Answer:
f'(1) = -64
Step-by-step explanation:
To find f'(1), we will be finding the f'(x) first which means the first derivative of f(x), we can find the derivative by using chain rule to this function.
The formula of chain rule is:
[tex]\displaystyle f(u) = u^n \to f'(u) = nu^{n-1}\cdot u'[/tex]
In simple explanation, we derive normally (power rule) then multiply by the derivative of inside (u).
Applying the formula, we will have:
[tex]\displaystyle{f'(x)=4(x^2-3)^{4-1}\cdot (x^2-3)'}\\\\\displaystyle{f'(x)=4(x^2-3)^{3}\cdot 2x}\\\\\displaystyle{f'(x)=8x(x^2-3)^{3}}[/tex]
Substitute x = 1 in the f'(x):
[tex]\displaystyle{f'(1)=8(1)(1^2-3)^3}\\\\\displaystyle{f'(1)=8(1-3)^3}\\\\\displaystyle{f'(1)=8(-2)^3}\\\\\displaystyle{f'(1)=8(-8)}\\\\\displaystyle{f'(1)=-64}[/tex]
Multiply.simplify your answer and write it as a mixed number 5•7/8
Answer:
it should be 4 3/8 but sorry if it's wrong <3
Tom made $171 for 9 hours of work. At the same rate, how many hours would he have to work to make 323 ?
Answer:
Your answer would be 17 because 171 divided by 9 is 19, so 323 divided by 19 would be 17.
Answer:
17 hoursStep-by-step explanation:
Tom made $171 for 9 hours of work. At the same rate, how many hours would he have to work to make 323 ?
we can solve with an equation171 : 9 = 323 : x
x = 9 * 323 : 171
x = 2907 : 171
x = 17
-------------------------
check
171 : 9 = 323 : 17
19 = 19
the answer is goodSolve for the value of v.
(9v-3) 84°
Answer:
v = 11
Step-by-step explanation:
(9v - 3) and 84 are a linear pair and sum to 180° , that is
9v - 3 + 84 = 180
9v + 81 = 180 ( subtract 81 from both sides )
9v = 99 ( divide both sides by 9 )
v = 11
Someone help with both pls
5.6x0.7
HElp I DUnNo hOW TO gEt the ANSWER
Ik it’s 3.92 but hOWWw??
Answer:2
Step-by-step explanation:
There is 2 decimal places because you see how many numbers there are behind each of the decimals when multiplying then add them and that’s how many numbers are behind the decimal in the problem
2 digit long multiplication.
__________________________________________
Long multiplication can seem very intimidating, especially if you're multiplying two numbers that are pretty large, or like in this case if you're using decimals. If you take it step by step, though, you'll be able to do long multiplication in no time.
[tex]\frac{\begin{matrix}\:\:&3&4&\:\:\\ \:\:&\:\:&5&6\\ \times \:&\:\:&\:\:&7\end{matrix}}{\begin{matrix}\:\:&3&9&2\end{matrix}}[/tex]
How do we determine where the decimal point goes?
[tex]5.6\mathrm{\:has\:}1\mathrm{\:decimal\:place}[/tex]
[tex]0.7\mathrm{\:has\:}1\mathrm{\:decimal\:place}[/tex]
[tex]\mathrm{Therefore,\:the\:answer\:has\:}2\mathrm{\:decimal\:places}[/tex]
[tex]=3.92[/tex] is your FINAL ANSWER!
__________________________________________
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What fraction of £1 is 17p?
Answer:
17 / 100 or 1 / 17
Step-by-step explanation:
Hope this helps :)
The required fraction of 17p in £1 is 17 / 100.
Given that,
To determine the fraction of £1 is 17p.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
What is the fraction?Fraction is defined as the number of compositions that constitutes the Whole.
Here,
£1 = 100p
p = 1 / 100
Multiply by 17 on both sides,
17p = 17 / 100
Thus, the required fraction of 17p in £1 is 17 / 100.
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Simplify y to the negative seventh power over x to the negative third power.
The expression is simplified to y ^-7/x^-3
What are algebraic expressions?Algebraic expressions are expressions comprising of variables, terms, factors, coefficients, constants.
These expressions are also made up of arithmetic operations such as;
AdditionSubtractionMultiplicationDivisionBracketFrom the information given, we have;
y to the negative seventh power over x to the negative third power
This can be represented as;
Negative seventh power = ^-7
Negative third power = ^-3
Substitute into formula
y ^-7/x^-3
Thus, the expression is simplified to y ^-7/x^-3
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the hypotenuse of an isosceles right triangle is $4\sqrt{2}$ units. how many square units are in the area of the triangle?
If hypotenuse of an isosceles right triangle is [tex]4\sqrt{2}[/tex] units, then the area of the triangle is 8 square units
Given,
The hypotenuse of an isosceles triangle =[tex]4\sqrt{2}[/tex]
An isosceles triangle is a triangle that has at least two sides of equal length
Consider the two equal sides as x
According to Pythagoreans theorem
[tex]x^{2} +x^{2} =(4\sqrt{2})^{2} \\2x^{2} =32\\x^2=16[/tex]
x=4 units
We know,
Area of two isosceles right triangle equal to the area of the square with same length
Area of the square = [tex]x^{2} =4^{2}=16[/tex] square units
Then the area of the triangle =[tex]\frac{16}{2}=8[/tex] square units
Hence, if hypotenuse of an isosceles right triangle is [tex]4\sqrt{2}[/tex] units, then the area of the triangle is 8 square units
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sketch the curve by using the parametric equations to plot points. indicate with an arrow the direction in which the curve is traced as t increases.
As t increases the curve is changing according to the plot points given by the parametric equations.
Define parametric equations?The coordinates of the points that make up a geometric object, such as a curve or surface, are frequently expressed using parametric equations; in this case, the equations are collectively referred to as a parametric representation or parameterization (alternatively spelled as parametrisation) of the object. It describes a collection of numbers that represent functions with one or more independent variables. The parameters used here are the independent variables. For the representation of the coordinates that make up geometric objects like curves and surfaces, parametric equations are used. Additionally, a curve that is not a function can be drawn using parametric equations.
The equations are
x=1-t²
y=2t-t²,-1≤t≤2
The sketch is in the diagram picture.
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1/5(10x−5)=5x−1 is the problem.
some one help please.
9th grade math
Solution of the equation [tex][\frac{1}{5(10x-5)} =(5x-1)][/tex] is [x = (-0.512788205961), (-0.187211794039)].
As per the question statement, our concerned equation is [tex][\frac{1}{5(10x-5)} =(5x-1)][/tex].
We are required to find the value of "x" that satisfied the equation. First, we will have to convert the given equation to the form of quadratic equation.
[tex][\frac{1}{5(10x-5)} =(5x-1)]\\or, 1=5(10x-5)*(5x-1)\\or, 1=5*5(2x-1)*(5x-1)\\or,1=25[(2x-1)(5x-1)]\\or,1=25(10x^{2} -2x-5x+1)\\or,1=25(10x^{2} -7x+1)\\or,1=250x^{2} -175x+25\\or,250x^{2} -175x+24=0\\[/tex]
Now, [(250x² - 175x + 24) = 0] is in the form of a quadratic equation.
Also, the formula to calculate the solutions of a standard quadratic equation [ax² + bx +c = 0] goes as [tex][x=(\frac{-b+\sqrt{(b^{2}-4ac) } }{2a}), (\frac{-b-\sqrt{(b^{2}-4ac) } }{2a}) ][/tex]
Comparing [ax² + bx +c = 0] with [(250x² - 175x + 24) = 0], we get
(a = 250), (b = 175) and (c = 24), and using these values in the above mentioned formula to calculate the solutions of quadratic equations, we get, [x = (-0.512788205961), (-0.187211794039)].
Quadratic Equations: In algebra, any polynomial equation whose highest degree is two and can be rearranged to the standard form of [ax² + bx + c = 0], where (a ≠ 0), is known as a quadratic equation.To learn about Quadratic Equations, click on the link below.brainly.com/question/1863222
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the distance from sacramento to fresno can be respresented as 2x+10 and the distance from fresno to san bernardino can be represented as 4c + 12. To Travel from sacramento to san bernardino is 340. How many miles is it to travel from Fresno to San Bernardino? Show your work below.
The distance travel from Fresno to San Bernardino is 224 miles.
What is distance?The distance of an object can be defined as the complete path travelled by an object .Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.
Given:
Distance from sacramento to fresno =2x+10
Distance from fresno to san bernardino= 4x + 12
Distance from sacramento to san bernardino = 340.
According to given question we have
Distance from sacramento to fresno+Distance from fresno to san bernardino=Distance from sacramento to san bernardino
2x+10 +4x + 12 =340.
Compare the like terms we get
6x+22=340
Subtract 22 from both sides we get
6x=318
x=53
So,
Distance from sacramento to fresno
=2x+10
=2*53+10
=106+10
=116
Distance from fresno to san bernardino
= 4x + 12
=4*53+12
=224
Therefore, the distance travel from Fresno to San Bernardino is 224 miles.
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There are 5 white balls,8 red balls ,7 yellow balls and 4 green balls in a container a ball is choosen at random.what is the probabilty of chooseing neither white or green? .
15/19 + 14/19 = 29/19
Step-by-step explanation:
Add the number of balls in the basket together.
Subtract the number of white balls from the sample space ( the total amount of balls) your answer is written over the sample space and the same process is done for the green ball
In 9 hours, Donna reads 45 chapters of a book. What is her rate in chapters per hour?
Answer:
Donna reads an average of 5 chapters each hour.
Step-by-step explanation:
45/9=5
Perimeter < 18.7 feet
4,1 ft
4.9 ft/
6.4 ft
x ft
Inequality:
Solution:
The solution to the inequality is x < 3.3
How to determine the solution to the inequality?The given parameters are:
Perimeter < 18.7 feet
Side lengths: 4.1 ft 4.9 ft 6.4 ft x ft
The perimeter of a shape is the sum of the side lengths
So, we have
Perimeter = 4.1 ft + 4.9 ft + 6.4 ft + x ft
Remove the unit
So, we have
Perimeter = 4.1+ 4.9 + 6.4 + x
Evaluate the sum
Perimeter = 15.4 + x
Recall that
Perimeter < 18.7 feet
So, we have
15.4 + x < 18.7
Subtract 15.4 from both sides
x < 3.3
Hence, the solution to the inequality is x < 3.3
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Pleaseeee hellp meeeee
Answer:
57,600 ft
Step-by-step explanation:
Please give an explanation along with your answer.
Answer: 1.19
Step-by-step explanation:
[tex]\displaystyle\\\frac{3\frac{1}{2}-1\frac{4}{5} }{1\frac{3}{7} }=\\\\\frac{\frac{3*2+1}{2} -\frac{1*5+4}{5} }{\frac{1*7+3}{7} } =\\\\\frac{\frac{6+1}{2}-\frac{5+4}{5} }{\frac{7+3}{7} } =\\\\\frac{\frac{7}{2}-\frac{9}{5} }{\frac{10}{7} } =\\\\\frac{\frac{7*5-9*2}{2*5} }{\frac{10}{7} } =\\\\\frac{\frac{35-18}{10} }{\frac{10}{7} } =\\\\\frac{\frac{17}{10} }{\frac{10}{7} } =\\\\\frac{17*7}{10*10} =\\\\\frac{119}{100} =\\\\1.19[/tex]
A parabola opening up or down has vertex (0, 1) and passes through (12, -17). Write its
equation in vertex form.
Simplify any fractions.
The equation of the parabola is y = (-3/2)x + 1.
The general vertex form of the equation of a parabola is y = a(x - h)2 + k
where (h, k) are the coordinates of the vertex
Here, we are given that vertex = (0, 1)
Thus, the equation of the parabola is-
y = a(x - 0)2 + 1
y = 2ax + 1
Also, we are given that the parabola passes through (12, -17).
Thus, (12, -17) must satisfy the equation of the parabola
⇒ -17 = 2a(12) + 1
-17 = 24a + 1
24a = -17 -1
24a = -18
a = -18/24
a = -3/4
Thus, the equation of the parabola becomes-
y = 2(-3/4)x + 1
y = (-3/2)x + 1
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When converting measurements in the metric system, you can move the decimal point to the left or to the right why? Select all that apply.
A When converting from smaller to larger units zero dividing by the power of 10
B Moving a decimal point is The same thing as adding or subtracting
C The metric system is based on powers of 10
DWhen converting some larger to smaller unit, you are applying by the power of 10
Answer:
C The metric system is based on powers of 10
Step-by-step explanation:
boy can mow a lawn in 90 minutes and his sister can mow the same lawn in 60 minutes. how long will it take for both mowing at the same time to mow the lawn?
The time taken by both to mow the lawn is 36 minutes.
This is a question of time and work.
It is given that:-
Time taken by boy to mow the loan = 90 minutes.
Time taken by girl to mow the loan = 60 minutes.
We have to find the time taken by both of them together to mow the lawn.
LCM(60,90) = 180
Let the total work to be done to mow the lawn be 180 units.
Hence,
Efficiency of boy = 180/90 = 2 units
Efficiency of girl = 180/60 = 3 units
Total efficiency = 2 + 3 = 5 units.
Hence, time taken by both of them to mow the lawn = 180/5 = 36 minutes.
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a dose was increased from 250 to 500 milligrams. what is the percent increase??
I got 1, so can anyone confirm if it's right or not please
Step-by-step explanation:
initally dose was 250 mg and then increased to 500 mg.
so, percent increase would be :-
(500-250)/250 * 100
= 1 %
so I guess u are correct.
The percentage increase in the size of the dosa is 100%
What is the percentage?The percentage is a ratio that can be expressed as a fraction of 100.
Given that, the size of the dosa is increased from 250 to 500.
The amount of increment is:
500 - 250
= 250
The percentage change is given by:
(250/250) × 100%
= 100%
Hence, the percentage increase in the size of the dosa is 100%
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Lois James' W-2 form is shown below.
રરરરર
1 Employed and code
PA
667438991
Acme, Inc
123 Man Street
Philadelphia, PA 19146
Lou James
632 Dodge Street
Philadelphia, PA 19145
Wage and Tax
Empre
471-29-2525
35-5427864
foW-2 Statement
Copy 1-For State, City, or Local Tax Department
A. $2018.40
D. $472.04
B. $32,554.76
C. $4465.71
32,554 76
999 43
2010
32,554 76
32,554 76
32.554 76
060
16 Laps
32,554 76
12e
the
124
4465 71
2018 40
Macato all
472 04
Department of the y
1400 18
How much did Lois have withheld from her yearly pay for Social Security?
20 Locatty cam
PHIL
ne Service
Answer:2018.40
Step-by-step explanation: i tried 472 and it was wrong and stated 2018 was correct.
Find the value of 3 + x when x = 5?
Answer: your mom
(x−5)(x−3)
Coach Murphy has the football team run stairs for practice. Each set of stairs has 75 steps. They have to do 6 sets and have already run 300 stairs.
Answer:
The run 750 steps
Step-by-step explanation
6x+300
x is 75
450+300
750
(-1)7 + (-1)8 + 1" + (-1)² + (-1)2n+1
Answer:
In the picrure
Step-by-step explanation:
If a₁ = 5 and a,, = 0,-1+5 then find the value of as.
Answer:
a1 = 6 and an = an-1 - 5
a2 = a2-1 - 5 = a1 - 5 = 1
a3 = a3-1 - 5 = a2 - 5 = -4, etc
Step-by-step explanation:
Solve for the value of c.
(20-3)
97°
i attached a pdf, hopefully it helps you understand!
(This is a Linear Programming Word problem) (Honors Algebra II)
You are screen printing t-shirts and sweatshirts to sell at the County Blues Festival and are working within the following constraints
- You have at most 1200 minutes to make shirts
- You want to spend no more than $600 on supplies
- You want to have at least 50 items to sell
- T-shirts take 10 minutes to make with a cost of $4 and a profit of $6
- Sweatshirts take 30 minutes to make with a cost of $20 and a profit of $20
How many T-shirts and how many sweatshirts should you make to maximize your profit?
How much is the maximum profit?
The maximum profit is 800, and the most T-shirts, sweatshirts, and hoodies you should produce is 10.
Linear programming: what is it?A mathematical model whose requirements are expressed by linear connections can be optimized using a technique known as linear programming. A particular type of mathematical programming is linear programming.
based on the available facts;
x= tshirt
y =sweatshirts
10x+20y≤1200
2x+20y≤600
x+y≥50
x≥0
y≥0
so p=6x+20y(objective function)
from above 10x+20y≤1200
20y/20=(-10x/20)+(1200/20)
y=-1/2+(60)
put y value in all formula
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There is a daily fee for renting a movin truck, plus a charge of $0.50 per mile driven. If driven 48 miles, it costs $64 to rent a truck. Write and solve an equation to find the daily fee
Answer:
Step-by-step explanation:
$0.50 x 48 + $64 = $88. Because of order of operations or PEMDAS, multiplication goes first, then comes addition. Hope you found this helpful!
Sally babysits for 3 hours on weekdays and charges $10 per hour. If she babysits for 65 days total, how much will she make?
If she babysits for 65 days total, she would make $1,950 in all
What is the earnings of Sally per day of babysitting?
The earnings that Sally realize from one day of babysitting is the pay per hour multiplied by the number of hours Sally works per day as shown below:
earnings per day=hourly rate*number of hours a day
hourly rate=$10
number of hours a day=3
earnings per day=$10*3
earnings per day=$30
Now, the earnings at she realizes from 65 days of babysitting can be determined as the earnings made in one day multiplied by the number of days she spent babysitting
earnings for 65 days=$30*65
earnings for 65 days=$1,950
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please solve this question (and explain how it works) thank you!
Answer:
Equation is 15(x-20) = 945
x = $83
Step-by-step explanation:
The cost of each lesson is $x
The discounted cost = x-20
Since 15 lessons cost 945,
the equation is
15(x-20) = 945
Simplifying by multiplying the term in brackets by 15:
15x - 15(20) = 945
15x - 300 = 945
Adding 300 on both sides isolates the 15 x term
15x = 945 + 300 = 1245
15x = 1245
Dividing both sides by 15 ,
x = 1245/15 = 83
So cost of lesson before discount is $83