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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
A teacher chooses two students in a class of 15 girls and 10 boys. The students are randomly chosen. What is the probability that the teacher chooses two girls?
1. 3/5
2. 3/7
3. 7/12
4. 7/20
Answer:
15/25 which simplifies to 3/5 which is the first answer
Step-by-step explanation:
(X^2 -6x -20)/(x+2)
Use long division
Answer:
The answer is x-8-4/x+2.
Step-by-step explanation:
I'm certain this is correct since I factored and have done everything required.
please do this for me
Answer:
63 degrees
Step-by-step explanation:
HINT: know that in a triangles angles add up to 180 degrees.
1. 96+21= 117
2. 180-117=63
3. 63 degrees
what is the circumference of a circle with an area of 20 pi
Answer:
28.1 units
Step-by-step explanation:
Area of circle= πr², where r is the radius.
Given that the area is 20π,
20π= πr²
Divide both sides by π:
20= r²
Square root both sides:
[tex]r = \sqrt{20} [/tex]
[tex]r = \sqrt{4(5)} [/tex]
[tex]r = ( \sqrt{4} )( \sqrt{5} )[/tex]
[tex]r = 2 \sqrt{5} [/tex]
Circumference of circle= 2πr
Substitute the value of r:
Circumference of the circle
[tex] = 2(\pi)( 2\sqrt{5} )[/tex]
[tex] = 4\pi \sqrt{5} [/tex]
= 28.1 units (3 s.f.)
subtract (3x^3-2x+5)-(-4x^3+3x-6)
Answer:
7x^3-5x+11
Step-by-step explanation:
(3x^3-2x+5)-(-4x^3+3x-6)
Distribute
3x^3-2x+5+4x^3-3x+6
Simplify
7x^3-5x+11
it's the logique
show that for all x >0
Answer:
See belowStep-by-step explanation:
We can show that for x = 0, both sides of the inequality get the value of 1.
With x > 0, the left side goes towards - ∞ with the negative slope and the right side is always positive.
I'll give a graphical solution.
Hope this helps.
5.32×10^5 solve it please need it by 12:00
Answer:
532,000
Step-by-step explanation:
10^5= 100,000
100,000 x 5.32
Move the decimal place 5 spaces to the right.
It gives you 532,000
Answer:
532000Step-by-step explanation:
5.32 × 10^5 =
532/100 × 100000 =
133/25 × 100000 =
532000
Which expression is equivalent to -p+2 -2p+ 8?
Answer:
- 3p + 10
Step-by-step explanation:
- p + 2 - 2p + 8 ← collect like terms
= (- p - 2p) + (2 + 8)
= - 3p + 10
Evaluate x(y+3)/(3+y)z for x = 2, y = 5, and z = 1.
4
3
2
1
Answer:
2
Step-by-step explanation:
hope this helps
Round 848704to the nearest thousand
Answer:
849000
Step-by-step explanation:
I used a site called Rounding to the Nearest Thousand Calculator. Sorry Brainly doesn't allow links:))) Happy Halloween!!
Relationship B has a greater rate than Relationship A. This graph represents Relationship A.
Which equations could represent Relationship B?
Select each correct answer.
y = 0.6x
y=23x
y=14x
y=34x
First-quadrant graph showing a ray from the origin through the points begin ordered pair 4 comma 2 end ordered pair and begin ordered pair 8 comma 4 end ordered pair.
Answer:
y = 0.6x
Step-by-step explanation:
Look what happens as we move from point (4, 2) to point (8, 4). The x coordinate increases by 4 and the y coordinate by 2. Thus, the slope of the line representing Relationship A is m = rise / run = 2/4, or 0.5.
The only one of the four possible answers that could be correct is y = 0.6x, which has a greater rate (slope) than does the given line (m = 0.5).
Answer: 0.6
2/3
3/4
I took the test and got those as my answer. Btw here's the image for proof :)
May I please receive help????
Please
Answer:
43°
Step-by-step explanation:
Equation:m∠ABD = m∠1 + m∠2
Substitute:
68° = m∠1 + (m∠1 + 18°)
Solve:68° = m∠1 + (m∠1 + 18°)
68° = 2(m∠1) + 18°
50° = 2(m∠1)
25 = m∠1
Solution:Know that we know that m∠1 is, we can add 18* to find m∠2
25° + 18° = 43°
-Chetan K
the shopkeeper sold a laptop having its cost price rupees 25000 at a profit of 25% find its selling price
Answer:
Let's see what we have here. A shopkeeper sold Item X for a his selling price (SP).
Let SP = x
Since the question says that Profit is 25% of the selling price, we have:
Profit = 25% SP = 0.25x
Now, we already know that:
Profit = SP - Cost
This part is the catch. To find out how much Item X originally cost,
Cost = SP - Profit = x - 0.25x = 0.75x
Now that we know the original cost of Item X, we can easily calculate the Real profit % using this formula:
= (Profit/Cost)*100
= (0.25x/0.75x)*100
= 33%
And there you have it. Hope I explained it clear enough.
Answer:
Step-by-step explanation:
Cost price = CP = ₹ 25,000
Profit% = 25%
Selling price = SP
[tex]SP =\dfrac{100+profit}{100}*CP\\\\\\=\dfrac{100+25}{100}*25000\\\\=\dfrac{125}{100}*25000[/tex]
= 125 * 250
= ₹31250
helpppppppppppppppp meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
a) = 4.198
b) = 4.146
Step-by-step explanation:
a) 15.444/6+0.232*7
do pemdas
=15.444/6+(0.232*7)
=(15.444/6)+1.624
=2.574+1.624
a) = 4.198
b) (1.709+0.364)*6/3
pemdas again
=(2.073) *6 / 3
=12.438 / 3
b) =4.146
Hope this helps :)
Answer:
A 4.198 and b is 2.073
Step-by-step explanation:
i hope this is right
Complete the table for y=2x-3
Answer:
See attachment also
Step-by-step explanation:
Let y be 0 at first.
Now let x be 0.
y | 0 -3
x | 1.5 0
Can someone help me with part b?
Step-by-step explanation:
the average rate of change of a function f in an interval [x-low, x-high] is
(f(x-high) - f(x-low)) / (x-high - x-low)
the year 2000 means t = 2000-1980 = 20
the year 2015 means t = 2015-1980 = 35
so, we have
(A(35) - A(20)) / (35 - 20)
((-0.6(35)² + 37.2×35 + 243) - (-0.6(20)² + 37.2×20 + 243)) / 15
((-735 + 1302 + 243) - (-240 + 744 + 243)) / 15
(810 - 747) / 15 = 63/15 = 4.2
the average change rate between 2000 and 2015 is 4.2.
that means that the use of nuclear energy in the USA increased by 4.2 billions of kilowatt hours per year during that period.
Any help please? Don’t understand
Help me.
Fraction questions
Answer:
a)
2 sections
b)
9 sections
Step-by-step explanation:
a) there are total 8 boxes
so, for fraction 1/4
1/4 × 2/2 = 2/8
therefore shade 2 sections.
b) there are total 15 sections so to shade 3/5 of this shape
3/5×3/3 = 9/15
therefore , shade 9 sections.
hope this answer helps you dear...take care!
Alex wrote the expanded form for the number 165.038 as “100 + 60 + 5 + 30 + 8.” Was he correct? If not, give the correct expanded form. P.S I really need the answer asap!
Answer:
no he is not correct.
the correct expanded form: 100+60+5+0.0+0.30+0.008
Step-by-step explanation:
Hope this helps also i learned about this r u in 5th grade
Alex's expanded form for the number 165.038 is not correct. The correct expanded form for the number 165.038 is 100 + 60 + 5 + 0.03 + 0.008.
The number 165.038 can be broken down into its individual place values:
Hundreds: 100
Tens: 60 (6 tens)
Ones: 5
Tenths: 0.03 (3 hundredths)
Hundredths: 0.008 (8 thousandths)
So, the correct expanded form for the number 165.038 is:
100 + 60 + 5 + 0.03 + 0.008
Hence, Alex's expanded form for the number 165.038 is incorrect. The correct expanded form is: 100 + 60 + 5 + 0.03 + 0.008.
To learn more on Number system click:
https://brainly.com/question/1763119
#SPJ3
t^(5)-10t+1=0 find the answer (≈)
Answer:
t: -1.80244705, 0.100001, 1.75234772
2
Rearrange terms
3
Subtract
6
6
6
from both sides of the equation
4
Simplify
5
Divide both sides of the equation by the same term
6
Simplify
James has a piece of construction paper with a length of 9/10 feet and a width of 2/3 feet.
What is the area of James's piece of construction paper?
Area = length x width
When you multiply fractions, multiply top number by top number and bottom number by bottom number:
9/10 x 2/3 = (9 x 2) / (10 x 3) = 18/30 this can be reduced by dividing both numbers by 6:
18/30 reduces to 3/5
Answer: 3/5 square feet
consider the following simplified algebraic expression 10x²y+6x²-7y²-6 which could be the original expression
Answer:
You technically can't do anything with it since it the algebraic expression doesn't factor.
Step-by-step explanation:
Help please! I can't understand this question!
Answer:
Step-by-step explanation:
y = 2x + 8
She know 8 songs. 8 will be the y-intercept and each month she learns 2 songs which will be the slope of the function.
Answer:
y=2x+8
Step-by-step explanation:
It's for how many songs he knows in total
2 songs a month so
songs he knows=2(number of months)+the 8 he already knows
please help !! find the area and perimeter. I KNOW HOW TO DO IT BUT I JUST DONT HAVE THE TIME RN!!
Answer:
Step-by-step explanation:
9.
Area = 15 × 5
Area = 75
perimeter = 15 + 6 + 15 + 6 = 42
10.
Area = (10 × 15) ÷ 2 = 75
perimeter = 18 + 10 + 15 = 43
11.
Area = (25 × 10) ÷ 2 = 125
perimeter = 31.6 + 25 + 11.2 = 67.8
please give me a brainliest answer
please help! & please explain your answer!!
Answer:
9Step-by-step explanation:
Plan A remains with $450 stable charge and Plan B is:
200 + 30x, with x being the number of physical training sessionsIn order Plan B to be cheaper we set an inequality:
200 + 30x < 45030x < 250x < 250/30x = 8.33 < 9Factorise; c cubed divided by c cubed?
HELP ASAP
Step-by-step explanation:
c³/c³ =1 .
hope this helps you.
Pls help me with this question!!!! Will mark the best answer brainliest!!!
Please what is the answer?
Answer: scale to measure the weight
Step-by-step explanation:
What is the missing side length of this right triangle? Type the answer in the box.
13 in.
5 in.
х
1
Answer:
13in
Step-by-step explanation:
remember it's the same angle width.
[tex]\sqrt3+2\sqrt2 - \sqrt6-4\sqrt2[/tex]
