals. Solution : 12 petals
( 2 ) To solve such problems we tend to use the equation [tex]z = x + y * i = r(cos\theta +isin\theta)[/tex] where [tex]r = \sqrt{x^2+y^2}[/tex] etc. Here I find it simpler to see each option, and convert each into it's standard complex form. It might seem hard, but it is easy if you know the value of (cos(5π / 3)) etc...
The answer here will be option c, but let's prove it,
cos(5π / 3) = 1 / 2,
sin(5π / 3) = [tex]-\frac{\sqrt{3}}{2}[/tex]
Plugging those values in for " [tex]8\left(\cos \left(\frac{5\pi }{3}\right)+i\sin \left(\frac{5\pi }{3}\right)\right)[/tex] "
[tex]8\left(-\frac{\sqrt{3}i}{2}+\frac{1}{2}\right)[/tex]
= [tex]8\cdot \frac{1}{2}-8\cdot \frac{\sqrt{3}i}{2}[/tex] = [tex]4-4\sqrt{3}i[/tex]
Hence proved that your solution is option c.
To find the distance AB across a river, a distance BC of 415 m is laid off on one side of the river. It is found that B = 112.2° and C = 18.3°. Find AB.
Answers
Answer:
AB or the distance across the river is about 171.36 meters.
Step-by-step explanation:
Please refer to the diagram below (not to scale). The area between the two blue lines is the river.
To find AB, we can use the Law of Sines. Recall that:
[tex]\displaystyle \frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c}[/tex]
BC (or a) is opposite to ∠A and AB (or c) is opposite to ∠C. Thus, we will substitute in these values.
First, find ∠A. The interior angles of a triangle must total 180°. Thus:
[tex]m\angle A + m\angle B + m\angle C = 180^\circ[/tex]
Substitute:
[tex]\displaystyle m\angle A + (112.2^\circ) +(18.3^\circ) = 180^\circ[/tex]
Solve for ∠A:
[tex]m\angle A = 49.5^\circ[/tex]
Substitute BC for a, AB for c, 49.5° for A and 18.3° for C into the Law of Sines. Thus:
[tex]\displaystyle \frac{\sin 49.5^\circ}{BC} = \frac{\sin 18.3^\circ}{AB}[/tex]
Since BC = 415 m:
[tex]\displaystyle \frac{\sin 49.5^\circ}{415} = \frac{\sin 18.3^\circ}{AB}[/tex]
Solve for AB. Cross-multiply:
[tex]\displaystyle AB \sin 49.5^\circ = 415\sin 18.3^\circ[/tex]
And divide:
[tex]\displaystyle AB = \frac{415\sin 18.3^\circ}{\sin 49.5^\circ}[/tex]
Use a calculator. Hence:
[tex]AB = 171.3648...\approx 171.36\text{ m}[/tex]
AB or the distance across the river is about 171.36 meters.
Use the equation p=6k+12 to find the value of p when k=9.
Answers
Next using the order of operations we can multiply 6 and 9 to get p=54+12.
Now we can simply add to get p=66
the answer is 66
Answer:
66
Step-by-step explanation:
when you plug in 9 for k. you do 6(9) which is 54. then add 12 to 54 and thats ur answer, 66.
will mark brainliest. PROMISE!! A stick has a length of $5$ units. The stick is then broken at two points, chosen at random. What is the probability that all three resulting pieces are longer than $1$ unit?
Answers
Answer:
0.16
Step-by-step explanation:
Length = 5 unitsNumber of broken sticks= 3Equal lengths = 5 units/3See the picture attached for reference.
As you see the best points are the green areas which covers 2 out of 5 zones.
Since it is same for both broken points, the probability of this is:
2/5*2/5 = 4/ 25 = 0.16Answer is 0.16
Simplify . 7+ the square root of 6(3+4)-2+9-3*2^2 The solution is
Answers
Answer:
7+sqrt(37)
Step-by-step explanation:
7+sqrt(6*(3+4)-2+9-3*2^2)=7+sqrt(6*7+7-3*4)=7+sqrt(42+7-12)=7+sqrt(37)
What is the missing digit?
820,107
– 65□,084
167,023
Answers
We can get this answer by subtracting the answer 167,023 from 820,107, we get 653,084.
you start at (5,3) you move down 4 units and up 6 units. where do you end?
Answers
You end up at the point (5, 5).
Identify the recursive formula for the sequence given by the explicit formula f(n) = 20 – 4(n − 1).
Answers
Answer:
[tex]\huge\boxed{f(n)=\left\{\begin{array}{ccc}f(1)=20\\f(n)=f(n-1)-4\end{array}\right}[/tex]
Step-by-step explanation:
[tex]f(n)=20-4(n-1)=20+(n-1)(-4)\\\\\text{It's an explicit formula of an arithmetic sequence:}\\\\f(n)=a_1+(n-1)(d)\\\\a_1-\text{first term}\\d-\text{common difference}\\\\\text{Conclusion:}\\\text{Next term}=\text{previous one}\ -4\\\\\text{The recursive formula:}\\\\\huge\boxed{f(n)=\left\{\begin{array}{ccc}f(1)=20\\f(n)=f(n-1)-4\end{array}\right}[/tex]
Answer:
Step-by-step explanation:
someone answered already
A charity organization is holding a food drive with a goal to collect at least 1,000 cans of
food by the end of the month. It currently has 565 cans from donations and is having an
event where 87 guests will attend and bring cans. Which solution set represents the
number of cans each guest must bring to meet the goal?
+
OA
++
0
1
2
3
4
5
6
7
8
9
10
---
+
OB. 4
+
0
1
2
3
4
5
6
7
8
9
10
OC.
+
1
2
3
5
6
7
8
9
10
OD. +
+
++
-
6
+
7.
+
0
1
2
3
4
5
8
9
10
Answers
Answer:
Each guest must bring 5 cans.
Step-by-step explanation:
1000-565=435
435/87=5
In empty set, n (A) = ………
Answers
Answer:
answer is
In empty set, n(A) = { }.
A rectangular parcel of land has an area of 6,000 ft2. A diagonal between opposite corners is measured to be 10 ft longer than one side of the parcel. What are the dimensions of the land, correct to the nearest foot? ft (smaller value) by ft (larger value)
Answers
Answer:
50ft by 120ft
Step-by-step explanation:
Area of a rectangle = L × W
6000ft² = L × W
L = 6000/W
When a diagonal line divides a rectangle into 2 right angled triangles, the diagonal line = Hypotenuse of either of the triangle and it is the longest side.
The formula for a right angle triangle =
a² + b² = c²( c = hypotenuse)
We are told in the question that:
A diagonal between opposite corners is measured to be 10 ft longer than one side of the parcel
Let us assume the side that the hypotenuse is longer than = Width
Hence, the Diagonal = (W + 10)²
Therefore
L² + W² = (W + 10)²
Since L = 6000/W
W² + (6000/W)² = (W + 10)²
W² + (6000/W)² = (W + 10) (W + 10)
W² + (6000/W)² = W² + 10W + 10W + 100
W² + (6000/W)² = W² + 20W + 100
W² - W² + (6000/W)² = 20W+ 100
6000²/W² = 20W + 100
6000² = W²( 20W + 100)
6000² = 20W³ + 100W²
20W³ + 100W² - 6000² = 0
20W³ + 100W² - 36000000 = 0
20(W³ + 5W² - 1800000) = 0
Factorising the quadratic equation,
20(W − 120)(W² + 125W + 15000) = 0
W - 120 = 0
W = 120
Therefore,
W(Width) = 120feet
Since the Width = 120 feet
We can find the length
6000ft² = L × W
L = 6000/W
L = 6000/120
L = 50 feet
The dimensions of the land, correct to the nearest foot is 50ft by 120ft
A hot air ballon is hovering 94 meters above the ground and begins to assend at a rate of 8 meters per second Let y be the height of the balloon in meters seconds after it begins to assend. Write an equation in slope-intercept form that models the height of the balloon. And how high is the ballon after 25 seconds?
Answers
Hi
let's call X amount of second going and Y the height reach by the ballon.
so Y=8X+94
f(x) = 8X+94
If you want to know how high will the ballon be in 25 seconds, remplace X by 25 and do the math. Have fun .
What is the mean of this data set?
A. 84
B. 85
C. 83
D. 88
Answers
Answer:
85
Step-by-step explanation:
Add to get total. divide by 4.
Answer:
B. 85
Step-by-step explanation:
Sorry for this very late response. But if anyone wasn't sure if 85 is the correct answer, it is. I can confirm this because I just took the test. I hope I could help! (:
Question:
If V7 - y = 6, then y =
A. -29
B. -5
C. 1
D. 29
[tex] \sqrt{7 - y = 6} [/tex]
Answers
Answer:
-29
Step-by-step explanation:
[tex] {\sqrt{7 - y }}^{2} = {6}^{2} [/tex]
[tex]7 - y = {6}^{2} [/tex]
y = 7-36
y = -29
how many pieces each 31/6 metres long can be cut fram a cloth 155/2 metres long ?
Answers
Answer:
?
Step-by-step explanation
my 4th person to ask a question
Find the union and interesection of each of the following A={3,6,9,12}, B ={6,8,9}
Answers
Answer:
Hello,
The answer would be,
A union B = {3,6,9,12}
and A intersection B= {6,9}
Answer:
[tex]\huge\boxed{ A\ union \ B = \{3,6,8,9,12\}}[/tex]
[tex]\huge\boxed{A\ intersection \ B = \{6,9\}}[/tex]
Step-by-step explanation:
A = {3,6,9,12}
B = {6,8,9}
A∪B = {3,6,9,12} ∪ { 6,8,9} [Union means all of the elements should be included in the set of A∪B]
=> A∪B = {3,6,8,9,12}
Now,
A∩B = {3,6,9,12} ∩ {6,8,9} [Intersection means common elements of the set]
=> A∩B = {6,9}
if 75% think the action is morally wrong, and we say there are 249 million adults in the country, how many believe that the action is morally wrong?
Answers
Answer: 186.75 million which is the same as saying 186,750,000
Work Shown:
75% = 75/100 = 0.75
75% of 249 million = 0.75*249 million = 186.75 million
186.75 million = 186.75*10^6 = 186,750,000
Answer:
186,750,000
Step-by-step explanation:
Take 75% of 249 million
.75 * 249,000,000
186,750,000
HELP ME!
A standard I.Q. test produces normally distributed results with a mean of 104 and a standard deviation of 16 for 52,000 students in grade 12 in the state. Approximately how many of these students would have I.Q.s above 140?
Answers
Answer: approx 1196 students.
Step-by-step explanation:
As known for normal distribution 95.4% of all results are situating at +-2*s distance from the mean. (s is the standard deviation)
2s=16*2=32 . The mean +2s= 104+32=136 = approx 140.
95.4% from 52000 = 49608 students. The residual amont ( which is out of the border mean+-2s)= 52000-49608=2392
Because of the normal distribution simmetry the number of the students which has IQ 140 and more is twice less than 2392.
N=2392:2=1196
Which expression is equivalent to 2(5)^4
Answers
Answer:
2·5·5·5·5
Step-by-step explanation:
2(5)^4 is equivalent to 2·5·5·5·5; 2 is used as a multiplicand just once, but 5 is used four times.
Answer the question that follow about the given sequence. “Does not exist” and “none” are valid answers. Blank answers will be counted incorrect. -33, -27, -21, -15, … a. Arithmetic/Geometric/Neither? b. State the Common Ratio or Common Difference. c. Find the explicit formula for the nth term d. Find the recursive formula for the nth term e. Value of the 10th term f. ∑ notation for the Infinite Series. g. Sum of the Infinite Series.
Answers
Answer:
it's an arithmetic sequence with common difference 6An=6n-39, A10=21Sn=3n'2-(39/2)nCompute the flux of the vector field LaTeX: \vec{F}=F → =< y + z , x + z , x + y > though the unit cubed centered at origin.
Answers
Assuming the cube is closed, you can use the divergence theorem:
[tex]\displaystyle\iint_S\vec F\cdot\mathrm dS=\iiint_T\mathrm{div}\vec F\,\mathrm dV[/tex]
where [tex]S[/tex] is the surface of the cube and [tex]T[/tex] is the region bounded by [tex]S[/tex].
We have
[tex]\mathrm{div}\vec F=\dfrac{\partial(y+z)}{\partial x}+\dfrac{\partial(x+z)}{\partial y}+\dfrac{\partial(x+y)}{\partial z}=0[/tex]
so the flux is 0.
The Rogers family drove 220 miles in 5.5 hours. How many miles would they drive at this same rate in 4 hours? A. 88 mi B. 147 mi C. 160 mi D. 179 mi Please show ALL work! <3
Answers
Answer:
160 miles
Step-by-step explanation:
We can use a ratio to solve
220 miles x miles
--------------- = ----------------------
5.5 hours 4 hours
Using cross products
220 *4 = 5.5x
880 = 5.5x
Divide each side by 5.5
880/5.5 = x
160 miles
Answer:
[tex]\large \boxed{\mathrm{C. \ 160 \ miles}}[/tex]
Step-by-step explanation:
We can solve this problem by ratios.
Let x be the missing value.
[tex]\displaystyle \frac{220}{5.5} =\frac{x}{4}[/tex]
Cross multiply.
[tex]5.5 \times x = 220 \times 4[/tex]
[tex]5.5x=880[/tex]
Divide both sides by 5.5.
[tex]\displaystyle \frac{5.5x}{5.5} =\frac{880}{5.5}[/tex]
[tex]x=160[/tex]
The quotient of 3 and the cube
of y+2
Answers
Answer:
[tex]\dfrac{3}{(y+2)^3}[/tex]
Step-by-step explanation:
Maybe you want this written using math symbols. It will be ...
[tex]\boxed{\dfrac{3}{(y+2)^3}}[/tex]
¿Cuál es la probabilidad de encontrar una persona que gane 6000 si en la empresa en donde trabaja el sueldo medio es de 3500 con una desviación de 1500?
Answers
Answer:
Question in English please I don't understand your language.
The question is attached, please help.
Answers
Answer:draw a triangle
Step-by-step explanation:
PLS HELP :Find all the missing elements:
Answers
Answer:
[tex]\large \boxed{\mathrm{34.2}}[/tex]
Step-by-step explanation:
[tex]\sf B= arcsin (\frac{b \times sin(A)}{a} )[/tex]
[tex]\sf B= arcsin (\frac{7 \times sin(40\°)}{8} )[/tex]
[tex]\sf B = 0.59733 \ rad = 34.225\°[/tex]
HELP PLEASEEEE!!!! ASAP
Answers
Answer:
6.22 sec
Step-by-step explanation:
h(t) = 105t-16t^2
For values of t for which height will be 34 feet can be obtained by substituting 34 in place of h(t) and solving for t
34=105t-16t^2, using quadratic formula we have t=1/32*(105±sqrt(8849)) which translates to - 0.34sec and 6.22sec but as time can't be negative, time is 6.22sec
Find the total area the regular pyramid. T.A=
Answers
Answer:
18√91 +54√3
Step-by-step explanation:
Name the point at the top of the pyramid "A", the point at the left front corner "B", and the one in the center of the hexagonal base "C". Then right triangle ABC is shown. The "base" BC of that triangle is the same measure as the front edge (6), because the diameter of a regular hexagon is equal to twice the side length.
Using the Pythagorean theorem, we can find the face edge length to be ...
AB^2 = BC^2 +AC^2
AB^2 = 6^2 +8^2 = 100
AB = √100 = 10
If we call the midpoint of the front edge "D", then we need to find the length of AD in order to determine the face area. Again, we can use the Pythagorean theorem.
AB^2 = BD^2 +AD^2
AD^2 = AB^2 -BD^2 = 10^2 -3^2 = 91
AD = √91
The area of one of the 6 lateral faces is ...
A = (1/2)bh = (1/2)(6)√91 = 3√91
The area of one of the 6 equilateral triangles that make up the base is ...
A = (√3)/4·s^2 = (√3)/4(6^2) = 9√3
Then the total area of the pyramid is ...
total area = 6 × (face area + partial base area)
= 6(3√91 +9√3)
total area = 18√91 +54√3
They are 10 ice cream flavors, 5 different toppings and it could be either in cup or in cone, how many 2-scoop combinations are possible?
Answers
Using the fundamental counting principle, it is found that: 50 2-scoop combinations are possible.
----------------------------------
The flavors and the toppings are independent, which means that the fundamental counting principle is used to solve this question, which states that if there are p ways to do a thing, and q ways to do another thing, and these two things are independent, there are p*q ways to do both things.
----------------------------------
In this question:
10 ice cream flavors.5 toppings.So,
[tex]10 \times 5 = 50[/tex]
50 2-scoop combinations are possible.
A similar question is found at https://brainly.com/question/24067651