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[tex] \huge \boxed{\mathfrak{Question} \downarrow}[/tex]
[tex] \huge \tt\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }[/tex]
[tex] \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}[/tex]
[tex]\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) } \\ [/tex]
To start solving this question, note that ⇨ for any 2 differentiable functions, the derivative of the quotient of the 2 functions will be the denominator multiplied by the derivative of the numerator minus the numerator again multiplied by the derivative of the denominator whole divided by the denominator². By doing all these steps, we'll get it as..
[tex]\frac{\left(x^{1}-5\right)\frac{\mathrm{d}}{\mathrm{d}x}(3x^{2}-2)-\left(3x^{2}-2\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{1}-5)}{\left(x^{1}-5\right)^{2}} \\ [/tex]
Remember that the derivative of the polynomial will be the sum of the derivatives of its terms. We know that, the derivative of a constant term is 0 & the derivative of [tex]ax^{n}[/tex] is [tex]nax^{n-1}[/tex]. So..
[tex]\frac{\left(x^{1}-5\right)\times 2\times 3x^{2-1}-\left(3x^{2}-2\right)x^{1-1}}{\left(x^{1}-5\right)^{2}} \\ [/tex]
Now, simplify it..
[tex]\frac{\left(x^{1}-5\right)\times 2\times 3x^{2-1}-\left(3x^{2}-2\right)x^{1-1}}{\left(x^{1}-5\right)^{2}} \\ = \frac{\left(x^{1}-5\right)\times 6x^{1}-\left(3x^{2}-2\right)x^{0}}{\left(x^{1}-5\right)^{2}} \\ = \frac{x^{1}\times 6x^{1}-5\times 6x^{1}-\left(3x^{2}x^{0}-2x^{0}\right)}{\left(x^{1}-5\right)^{2}} \\ = \frac{6x^{1+1}-5\times 6x^{1}-\left(3x^{2}-2x^{0}\right)}{\left(x^{1}-5\right)^{2}} \\ = \frac{6x^{2}-30x^{1}-\left(3x^{2}-2x^{0}\right)}{\left(x^{1}-5\right)^{2}} \\ = \frac{6x^{2}-30x^{1}-3x^{2}-\left(-2x^{0}\right)}{\left(x^{1}-5\right)^{2}} \\ = \frac{\left(6-3\right)x^{2}-30x^{1}-\left(-2x^{0}\right)}{\left(x^{1}-5\right)^{2}} \\ = \frac{3x^{2}-30x^{1}-\left(-2x^{0}\right)}{\left(x^{1}-5\right)^{2}} \\ = \frac{3x^{2}-30x-\left(-2\right)}{\left(x-5\right)^{2}} \\ = \large \boxed{\boxed{ \bf \frac{3x^{2}-30x + 2}{\left(x-5\right)^{2}} }}[/tex]
You can further simplify the answer to [tex]\underline{\underline{\frac{146}{\left(x-5\right)^{3}}}}\\[/tex]__________________
Hope it'll help you!
ℓu¢αzz ッ
GIVING BRAINLIST!!! SHORT QUESTION PLS ANSWER
Answer:
Terms:4x, -2x
Coefficients:4, 2
Constant:3
(−m
2
+6)+(−4m
2
+7m+2)
Following are calculation to the given eqution:
Given:
[tex]\bold{(-m^2+6)+(-4m^2+7m+2)}[/tex]
To find:
Solve the equation.
Solution:
[tex]\to \bold{(-m^2+6)+(-4m^2+7m+2)}\\\\\to \bold{-m^2+6-4m^2+7m+2}\\\\\to \bold{-5m^2+7m+8}\\\\\to \bold{-1(5m^2-7m-8)}\\\\[/tex]
Therefore, the final solution is "[tex]-1(5 m^2-7m-8)[/tex]".
Learn more:
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Answer this question I will try to give brainliest but I don't know how so no promises.
Answer:
d. 4x+12
Step-by-step explanation:
distribute the 4
4*x =4x
4*3=12
therefore its
4x+12
Answer:
D
Step-by-step explanation:
4(x+3)
(4 times x) + (4 times 3)
4x + 12 = D
1. Find the product of 4 X 2 X 3 two different ways.
Answer:
6 x 4
8 x 3
The product: 24
Hope This Helps! •v•
Step-by-step explanation:
Answer:
6 x 4
8 x 3
The product: 24 K12 is how i know thx bye! :D
A school had 180 boys and 240 girls attending
(a) What is the ratio of boys to girls?
(b) What is the ratio of girls to boys?
(c) What is the ratio of students to boys?
(d) What is the ratio of girls to students?
Answer:
a. ratio is 180:240
B. ratio is 240:180
C. ratio is 420:180
d. ratio is 240:420
Hope this helps!!
Solve the equation. ( − 6 ) ( − 2 ) ( − 1 ) =
Answer:
-12
Step-by-step explanation:
Can someone pls help me :(( tysm if u do and i have 7 khan academy’s and there only 4 questions on each on can someone pls help me on them there all due by 12 tn and i dont know who else to ask for help tysm if u do:c
Answer:
-8
Step-by-step explanation:
I’ll substitute x for the blank space:
-2 = x + 6
-2 - 6 = x
x = -8
-8 + 6 = -2 ✅
The volume of this cone is 540π. Work out the height,h, of the cone, radius=9cm
Answer:
h = 20
Step-by-step explanation:
540π = 1/3 . h . π . 9^2
get rid of π
540 = 1/3 . h . 9^2
multiply by 3 to get rid of 1/3
3 . 540 = h . 9^2
1620 = h . 81
divide by 81
1620/81 = h
20 = h
Hope that helps :)
Please I need help the question is angle sum theorem
Answer:
x=80, y=55
Step-by-step explanation:
x is on a line so 180-100=80
x= 80
angles of a triangle are 180 so 180-45-80=55
y=55
-9 ÷ 7.2 as a decimal
Hi, I was absent yesterday on my math class and I missed the whole lesson of yesterday , teacher gave us homework on delta math and I still quite do not understand how to solve it please help!
work out the surface area of this cylinder
8cm diameter
16.8cm height
describe rule for pattern 10, 30, 90, …
Answer:
it go by 20 then 30
Step-by-step explanation:
Answer:
see explanation
Step-by-step explanation:
Each term is 3 times the previous term, that is
30 = 10 × 3 = 30
90 = 30 × 3 = 90
There is a common ratio between consecutive terms meaning the sequence is geometric.
The sum of two consecutive odd numbers is 1408. What are the numbers?
Put the smaller number first comma then the larger number.
Answer:
703,705
Step-by-step explanation:
divide 1408 by 2
add one for one number
subtract one for the other
[(3x-2)(x+6)]-[(x-1)(2x)]=103 steps
Let's solve your equation step-by-step.
(3x−2)(x+6)−(x−1)(2x)=103
Step 1: Simplify both sides of the equation.
x2+18x−12=103
Step 2: Subtract 103 from both sides.
x2+18x−12−103=103−103
x2+18x−115=0
Step 3: Factor left side of equation.
(x−5)(x+23)=0
Step 4: Set factors equal to 0.
x−5=0 or x+23=0
x=5 or x=−23
Answer:
x=5 or x=−23
(8.1 x 10⁻⁴) - (9.5 x 10⁻⁵)
Answer:
[tex]7.15*10^{-4}[/tex]
Step-by-step explanation:
[tex](8.1*10^{-4})-(9.5*10^{-5})=0.00081-0.000095\\\\=0.000715 = 7.15*10^{-4}[/tex]
Work out the area of a rectangle with base,b= 32mm and perimeter,P= 78mm.
Answer:
224
Step-by-step explanation:
b = 32, h = 7 is the solution to P = 78. Hence, 7*32 = 224 is the answer
Please someone brilliant answer this!!!
Eighteen plumbers can install 540 water lines in six weeks. How long will it take twelve plumbers to install the same number of lines?
It will take twelve (12) plumbers 9 weeks to install the same number of lines
From the question,
We have that, 18 plumbers can install 540 water lines in 6 weeks,
To determine how long it will take 12 plumbers to install the same number of lines,
First, we will determine how long it will take 1 plumber.
If 18 plumbers can install 540 water lines in 6 weeks
Then,
1 plumber will install 540 water lines in 18 × 6 weeks
18 × 6 weeks = 108 weeks
∴ It will take 1 plumber 108 weeks to install 540 water lines
Now, for the number of weeks it will take 12 plumbers
If 1 plumber can install 540 water lines in 108 weeks
Then,
12 plumbers will install 540 water lines in [tex]\frac{108}{12}[/tex] weeks
[tex]\frac{108}{12} = 9 \ weeks[/tex]
Hence, it will take twelve (12) plumbers 9 weeks to install the same number of lines
Learn more here: https://brainly.com/question/18880656
What is the slope of the line on the graph?
Enter your answer in the box.
Please help me!
Answer:
6
Step-by-step explanation:
We can use the points on the line to find the slope
(0,-1) and (1,5)
Using the slope formula
m = ( y2-y1)/(x2-x1)
= (5 - -1)/(1-0)
= (5+1)/(1-0)
= 6/1
= 6
Answer:
m = 6 units
Step-by-step explanation:
To get from point (0, -1) to point (1, 5) that are on the line we have to go up 6 units and 1 unit to the right
slope = rise /run = 6/ 1 = 6
Can u help me with this please it’s due in 5 mins. Find value of x.
Answer:
x = 35°
Step-by-step explanation:
Co-interior angles add up to 180°, so:
2x + 43 + 2x - 3 = 180° (now, simplify)
4x + 40 = 180° (subtract 40 from both sides)
4x = 140° (divide both sides by 4)
x = 35°
Hope this helps!
Answer:
x=35
Step-by-step explanation:
given: two lines cut by a transversal to find x
solution: the given two angles are supplementary since they are consecutive interior angles.
(2x+43)+(2x-3)=180°
⇒ 4x+40=180°⇒4x=140°
⇒x=[tex]\frac{140}{4}[/tex]=35
hope this helps :)
Here's a question ~
Two lines passing through the point (2 , 3) intersect each other at an angle of 60° . If slope of one line is 2, then find the equation of the other line ~
note : there are two possible slopes !
Need Proper Explanation ~
Answer:
[tex]\sf\longmapsto \: ( \sqrt{3} - 2)x + (2 \sqrt{3 } + 1)y = - 1 + 8 \sqrt{3} [/tex]
Step-by-step explanation:
It is given that –
Slope of the first line is–
[tex]\sf\longmapsto \: m_{1} = 2[/tex]
Let,
the slope of the Another line be –
[tex]\sf\longmapsto \: m _{2}[/tex]
Now,
The angle between the two lines is 60°.
Let's start solving!
[tex]\sf\longmapsto \: \tan(60°) | \frac{ m_{1} - m_ {2} }{1 + m_{1} m_ {2}} | [/tex]
[tex]\sf\longmapsto \: \sqrt{3} = | \frac{2 -m_{2} }{1 + 2m_{2}} | [/tex]
[tex]\sf\longmapsto \: \sqrt{3} = ± \: \: ( \frac{2 -m_{2} }{1 + 2m_{2}} )[/tex]
[tex]\sf\longmapsto \: \sqrt{3} = \frac{2 -m_{2} }{1 + 2m_{2}} [/tex]
[tex]\sf\longmapsto \: \sqrt{3} (1 + 2m_{2}) = 2 - m_{2}[/tex]
[tex]\sf\longmapsto \: \sqrt{3} + 2 \sqrt{3} m_{2} + m_{2} = 2[/tex]
[tex]\sf\longmapsto \: m_{2} = \frac{2 - \sqrt{3} }{(2 \sqrt{3} + 1) } [/tex]
The equation of line passing through point (2,3) and having a slope of –
[tex]\sf\longmapsto \: m_{2} = \frac{(2 - \sqrt{3} )}{2 \sqrt{3} + 1 } [/tex]
is–
[tex]\sf\longmapsto \: (y - 3) = \frac{2 - \sqrt{3} }{2 \sqrt{3} + 1 } (x - 2)[/tex]
[tex]\sf\longmapsto \: ( 2\sqrt{3} + 1)y - 3(2 \sqrt{3} + 1) = (2 - \sqrt{3} )x - 2(2 - \sqrt{3} [/tex]
[tex]\sf\longmapsto \: ( \sqrt{3} - 2)x + (2 \sqrt{3 } + 1)y = - 1 + 8 \sqrt{3} [/tex]
Hence the equation of the other line is -
[tex]\sf\longmapsto \: ( \sqrt{3} - 2)x + (2 \sqrt{3 } + 1)y = - 1 + 8 \sqrt{3} [/tex]
Solving Equations with the Variable on Each Side
Justify each step.
a.
b.
1. 4k-3=2k + 5
4k-3-2k= 2k +5 - 2k
2k-3 = 5
2k-3+3=5+3
2k=8
2k_8
2 2
k=4
C.
d.
e.
f.
Answer:
See below
Step-by-step explanation:
4k - 3 = 2k + 5 Given
4k - 3 -2k = 2k + 5 - 2k Addition (added -2k to both sides )
4k - 2k - 3 = 2k - 2k + 5 Commutative (changed the order of the terms)
2k - 3 = 0 + 5 Addition/ Identity
2k - 3 = 5 Addition
2k - 3 + 3 = 5 + 3 Addition (added 3 to both sides)
2k + 0 = 8 Addition
2k = 8 Identity
Which table was created using the equation y=5x-4
How to draw 0.15+0.36 using a quick picture
Answer:
heres my photo + answer
Step-by-step explanation:
0.15
+ 0.36
____
Giving brainlyest .... .....
Answer:
4.475 is the answer.
Step-by-step explanation:
also hide your tabs just in case ;)
Answer:
4.475 believe me i did k12 before plz give me brainlyiest explanation:
An object is launched at 9.8 meters per second (m/s) from a 308.7-meter tall platform. The function that represents the object's height s at time t seconds after launch is
s(t) = −4.9t2 + 9.8t + 308.7,
where s is in meters. When does the object strike the ground?
this is the full answer for you're Q
please give me good
The time taken by the object to hit the ground will be 9 seconds.
What is a quadratic equation?A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.
Given that an object is launched at 9.8 meters per second (m/s) from a 308.7-meter tall platform. The function that represents the object's height s at time t seconds after launch is
s(t) = −4.9t²+ 9.8t + 308.7
To find the time taken put the function equal to zero.
−4.9t²+ 9.8t + 308.7 = 0
t² - 2t - 63 = 0
t² - 9t + 7t - 63 = 0
t ( t - 9 ) +7 ( t - 9 ) = 0
( t - 9 ) ( t + 7 ) = 0
t = 9 and -7(ignore)
t = 9 seconds
Therefore, the time taken by the object to hit the ground will be 9 seconds.
To know more about a quadratic equation follow
https://brainly.com/question/2264627
#SPJ2
find the measure of the indicated angle
Answer:
Angle A is also the measurement of 48 degrees because the dashes on the triangle lines indicate that they are the same.
Step-by-step explanation:
what is the recurring decimal of 0.68
Answer:
0.68 repeating as a fraction
0.68 repeating as a fraction
Directions: Convert the equations from standard form to slope intercept form.
Answer:
Write in slope-intercept form, [tex]y=mx+b[/tex].
5. [tex]y=2x+7[/tex]
6. [tex]y=-\frac{5}{3} x+4[/tex]
7. [tex]y=x-1[/tex]
8. [tex]y=\frac{1}{3}x +5[/tex]
9. [tex]y=\frac{4}{5}x -2[/tex]
10. [tex]y=-\frac{7}{3}x + 6[/tex]
Find an ordered pair (x, y) that is a solution to the equation
3x+y=7
(x,y) = 0.0
X 00
?
Answer:
(0, 7) is an ordered pair solution to 3x + y = 7
Step-by-step explanation:
Given the equation 3x + y = 7, find a solution (ordered pair).
There are an infinite number of possible solutions. Let's focus on just one:
Let x = 0. Then y = 7, and (0, 7) is an ordered pair solution to 3x + y = 7