If you ever swam in a pool and your eyes began to sting and turn red, you felt the effects of an incorrect pH level. pH measures the concentration of hydronium ions and can be modeled by the function p(t) = −log10t. The variable t represents the amount of hydronium ions; p(t) gives the resulting pH level.
Water at 25 degrees Celsius has a pH of 7. Anything that has a pH less than 7 is called acidic, a pH above 7 is basic, or alkaline. Seawater has a pH just more than 8, whereas lemonade has a pH of approximately 3.
Create a graph of the pH function either by hand or using technology. Locate on your graph where the pH value is 0 and where it is 1. You may need to zoom in on your graph.
The pool maintenance man forgot to bring his logarithmic charts, and he needs to raise the amount of hydronium ions, t, in the pool to 0.50. To do this, he can use the graph you created. Use your graph to find the pH level if the amount of hydronium ions is raised to 0.50. Then, convert the logarithmic function into an exponential function using y for the pH.
The pool company developed new chemicals that transform the pH scale. Using the pH function p(t) = −log10t as the parent function, explain which transformation results in a y-intercept and why. You may graph by hand or using technology. Use complete sentences and show all translations on your graph.
p(t) + 1
p(t + 1)
−1 • p(t)
Answers
For a better understanding of the explanation provided here, please go through the graphs in the attached files. The first file contains the explanations to the first part of the question and the second file contains the three graphs required to explain the second part (the y intercept part) of the question.
It has been given to us that the pH concentration equation is:
[tex] p(t)=-log_{10}t [/tex]
where, The variable t represents the amount of hydronium ions and p(t) gives the resulting pH level.
As can be seen from the first graph, pH is 1 when the amount of hydronium ions, t is 0.1. This is as expected, because, from the concept of logarithms we know that:
[tex] log_{10}(0.1)=log_{10}(\frac{1}{10})=log_{10}(10^{-1})=-1\times log_{10}10=-1\times 1=-1 [/tex]
Thus, [tex] p(0.1)=-1\times-1=1 [/tex]
Again, the value of pH, p(t) is 0 when the concentration of the Hydronium ions, t is 1. This, again, is as expected, because, from the concept of logarithms we know that [tex] log(1)=0 [/tex].
If the pool maintenance man uses our graph and needs to find the the pH level if the amount of hydronium ions is raised to 0.50, then to do so, the pool maintenance man must draw a vertical line from t=0.5 and check the x coordinate of the point where this vertical line intersects the p(t) graph. As we can see from the graph this roughly comes out to be the horizontal line y=0.3.
Let us now move on to the second part of the question. For a better understanding of this part please go through the second graph which has been attached. This graph contains all translations on the original graph and the explanation to each one of them is provided below:
Let us start with the last one, -p(t). We know that, since, [tex] p(t)=-log_{10}(t) [/tex], therefore, [tex] -p(t)=log_{10}(t) [/tex], simply a vertical "flip" or reflection of the original graph. And because the original graph did not have a y intercept, this graph too will not have a y intercept.
Let us now move on to the first one. Here, [tex] p(t)+1=-log(t)+1 [/tex]. This graph will simply move the original graph vertically up by 1 unit and that will not have any bearing on the y intercept and thus, the graph of p(t)+1 will again, not have a y intercept.
Finally, let us move on to the graph of the equation p(t+1). As can be seen, this graph has a y intercept at the origin when t=0. This is because:
[tex] p(t+1)=log_{10}(t+1) [/tex]
and when t=0, [tex] p(t+1)=p(0+1)=log_{10}(0+1) [/tex]
[tex] p(1)=log_{10}(1)=0 [/tex]
Thus, when t=0, p(t+1)=0 too and thus we have a y intercept.
Therefore, out of the three transformations, only the middle transformation results in a y-intercept, the explanation for which has been provided.
Related Questions
Find two numbers, if
Their sum is 3/5 and their difference is 7 1/5
Answers
.. x + y = 0.6
.. x - y = 7.2
Add these equations to get
.. 2x = 7.8
.. x = 3.9
Then you can find y from
.. y = 0.6 -3.9 = -3.3
The two numbers are -3.3 and 3.9.
Answer:
3.9 and -3.3
Step-by-step explanation:
helpppppppppppppppppppp
Answers
For the function:
y = exp (x) -4
We see that for x = 0 we have:
y = exp (0) -4
y = 1-4
y = -3
Which is consistent with the graph.
Answer:
y = exp (x) -4
option 4
William works at a nearby electronics store. He makes a commission of 6 % 6%6, percent on everything he sells. If he sells a computer for $ 7 6 4 . 0 0 $764.00dollar sign, 764, point, 00, how much money does William make in commission?
Answers
$ 764 ----> 100%
$ x --------> 6%
We clear the value of x:
x = (6/100) * (764)
x = 45.84 $
Answer:
William makes $ 45.84 in commission
Answer:
x = 45.84 $
late but i need points
Step-by-step explanation:
I need help with this one
Answers
So this is False
There are 18 animals and 40 legs in all so lets see how many cows could be born. 4,8,16,12,24,28,32,36,40. so there could be 9 cows and now lets see on chickens 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40. so the could be 20 chickens so if u think. i think the ancewer is 30 chickens and 10 cowws thx!!!!
Answers
Given information
--------------------------------------
Total animals = 18
Total legs = 40
--------------------------------------
Assumed all are chickens
--------------------------------------
Total legs = 18 x 2 = 36
--------------------------------------
Calculate extra legs
--------------------------------------
40 - 36 = 4
--------------------------------------
Difference in legs between the cow and chicken
--------------------------------------
4 - 2 = 2
--------------------------------------
Find the number of cows
--------------------------------------
4 ÷ 2 = 2
--------------------------------------
Find the number of chickens
--------------------------------------
18 - 2 = 16
--------------------------------------
Answer: 16 chickens and 2 cows
--------------------------------------
Tim predicts he will get 98 points on the next exam. If Tim actually earned 62 points, what was Tim's percent error? Round your answer to the nearest tenth of a percent.
Answers
original #= 98
new #= 62
% change= (62-98)/98 x 100
= -36/98 x 100
= -0.36734 x 100
= -36.73%
Rounded to nearest 10th of %= -36.7%
CHECK:
= 98 - (98 * 36.73%)
= 98 - (98 * 0.3673)
= 98 - 36
= 62 new #
ANSWER:
Her percent error was 36.7% (rounded to the nearest tenth of a percent). The negative indicates a decrease.
Hope this helps! :)
Answer: 58.1
Step-by-step explanation:
98 - 62 / 62 = rounds to 58.1 Thank me Later..
Which of the following is the image of A after a rotation of -90° about the origin?
(0, -2)
(0, 2)
(-2, 0)
Answers
Answer:
Option A. (0, -2)
Step-by-step explanation:
In the given graph coordinates of point A are (2, 0).
Now this point is rotated by -90° about the origin, that means rotation has been done clockwise by 90°.
Now after rotation this point A will lie on the negative side of the y-axis and the new coordinates become (0, -2).
Therefore, option A. (0, -2) is the correct option.
What happens to the surface area of a rectangular prism when each of the dimensions is doubled? (1 point) i?
Answers
Final answer:
The surface area of a rectangular prism increases by four times when each of the dimensions is doubled because surface area scales in proportion to the square of the linear dimensions.
Explanation:
When the dimensions of a rectangular prism are doubled, the surface area of the prism increases by a factor of four. This is because the surface area is proportional to the square of the linear dimensions. If the length, width, and height of the prism are doubled, the new surface area (A') compared to the original surface area (A) is calculated as follows:
A' = 2l × 2w + 2l × 2h + 2w × 2h
A' = 4(lw + lh + wh)
A' = 4A
Thus, if each dimension is doubled, the surface area increases by four times.
(x+10)+(3x+2)=180
What is x
Answers
To solve this problem, we need to simplify.
(x + 10) + (3x + 2) = 180
x + 3x + 10 + 2 = 180
We combine like terms first:
4x + 12 = 180
And isolate x.
4x = 168
Now, we divide both sides of the equation by 4 to solve for x.
x = 168 ÷ 4
x = 42
Hope this helps!
Step 1: Simplify both sides of the equation.x+10+3x+2=180(x+3x)+(10+2)=180 (Combine Like Terms)4x+12=1804x+12=180
Step 2: Subtract 12 from both sides.4x+12−12=180−124x=168
Step 3: Divide both sides by 4.4x/4=168/4
x=42
A family on vacation drives 123 miles in 2 hours, then gets stuck in traffic and goes 4 miles in the next 15 minutes . The remaining 191 miles of the trip take 3 3/4 hours. What was their average rate of speed to the nearest tenth of a mile per hour ?
Answers
The average speed of an object is the total distance traveled by the object divided by the elapsed time to cover that distance.
Total distance traveled = 123 miles + 4 miles + 191 miles = 318 miles
Total time taken = 2 hours + 15 minutes + [tex] 3\frac{3}{4} [/tex] hours
= 2 hours + [tex] \frac{15}{60} [/tex] hour + [tex] \frac{15}{4} [/tex] hours
= [tex] 2+\frac{1}{4}+\frac{15}{4} [/tex] hours
=[tex] 2+\frac{16}{4} [/tex] hours
= 6 hours
Average speed = Total distance [tex] \div [/tex] Total time
= [tex] \frac{318}{6} [/tex] mile per hour
= 53 mile per hour.
The average speed of an object is the total distance traveled by the object divided by the elapsed time to cover that distance.
Total distance traveled = 123 miles + 4 miles + 191 miles = 318 miles
Total time taken = 2 hours + 15 minutes + [tex] 3\frac{3}{4} [/tex] hours
= 2 hours + [tex] \frac{15}{60} [/tex] hour + [tex] \frac{15}{4} [/tex] hours
= [tex] 2+\frac{1}{4}+\frac{15}{4} [/tex] hours
=[tex] 2+\frac{16}{4} [/tex] hours
= 6 hours
Average speed = Total distance [tex] \div [/tex] Total time
= [tex] \frac{318}{6} [/tex] mile per hour
= 53 mile per hour.
Check my answers please?
1. What are the first five terms of the sequence given by the formula a_n=6n+1
a. 7,13,19,25,31
b.1,7,13,19,25
c. 6,12,18,24,30 <---
d.13,19,25,31,37
3. Write an explicit definition for the sequence -3, 1, 5, 9,...
a. a_n=-3+4(n-1)
b. a_n=-3+ 4n <---
c. a_n= -3+(n-1)
d. a_n= -3+4(n+1)
7. what is the 12th term of the sequence 20,16,12,...
a. -30
b. -20
c. -28
d. -24 <----
8. Find the missing term of the arithmetic sequence 20, __, 32,...
a.42
b.18
c.34 <----
d. 36
10. what is the 10th term of the sequences 625,125,25,...
a. 1/3,125
b. 1/
Answers
3. Correct answer is a (a(n)=-3+4(1-1)=-3).
7. The pattern is to reduce the previous value by 4, thus the 12th term of the sequence is -24 (a(n)=20 - 4(n-1)=20 - 4(12-1)=-24).
8. Missing term is 26 (32+20=52; 52/2=26).
10. Pattern is 625/1=625; 625/5=125; 125/5=25; 25/5=5, thus. the 10th term is 1/3125 (answer a).
n quadrilateral LMNO, LO ∥ MN. What additional information would be sufficient, along with the given, to conclude that LMNO is a parallelogram? Check all that apply. ML ∥ NO ML ⊥ LO LO ≅ MN ML ≅ LO MN ⊥ NO
Answers
Answer: The correct options are
(A) ML ∥ NO,
(C) LO ≅ MN.
Step-by-step explanation: Given that in quadrilateral LMNO, LO ∥ MN.
We are to select the correct additional information that would be sufficient along with the given information to conclude that LMNO is a parallelogram.
PARALLELOGRAM: A parallelogram is a quadrilateral if ine of the following conditions are satisfied:
(i) Two pairs of opposite sides parallel
or
(ii) one pair of opposite sides parallel and congruent.
The given condition is
LO ∥ MN.
So, the other additional sufficient condition will be
either the other pair of opposite sides parallel, i.e., ML ∥ NO,
or
the same pair of parallel sides are congruent, i.e, LO ≅ MN.
Thus, the correct statements are ML ∥ NO and LO ≅ MN.
Option (A) and (C) are correct.
Answer:
a and c
Step-by-step explanation:
A triangular playground has angles with measures in ratio 8: 3: 9 what is the measure of the smallest angle
Answers
20x = 180
x = 180/20
x = 9
The smallest angle is: 3×9 = 27 degrees
Note: 180 degrees is the sum of angles in a triangle
Answer:
The measure of the smallest angle is 27°
Step-by-step explanation:
The triangle has angles with measure ratio 8:3:9, so the sizes of the angles are going to change depends on the ratio.
Let’s name the common value as “α”.
Basing on the angle-sum property, we already know that the sum of the angle in a triangle is 180°.
The measure of each one are:
8α, 3α, 9α
The sum of these is 180°.
Then,
8α + 3α + 9α = 180°
Let’s sum similar values:
20α =180°
α= 180°/20
α= 9
Replacing values, we going to find the measure of each angle:
8(9) = 72°
3(9) = 27°
9(9) = 81°
The measure of the smallest angle is 27°
What is the simplest form of root 3.025
Answers
Explanation:
1) By convention if you do not mention the index of the root it is square root.
2) By definition the square root of a number x is the numberwhose square is the original number, i.e.
√3025 = 55 because 55^2 = 3025.
3) 3025 is a perfect square because it is the square of a whole numbe.
4) It is easy to find the square root of a perfect square, but if the number is not easily reknownm as a perfect square you will have to probe with several numbers until finding the square root.
For example, you might easily realize that 50^2 is 2500, and that 60^2 is 3600, so you start testing numbers greater thatn 50 and less than 60 until you get 55^2 = 3025.
5) How can you simplify a radical? If you know the properties of radicals you can simplify a radical easily.
You start by decomposing 3025 into its prime factors.
That will result into:
[tex]3025 =5^2{11}^2[/tex]
Then, by radical properties:
[tex] \sqrt{5^2{11}^2} = \sqrt{5^2} \sqrt{{11}^2} =(5)(11)=(55)[/tex]
So, the simplest form of √3025 is 55.
Which calculation can be used to find the value of y in the equation y^3 = 27?
y equals 27/3
y equals cube root of 27
y equals square root of 27 divided by 3
y equals square root of 27
Answers
another answer is
y equals square root of 27 divided by 3
Provided it is square root of (27 divided by 3)
PLEASE HELP ASAP!!! WILL GIVE BRAINLIEST!!!
Two florist purchased flower bouquets and vases at the same store. The first florist bought 2 flower bouquets and 2 vases for a total of $12.50. The second florist bought 8 flower bouquets and 2 vases for a total of $29.00.
Let b represent the cost of one flower bouquet and v represent the cost of one vase. Write AND SOLVE a system of equations to find the price of each type of arrangement. SHOW ALL WORK!
THANKS FOR ALL YOUR HELP
Answers
8f + 2v = $29.00
-2f. - 2v = -12.50
8f + 2v = 29.00
6f = $16.50
f= $2.75 each flower bouquet
2(2.75) + 2v = 12.50
5.50 + 2v = 12.50
2v = $7.00
v = $3.50 each vase
you owe $1,945.61 on a credit card that has an 11.2% APR. the minimum payment due is $156.00. you decide to pay $300.00. how much do you save in interest by paying more than the minimum, assuming you make both payments at the beginning of the month?
$,
Answers
Answer:
$1.344
Step-by-step explanation:
APR represents annual percentage rate, and it specifies the amount of interest that would accrue on a loan over a specified period.
Extra amount paid = $300 - $156 = $144
Annual interest that would have been paid on the extra $144 = $144 * 11.2/100= $16.128
this amount on monthly basis is $16.128/12 = $1.344
Evaluate the expession. x=12, y=8, z=3 4x-yz
Answers
x=12, y=8, z=3
4x-yz = 4(12) - (8)(3)
4x-yz = 48 - 24
4x-yz = 24
The value of the given expression is 24.
The given expression is 4x-yz.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
Put, x=12, y=8 and z=3 in the given expression, we get
4x-yz = 4×12 - 8×3
= 48 - 24
= 24
Therefore, the value of the given expression is 24.
To learn more about an expression visit;
https://brainly.com/question/28170201.
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Emily’s pet snake is 5 feet long. Kristen’s snake is 50 inches long. Kristen says her snake is much longer because 50 is so much bigger than 5. Is Kristen right? Why or why not?
Answers
Which equation finds the value of x in the triangle below?
Answers
1) cot 70=x/12
Cot 70=[opposite side]/[adyacent side]=x/12
The option 1 is correct
2) cot 70=12/x
Cot 70=[opposite side]/[adyacent side]=x/12
The option 2 is not correct
3)sec 20=x/12
Sec 20 =1/cos20
Cos 20==[opposite side]/[hypotenuse]=12/z
1/(1/cos20)-------> 1/(12/z)------> z/12
The option 3 is not correct
4) sec 20=12/x
Sec 20 =1/cos20
Cos 20==[opposite side]/[hypotenuse]=12/z
1/(1/cos20)-------> 1/(12/z)------> z/12
The option 4 is not correct
the correct value is
1) cot 70=x/12
Answer:
A: cot 70 degrees = x/12
Step-by-step explanation:
on edg... Good Luck!!!
The mean weight of five complete computer stations is 167.2 pounds. The weights of four of the computer stations are 158.4 pounds, 162.8 pounds, 165 pounds, and 178.2 pounds respectively. What is the fifth computer station?
Answers
The mean weight of five complete computer stations is 167.2 pounds.
The weights of four of the computer stations are 158.4 pounds, 162.8 pounds, 165 pounds, and 178.2 pounds.
We have to determine the weight of fifth computer station.
Let the weight of fifth computer station be 'x' pounds.
Mean is calculated by sum of all the observations divided by the total number of observations.
So, [tex] \frac{158.4+162.8+165+178.2+x}{5}=167.2 [/tex]
[tex] \frac{664.4+x}{5}=167.2 [/tex]
[tex] {664.4+x}=167.2 \times 5 [/tex]
[tex] {664.4+x}=836 [/tex]
x= 171.6 pounds
The weight of fifth computer station is 171.6 pounds.
To find the weight of the fifth computer station, subtract the sum of the weights of the four given stations from the mean weight.
Explanation:The mean weight of five complete computer stations is 167.2 pounds. To find the weight of the fifth computer station, we can calculate the sum of the weights of all five stations and then subtract the sum of the weights of the four given stations. The weight of the fifth station can be found by subtracting the sum of the weights of the four given stations from the mean weight.
Sum of the weights of all five stations = 5 * 167.2 pounds
Sum of the weights of the four given stations = 158.4 pounds + 162.8 pounds + 165 pounds + 178.2 pounds
Weight of the fifth station = Sum of the weights of all five stations - Sum of the weights of the four given stations
Learn more about Mean Weight here:https://brainly.com/question/23580532
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HELP!!! WILL MARK BRAINLIEST IF YOUR RIGHT!!! LOOK AT THE IMAGE FOR THE QUESTION AND ANSWER CHOICES
Answers
√3 ≈1.732, 17/10=1.7
convert all the fraction into decimals, you'll see C is the closest to 1.732
Lines AB and CD are parallel. If the measure of W equals 129°, what is the measure of X?
Answers
Identify the GCF of 10x4y3 − 5x3y2 + 20x2y.
10x2y
10x3y
5x2
5x2y
Answers
The strategy for expressions with variables is still to factor out the greatest term.
For [tex]10x^4y^3-5x^3y^2+20x^2y[/tex], we look for the largest factor in each term.
For [tex]10x^4y^3[/tex], the largest factors are [tex]x^4[/tex] and [tex]y^3[/tex]. We'll come back to the coefficients in a minute.
For [tex]-5x^3y^2[/tex], the largest factors are [tex]x^3[/tex] and [tex]y^2[/tex]. Now, looking back to the previous term and also considering the coefficients, the largest factor of the two is [tex]5x^3y^2[/tex]. You could rewrite the first term as [tex](5x^3y^2)(2xy)[/tex] and the second term as [tex]-1(5x^3y^2)[/tex].
Now, we consider the last term, [tex]20x^2y[/tex]. The largest factor common to the two other terms is [tex]5x^2y[/tex].
And that's our final answer for the GCF (answer D).
The GCF of the given expression is:
[tex]5x^2y[/tex]
Step-by-step explanation:The GCF ( greatest common factor ) is the greatest divisor which divides all the terms completely.
Here we have the expression as:
[tex]10x^4y^3-5x^3y^2+20x^2y[/tex]
Here we see that the factors of the first term are:
[tex]10x^4y^3=2\times 5\times x\times x\times x\times x\times y\times y\times y[/tex]
The factor of the second term is:
[tex]-5x^3y^2=-1\times 5\times x\times x\times x\times y\times y[/tex]
and the factor of the third term is:
[tex]20x^2y=2\times 2\times 5\times x\times x\times y[/tex]
i.e. the factor which is common to all the three terms are:
[tex]5\times x\times x\times y=5x^2y[/tex]
Hence, the GCF is: [tex]5x^2y[/tex]
Complete the synthetic division problem below. What is the quotient in polynomial form?
Answers
We bring down the first number inside the box, 2, unchanged.
_______
-1| 2 7 5
_______
2
Now we multiply that 2 by the number outside, -1:
_______
-1| 2 7 5
-2
2
Now we add the two numbers in the middle column:
________
-1| 2 7 5
-2
2 5
Multiply the 5 we brought down by the -1:
________
-1| 2 7 5
-2 -5
2 5
Add the numbers in the last column:
________
-1| 2 7 5
-2 -5
2 5 0
The 3 numbers under the box represent the coefficients of x² and x, as well as the constant. When we finish, we no longer have an x², but start at the next level down, which would be x. 2 would be the coefficient of x and 5 would be the constant, with 0 remainder.
if f(x)=5x-1 thenF-1(x)
Answers
How much would Kendra have in her account after three years if she started with $500 and earned 2 percent interest compounding annually?
Answers
A time period of 3 years would be $30.
I hope I helped you!
Answer:530.6
Step-by-step explanation:
PLEASE HELP ME ON THIS QUESTION AND DON'T FORGET TO EXPLAIN!!!
Please show ur work and correct answer will get brainliest
Answers
f(x) [3rd one down] added to the middle g(x) should give you h(x)
f(x)_down 3 + g(x)_middle_g(X)_second column = -2x + 3 + 7x - 9 Now collect the like terms.
f(x) + g(x) = 5x - 6 which is h(x).
These guys sure believe in reading problems.
n a recent survey of 50 10-year olds, it was discovered that 14 liked both McDonald's and Burger King. Overall, 36 of the children surveyed liked McDonald's and 24 liked Burger King. How many of the children surveyed did not like either restaurant? Please show your statistical thinking to support your answer.,
Answers
Given f(x) =10x-2x find f(7)
Answers
10(7) -2(7)
70 - 14
56
f(7) = 56