[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
The formula for slope according to first principle is :
[tex] \qquad \sf \dashrightarrow \: \[ \displaystyle\lim_{x\to0} \: \: \sf \frac{f(x + h) - f(x)}{h} \][/tex]
[tex] \qquad \sf \dashrightarrow \: \[ \displaystyle\lim_{x\to0} \: \: \sf \frac{ log(x + h) - log(x)}{h} \][/tex]
[tex] \qquad \sf \dashrightarrow \: \[ \displaystyle\lim_{x\to0} \: \: \sf \frac{ log( \frac{x + h}{x} ) }{h} \][/tex]
[tex] \qquad \sf \dashrightarrow \: \[ \displaystyle\lim_{x\to0} \: \: \sf \frac{ log( \frac{ h}{x} + 1 ) }{h} \][/tex]
[tex] \qquad \sf \dashrightarrow \: \[ \displaystyle\lim_{x\to0} \: \: \sf \frac{ log( \frac{ h}{x} + 1 ) }{ \frac{h}{x} \times x} \][/tex]
[tex] \qquad \sf \dashrightarrow \: \[ \displaystyle\lim_{x\to0} \: \: \sf \frac{1}{x} \bigg(\frac{ log_{e} ( \frac{ h}{x} + 1 ) }{ \frac{h}{x} \times log_{e}(10) } \] \bigg)[/tex]
[tex] \qquad \sf \dashrightarrow \: \[ \dfrac{1}{x \: log_{e}(10) } \displaystyle\lim_{x\to0} \: \: \sf \bigg(\frac{ log_{e} ( \frac{ h}{x} + 1 ) }{ \frac{h}{x} } \] \bigg)[/tex]
[tex] \qquad \sf \dashrightarrow \: \[ \dfrac{1}{x \: log_{e}(10) } [/tex]
Now, the best estimate of slope is at x = 20 :
[tex] \qquad \sf \dashrightarrow \: \[ \dfrac{1}{20\times 2.303} [/tex]
[tex] \qquad \sf \dashrightarrow \: \[ \dfrac{1}{46.06} [/tex]
[tex] \qquad \sf \dashrightarrow \: \approx0.0217[/tex]
Help please!!!!!!!!!!
Answer:
y= -1/5x+3
I hope that this helps! :)
How to attach multiple photos?
Answer:
click the paperclip
Step-by-step explanation:
you can click the paperclip and paste multiple pictures
An airplane is preparing to land at an airport. It is46,400 feet above the ground and is descending at the rate of3,100 feet per minute. At the same airport, another airplane is taking off and will ascend at the rate of 2,700 feet per minute. When will the two airplanes be at the same altitude and what will that altitude be?
The time when the two airplanes would have the same altitude is 8 minutes. The altitude would be 21,600 feet.
What is the altitude?The equation that can be used to represent the altitude of the descending plane is: feet above the ground - (rate of descent x number of minutes)
46,400 - (3100 x t)
The equation that can be used to represent the altitude of the ascending plane is: rate of ascent x number of minutes
2700 x t
Where t is the number of minutes
When both airplanes are of the same altitude, the above equations will be equal: 2700t = 46,400 - 3100t
In order to determine the value of t, take the following steps:
Combine similar terms: 2,700t + 3,100t = 46,400
Add similar terms : 5,800t = 46,400
Divide both sides by 5,800 : t = 46,400 / 5,800
t = 8 minutes
Altitude = 2700 x 8 = 21,600 feet
To learn more about mathematical equations, please check: https://brainly.com/question/26427570
#SPJ1
8x-(14x - 12) = 48 - 6x
Diego tried to solve the equation 13(x+15)=3
Answer:
x=0.107
Step-by-step explanation:
First we distribute 13 to x and 15. That gives us 13x+15x=3. Now we add 13x and 15x, that gives us 28x=3. Now we divide by 28 on both sides. That gives us x=0.107
During her senior year, Courtney took both the SAT and ACT. She scored 680 on the SAT math test and 27 on the ACT math test. Scores on the math section of the SAT vary from 200 to 800, with a mean of 528 and standard deviation of 117. Scores on the math section of the ACT vary from 1 to 36, with a mean of 20.5 and a standard deviation of 5.5.
Calculate Courtney's standardized score (z-score) on each test. Which of her two test scores was better, relatively speaking? Explain your reasoning.
Her z-scores are given as follows:
SAT: 1.30.ACT: Z = 1.18.Due to the higher z-score, she was relatively better on the SAT.
What is the z-score formula?The z-score of a measure X of a distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.For the SAT test, the parameters are given as follows:
[tex]X = 680, \mu = 528, \sigma = 117[/tex]
Hence her z-score is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (680 - 528)/117
Z = 1.30.
For the ACT test, the parameters are given as follows:
[tex]X = 27, \mu = 20.5, \sigma = 5.5[/tex]
Hence her z-score is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (27 - 20.5)/5.5
Z = 1.18.
Due to the higher z-score, she was relatively better on the SAT.
More can be learned about z-scores at https://brainly.com/question/25638875
#SPJ1
HELP ME SOLVE THIS PLEASE! I WILL GIVE BRAINLYEST
Answer:
Step-by-step explanation:
y keeps adding 6 while x keeps adding 3
At the mini-mart, Kathy spent $1.39 for a muffin, $2.99 for milk, and $0.99 for a bag of chips. About how much did he spend?
$5.00
$3
$4.00
$5.37
Answer:
$5.37
...............
What is the area of ABC? Round to the nearest tenth of a square unit.
Answer:
I can't see the photo very well.
HELL DONT TELL ME BS
DONt
Answer: D , see below
Step-by-step explanation:
remember the power rules
(a^b)^c= a^(b*c)
answer is(10^10)(7^25) is choice D
Answer:
THe answer is d
Compute the sum of all nine 2-digit numbers with a ones digit of 6.
Sum of all nine number = 438
Step-by-step explanation:
Given :
2 Digit Number whose ones place is 6.
Solution :
Nine numbers are - 16,26,36,46,56,66,76,86,96
Sum of all nine number = 16+26+36+46+56+76+86+96 = 438
For more information, refer the link given below
https://brainly.com/question/13013054?referrer=searchResults
Is 3abc an expression?
Answer:
yes
Step-by-step explanation:
an expression is like an equation without the equal sign, or according to the Oxford Dictionary: "a collection of symbols that jointly express a quantity."
Answer:
Yes
Step-by-step explanation:
An expression is a collection of symbols that jointly express a quantity, which means a set of symbols that equals a number. a,b, and c are all variables, meaning that its a expression
Y - 58 = -43
Helppppp
Answer:
y = 15
Step-by-step explanation:
y - 58 = -43
add 58 to both sides
y = 15
Answer:
y = 15
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define Equation
y - 58 = -43
Step 2: Solve for y
Add 58 on both sides: y = 15Step 3: Check
Plug in y into the original equation to verify it's a solution.
Substitute in y: 15 - 58 = -43Subtract: -43 = -43Here we see that -43 does indeed equal -43.
∴ y = 15 is the solution to the equation.
Laura has 1425 dollars in her bank account this amount reflects a 14% increase what was her original amo
I need to find the invalid input in this but I'm having trouble finding it anyone got any ideas?
The mistake made by the given solution is that it squared the imaginary letter i to get i² = -1 instead of recognizing i has no square attached to it.letter i to get i² = -1 instead of recognizing i has no square attached to it.
How to simplify complex numbers?We are given the complex number equation as;
(16 - 3i) + (4 + 2i)
Open the bracket to get;
16 - 3i + 4 + 2i
Collect like terms to get;
(16 + 4) + (2i - 3i)
Simplify to get;
20 + (-i)
= 20 - i
Now, the mistake made by the given solution is that it squared the imaginary letter i to get i² = -1 instead of recognizing i has no square attached to it.letter i to get i² = -1 instead of recognizing i has no square attached to it.
Read more about Complex Numbers at; https://brainly.com/question/10662770
#SPJ1
Weight is a measure of force affected by gravity. The Moon’s gravity is less than Earth’s gravity, so objects weigh less on the Moon than on Earth.
How much do you think a cat will weigh on the Moon? Explain your reasoning.
9514 1404 393
Answer:
about 1.5 pounds
Step-by-step explanation:
The moon's gravity is about 1/6 that of Earth, so a 9-lb cat would weigh about 9/6 = 1.5 pounds on the moon.
PLEASE HELP!!!
Which of the following relationships represents a function?
A.
x -6 5 -2 -2
y 8 6 8 7
B.
x -6 5 -6 7
y 8 8 14 7
C.
x -6 5 -3 10
y 8 6 14 8
D.
x -6 5 -2 5
y 8 6 8 7
Answer:
c
Step-by-step explanation:
hehehehhehrhehheheh
HELP ME FAST PLEASE!!
If -x is positive, then -x>0??
TRUE OR FALSE???
Answer:
true because if it's positive it's greater than zero
Step-by-step explanation:
pls help me with this i need help with this
The measure of the missing angle is 118 degrees
What are quadrilateral?Quadrilateral are figures that have sides and angles
For two parallelograms to be equal, the ratio of the sides must be equal to a constant
Also, all the measure of the angles must be equal. From the given parallelogram, the measure of the angles must be equal that is;
x = 118 degrees
Hence the measure of the missing angle is 118 degrees
Learn more on similar sides here:https://brainly.com/question/24184322
#SPJ1
Answer:
118degrees
Step-by-step explanation:
How many cm in 12.7 inch
What is the equation in standard form of the line y - 5 =
5=(x + 6)?
2y-10=3x + 18
2y = 3x + 28
3x - 2y = -28
3x = 2y - 28
Answer: 5(2x + 3). = 2x2 + 3x − 10x − 15 ... 5. Expand. 1. 2. (2y – 8). 6. Expand and simplify. ... 28 g. 72 h. 162. 2. Simplify. a. +. 72. 162 b. −. 45 2 5.
Step-by-step explanation:
Of the 450 parking spaces in a parking
lot 8% of the spaces are reserved for
handicapped parking. Of those parking
spaces NOT reserved for handicapped
parking, 18 are suitable for compact cars
only. How many spaces that are NOT
reserved for handicapped parking are
suitable for noncompact cars?
A. 432
B. 424
C. 414
D. 396
E. 369
Answer:
D. 396
Step-by-step explanation:
8/100 × 450 = 414
414 - 18 = 396
Answer:
answer could be e. 369
Step-by-step explanation:
762×819 _7299
what is the measure of DE?
Answer:
C: 41°
Step-by-step explanation:
ACB ≅ BDE
he height of Niagara Falls is 56 meters. How many
kilometers high is Niagara Falls?
Answer:
0.056 kilometers
Step-by-step explanation:
Frosty rolled around the track for laps in 10 minutes
A.how many minutes per lap is that be
B.how many laps per minute is that
C.if Frosty holds 40 laps at the same rate how long take does it take him
Answer:
In bold below.
Step-by-step explanation:
A . 10/4 = 2.5 minutes per lap.
B. Laps per minute = 1 / 2.5 = 0.4 laps per minute.
C. Time taken for 40 laps = 40 / 0.4 = 100 minutes.
(-3)(3) + ? = -8
What value makes it true
-1
1
-17
17
Answer:
1
Step-by-step explanation:
-3*3=-9+1=-8
Evaluate the expression for y= -1 -13y-16
Answer: y = -17/14
Step-by-step explanation:
y = -1 -13y - 16
First we must isolate the variable:
y+13y = -1 - 16
Next we must add like terms:
14y = -17
Finally, divide 14 on both sides:
14y/14= -17/14
Answer: y = -17/14
Hope this helps
find slope from table find slope from graph use slope formula
Answer:
To find the slope of both graph and table, you would have to know the coordinates of both.
Step-by-step explanation:
The formula is: m= y2-y1/x2-x1
Let's say that the graph/table says one point lays on (2,9) and the other is (-3,4). You would use the formula to get your slope.
m= 9-4/(-3)-2
m=5/-5
m= -1
Answer:
rise over run
Step-by-step explanation:
2) In A ABC , if LA = 60° , LB = 450 then find tc.
In ∆ABC,
Angle A = 60°
Angle B = 45°
To Find:The measurement of Angle C.
We know that the sum of all the interior angles of a triangle is 180°.
Explanation:Angle A + Angle B + Angle C = 180°
By putting the respected values, we get
60° + 45° + Angle C = 180°
or, 105° + Angle C = 180°
By transposition method, we get
Angle C = 180° - 105°
Angle C = 75°
Answer:The measurement of Angle C is 75°
Need answer asap........
Answer:
So you need to use PEMDAS, Mom is correct but the dad is not correct
Step-by-step explanation:
He needed to subtract before he added, basically from left to right first come first serve.