If you know the rules for differentiation, then
[tex]f(x)=\dfrac7x\implies f'(x)=-\dfrac7{x^2}\implies f'(1)=-7[/tex]
If you don't, you can use the definition of the derivative to first find [tex]f'(x)[/tex]:
[tex]f'(x)=\displaystyle\lim_{h\to0}\frac{\frac7{x+h}-\frac7x}h=\lim_{h\to0}\frac{7x-7(x+h)}{hx(x+h)}=-\lim_{h\to0}\frac7{x(x+h)}=-\dfrac7{x^2}[/tex]
Plug in [tex]x=1[/tex] to get the same result.
Or, you can directly compute the value of the derivative using the limit definition:
[tex]f'(1)=\displaystyle\lim_{x\to1}\frac{\frac7x-7}{x-1}=\lim_{x\to1}\frac{7(1-x)}{x(x-1)}=-\lim_{x\to1}\frac7x=-7[/tex]
Solve for x: the quantity of x plus 20 over 2 = 3x
Answer:
x = 4
Step-by-step explanation:
For this problem, we simply need to convert the words into the left hand side of the equation and solve for x:
The quantity of implies a grouping
x plus 20 is the quantity
And we want the quantity over 2 all equal to 3x:
( x + 20 ) / 2 = 3x
( x + 20 ) = 6x
20 = 5x
4 = x
And now we can check to see if x is correct by plugging back into the equation:
( x + 20 ) / 2 = 3x
( (4) + 20 ) / 2 ?= 3(4)
( 24 ) / 2 ?= 12
12 == 12
Therefore, we have shown the value of x to be equal to 4.
Cheers.
Answer:
x+20/2=3x.
6x=x+20.
6x-x=20.
5x=20.
x=4.
The formula for the area of a triangle is, 1 А A= bh Calculate the height of a triangle when A= 24 m2 and b = 8 m.
I hope this helps you
A=1/2.b.h
given Area is 24 and base is 8
24=1/2.8.h
24=4.h (divide 4 both of sides)
h=6 (height)
7(6+5n) + 5(7 + n) = 37
I need help please
Answer:
or, 42+35n+35+5n=37
or, 77+40n=37
or, 40n=40
so, n=1
Step-by-step explanation:
hope it helps you
4. Bill Watson is the Swanton Village computer technician. He earns $22.22 per hour. What is his straight-time pay for a 36-hour week?
Answer:
$799.92
Step-by-step explanation:
To find his pay, multiply the number of hours he worked by his pay per hour:
22.22(36)
= 799.92
So, his pay was $799.92
A delivery driver reported that he was 280 miles away from headquarters.
The driver can expect to travel 50 miles per hour. How long will it take
to return?
Answer:
5.6 hoursStep-by-step explanation:
Using the formula for calculating speed expressed as shown;
Speed = Distance/Time
Given parameters
Distance = 280miles
Speed = 50miles/hour
Required
Time it will take t return
From the formula above, Time = Distance/ Speed
Substituting the given parameters
Time = 280/50
Time = 5.6 hours
Hence the time it will take the driver to return is 5.6hours
Is 5 1/
25 rational or irrational? Explain
Answer:
rational
Step-by-step explanation:
Hello!
A rational number can be expressed as a ratio of two numbers in p/q form
A irration number cannot be expressed this way
5 1/25 is a rational number since it can be expressed as a ratio of two numbers which is 126/25.
Hope this helps!
[tex]\frac{51}{25}[/tex] is a rational number.
Rational numbers is a mathematical term that refers to the set of numbers that is expressed in a common fraction a / b. It can also be characterized because the denominator is not zero. For example
[tex]\frac{2}{8}[/tex], [tex]\frac{5}{10}[/tex], [tex]\frac{3}{9}[/tex]
On the other hand, irrational numbers are a set of numbers that cannot be expressed as a fraction. For example
π = 3.14159265358979323846…
According to the above, it can be inferred that the number [tex]\frac{51}{25}[/tex] is rational because it is expressed as a fraction.
Learn more in: https://brainly.com/question/17450097
Need help Only 5 questions
Answer:
for question no 5
answer is 1/10
Simplifying Square Roots of Negative Numbers √-100 = + i
Answer:
10i.
Step-by-step explanation:
We can rewrite sqrt(-100) as sqrt(-1) multiplied by sqrt(100).
sqrt(-1) is i and sqrt(100) is 10, so sqrt(-100) is 10i.
Answer:
0 + 10i
Step-by-step explanation:
for edge
Michael, Nate, Ben, and Andrew are running a relay race. In order to complete the race, they must run exactly 4 laps. Since Michael is the fastest of the four, he runs 1 1/3 laps. Nate then runs 1/2 lap, followed by Ben running 3/4 lap. How many laps must Andrew run to complete the race? Express your answer as a mixed number.
Answer:
Andrew must run 1 5/12 Laps to complete the race.
Step-by-step explanation:
Total lap run by Michael, Nate, Ben, and Andrew = 4 laps
laps run by Michael = 1 1/3 laps =(3+1)/3 = 4/3 laps
laps run by Nate =1/2 laps
laps run by ben =3/4 laps
Let laps run by Andrew = x
therefore
laps run by Michael + laps run by Nate + laps run by ben + laps run by Andrew = 4 laps
4/3 + 1/2 + 3/4 + x = 4
LCM of 3,2 and 4 is 12
=> (4*4 + 6*1 + 3*3+12x)/12 = 4
=> (16+6+9+12x)/12 = 4
=> 31+12x = 12*4 = 48
=> 12x = 48-31= 17
=> x = 17/12 = 1 5/12
Thus, Andrew must run 1 5/12 Laps to complete the race.
If (1,-1) is a point on the line 2x-(2a+5)y=5 then find the value of a
Answer:
a = - 1Step-by-step explanation:
Since ( 1 , -1) is a point on the line 2x-(2a+5)y=5 we can substitute it into the equation to find a
We have
2(1) - (-1)(2a + 5) = 5
Multiplying two negatives make a positive
That's
2 + 2a + 5 = 5
2a + 7 = 5
Group like terms
Send the constants to the right side of the equation
That's
2a = 5 - 7
2a = - 2
Divide both sides by 2
That's
[tex] \frac{2a}{2} = \frac{ - 2}{2} [/tex]We have the final answer as
a = - 1Hope this helps you
Solve the equation x/2-6=y for x
Answer:
x = 2y + 12Step-by-step explanation:
x/2 - 6 = y+6 +6
x/2 = y + 6×2 ×2
x = 2(y + 6) x = 2y + 12rose had $1000 in her bank account when she was 8 year old. each birthfay her grandma gave rose $20 until she turned 21
Answer:
1260
Step-by-step explanation:
Subtract 21 from 8,to get 13.Multiply 13 to the 20 dollars,when you do that you get 260.You add the 260 and the 1000 dollars together.
I NEED HELP FAST PLEASE
Answer:
The sum is
[tex]6 \sqrt{5} [/tex]
Step-by-step explanation:
Hey, there!!
Let's simply work with it,
[tex] = 4 \sqrt{5} + 2 \sqrt{5} [/tex]
As their bases are same, simply add them like,
[tex] = (4 + 2) \sqrt{5} [/tex]
[tex] = 6 \sqrt{5} [/tex]
Hope it helps...
Answer: 6[tex]\sqrt{5}[/tex]
Step-by-step explanation:
first collect like terms: 4[tex]\sqrt{5}[/tex] + 2[tex]\sqrt{5}[/tex] equals to (4+2)[tex]\sqrt{5}[/tex] , then just add 4 and 2 which equals to 6[tex]\sqrt{5}[/tex]
A camera shop stocks eight different types of batteries, one of which is type A76. Assume there are at least 31 batteries of each type. (a) How many ways can a total inventory of 31 batteries be distributed among the eight different types
Answer: 12,620,256
Step-by-step explanation:
Given: The camera shop socks eight different types of batteries and there re at least 31 batteries of each type.
Here we want to select r= 31 batteries from n= 8 kinds of batteries, then formula we use to find number of ways is [tex]^{n+r-1}C_r=\ ^{31+8-1}C_{31}[/tex]
[tex]=^{38}C_{31}=\dfrac{38!}{31!(38-31)!}\\\\=\dfrac{38!}{31!7!}\\\\=\dfrac{38\times37\times36\times35\times34\times33\times32\times31!}{31!\times5040}\\\\=12620256[/tex]
Hence, the number of ways can a total inventory of 31 batteries be distributed among the eight different types = 12,620,256
Cora started her math homework at 3:39 P.M. She finished all the problems at 4:12 P.M. How long did Cora spend doing her math homework?
Answer:
She spent 33 minutes on her homework
Step-by-step explanation:
Answer:
33 minutesStep-by-step explanation:
An hour is 60 minutes.
Taking 39 away from 60...
39 - 60 = 21
and adding 12 to it.
21 + 12 = 33
We have our answer:
33 minutesI'm always happy to help :)the hypothenus of a right angle triangle is 13cm. if one other side of the triangle is 1cm shorter than the hypothenus, calculate the third side of the triangle
Answer:
5 cm.
Step-by-step explanation:
Let the lengths of the other 2 sides be 13-1 = 12 and x cm.
Then by Pythagoras:
13^2 = 12^2 + x^2
x^2 = 13^2 - 12^2
x^2 = 169 - 144 = 25
x = √25
x = 5 cm.
Step-by-step explanation:
Hey, there!!
As per your question,
There is a Right angled triangle, whose hypotenuse is 13 cm, one side is (13-1)=12 cm.
another side = ?
Let ABC be a Right angled triangle, taking angle "theta" as a refrence angle.
Hypotenuse (h)= 13 cm.
base ( b) = x
perpendicular (p)= 12cm.
By Pythagoras relation we get,
[tex]b = \sqrt{ {h}^{2} - {p}^{2} } [/tex]
[tex]b = \sqrt{ {13}^{2} - {12}^{2} } [/tex]
[tex]b = \sqrt{169 - 144} [/tex]
Therefore, base is 5 cm. Or the third side is 5 cm.
Hope it helps...
Write an English phrase that would translate into the following mathematical expression. 7z-4
Answer: Four is less than seven times z
Step-by-step explanation:
y
A
B
4
Analyze the pre-image ABCD. What are the vertices of
the final image if T_1,-2y = x is applied to figure
ABCD?
A"
B"(3, 2)
C"
D"
2
D
с
<
*
-2
-2
Answer:
A"(3, 0), B"(3, 2), C"(1, 1), D"(1, -1)
Step-by-step explanation:
Coordinates of A,B,C and D are,
A(2, 4), B(4, 4), C(3, 2) and D(1, 2)
Rule for the reflection over a line y = x,
(x, y) → (y, x)
Therefore, new image of ABCD will be,
A(2, 4) → A'(4, 2)
B(4, 4) → B'(4, 4)
C(3, 2) → C'(2, 3)
D(1, 2) → D'(2, 1)
Rule for translation [tex]T_{-1, -2}[/tex],
(x, y) → (x - 1, y - 2)
By this rule image of A'B'C'D' will be,
A'(4, 2) → A"(3, 0)
B'(4, 4) → B"(3, 2)
C'(2, 3) → C"(1, 1)
D'(2, 1) → D"(1, -1)
Jane is saving to buy a cell phone
$35 a month from her allowance
Does it make sense to represent to
and the number of months with a
your answer.
She is given a $100 gift to start and saves
after 1 month, Jane has saved $135.Does it make sense to represent the relationship between the amount saved
ne constant rate? Why or why not? Explain.
Answer:
Yes
Step-by-step explanation:
Since it is mentioned that Jane saved $35 in a month from her allowance also the starting amount is $100 and she saved $135 after month
So based on the above information, yes it makes the sense as it represents the relation between the saving amount and number of months considering one constant rate as it she saves the similar money amount for every month
Therefore, it is linear
there is a pattern (2,4) (4,6) (6,9) (8,12) what is the 8th group
Answer:
(2,4) (4,6) (6,9) (8,12)
First bracket : Add 2
Second bracket : Add 2
Third bracket : Add 3
Fourth bracket: Add 4
This is all I know
HELPPPP please !!!!!,!!?
Mercury has the greater density than that of Venus .
Answer:
mercury has higher density than venus
5. There are 2 green blocks, 3 blue blocks, and 5 yellow blocks in a bag. What is the
likelihood that if one block is randomly chosen it will be either green or blue?
A. Unlikely
B. Likely
C. Certain
D. Equally Likely or Unlikely
Answer:
D
Step-by-step explanation:
equally likely or unlikely because it is 50%
Answer:
It is D hope this helps bud :)
Step-by-step explanation:
1/3 + a + 5/4. what is A
Answer:
a = -1.58
Step-by-step explanation:
1/3 +a+5/4 =0
1/3+5/4= -a
4+15/12 = -a
19/12 = -a
1.58= -a
1.58/-1 = -a/-1
-1.58 = a
Find the slope of the line containing the points (-5,-4) and (-3,-6)
Q1. Helen can collect 240 flowers in 20 minutes. How many flowers can
she collect in 35 minutes?
Answer:
420 flowers
Step-by-step explanation:
20 minutes = 240 flowers
1 minute =240/20 flowers
35 minutes = (240*35)/20 flowers
The answer is 420 flowers.
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Helen can collect 240 flowers in 20 minutes.
You need to find the number of flowers she can collect in 35 minutes.
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1: Find the unit rate of Helen collecting flowers. To find the unit rate, just divide 240 by 20, to see how many flowers she can collect per minute.
2: Multiply the number of flowers Helen can collect in 1 minute by 35 (since 1 times 35 is 35).
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1: 240 divided by 20 is 12. Helen can collect 12 flowers per minute. The unit rate of Helen collecting flowers is 12 flowers per minute.
2: Since Helen can collect 12 flowers per minute, you need to find out how many she can collect in 35 minutes. To get from 1 minute to 35 minutes, you multiply 1 by 35. So you need to multiply 12 by 35 as well. 12 times 35 is 420. So Helen can collect 420 flowers in 35 minutes.
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Why is
[tex] \sqrt{2x} [/tex]
is not a polynomial but
[tex] \sqrt{2}x [/tex]
is a polynomial?
Answer:
Only natural numbers (i.e., non-negative integers) can be the exponents of variables in a polynomial.
Step-by-step explanation:
The exponent of variables in a polynomial should be natural numbers ([tex]0[/tex], [tex]1[/tex], [tex]2[/tex], [tex]3[/tex], [tex]\dots[/tex].)
[tex]\sqrt{2\, x}[/tex] is equal to [tex]\sqrt{2}\, x^{1/2}[/tex]. In this expression, [tex]x[/tex] is the variable. Its exponent is [tex]1/2[/tex], which isn't a natural number. On the other hand, [tex]\sqrt{2}\, x[/tex] is equivalent to [tex]\sqrt{2}\, x^{1}[/tex]. The exponent of variable [tex]x[/tex] is [tex]1[/tex], which is indeed a natural number.[tex]\sqrt{2\, x}[/tex] isn't a polynomial because the exponent of variable [tex]x[/tex] isn't a natural number. On the other hand, [tex]\sqrt{2}\, x[/tex] is indeed a polynomial over the set of real numbers.
Identify the slope and the y-intercept of the linear equation. Y=4x+7
Answer:
Hey there!
The slope of the line is 4, and the y-intercept is (7,0)
Let me know if this helps :)
Does anyone know this?
Answer:
[tex]\Huge \boxed{-2}[/tex]
Step-by-step explanation:
[tex]f(x)=-2x^2-2x+10[/tex]
For f(2), the input of the function is 2.
Let x = 2.
[tex]f(2)=-2(2)^2-2(2)+10[/tex]
Evaluate.
[tex]f(2)=-2(4)-2(2)+10[/tex]
[tex]f(2)=-8-4+10[/tex]
[tex]f(2)=-2[/tex]
Answer:
[tex]f(x) = - 2 {x}^{2} - 2x + 10[/tex]
put the value of x = 2
[tex]f(2) = - 2( {2}^{2} ) - 2(2) + 10[/tex]
[tex] f(2) = - 8 - 4 + 10[/tex]
[tex]f(2) = - 12 + 10[/tex]
[tex]f(2) = - 2[/tex]
hope it helps u
Explain how you can use absolute value to tell wether the sum of two integers is positive or negative
Step-by-step explanation:
Using absolute value to tell wether the sum of two integers is positive or negative.
Suppose we have a positive integer,
x and a negative interger, -x and we want to find their sum, we take the absolute values of each of the integers, that is |x| and |-x|. Then we subtract these values: |x| - |-x|. If the larger integer is positive, the result of the difference is positive, but if the larger number is negative, the result of the difference is negative.
For any integer x, x + (-x) = 0
4 1/2 + 5 1/2= what
Answer:
10
Step-by-step explanation:
4 1/2 + 5 1/2= 4+5+1/2+1/2=4+5+1=10
Answer:
10Step-by-step explanation:
[tex]4\frac{1}{2}+5\frac{1}{2}\\\\\mathrm{Add\:whole\:numbers}\:4+5:\\\quad 9\\\\\mathrm{Combine\:fractions}\:\frac{1}{2}+\frac{1}{2}:\\\quad 1\\\\=9+1\\\\=10[/tex]