Answers
Answer:
[tex]\left(x-5\right)^6\left(x+3\right)^3\left(11x+1\right)[/tex]
and
[tex]x=5,\:x=-3,\:x=-\frac{1}{11}[/tex]
Step-by-step explanation:
This problem is slightly more difficult.
We start off with the product rule. If y = v*u then in the case:
[tex]u=\left(x+3\right)^4,\:v=\left(x-5\right)^7[/tex]
[tex]=> \frac{d}{dx}\left(\left(x+3\right)^4\right)\left(x-5\right)^7+\frac{d}{dx}\left(\left(x-5\right)^7\right)\left(x+3\right)^4[/tex]
Now we apply the chain rule:
[tex]\frac{d}{dx}\left(\left(x+3\right)^4\right) = 4\left(x+3\right)^3\frac{d}{dx}\left(x+3\right)\\= 4\left(x+3\right)^3\cdot \:1\\= 4\left(x+3\right)^3[/tex]
We can apply the chain rule again for this second bit:
[tex]\frac{d}{dx}\left(\left(x-5\right)^7\right) = 7\left(x-5\right)^6\frac{d}{dx}\left(x-5\right)\\= 7\left(x-5\right)^6\cdot \:1\\= 7\left(x-5\right)^6[/tex]
So now we are left with this long equation:
[tex]4\left(x+3\right)^3\left(x-5\right)^7+7\left(x-5\right)^6\left(x+3\right)^4[/tex]
Which we can actually factor:
[tex]4\left(x+3\right)^3\left(x-5\right)^7+7\left(x-5\right)^6\left(x+3\right)^4 = \left(x-5\right)^6\left(x+3\right)^3\left(4\left(x-5\right)+7\left(x+3\right)\right) \\= \left(x-5\right)^6\left(x+3\right)^3\left(11x+1\right)[/tex]
...And for the second bit, if we equate to 0, we can apply the Zero Product Property to get all the x values:
[tex]\left(x-5\right)^6\left(x+3\right)^3\left(11x+1\right)=0,\\x=5,\:x=-3,\:x=-\frac{1}{11}[/tex]
Related Questions
CAN SOMEONE HELP MEEE
Answers
Answer:
Step-by-step explanation:
swimming pool is circular hence we have
circumference= 2*pi*d/2 ( r=d/2)
36 feet = 2*(3.14)*d/2
36=3.14d
d=36/3.14
d=11.46 feet
2 4/3 ÷ 1 8/7 Find each quotient. Write the answer as a fraction in simplest form.
Answers
Answer:
It equals 1 5/9
Step-by-step explanation:
Hope this helps :)
8/15-3/15 what’s the answer
Answers
Answer:
1/3
Step-by-step explanation:
8/15-3/15=5/15=1/3
whats the radius for 3(x-1)^2+3(y+3)=243
Answers
3(x-1)2+3y+9=243
3(x2-1)+3y+9=243
3x2-3+3y+9=243
32+3y-3+9=243
32+3y=243+3-9
3y(y+1)=237
PLEASE HELP
it hasn’t been a good day and i don’t feel like doing this
Answers
Answer:
Both are quadrant
Step-by-step explanation:
A 20-foot ladder leans up against the side of a building so that the foot of the ladder is 10 feet from the base of the building. How far up the
building does the ladder reach? Round your answer to the nearest tenth.
18.1
17.3
15.9
16.4
Answers
Answer:
17.3
Step-by-step explanation:
To solve this equation, you need to use the pythagorean theorem which is:
[tex]a^{2} +b^{2}= c^{2}[/tex]
a= length
b= height
c= hypotenuse
First, substitute in your values for the equation:
[tex]10^2+b^{2} =20^{2}[/tex]
Then, use the squares in the equation:
[tex]100+b^{2} =400[/tex]
Then, subtract 100 from both sides to isolate b:
[tex]b^{2} =300[/tex]
Finally, square root both sides to get your answer:
[tex]b=17.3205080757[/tex]
Then round to the nearest tenth which gives you 17.3.
Answer: 17.3 ft
Step-by-step explanation:
Which recursive formula represents the geometric sequence?
25, 20, 16,
Answers
Answer:
Step-by-step explanation:
[tex]a_n=\frac{4}{5}(a_{n-1})[/tex]
11. Mr. Dawley bought 2 Hydroflask water bottles at $2.49 each
and 3 Rubik's cubes for $1.75 per cube. How much did he
pay
for
the water bottles and the cubes?
Answers
Answer:
$10.23
Step-by-step explanation:
2 hydroflasks for 2.49 dollars each is equal to $4.98 and 3 Rubik's cubes for 1.75 dollars each is equal to $5.25 and when you add both of them, you get $10.23
Then multiply $1.75 times 3=?
Then add the answers from #1 and #2 together and that should be your answer.
Hope this helps
What is the value of x?
Round your answer to the nearest tenth.
Answers
Answer:
2.4
Step-by-step explanation:
Because of AA Similarity, we have BDC is similar to FHG. We know that FH is 2/5 times BD so FG is 2/5 times BC which is 6*2/5 = 12/5 = 2.4
The Thornton family is going hiking tomorrow. To get ready, Mrs. Thornton is making trail mix. She mixes 7 cups of nuts, 2 cups of chocolate chips, and 3 cups of raisins. Mrs. Thornton splits the trail mix evenly into 6 bags, one for each family member.
Answers
Answer:
7+2+3=12 pounds in totak
12÷6=2 pounds in each bag
6. On Saturday, you bowl at Mar Vista Bowl, where renting shoes
costs $2 and each game bowled is $3.50. On Sunday, you bowl at
Pinz where the shoe rental is $5 and each game bowled is $3.25. If
you spent the same amount each day, how many games, g, were
bowled? Define variables.
Answers
Answer:
3.50 +3.25 = 6.75
Sory If wrong :)
I hope This Help'S
A rectangular prism. The prism has a length of 4 units, width of 2 units, and height of 1 unit.
The two-dimensional net of a rectangular prism is shown at the left. What is the prism’s surface area?
Answers
Answer:
28 is the total surface area!!
Step-by-step explanation:
A = 2(wl + hl + hw)
A building has 23 floors of offices above
ground and 5 floors below ground,
Nathan parks on the 2nd floor below
ground and has an office on the 18th
floor. The ground floor is floor zero,
Which absolute value expression
represents how many floors he must go
up to get from his car to his office?
a. -51 +1 231
b.|-2| + |18|
c. |-5| + |18|
d.|-2| + 231
Answers
Answer:
The correct answer would be letter B.
Answer:
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb
Step-by-step explanation:
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb
Brian is standing on a platform that is 4 feet above the surface of a pool. He jumps into the pool and reaches a depth of 7 feet below the surface.
Write an inequality that compares Brian's distance above and below the surface of the pool.
Answers
Answer:
7×4=28
Step-by-step explanation:
hope this helps you out
plz answer only if you know you are correct
Answers
Answer:
y=50x
Step-by-step explanation:
find the slope of the line. it goes through the origin so there is no y-intercept.
what grade is this for?
hope this helps
WHAT I CAN DO
Read, analyze and solve.
1. Cesar invited 300 kids in the party. Only 15% of the kids did notshow up. How
many kids came to the party?
2. Rosa got 20% of an 80 item test incorrectly. How many items did she get
correctly?
3. There were 50 pupils in Grade Ill. If 28% of the pupils were absent, how many
pupils were present?
4. Out of 50 pupils, only 48 pupils joined the educational fieldtrip. What percent
joined the trip?
5. Among the 50 pupils in a Grade 6 class, 6% are left-handed. How many are left-
handed?
Answers
1.
300 x 0.15 = 45
300 - 45 = 255
255 kids came to the party
//
2.
80 x 0.20 = 16
80 - 16 = 64
She got 64 items correctly
//
3.
50 x 0.28 = 14
50 - 14 = 36
36 pupils were present
//
4.
48 / 50 = 0.96
0.96 x 100 = 96.0%
96% joined the trip
//
5.
50 x 0.06 = 3
3 pupils are left handed
PLEASE HELP!! THIS IS ON HEGARTY MATHS AND I DON'T UNDERSTAND IT!!Mean 2
Answers
Answer:
The mean temperature is
Mean = total temperatures / no of days
Mean = - 5 + 2 + 4 - 3 + 7 + 9 - 3 + 0 + 6 + 2/ 10
Mean = 19 / 10 = 1.9
Step-by-step explanation:
Answer:
0.1
Step-by-step explanation:
First, add all the numbers:
-5 -4 -2 -2 -1 0 1 2 3 9
You get 1
Then you have to divide the answer by how many numbers there are:
Numbers = 10
1÷10 = 0.1
Hope this helps
4. Which of the following graphs represents y = x-2?
HURRRY PLSSSS. I NEED IT ASAP
Answers
Answer:
B
Step-by-step explanation:
when it says -2 that means you go straight down
Answer:
B
Step-by-step explanation:
-2 in the equation is the y intercept and the slope is positive so graph B is the only possible answer
Manny needs to solve the equation x2 – 8x – 24 = 0 by completing the square. Which pair of steps is the most efficient way to begin?
Answers
Answer:
B
Step-by-step explanation:
So for some reason the person didn't put the equations... I had the same question so here they are.
A.x^2 – 8x = 24
x2 – 8x + 4 = 24 + 4
B.x^2 – 8x = 24
x2 – 8x + 16 = 24 + 16
C.x^2 – 8x = 24
x2 – 8x + 64 = 24 + 64
D.x^2 – 8x = 24
x2 – 8x + 144 = 24 + 144
Good luck!
The quadratic equation can be solved by completing square method. The steps to solve the given equation are explained in detail.
What is a quadratic equation?The general form of a quadratic equation is given as ax^2 + bx + c = 0.
Here, a ≠ 0 and b and c are integers.
The degree of a quadratic equation is 2.
The given equation is,
x^2 - 8x -24 = 0
To solve this equation by completing square method, it has to be transformed into the form of (a + b)^2.
The steps for this method are given as follows,
(i) Find the coefficient of x^2. The square root of the this coefficient is the value of a.
(ii) Find the term containing non-square part. In the given case it is -8x.
(iii) Compare the coefficient of this term with 2ab. it gives,
2ab = -8
=> 2 × 1 × b = -8
=> b = -4
(iv) Write the equation in the form of a^2 + 2ab + b^2 leaving the remaining term as it is. For the given equation it can be written as,
x^2 - 8x + 4^2 - 40 = 0
=> x^2 - 8x + 4^2 = 40
(v) Now, write the equation in terms of (a +b)^2 and get the solution. In this case it is written as,
(x - 4)^2 = 40
=> x - 4 = ±√40
=> x = 4 ±√40
To know more about quadratic equation click on,
https://brainly.com/question/17177510
#SPJ5
Write 3 60/79 as an improper fraction.
Answers
3 60/79
•Finding the top part of the fraction
#Firstt times 79 with 3
79× 3 = 237
#Then, u plus it with 60
237 + 60 = 297
•Bottom part
#The bottom part of the fraction stay the same so,
297/79
Answer : 297/79#Hope my answer is correct cuz i dont use calc to do this
the two lines below are parallel if the slope of the red line is 5 what is the slope of the green line
Answers
Answer:
5
Step-by-step explanation:
Since the two lines are parallel, they must have the same slope. This means that the slope of green line must be 5 just like the red line. You can also use the slope formula (rise/run) or change in y divided by change in x.
Find (g o f)(-1). *
f(x) = x2 + 2x – 3
g(x) = x - 5
O A. -11
OB.-4
Oc.o
O D.-9
Answers
Answer:
D -9
Step-by-step explanation:
(g o f)(-1) = g(f(-1))
f(-1) = [tex]f(-1) = (-1)^{2} + 2(-1) - 3\\= 1 - 2 - 3\\= -4[/tex]
g(-4) = -4 - 5 = -9
So, (g o f)(-1) = -9
Please help
-3x= y
-9x - 5y = - 48
Answers
Answer:
i can teach you how to solve it on calculator if u want
8.6 x10^-9 in standard form
Answers
-9 in power means that the value is in fractional and the 10 base is multipied 9 times and put it on denominator.
8.6 = 86 x 10^-1
Let's multiply :
86 x 10^-1 x 10^-9
= 86 x 10^-10
= 86/10000000000
=0,0000000086
Note : if you don't know about how 10^-1 x 10^-9 returns 10^-10, it's because of exponential rules. If the base are same wuth each other, then just do the addition operation in the exponent like this :
10^(-1+(-9))
= 10^(-1-9)
=10^-10
Hope it helps :)
Write an equation of a line in the form y=mx+b that together with the equation x+3y=9 forms a linear system that has no solutions.
Answers
Answer:
I love algebra anyways
The ans is in the picture with the steps how i got it
(hope this helps can i plz have brainlist :D hehe)
Step-by-step explanation:
what is the solution of 9x+4<7-3n IF X is an element of whole number
Answers
Answer: if you want me to solve for n or x here
Step-by-step explanation: hope this help:)
Help please! I don't really understand :/
Answers
Josie 10.50 per hour many hours would she have worked once she got 175
Answers
:D please help mee☺️
Answers
Answer:
115
Step-by-step explanation:
The angle of a straight line is 180°. so all you have to do is subtract 65 from 180 and get 115.
Answer:
<7=115 degrees
Step-by-step explanation:
Since <8 = 65 degrees, and <7 and <8 are straight angles, then 180-65 = 115
66.6% recurring is what as a fraction
Answers
Answer:
wfe
Step-by-step explanation:
333/500
Answer:
2/3
Step-by-step explanation:
2/3=0.6666666667 or 0.6 recuring