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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
The expression - 250 + 16z represents a submarine that began at a depth of 250 feet below sea level
and ascended at a rate of 16 feet per minute. What was the depth of the submarine after 9 minutes?
Express the values below I’m scientific notation 52,800g, 255.6m, 0.04109cm!?
Answer:
1) 5.28 x 10^4 g
2)2.556 x 10^2 m
3)4.109 × 10^-2cm
Have a nice day!!!!!
Answer:
52,800 in scientific notation is [tex]5.28[/tex] × [tex]10^4[/tex].
255.6 in scientific notation is [tex]2.556[/tex] × [tex]10^2[/tex].
0.04109 in scientific notation is [tex]4.109[/tex] × [tex]10^{-2}[/tex].
HELP PLEASE!!
Write a recursive rule for an=1/3•4^n-1
A.) an=1/3•an-1
B.) an=4•1/3an-1
C.) an=1/3•4an-1
D.) an=4•an-1
Answer:
D.) an = 4 * an-1
Step-by-step explanation:
a(n) = (1/3) * 4^(n-1)
a(n-1) = (1/3) * 4^(n-1-1) = (1/3) * 4^(n-2)
Thus,
a(n) = (1/3) * 4 * 4^(n-2) = 4 * [(1/3) * 4^(n-2)] = 4 * a(n-1), so that
a(n) = 4 * a(n-1).
mr. tyler has a total of $5,000 in savings account and in a mutual fund. If he has x dollars in the savings account, how much dollars does he have in the mutusl fund?
Mr. Tyler has $(5000 - x) in the mutual fund, where is amount in the saving account.
If Mr. Tyler has $5,000 in total, and x dollars in the savings account.
The amount he has in the mutual fund can be calculated by subtracting the amount in the savings account from the total amount.
Amount in the mutual fund = Total amount - Amount in the savings account
Here, Total amount = $5000 and Amount in the savings account = x
Substituting the values back to the formula as
Amount in the mutual fund = $5,000 - x
So, Mr. Tyler has $(5000 - x) in the mutual fund.
Learn more about Mutual Fund here:
https://brainly.com/question/22525531
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write the equation of the line parallel to the given line y = 2x - 4
Answer:
y=2x-8
Step-by-step explanation:
Plot the line and use the parallel slope to create the line and then find the y-intercept
guys pls help me!!!!!!
Answer:
X would also be 59° due to the Corresponding property.
Help help help help help help help
I) Degree Yes No m b
6) 1 √ 1 10
7) 1 √ 5 -1
8) 2 √
II)
9) x = 1,y = 3, 3x
x = 2,y = 6, 3x
x = 3,y = 9, 3x
It's a linear equation because it has 1 degree of function.
f(x) = 3x + 0.
10) x = -2,y = 4,x²
x = -1,y = 1,x²
x = 0,y = 0,x²
It's not linear a linear equation because it has 2 degree of function.
A)
1. m = -2/3 , b = 4
y = mx + b
y = -2/3x + 4
Values;
x= 0,y = 4 (0, 4)
x=1,y=10/3 (1,10/3)
x=2, y= 8/3 (2, 8/3)
x=3, y=2 (3, 2)
x=4, y=4/3 (4, 4/3)
The graph is the 1st one above.
2. a = -2 , b = 3
y = mx + b
at y = 0, x = -2
0 = m(-2) + 3
-3 = -2m
m = 3/2
y = 3/2x + 3
Values;
x = -2, y=0, (-2, 0)
x = -1, y = 3/2, (-1, 3/2)
x = 0,y = 3, (0, 3)
x = 1,y = 9/2, (1, 9/2)
x = 2, y = 6, (2, 6)
The graph is the 2nd one above.
Which expression is equivalent to 5 to the power of 6
5^6
Answer:
5^6
5^6 is the same thing as
5^6=5×5×5×5×5×5
=5×5=25×5=125×5=625×5=3125×5=15625
5^6= 15625
Answer:
125 * 125
Step-by-step explanation:
do 125 x 125 = 15625
Ken bought a new car and had to borrow $6,500 from the bank. The bank charged
Ken 3.7% in simple interest for the 5 years Ken had the bank loan. What's the total
amount Ken will have to repay the bank?
Answer: 65005.037
Step-by-step explanation:
I=?
P=6,500
R=037
T=5 years
I= 6,500+037+5= 65005.037
a man earned $180 for working 14 hours. How many hours must he work to earn 300
Answer:
it would be roughly 24 hours
Step-by-step explanation:
180÷14
12.8571428571
simplify to 12.85
12.85× X = 300
X=24
can somebody please just help me do not answer if you do not know
Answer:
it could be 34 , 34 and 82
or 34 , 73 and 37
Step-by-step explanation:
angles in a triangle add up to 180. in and isosceles triangle two angles are always the same so there will be 2 possible outcomes.
pls mark brainalist
9. The repair order is a legal document because
People say it’s B or C, which one is correct.
Correct gets brainliest!!!
Answer:
C is the correct answer cos it is paid by the customer
how to solve the attachment question?
Answer:
y = 100 - 0.08^ x
Step-by-step explanation:
a line containing the points (4, y) and (-3, 2) has a slope of 3/2.
Answer:
y=14.5
Step-by-step explanation:
A slope of 3/2 means that for every unit it moves to the right, it will move 1.5 units up. The x of 4 is 7 more than the -3 of our other point. 7*1.5=12.5, and 12.5+2=14.5.
Simplify to create an equivalent expression
-5(3p+3) + 9(-7+p)
The answers are:
A)-5p-78
B)-6p-78
C)-6p-48
D)-6p+78
Brainlest Evaluate (-2-2-1/2)³
Answer:
[tex]\sf\longmapsto \: \frac{ - 792}{8} [/tex]
Step-by-step explanation:
[tex]\sf\longmapsto \: (−4− \frac{1}{2} ) {}^{3} [/tex]
[tex]\sf\longmapsto \: (− \frac{9}{2} ) {}^{3} [/tex]
[tex]\sf\longmapsto \: \frac{ - 729}{8} [/tex]
[tex]\sf\longmapsto \: Decimal: -91.125[/tex]
What is the equation of a line that passes through the point (8, -2) and is parallel to the line whose equation is 3x + 4y = 15?
Answer:
y = -3/4x + 4 or 3x + 4y = 16
Step-by-step explanation:
Step 1
Find the slope of the given line
we have
3x + 4y = 15
Isolate the variable y
Subtract 3x from both sides
3x + 4y -3x = 15-3x
Divide by 4 both sides
y = -3/4x + 15/4
the slope of the given line is
m = -3/4
Step 2
Find the equation of the line that passes through the point and is parallel to the given line
we know that
if two lines are parallel, then their slopes are equal
The equation of the line into point-slope form is equal to
y - y₁ = m(x-x₁)
we have
m= -3/4
(x1,y1) = (8,-2)
substitute in the equation
y + 2= -3/4(x-8)
y = -3/4x + 6 - 2
y = -3/4x + 4 or 3x + 4y = 16
therefore
the answer is
y = -3/4x + 4
or
3x + 4y = 16
An insect's head accounts for approximately 60% of its total mass. If the insect weighs 40 g, what is the mass
of its head?
Answer:
24 g
Step-by-step explanation:
60/100x40
2400/100
24
The sum of the real numbers x and y is 11. Their difference is 5. What is the value of xy?
Answer:8
Step-by-step explanation:
Answer:
xy=24
Step-by-step explanation:
x+y=11
x-y=5
x=y+5
y+5+y=11
2y=6
y=3
x=8
xy=24
Evaluate. 2 > 8 - 4/3h
Answer: h>9/2
Step-by-step explanation:
helpppppppppppppppppppppppppppppp meeeeeeeeeeeeeeeeeee plsssssssssssssssssssssss there is more but plss help mee
Answer: The attachment is a bit difficult to read, and long. I'll make some suggestions and add some detail to a few of the problems, but would ask that these suggestions be applied to other problems to find the answers.
Step-by-step explanation:
9. Coinciding lines line on top of each other. I.e., they are the same equation. If we take A, for example, we can reduce the second expression by dividing by 2: (2x+4y=6)/2 = (x + 2y = 3). This matches the first expression (x + 2y = 3). ! Whoa, that went fast.
10. (x+8)(x-8) = x² +8x -8x - 64 = x² - 64
11. I don't have the time to explain how one can factor, but practice is important. And I don't know if this is completely factored, but it matches one of the options. Try (n-2)(n²+2n + 4) [n³ +2n² +4n - 2n² -4n -8 = n³ - 8. It works.
12. The denominators are the same, so add the numerators and keep the denominator. (7x+4y)/x²y
13. The slope is the "Rise" over the "Run." (3,4), (8,-1) Rise = (-1 - 4) = -5. Run = (8-3) = 5 Slope = -(5/5) = -1
14. A line with a positive slope will move upwards as x increases. We can eliminate options C and D immediately. That leaves A and B. The line we are looking for is y = 5x + b. We are not given b, the y-intercept, so determine the slopes of both lines: I get 4 for A and 5 for B. To confirm B is correct, we could calculate b for y=5x+b by using given point, (2,3). 3 = 5*2 + b, b = -7. We can't see this point (0,-7) on the graph, but it appears correct. B is the best answer.
15. The line will have the form of y=mx+b. Calculate m, the slope, from the two points (3,1) and (4,7). Rise = 6, Run = 1 Slope = 6. y=6x+b. Find b by using either of the given poins and solving for b. I'll choose (3,1). y=6x+b; 1 = 18 + b; b = -17. The equation is y=6x-17. Rearrange option A (y =6x - 17).
16. The second value in each factor must, when multiplied together, equal the final term of the original expression, -9y². I see only one option for which that is true, C. Multiply the two factors in C to be certain, and you'll find they result in the correct expression.
in fiq Q.3 measure the angle which the ladder makes with (I) the ground (2) the wall
Step-by-step explanation:
for measuring the angle use the protractor !
What is an equation of the line that passes through the points (2,6) and (1, 1)?
Answer: y=5x+b
Step-by-step explanation:
I used the slope intercept equation, which supplied me the solution.
m=5
b=0
What is a correct congruence statement for the triangles shown?
Enter your answer in the box.
ΔQDJ=Δ____
Answer:
GAP but if not that AGP
Step-by-step explanation:
Answer:
ΔQDJ ≅ GAPStep-by-step explanation:
Use the order of corresponding vertices.
Q and G, D and A, J and P are corresponding considering the marks on the lines.
ΔQDJ ≅ GAPwhich is colder -3°c or -2°c
Answer:
-2 is colder
Step-by-step explanation:
Becuase when you get to the negative the Closest number to 0 is greater which means -2 is closer to 0 which makes it colder.
(Hope this helps can I pls have brainlist (crown)☺️)
LY!
Fill in the missing numbers to complete the pattern:
2.6, 3.1,
4.6, 5.1
HELP RN PLEASE!!!!!!!!
Step-by-step explanation:
this is the answer
hopes it helps
Solve the equation. 9 ( − 2 ) =
Answer:
- 18
Step-by-step explanation:
9 ( - 2 )
= 9 x ( - 2 )
= - 18
Therefore, - 18 is the answer of the given equation.
Answer:
-18
Step-by-step explanation:
the parentheses mean to multiply, so 9 times 2 is 18, but since it is a negative and a positive that you're multiplying, then it would be negative 18
the average age of teacher at school is 36 years.mr Smith age is 11/9 of the average. how old is Mr Smith?
Answer: 44
Step-by-step explanation:
I'm positive this is right! Have a good day! Hope this helps! Please give brainliest, i would help a lot if you did, but its fine if you don't Just have a good rest of the day!
Write 6^7 + 6^5 + 11 in base six. Use the digits 0, 1, 2, 3, 4, 5
Answer:
Sorry I don't remember the answer