Answer:
t = (400 + 20c)/(8+c)weighted sum of temperatures4 cupsStep-by-step explanation:
You want an equation for the temperature of 8 cups of hot (50 °C) water combined with c cups of cold (20 °C) water, along with an explanation of it. Then you want the number of cups required to reduce the temperature to 40 °C.
(a) EquationAssuming constant heat capacity and volume as a function of temperature, the temperature of the mix will be the weighted average of the temperatures of the contributors. That is c cups of water at 20 °C combined with 8 cups of water at 50 °C will have a temperature (t) of ...
t = (20c +8(50))/(c+8)
t = (20c +400)/(c +8)
(b) ExplanationThe thermal energy contained in the water is assumed to be jointly proportional to its volume and its temperature. The combined thermal energy of the mixture will be the total of that of its contributors.
That is, the temperature of the mix is the weighted sum of the temperatures of the contributors, the weights being their respective volumes.
(c) 40°The value of c for a temperature of 40 °C is ...
40 = (20c +400)/(c+8)
2(c +8) = c +20) . . . . divide by 20, multiply by (c+8)
2c +16 = c +20 . . . . eliminate parentheses
c = 4 . . . . . . . . . . . . subtract (c+16)
4 cups of cold water must be added to reduce the temperature ot 40 °C.
(a) t = (400 + 20c)/(8+c)
(b)weighted sum of temperatures
(c) 4 cups
What is an equation?An equation is a statement that asserts the equality of two expressions, the expressions are written one on each side of an '=' equal to sign.
Let t be the temperature of water.
Let c be the number of cold cup of water at 20°C
(a)c cups of water at 20 °C combined with 8 cups of water at 50 °C will have a temperature (t) of
[tex]t= \frac{20c+8*50}{c+8}[/tex] --------(1)
(b)The temperature of the mix is the weighted sum of the temperatures of the contributors, the weights being their respective volumes.
(c)The value of c for a temperature of 40 °C is
40 = (20c +400)/(c+8)
2(c +8) = c +20) . . . . divided by 20, multiply by (c+8)
2c +16 = c +20 . . . . eliminate parentheses
⇒ c = 4
Hence, the required equation is [tex]t= \frac{20c+8*50}{c+8}[/tex] and for part (c) 4 cups.
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PLEASE ANSWER ASAP
Farm Land
You are buying 60 acres of farm land at a cost of $685,000.
What is the cost per acre?
$
per acre
What would the cost be for 50 acres?
$
Round your answers to the nearest dollar as needed.
please help me will give u extra points :)
•
Answer:
Ok
Step-by-step explanation:
Find the sum a + (a + 1) + (a + 2) + ... + (a + n - 1) in terms of a and n.
Part (b): Find all pairs of positive integers (a,n) such that n greater than 2 and a + (a + 1) + (a + 2) + ... + (a + n - 1) = 100.
(a) The sum a + (a + 1) + (a + 2) + ... + (a + n - 1) is Sn = n/2 * (a + n)
It can be represented as the sum of an arithmetic series. The nth term of the series is (a + n - 1) and the first term is a.
The common difference between consecutive terms is 1. The formula to calculate the sum of an arithmetic series is:
[tex]Sn = n/2 * (2a + (n - 1)d)[/tex]
Where n stands for the number of terms, a will be the first term, and d is a common difference. By substituting the values for n, a, and d, we'll get:
Sn = n/2 * (2a + (n - 1) * 1)
Sn = n/2 * (2a + n - 1)
Sn = n/2 * (a + n)
(b) The pairs of positive integers (a,n) that will fulfill the conditions are (10,10), (15,8), and (20,6).
To find all pairs of positive integers (a,n) such that n is greater than 2 and a + (a + 1) + (a + 2) + ... + (a + n - 1) = 100, we can rearrange the formula from the above problem part (a) to solve for a:
Sn = n/2 * (a + n) = 100
a = 2 * (100/n) - n
Since a must be a positive integer, we can use trial & error to find all possible values of n that make a positive integer. Here are some of the solutions:
For n = 10, a = 10.
For n = 8, a = 15.
For n = 6, a = 20.
So the pairs of positive integers (a,n) that satisfy the conditions are (10,10), (15,8), and (20,6).
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A company studied the number of lost-time accidents occurring at its Brownsville, Texas, plant. Historical records show that 9% of the employees suffered lost-time accidents last year. Management believes that a special safety program will reduce such accidents to 5% during the current year. In addition, it estimates that 15% of employees who had lost-time accidents last year will experience a lost-time accident during the current year.
a. What percentage of the employees will experience lost-time accidents in both years (to 2 decimals)? %
b. What percentage of the employees will suffer at least one lost-time accident over the two-year period (to 2 decimals)? %
answer-
577468-64753=57623546
a student runs an experiment to test how microwave power and temperature affect popping. each bag of popcorn can be popped for 3 minutes or 4 minutes. the microwave power can be set to low, medium, and high. each combination of time and power is tested on one bag of popcorn and the number of unpopped kernels is recorded. The number of treatments in this experiment are:
• 12
• 6
• 4
Option • 12 is the answer .The number of treatments in the experiment is 12.
The understudy is directing a trial to comprehend the connection between microwave power and time on the quantity of unpopped bits in a pack of popcorn. There are three degrees of microwave power: low, medium, and high. Each sack of popcorn can be popped for either 3 minutes or 4 minutes, which provides us with a sum of double cross variables. To cover every one of the potential mixes of time and power, the understudy runs 12 distinct medicines (3 degrees of force x 2 degrees of time). Every treatment addresses one sack of popcorn that is popped for a particular time frame and with a particular power setting. The quantity of unpopped parts is recorded for every treatment, and the outcomes are utilized to make determinations about the impacts of microwave power and time on the quantity of unpopped pieces.
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At a certain bakery, the price of each doughnut is $1.S0. Let the random variable D represent the number of doughnuts a typical customer purchases each day. The expected value and variance of the probability distribution of' D are 2.6 doughnuts and 3.6(doughnuts) respectively. Let the random variable P represent the price of the doughnuts that a typical customer purchases each day. Which of the following is the standard deviation, in dollars, of the probability distribution of P? (A) 1.5(3.6) 1.513.6 Vi.5(3.6) 1.502.6) 1.512.6
The standard deviation of the probability distribution for the given price of each doughnut and the variance is equal to $√1.50 × 3.6.
Price of the each doughnut 'P' = $1.50
Expected value of the probability distribution of the doughnut = 2.6
Variance of the probability distribution = 3.6
Price of the variance of the probability distribution is equal to
= Price of each doughnut × Variance
= 1.50 × 3.6
Standard deviation of the probability distribution is equal to
= √ Price of the variance of the probability distribution
= √1.50 × 3.6 dollars.
Therefore, the standard deviation of the probability distribution is equal to
$√1.50 × 3.6.
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in the diagram below find the value of x and hence find tb
Answer:
x = 11 , TB = 12 cm
Step-by-step explanation:
given a tangent and a secant from an external point to the circle, then
the square of the measure of the tangent is equal to the product of the measures of the secant's external part and the entire secant, that is
TC × TB = TA²
3(3 + x - 2) = 6²
3(x + 1) = 36 ( divide both sides by 3 )
x + 1 = 12 ( subtract 1 from both sides )
x = 11
then
TB = TC + CB = 3 + (11 - 2) = 3 + 9 = 12 cm
The ages of the students in an art class at the community center are listed below. 9, 11, 14, 14, 16, 21, 24, 26, 32, 33, 37, 38, 38, 52, 53, 55 Complete the frequency table
According to the information, the frequency table would look like this: 0 - 9 = 1, 10 - 19 = 4, 20 - 29 = 3, 30 - 39 = 5, 40 - 49 = 0, 50 - 59 = 3.
How to identify the frequency of student ages?To identify the frequency of the ages of the students we must analyze the information on the age of each student. Once we have this information we must classify each student in a range. Later we must count how many students we have in each range to identify the frequency.
0 - 9 = 110 - 19 = 420 - 29 = 330 - 39 = 540 - 49 = 050 - 59 = 3Learn more about frequency in: https://brainly.com/question/5102661
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A triangular prism and two nets are shown:
Which is the correct net of the prism and what is the surface area of the prism? (1 point)
A. Net B with 184 square inches
B. Net B with 248 square inches
C. Net A with 268 square inches
D. Net A with 540 square inches
The surface area of the triangular prism will be 540 square inches. Then the correct option is D.
What is the surface area of a triangular prism?Let h be the height and b be the base of the triangle. Let L₁, L₂, and L₃ be the length and W be the width of the rectangle. Then the surface area of the triangular prism will be given as,
Surface area = 2 Area of triangle + 3 Area of rectangle
Surface area = (h x b) + (L₁ + L₂ + L₃) x W
The surface area of the triangular prism is given as,
SA = (5 x 12) + (5 + 12 + 13) x 16
SA = 60 + 30 x 16
SA = 60 + 480
SA = 540 square inches
The surface area of the triangular prism will be 540 square inches. Then the correct option is D.
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Let P(t)=36(1−e^(−kt))+56
represent the expected score for a student who studies t
hours for a test. Suppose k=0.24
and test scores must be integers.
The highest integer that the student can possibly score is given as follows:
92.
If the student does not study, the grade that he should expect is of:
56.
What is the exponential function?The exponential function for this problem is defined as follows:
P(t) = 36(1 - e^(-0.24t)) + 56.
In which:
t is the number of hours studied for the test.P(t) is the expected grade.The highest grade is for large values of t, meaning that e^(-0.24t) = 0, and thus:
P(t) = 36 + 56
P(t) = 92.
If the student does not study, we have that t = 0, hence the grade is given as follows:
P(0) = 36(1 - e^(-0.24 x 0)) + 56
P(0) = 0 + 56
P(0) = 56.
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Amy is painting one wall in her dining room. The wall is 10 feet by 13 feet. A gallon of paint covers 60 square feet. The hardware store only sells paint by the gallon, meaning that partial gallons cannot be purchased. Given this, how many gallons of paint will Amy need to purchase
Answer:
3
Step-by-step explanation:
Since the wall is two different lengths, it assumes the wall is a rectangle
Angle of a rectangle is L x W
Which means 10x13 = 130
Since every gallon covers 60 square feet, we need to divide that 130 by 60
(130)/(60) = 2.2
Since they dont sell partial gallons, she would have to buy 3 gallons of paint
Nathan's lawnmower uses of a tank of gas to cut three one-acre
lawns. How many one-acre lawns can he cut with a full tank of
gas? Explain.
Nathan can cut 3 one-acre lawns with a full tank of gas
What is Cross multiplying fractions?
Cross multiply fractions by multiplying one fraction's denominator by the second fraction's numerator and then comparing the two values. The larger fraction is the one with the higher value.
Since Nathan's lawnmower uses one tank of gas to cut three one-acre lawns, it means that he can cut one one-acre lawn with 1/3 of a tank of gas. So, if he has a full tank of gas, he can cut one-acre lawns equal to the number of times 1/3 fits into a full tank. In other words, he can cut a full tank of gas divided by 1/3 of a tank of gas.
The number of one-acre lawns Nathan can cut with a full tank of gas is:
1 tank / (1/3 tank) = 3 one-acre lawns.
So, Nathan can cut three one-acre lawns with a full tank of gas.
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It takes you 36 seconds to walk from the first (ground) floor of a building to the third floor. How long will it take you to walk from the first floor to the sixth floor (at the same pace, assuming all floors have the same height)?
Answer:
72 seconds.
The 6th floor is 2 times the amount of walking from the ground floor to the third, so the time to walk to the 6th floor will be twice as long too.
36 * 2 = 72
Step-by-step explanation:
Hope it helps! =D
IVE BEEN RACKING MY BRAIN FOR 2 DAYS ON HOW TO WORK THIS PROBLEM OUT I CANT SEEM TO GET HOW ITS DONE FRUSTRATING!!!! PLEZZZ ANYONE I JUST WANT TO GIVE UP
Bill scheduled himself from 8:00 AM-1:00 PM Sunday through Wednesday. On Wednesday, he needed to release his intervals from 11:00 AM-1:00 PM at the last minute. He serviced all of the other time for which he posted. What was his overall Commitment Adherence percentage? Enter whole numbers (no decimals) only.
Bill's overall Commitment Adherence percentage was 64%.
What was his overall Commitment Adherence percentage? To find the overall Commitment Adherence percentage, we need to find the total time Bill committed to work and the total time he actually worked.Total time committed: 5 days * 5 hours per day = 25 hoursTotal time actually worked: 4 days * 5 hours per day - 2 hours = 16 hoursThe overall Commitment Adherence percentage is then:Adherence Percentage = (Total time actually worked / Total time committed) * 100Adherence Percentage = (16 / 25) * 100 = 64%So Bill's overall Commitment Adherence percentage was 64%.To learn more about percentage refer:
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Help on math for 10 points
Answer:
2
Step-by-step explanation:
SV = TU
x+3 = 4x-3
6=3x
x=2
Hello!:
In a parallelogram:
--> the sides parallel to each other are equal in length
--> so sides SV and TU are equal lengths
--> which in equation form
[tex]SV=TU\\x+3=4x-3\\4x-x=3+3\\3x=6\\x=2[/tex]
Thus if SV = x + 3, then:
[tex]SV=x+3=2+3=5[/tex]
The length of SV is 5
Answer: 5
a cell phone company charges $35 per month for an unlimited data plan and charges a one time $100 activation fee. your parents will only spend a maximum of $485. write and solve an inequality that represents the total months (m) your parents will pay for the phone
The number of months (m) your parents will spend paying for the phone, and then x≤11, by solving the inequality.
What is meant by inequality?In mathematics, inequality refers to a relationship between two expressions or values that is not equal to one another. So, inequality develops as a result of imbalance.The equals sign in the equation-like statement 5x 4 > 2x + 3 has been replaced by an arrowhead. This is a prime instance of inequality. This indicates that the left half, 5x 4, is larger than the right part, 2x + 3, in the equation.Less than symbol (), greater than symbol (>), more than or equal to symbol (), less than symbol (), and not equal to symbol () are the five inequality symbols used in mathematics.Therefore,
Set the months to X based on the information from the query, and we have
35X + 100 ≤ 485
then we can have
35x ≤ 485 -100
35x≤385
x≤385/35
x≤11
Consequently, we may state that the parents will pay for the phone for a total of 11 months.
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in 2013, kai renters a 2-bedroom apartment for $836. last year, 2022, kai renewed her lease and the rent had increased to $1549. if the rise in rent for kai’s apartment was liner how much was her rent payment in 2016
Based on the slope, which describes a linear equation, the rent payment of Kai in 2016, was $1,073.66.
What is a linear equation?A linear equation is an algebraic equation written in the form of y=mx+b.
A linear equation involves a constant and a first-order term, where m is the slope and b is the y-intercept.
Kai's rental payment in 2013 = $836
Kai's rental payment in 2022 = $1,549
Slope = Rise/Run
Rise (Difference in rent between the two periods = $713 ($1,549 - $836)
Run = (Difference in the years) = 9 (2022 - 2013)
Slope = $79.22 ($713/9)
Let the number of years between 2013 and the stated year = x
Run = 3 (2016 - 2013)
Linear Equation:y = mx + b
Rent in x years = 836 + 79.22x
= 836 + 79.
= $1,073.66 (836 + 79.22(3)
Thus, solving the linear equation, Kai's rental payment in 2016 was $1,073.66.
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At Aaron's Automobile's, Bob sold $150,000 worth of cars last month. If Bob earns a 5% commission on his sales, how much did he make in
commission last month?
Bob's commission was
Answer: 7,500
Step-by-step explanation: 5% of 150,000 is 7,500.
WILL GIVE 30 POINTS
Suppose f is a function that takes a real number x and performs the following steps in the order given:
(1) add 8
(2) take the square root
(3) subtract 9
(4) divide into 12
f(x)=?
Answer: f(x) = (x+8)^(1/2) - 9 / 12
Step-by-step explanation:
To find f(x), we need to apply the steps given in the problem in the order they are presented.
First, we add 8 to the input value x. This step is represented by the term x+8.
Next, we take the square root of the result from step 2. This step is represented by the exponent (1/2) on the term x+8.
Next, we subtract 9 from the result of step 3. This step is represented by the term -9.
Finally, we divide the result of step 4 by 12. This step is represented by the division operator '/' and the denominator 12.
So f(x) is a function that takes the input x, adds 8, takes the square root, subtracts 9, and divides by 12.
Answer:
f(x) = [√(x + 8) - 9]/12
Step-by-step explanation:
The expression f(x) begins with ->
Step 1: x + 8
Step 2: √(x + 8)
Step 3: √(x + 8) - 9
Step 4: [√(x + 8) - 9]/12
The equation is now:
f(x) = [√(x + 8) - 9]/12
You purchase a plant and begin measuring its height each day. This plant grows the same
amount each day. When you got it, it was 10 cm tall. The next day it was 13 cm tall. The day
after that it was 16 cm tall. How tall will it be one week after you purchased it?
Answer:
31 cmStep-by-step explanation:
Initial height is 10 cm and daily growth rate is 3 cm as:
13 - 10 = 3 and16 - 13 = 3After one week the plant will be:
10 + 7*3 = 10 + 21 = 31 cm tallIf the bisector of an angle of a triangle bisects the opposite side, the is the triangle isosceles. If true then enter 1 else if False enter 0
The statement given is true. When the bisector of an angle of a triangle bisects the opposite side, the is the triangle isosceles.
In the attached picture of ΔABC, we can see that AD is the bisector of ∠A that meets BC in D, so that BD = DC.
Now, we need to prove that AB = AC.
As construction, produce AD to E so that AD = DE, and then join CE.
So, in ΔABD and ΔECD, we have:
BD = CD
AD = ED
and ∠ADB = ∠EDC because those are vertically opposite angles.
Consequently, based on SAS congruence criterion, ΔABD ≅ ΔECD.
Thus, AB = EC and ∠BAD = ∠CED. And also, ∠BAD = ∠CAD.
For that reason, it means ∠CAD = ∠CED, and AC = EC.
Hence, AB = AC. It is proved that the triangle is isosceles.
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Question 12: Hannah baked some chocolate, strawberry and vanilla cupcakes.
She baked four times as many chocolate as strawberry cupcakes.
She baked three times as many chocolate as vanilla cupcakes.
Altogether Hannah made 152 cupcakes.
How many cupcakes of each flavour did Hannah make?
Let's call the number of strawberry cupcakes "s".
So the number of chocolate cupcakes is 4s and the number of vanilla cupcakes is 3s.
Altogether, Hannah made s + 4s + 3s = 8s cupcakes.
We know that Hannah made 152 cupcakes, so 8s = 152
Therefore, s = 19
So Hannah made 19 strawberry cupcakes, 4 * 19 = 76 chocolate cupcakes, and 3 * 19 = 57 vanilla cupcakes.
A pile is a post-like support made of timber, steel, or concrete used in foundations that are driven deep into the ground to support structures such as piers. While the tide is out, a pile at Old Pier in Naples Florida, casts a shadow that is 31 inches long. At the same time, a person standing on the shore who is 6 feet 4 inches tall casts a shadow that is 45 inches long. How much of the pile is above the water? Round your answer to the nearest feet and inches.
The height of the pile above the water is 4 feet 4 inches.
What are ratio and proportion?A ratio is a comparison between two similar quantities in simplest form.
Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.
In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.
We know 1 foot is equal to 12 inches.
6 feet 4 inches = 6×12 = 4 = 76 inches.
let, The height of the pole above the sea is 'x' inches.
Therefore,
x : 31 : : 76 : 45.
x/31 = 76/45.
x = 31×1.68.
x = 52. 35 inches.
or 4 feet 4 inches.
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Is 14 or 18 the solution of the equation 7x-20+78
Answer:
the answer is 7x + 58
Step-by-step explanation:
7x - 20 + 78
=7x + 58.
remember your question is algebra.
36 9/10 − 18 6/10
Please help
Thanks :)
Answer:
i believe the answer is 18 3/10
Step-by-step explanation:
PLSSSS HELPPPP ME TY
Answer:
Below
Step-by-step explanation:
Volume of a cylinder = pi r^2 h
the volume of this FULL pool = 2 x 56.52 = 113.04 ft^3
the radius is 1/2 of the diameter = 3 ft
V = pi r^2 h <======re-arrange to
V / (pi r^2) = h
so your equation at the bottom would be
113.04 ÷ 3^2 ÷ 3.14
Now rearrange the equation you wrote above so that P is written in terms of E and S . The quantity of pizza he buys can be represented by the equation ________ .
The equation representing the amount spend on salad and pizza is E = 5S + 2P , P in terms of E and S is P = (1/2)(E - 5S) and the completion of table is given by:
Budget Bowls of salad Slice of pizza
$40.00 0 20
$40.00 4 10
$40.00 8 0
Let 'E' represents the dollars spends on salad and pizza.
'S' represents the bowls of salad, 'P' represents the slice of pizza
Cost of bowl of salad = $5.00
Cost of slice of pizza = $2.00
Equation represents dollars spends on salad and pizza is :
E = 5S + 2P
Equation representing P in terms of E and S is:
P = (1/2)(E - 5S)
If E = $40.00
Then to make equation true value of S and P for the table is:
E = $40.00
S = 0
40 = 5(0) + 2P
⇒P = 20
E = $40.00
S = 4
40.00 = 5(4) + 2P
⇒P = 10
E = $40.00
P = 0
40.00 = 5S + 2(0)
⇒S = 8
In table form:
Budget Bowls of salad Slice of pizza
$40.00 0 20
$40.00 4 10
$40.00 8 0
Therefore, the equation representing total amount of money spend is
E = 5S + 2P , representation of P in terms of E and S is P = (1/2)(E - 5S) and complete table is equal to :
Budget Bowls of salad Slice of pizza
$40.00 0 20
$40.00 4 10
$40.00 8 0
Paolo is buying salad and pizza for a company lunch. Suppose that a bowl of salad costs $5.00, and slice of costs $2.00.Let E be the amount in dollars that Paolo spends on salad and pizza. If Paolo buys S bowls of salad and P slices of pizza, then the total amount of money he spends E can be represented by the equation _____.Now rearrange the equation you wrote above so that P is written in terms of E and S. The quantity of pizza he buys can be represented by the equation _____.Suppose Paolo has $40.00 to spend on salad and pizza; that is E = $40.00Complete the following table with values of S or P that make the equation true. To complete the first row, determine the number of pizza slices Paolo can purchase with $40.00, when the number of salad bowls he purchases is 0.Budget (Dollars) Salad (Bowls) Pizza (Slice)40.00 0 _____40.00 4 _____40.00 _____ 0
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I added a screenshot.
The solution is Option C.
The value of the set n ( A' ∪ B' ) = n ( A ∩ B )' = 15
What is union and intersection of sets?The union of two sets A and B is the set of all those elements which are either in A or in B, i.e. A ∪ B, whereas the intersection of two sets A and B is the set of all elements which are common. The intersection of these two sets is denoted by A ∩ B
The union of two sets is a new set that contains all of the elements that are in at least one of the two sets
The intersection of two sets is a new set that contains all of the elements that are in both sets
Given data ,
From the Venn diagram , we get
n ( A ) = { 3 , 1 }
n ( B ) = { 7 , 1 }
And , n ( A ∩ B ) = { 1 }
And , the universal set n ( U ) = { 5 , 3 , 1 , 7 }
From the set theory , we get
Now , the value of n ( A' ∪ B' ) = n ( A ∩ B )'
n ( A ∩ B )' = n ( U ) - n ( A ∩ B )
n ( A ∩ B )' = { 5 , 3 , 1 , 7 } - { 1 }
So , n ( A ∩ B )' = { 3 , 7 , 5 }
And , n ( A ∩ B )' = 3 + 7 + 5 = 15
Hence , the set n ( A ∩ B )' is 15
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Rewrite e^-2.5 =h as an equivalent logarithmic equation. Enclose arguments of functions in parentheses and include a multiplication sign between terms. For example, c*ln(h).
In mathematical terms, the equation e^-2.5 = h states that the exponential value of -2.5 (e^-2.5) is equal to the variable h. To convert this equation into its logarithmic form, we can take the natural logarithm of both sides of the equation. The natural logarithm, represented by the function ln, returns the power to which e must be raised to obtain a given number.
So, taking the natural logarithm of both sides of the equation, we have:
ln(e^-2.5) = ln(h)
Since ln(e^x) = x, we can simplify the left side of the equation:
ln(h) = -2.5
Thus, the logarithmic equivalent of the equation e^-2.5 = h is ln(h) = -2.5.
The logarithmic equation ln(h) = -2.5 can be interpreted as follows: the natural logarithm of h is equal to -2.5. In other words, h is the result of raising e to the power of -2.5. To find the value of h, we can use the exponential function:
h = e^-2.5
Therefore, the original equation e^-2.5 = h and the logarithmic equation ln(h) = -2.5 are mathematically equivalent and can be used interchangeably.
It is worth mentioning that logarithms are used in many areas of mathematics and science, including engineering, finance, and physics. They allow us to simplify complex calculations and to solve problems that are otherwise difficult or impossible to solve.
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pls help
Which angle is supplementary to
∠FAE?
Answer:
<FAB
Step-by-step explanation:
Supplemental angles add to 180. They make a straight line.
Supplementary angles add up to 180°. Using this knowledge, write an equation with the given information:
x°+45°=180°
Subtract 45° from both sides:
x°=135°
We now know that we're looking for an angle in the figure that equals 135°. Notice that ∠BAF accomplishes this, therefore ∠BAF is supplementary to ∠FAE.
