We are given the expression √4x^2+100 and the substitution x/5=tan(θ). Our goal is to use the substitution to write the expression as a trigonometric expression and simplify as much as possible.
First, let's substitute x/5=tan(θ) into the expression:
√4(tan(θ)*5)^2+100
Next, let's simplify the expression:
√4(25tan^2(θ))+100
√100tan^2(θ)+100
Now, let's factor out 100 from the expression:
√100(tan^2(θ)+1)
10√tan^2(θ)+1
Finally, let's use the trigonometric identity 1+tan^2(θ)=sec^2(θ) to simplify the expression further:
10√sec^2(θ)
10sec(θ)
Therefore, the expression √4x^2+100 can be written as 10sec(θ) using the substitution x/5=tan(θ).
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The owner of a beverage company wants to determine whether two of his machines are filling bottles with the correct amount of liquid. He randomly selects 20 bottles filled by each of the two machines and measures the number of ounces that the bottles contain. The histograms below show the data. If the machines are designed to dispense between 5 and 6 ounces into a bottle, which machine appears to be doing a better job? Explain how you determined your answer.
Based on the histograms, it appears that Machine B is doing a better job of dispensing the correct amount of liquid.
What is histogram?The most common graph for displaying frequency distributions is a histogram.
To begin, Machine B's histogram is more symmetrically distributed around the 5.5-ounce mark, which is the target fill level.
Machine A's histogram, on the other hand, is skewed to the right, indicating that it is more likely to dispense more than 5.5 ounces.
Second, Machine B's histogram has a narrower spread, with most measurements falling between 5.4 and 5.6 ounces.
This indicates that the machine fills the bottles consistently within a narrow range of the target fill level.
Thus, the histogram for Machine A, on the other hand, has a wider range, with some measurements falling below 5.4 ounces and others exceeding 5.6 ounces, indicating a less consistent performance.
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Your question seems incomplete, the probable complete question is:
Could someone please explain how to do this? My teacher wasn't clear, so I don't know how.
Check the picture below.
[tex]\boxed{4} \\\\\\ (x+3)^2~~ = ~~[(x-1)+10](x-1)\implies x^2+6x+9~~ = ~~(x+9)(x-1) \\\\\\ x^2+6x+9~~ = ~~x^2+8x-9\implies 6x+9=8x-9\implies 9=2x-9 \\\\\\ 18=2x\implies \cfrac{18}{2}=x\implies 9=x[/tex]
Assume 4 years of monthly data was used to create a seasonally-adjusted forecasting model. The trend equation for the 4 years was found to be: y = 65 + 6.7X.
Seasonal factors are reported. Compute a seasonally-adjusted forecast for quarter 4 of year 5.
QTR1 QTR2 QTR3 QTR4
0.12 0.35 0.42 0.1
a. 10.8
b. 98.5
c. 24.5
d. 17.2
The seasonally-adjusted forecast for quarter 4 of year 5 is 91.9
The seasonally-adjusted forecast for quarter 4 of year 5 can be calculated by using the following equation:
Seasonally Adjusted Forecast = Trend Equation + Seasonal Factors
= 65 + 6.7X + 0.1
= 65 + 6.7X + 0.1
= 65 + 6.7*4 + 0.1
= 65 + 26.8 + 0.1
= 91.9
Therefore, the seasonally-adjusted forecast for quarter 4 of year 5 is 91.9.
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In AWXY, w = 55 inches, m/W=162° and m/X-9°. Find the length of y, to the
nearest 10th of an inch.
The length of y for the triangle is 27.8 in
How to find the length of y?The sine rule is for solving triangles which are not right-angled in which two sides and the included angle are given. The following are cosine rule formula:
w/sinW = x/sinX = y/sinY
where w, x and y are the lengths and W, X and Y are the angles
Given: w = 55 inches, m∠W = 162° and m∠X= 9°
m∠Y = 180 - 162 - 9 = 9° (angle sum in a triangle)
Using the formula:
w/sinW = y/sinY
55/sin162° = y/sin9°
y = (55*sin9°)/sin162°
y = 27.8 in
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Select the correct answer from each drop-down menu.
Consider quadrilateral EFGH on the coordinate grid.
-6
E
-4
1
LL
F
>+
Y
6-
2-
O
-4-
-6-
H
-N
G
05.
6
In quadrilateral EFGH, sides FG and EH are
are
X
because they
The area of quadrilateral EFGH is closest to
✓square units.
Sides EF and GH
First box ( not congruent, congruent).
Second box ( each have a length of 5.83, each have a length of 7.07, have different lengths)
Third box ( not congruent, congruent with lengths of 4.24, congruent with length of 5.83)
Fourth box (41, 34, 25, 30)
In quadrilateral EFGH, sides FG and EH are congruent because they each have a length of 7.07. Sides EF and GH are not congruent. The area of quadrilateral EFGH is closest to 41 square units.
How to calculate the distance between the two points?For the width, we would determine the distance between the vertices F (-1, 4) and G(4, -1)
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance FG = √[(4 - (-1))² + (-1 - 4)²]
Distance FG = √[5² + (-5)²]
Distance FG = √50
Distance FG = 7.07 units.
Distance EH = √[(1 - (-4))² + (-4 - 1)²]
Distance EH = √[5² + (-5)²]
Distance EH = √50
Distance FG = 7.07 units.
For the length, we would determine the distance between the vertices E (-4, 1) and F (-1, 4)
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance EF = √[(-1 - (-4))² + (4 - 1)²]
Distance EF = √[3² + (3)²]
Distance EF = √9
Distance EF = 3 units.
Distance HG = √[(4 - 1)² + (1 - (-4))²]
Distance HG = √[3² + (5)²]
Distance HG = √34 units.
Mathematically, the area of a rectangle can be calculated by using this formula:
Area of rectangle = length × width
Area of rectangle = √34 × 7.07
Area of rectangle = 41.22 square units.
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The cargo bed of a commercial truck is shaped like a rectangular prism. The dimensions are shown. Billy has 80 cubic meters of mulch to take to his house. How many trips will he have to make until all the mulch is at his house?
Answer:
We need to find out how many trips Billy needs to make to transport 80 cubic meters of mulch. Since we know the dimensions of the cargo bed, we can find its volume and then divide the total volume of mulch by the volume of the cargo bed to find the number of trips.
The volume of the cargo bed is:
V = l × w × h
where l is the length, w is the width, and h is the height. Using the dimensions given in the diagram, we get:
V = 4 m × 2.5 m × 1.5 m = 15 cubic meters
Now we can divide the total volume of mulch by the volume of the cargo bed to find the number of trips:
Number of trips = total volume of mulch / volume of cargo bed
Number of trips = 80 cubic meters / 15 cubic meters ≈ 5.33
Since Billy cannot make a fractional number of trips, he will need to make 6 trips to transport all the mulch to his house.
Helpppp pleasee ill give everything please see the photo (find the missing angle. Round to the nearest degree
Answer:
64.15°
Step-by-step explanation:
here
theta = 64.15°
( solution in picture)
By what will the product of 2 numbers decrease if one of the numbers is decreased by 25% and the other number is decreased by 50%
Answer:
62.5%
Step-by-step explanation:
the product of the two numbers=xy
the product of the altered numbers=(0.75x)(0.5y) OR 0.375xy
finally you subtract this from one to get your decrease: 1-0.375=0.625
then simply convert that to a percent, leaving you with 62.5%. hope this helps!
Ben has scored 15 points. He has 8 points more than Greg. Which equation can be used to determine
The equation that can be used to determine Greg's score is 15 - 8 = x. This equation shows that if you subtract 8 points from Ben's score of 15 points, you will get Greg's score.
Step-by-step explanation:
In conclusion, the equation 15 - 8 = x can be used to determine Greg's score.
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1. in a survey of 290 university applicant, 181 applied ESUT. 142 applied for UNN, 117 applied for FUTO, and each admission into at least one of the three universities. If 75 applie and UNN, 60 applied for ESUT and FUTO, and 54 for UINN a a. Draw a Venn diagram to illustrate this information. b. How many applicant applied All three universities il Exactly two universities PLASU towns.
a Draw a Venn diagram to illustrate the information
b how many applicant applied
I all three universities
ii Exactly two universities
III plasu
Answer:
a. Here is a Venn diagram to illustrate the information:
markdown
ESUT
/ \
FUTO UNN
\ /
\ /
(X)
where (X) represents the number of applicants who applied to all three universities.
b. To find the number of applicants who applied to all three universities, we can use the formula:
scss
Total = ESUT + FUTO + UNN - (Exactly two) - (None) + (All three)
We know that:
makefile
ESUT = 60 + 54 + (All three)
UNN = 75 + (All three)
FUTO = 54 + 60 + (All three)
Total = 290
Substituting these values, we get:
scss
290 = (60 + 54 + All three) + (54 + 60 + All three) + (75 + All three) - (Exactly two) - (None) + (All three)
Simplifying, we get:
scss
290 = 249 + 2(All three) - (Exactly two) - (None)
We also know that:
scss
None = Total - (ESUT + FUTO + UNN) = 290 - (181 + 142 + 117) = -150
This negative value means that there are no applicants who did not apply to any of the universities. This is a contradiction, so we must have made an error in our calculations.
Therefore, we cannot find the number of applicants who applied to all three universities or exactly two universities.
expand the expression log6x^2
Answer:
log(2)+log(3)+2log(x)
you should try downloading an app called math away
i don't know if it's right but I got the answer from a reliable source
Help me. giving brainliest!!!
Answer: 709 milliliters
Step-by-step explanation:
It is just the sum of the numbers so,
236 + 473 = 709
709 milliliters
Hope this helps!
Answer:
709 millimeters
Step-by-step explanation:
Add it up 236 = 473 = 709
A recipe uses 2 cups of milk to make 6 servings. If the same amount of milk is used for each serving, how many servings can be made from one gallon?
1 gallon
=
1 gallon=
4 quarts
4 quarts
1 quart
=
1 quart=
2 pints
2 pints
1 pint
=
1 pint=
2 cups
2 cups
1 cup
=
1 cup=
8 fluid ounces
8 fluid ounces
Before you try that problem, answer the question below.
How many cups will you need to find the number of servings for?
Step-by-step explanation:
How many cups of milk are in a gallon = 16
If a recipe uses 2 cups for 6 servings, then he will make 48 servings from a gallon.
1 quart is 4 cups of milk, a gallon contains 4 quarts
1 pint is 2cups, a gallon contains 8pints of milk
From the question 1 gallon is 4 quarts or 8pints or 48servings
The box plots display the math scores for two 7th grade math classes. which statement is best supported by the information in the box plots? A, the range for Mrs. Morales‘s class is greater than the range for Mr. Florez‘s class  B, the data for Mr. Flores’s class are more symmetrical than the data for Mrs. Morales‘s class C, the median score for Mrs. Morales’s class is equal to the median for Mr. Flores’s class  D, the interquartile range for Mr. Flores‘s class is greater than the interquartile range for Mrs. Morales‘s class 
Therefore, the best statement supported by the information in the box plots is statement B, "the data for Mr. Flores’s class are more symmetrical than the data for Mrs. Morales's class."
What is box plot?A box plot, also known as a box-and-whisker plot, is a graphical representation of the distribution of numerical data. It displays the five-number summary of a dataset, which includes the minimum value, the first quartile (Q1), the median, the third quartile (Q3), and the maximum value.
Here,
From the box plots, we can make the following observations:
A) The range for Mrs. Morales's class appears to be 100-50 = 50.
The range for Mr. Florez's class appears to be 95-55 = 40.
Therefore, statement A is not supported by the information in the box plots.
B) The box plot for Mr. Flores's class is more symmetrical than the box plot for Mrs. Morales's class, which is skewed to the left.
Therefore, statement B is supported by the information in the box plots.
C) The median score for Mrs. Morales's class appears to be between 70 and 75.
The median score for Mr. Florez's class appears to be between 75 and 80.
Therefore, statement C is not supported by the information in the box plots.
D) The interquartile range for Mrs. Morales's class appears to be between 60 and 80, which is a range of 20.
The interquartile range for Mr. Florez's class appears to be between 65 and 85, which is also a range of 20.
Therefore, statement D is supported by the information in the box plots.
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Use The Compound Interest Formula \( A=P\Left(1+\Frac{R}{N}\Right)^{N T} \) To Solve. Round To Two Decimal Places. Find The Accumulated Value Of An Investment Of $ 20,000 At 6% Compounded Annually For 16 Years. A. $ 39,200.00 B. $ 38,000.00 C. $ 47,931.16 D. $50,807.04
The accumulated value of an investment of $20,000 at 6% compounded annually for 16 years is $50,807.04. The correct answer is D.
To find the accumulated value of an investment of $20,000 at 6% compounded annually for 16 years, we need to plug in the given values into the compound interest formula: A = P(1 + r/n)^nt
Given values:
P = $20,000 (principal amount)
R = 6% (annual interest rate)
N = 1 (number of times interest is compounded per year)
T = 16 (number of years)
Plugging in the given values into the formula:
A = 20000(1 + (0.06/1))^(1)(16)
Simplifying the equation:
A = 20000(1.06)^16
Using a calculator to find the value of A:
A = $50,807.04
Therefore, the accumulated value is D. $50,807.04.
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∟A= 7x + 24° , ∟B = 3x + 92° Solve for x and then find the measure of ∟A:
∟A=_____°
Measure of ∟A is 119°
To solve for x, we must use the fact that the angles have the same measure, so ∟A = ∟B.
Substitute 7x + 24° for ∟A and 3x + 92° for ∟B and set them equal to each other:
7x + 24° = 3x + 92°
Subtract 3x from both sides:
7x - 3x = 92° - 24°
4x = 68°
Divide both sides by 4 to solve for x:
x = 17°
Now that we have x, we can substitute 17° for x into the original equation for ∟A to find its measure:
∟A = 7x + 24°
∟A = 7(17°) + 24°
∟A = 119°
Therefore, the measure of ∟A is 119°.
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(Written assignment) A student was asked to simplify the following rational expression:
(x^2+3x+2)/(x^2+6x+8)
Here is the student’s work, in which the expression was simplified incorrectly:
Questions for thought:
1. Please explain the student’s mistake and why it is incorrect.
2.This type of mistake is common in Algebra, why do you think it is so common?
3.Have you ever made a mistake like this?
4. If you have made a mistake like the one shown above, what helped make you stop making this mistake?
5.What advice would you give future Algebra 2 students to help stop them from making mistakes like this?
You do not have to answer all the questions in your response. As long as your answer has AT LEAST FIVE (5) COMPLETE SENTENCES you will get brainliest
Answer:
The student factored the numerator and denominator incorrectly. Instead of factoring to (x+1)(x+2)/(x+4)(x+2), they factored to (x+1)(x+2)/(x+4)(x+2) = (x+1)/x+4.
Factoring polynomials can be a difficult skill to master, and mistakes in factoring can lead to errors in simplifying rational expressions. Additionally, students may rush through factoring or not double-check their work, leading to careless errors.
Students can avoid mistakes like this by practicing factoring polynomials regularly and double-checking their work. It can also be helpful to write out each step clearly and show all work, so mistakes can be caught more easily.
My advice would be to practice factoring polynomials regularly, and double-check your work when simplifying rational expressions. Also, it is important to take your time and show all work, so mistakes can be caught more easily.
create number patterns using numbers between 100-300
what is the rule multiplying with different signs
Answer:
When you multiply two numbers with different signs (positive and negative), the result is always negative.
This can be understood in terms of the basic properties of multiplication and the fact that a negative number is essentially the opposite of a positive number. When you multiply a positive number by a positive number, the result is positive because both numbers are pointing in the same direction along the number line. When you multiply a negative number by a negative number, the result is also positive because both numbers are pointing in the opposite direction along the number line, and multiplying them together "flips" them back to the positive side. However, when you multiply a positive number by a negative number, the two numbers are pointing in opposite directions along the number line, and so their product is negative.
Therefore, the rule for multiplying two numbers with different signs is that the product is always negative.
Step-by-step explanation:
if tan t = 11/7 and 0≤ t≤????/2 find sin t, cost, csc t, sect, and cott. To enter the square root of a number, type "sqrt(a)". For example, type "sqrt(2)" to enter √2. sin t = cos t = csc t = sec t = cot t =
The hypotenuse is sqrt(11^2 + 7^2) = sqrt(170). Then, sin t = 11/sqrt(170), cos t = 7/sqrt(170), csc t = sqrt(170)/11, sec t = sqrt(170)/7, and cot t = 7/11.
Since we know that tan t = 11/7, we can use the Pythagorean identity (sin^2 t + cos^2 t = 1) to find the other trigonometric functions. First, we will find sin t and cos t:
tan t = 11/7 = opposite/adjacent = sin t/cos t
sin t = 11*cos t
cos t = 7*sin t
Substituting the second equation into the first equation:
sin t = 11*(7*sin t)
sin^2 t = 121*sin^2 t
121*sin^2 t - sin^2 t = 0
120*sin^2 t = 0
sin^2 t = 0/120
sin^2 t = 0
sin t = 0
Since sin t = 0, cos t = 1. Now we can find the other trigonometric functions:
csc t = 1/sin t = 1/0 = undefined
sec t = 1/cos t = 1/1 = 1
cot t = 1/tan t = 1/(11/7) = 7/11
So, the values of the trigonometric functions are:
sin t = 0
cos t = 1
csc t = undefined
sec t = 1
cot t = 7/11
Note: Another way to find the values of the trigonometric functions is to use the Pythagorean Theorem to find the hypotenuse of the right triangle with sides 11 and 7.
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This morning the temperature was -5 °F. How much must the temperature change to reach 0 °F?
Answer:
5°
Step-by-step explanation:
because: -5°+5°=0° I think
Answer:
5 degrees
Step-by-step explanation:
-5+5=0
Suppose you deposit $800 in an account with an annual interest rate of 10 % compounded quarterly.
Use the nt formula A = P(1+ -) and round each answer to 2 decimal places, if necessary.
a. Find an equation that gives the amount of money in the account after t years. A(t) =
b. Find the amount of money in the account after 5 years. After 5 years, there will be $ in the account.
c. How many years will it take for the account to contain $1600? It will take years for there to be $1600 in the account. d. If the same account and interest were compounded continuously, how much money would the account contain after 5 years? With continuous compounding interest, there would be $ in the account after 5 years.
So, with continuous compounding interest, there would be $1324.46 in the account after 5 years.
A(t) = P(1 + r/n)^(nt)
a. To find an equation that gives the amount of money in the account after t years, we can plug in the given values for P, r, and n into the formula. P is the initial deposit, r is the annual interest rate, and n is the number of times the interest is compounded per year. So, the equation will be:
A(t) = 800(1 + 0.10/4)^(4t)
b. To find the amount of money in the account after 5 years, we can plug in t = 5 into the equation and solve for A(t):
A(5) = 800(1 + 0.10/4)^(4*5)
A(5) = 800(1.025)^20
A(5) = 1303.04
So, after 5 years, there will be $1303.04 in the account.
c. To find how many years it will take for the account to contain $1600, we can set A(t) = 1600 and solve for t:
1600 = 800(1 + 0.10/4)^(4t)
2 = (1.025)^4t
log(2) = 4t*log(1.025)
t = log(2)/(4*log(1.025))
t = 7.22
So, it will take 7.22 years for there to be $1600 in the account.
d. If the same account and interest were compounded continuously, we can use the formula A(t) = Pe^(rt) to find how much money would be in the account after 5 years:
A(5) = 800e^(0.10*5)
A(5) = 800e^0.5
A(5) = 1324.46
So, with continuous compounding interest, there would be $1324.46 in the account after 5 years.
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(a) The equation that gives the amount of money in the account after t years is A(t) = 800(1.025)^4t.
(b) After 5 years, there will be $1304.56 in the account.
(c) It will take 7.24 years for there to be $1600 in the account.
(d) With continuous compounding interest, there would be $1340.95 in the account after 5 years.
a. The equation for the amount of money in the account after t years is A(t) = 800(1 + 0.10/4)^(4t) = 800(1.025)^4t. This is derived from the formula A = P(1+ r/n)^(nt), where P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.
b. To find the amount of money in the account after 5 years, we can plug in the values into the equation from part a. A(5) = 800(1 + 0.10/4)^(4)(5) = 800(1.025)^20 = $1304.56. Therefore, after 5 years, there will be $1304.56 in the account.
c. To find how many years it will take for the account to contain $1600, we can set the equation from part a equal to 1600 and solve for t. 1600 = 800(1 + 0.10/4)^(4t) => 2 = (1.025)^4t => 4t = log(2)/log(1.025) => t = 7.24 years. Therefore, it will take 7.24 years for there to be $1600 in the account.
d. If the same account and interest were compounded continuously, the formula for the amount of money in the account after t years would be A(t) = 800e^(0.10t). To find how much money the account would contain after 5 years, we can plug in the values into this equation. A(5) = 800e^(0.10)(5) = $1340.95. Therefore, with continuous compounding interest, there would be $1340.95 in the account after 5 years.
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I need help please, I dont know how to do this
m=2
because in the other equation, the digit next to x is 2 so m must be 2
tear production rate reduced normal none astigmatism no yes soft spectacle prescription myope hypermetrope hard none Decision trees for the labor data wage increase Ist year <= 2.5 > 2.5 bad statutory holidays >10 < 10 wage increase Ist year good wage increase 1st year <= 2.5 > 2.5 working hours per week statutory holidays bad good <= 36 > 36 > 10 <= 10 bad health plan contribution good wage increase Ist year none half full <%3D4 bad good bad bad good 17 2nd_Heart Attack Yes Yes Q1. Given the following data table, answer the questions: (5 Marks) Marital Weight Stress Trait Age Gender Cholesterol Status Category Level Anxiety 60 Yes Female Overweight 150 High 50 69 Yes Male Overweight 170 Normal 60 52 No Female Normal 174 High 35 66 Yes Male Overweight 169 Normal 60 70 Yes Female Overweight 237 Normal 65 52 No Female Normal 174 High 35 58 Yes Male Normal 140 Normal 45 No Yes Yes No No (a) Explain the table with respect to rows and columns. Also, explain what is the meaning of rows and columns in any data table. (b) Which problem can be solved using above data table? (c) Prepare decision table for the above table. NEED ITS ACCURATE SOLUTION. ONLY THEN I WILL UPVOTE IT.
(a) Each row represents a different individual and Each column represents a different variable or characteristic. (b) Identifying the relationship between different variables and the likelihood of a person having a heart attack, this problem can be solved using this data table.
(a) The table is organized into rows and columns. Each row represents a different individual and includes information about their age, gender, weight category, cholesterol level, marital status, stress level, and anxiety trait. Each column represents a different variable or characteristic, such as age, gender, weight category, etc. The rows and columns are used to organize the data and make it easier to read and understand.
(b) The problem that can be solved using this data table is identifying the relationship between different variables and the likelihood of a person having a heart attack. For example, the table can be used to determine if there is a correlation between age, gender, weight category, cholesterol level, marital status, stress level, and anxiety trait and the likelihood of a person having a heart attack.
(c) Decision table for the above table:
| Age | Gender | Weight Category | Cholesterol Level | Marital Status | Stress Level | Anxiety Trait | Heart Attack |
|-----|--------|-----------------|-------------------|----------------|--------------|---------------|--------------|
| 60 | Female | Overweight | 150 | Yes | High | Yes | Yes |
| 69 | Male | Overweight | 170 | Yes | Normal | Yes | Yes |
| 52 | Female | Normal | 174 | No | High | Yes | No |
| 66 | Male | Overweight | 169 | Yes | Normal | No | Yes |
| 70 | Female | Overweight | 237 | Yes | Normal | No | Yes |
| 52 | Female | Normal | 174 | No | High | Yes | No |
| 58 | Male | Normal | 140 | Yes | Normal | No | No |
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Find an equation of the line parallel to y = 3x - 3 and that passes through the point (3, 2)
The solution is, the equation of a line parallel to y=3x-3 and passing through point (3,2) is y=3x-7.
What is a straight line?A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.
here, we have,
The equation of the given line is,
y=3x-3 ....1
We have to find the equation of a line parallel to y=3x-3 and passing through the point (x1, y1)=(3,2).
The general equation of a line is,
y = mx+c ....2
Here, m is the slope of the line.
Comparing equations (1) and (2), we find that the slope of the line
y=3x-3 is m=3.
The slope of two parallel lines are always equal.
Hence, the slope of a line parallel to the line y=3x-3 is also m=3.
Now, the formula for the point slope form of the equation of a line can be written as,
y - y1 = m (x - x1)
Substitute m=3, x1=3 and y1=2 in the above equation to find the equation of a line parallel to y=3x-3 and passing through point (3,2) is,
y-2 = 3(x - 3)
Therefore, the equation of a line parallel to y=3x-3 and passing through point (3,2) is y=3x-7.
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Given f(x)=x2−2x+3, and a point a in the domain of f. We wish to compute f′(a) using the definition
f′(a)=limh→0 f(a+h)−f(a)/h. Notice this is an indeterminate of the form 0/0 (a) Simplify f(a+h)−f(a)/h= FORMATTING: The answer must be a polynomial in a and h in its simplest form. (b) Compute f′(a)=limh→0 f(a+h)−f(a)/h
2a + 2h
(a) Simplifying, we get f(a+h)−f(a)/h = (a+h)2−2(a+h)+3 − (a2−2a+3) / h = (2a+2h)h/h = 2a + 2h.
(b) We now use the definition of the derivative to compute f'(a) = limh→0 (2a + 2h) = 2a.
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The quotient of x and 3 plus 24 PLEASE HELP
Answer:
(24 divided by 3) + x
Step-by-step explanation:
i did it
This is the graph of a function in the form. f(x)=a*b^x. What is the function?
A = f(x)=3^x.
B = f(x)=2*3^x.
C = f(x)=3*(0.1)^x
D = f(x)=(0.2^x)
An equation of the function include the following: C. f(x) = 3×(0.1)^x.
What is an exponential function?In Mathematics, an exponential function can be modeled by using this mathematical expression:
f(x) = ab^x
Where:
a represents the base value or y-intercept.x represents time.b represents the rate of change.By critically observing the graph of this exponential function, we can logically deduce that the base value of this exponential growth function is at (0, 3) and its domain includes all real numbers i.e -∞ < x < ∞.
Therefore, the required exponential function is given by:
f(x) = 3(0.1)^x
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You must SHOW ALL YOUR WORK for full points. Write your answer as an (x,y) ordered pair.
2x + 3y = 7
-2 + 1y = -11
Must be done in both elimination method and substitution method.
The solution to the equation is (5, -1)
How to determine the solution to the equationFrom the question, we have the following parameters that can be used in our computation:
2x + 3y = 7
-2x + 1y = -11
Add to eliminate x
So, we have
4y = -4
Divide both sides by 4
y = -1
Recall that 2x + 3y = 7
Substitute the known values in the above equation, so, we have the following representation
2x - 3 = 7
So, we have
2x = 10
Divide
x = 5
For the substitution method, we have
2x + 3y = 7
-2x + y = -11
The second equation becomes
y = 2x - 11
By substitution, we have
2x + 6x - 33 = 7
So, we have
8x = 40
x = 5
Recall that
y = 2x - 11
So, we have
y = 2 * 5 - 11
y = -1
Hence, the solution is (5, 2)
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Martina can run 3 miles without stopping. Last year she could run 3,640 yards witho stopping. How many more feet can Martina
Martina can run 4,920 more feet this year compared to last year.
Martina can run 3 miles without stopping. Last year she could run 3,640 yards without stopping. We need to find out how many more feet Martina can run this year compared to last year.
First, we need to convert both measurements to the same unit so that we can compare them. We will convert both measurements to feet.
1 mile = 5,280 feet
1 yard = 3 feet
So, 3 miles = 3 x 5,280 feet = 15,840 feet
And, 3,640 yards = 3,640 x 3 feet = 10,920 feet
Now, we can subtract the number of feet Martina could run last year from the number of feet she can run this year to find out how many more feet she can run this year.
15,840 feet - 10,920 feet = 4,920 feet
Therefore, Martina can run 4,920 more feet this year compared to last year.
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