Answer: 9
Step-by-step explanation:
assuming that each box is 1 square inch then, you would get 9 square inches.
0,5 go down three to get 0,2
0,2 go left three to get -3,2
-3,2 go up three to get -3,5
-3,5 go right three to get 0,5
so you end up with a 3-by-3 box
if a + b is equals to 5 and a x b is equal to 6 then what is the value of a and b
Answer: 2 and 3, or 3 and 2
Step-by-step explanation:
a + b = 5 so a = 5 - b
Substitute a = 5 - b into ab = 6; (5 - b)b = 6
5b - [tex]b^{2}[/tex] = 6
[tex]b^{2}[/tex] - 5b + 6 = 0
(b - 2)(b - 3) = 0
So b is either 2 or 3
So a is either 3 or 2 depending on what b is
Graduate management aptitude test (gmat) scores are widely used by graduate schools of business as an entrance requirement. suppose that in one particular year, the mean score for the gmat was 473, with a standard deviation of 104. what values are three standard deviations within the mean?
The values that exist two standard deviations above and below the mean are 681 and 265.
How to determine the values?The given parameters exist:
Mean = 473
Standard deviation =104
The values above and below the mean exist calculated utilizing:
[tex]$x=\bar{x} \pm n \sigma$[/tex]
In this case n = 2.
So, we have, [tex]$x=\bar{x} \pm 2 \sigma$[/tex]
The value above is:
x = 473 + 2 [tex]*[/tex] 104 = 681
The value below is:
x = 473 - 2 [tex]*[/tex] 104 = 265
Therefore, the values that exist two standard deviations above and below the mean are 681 and 265.
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(FIRST PERSON TO ANSWER GETS BRAINLIEST!!!) A student earned $2500.75 at his summer job making $12.50 per hour. Let h represent the number of hours the student worked. Which of the following equations could be used to determine how many hours the student worked at his summer job? (answer choices and question is below)
Answer:
[tex]12.50 \space\ h = 2500.75[/tex]
Step-by-step explanation:
We know from the question that the student earned $12.50 per hour.
Using this information, we can say that if the student worked for h hours, they would make a total of 12.50 × h dollars.
We also know that the total money they earned is $2500.75.
∴ Therefore, we can set up the following equation:
[tex]\boxed {12.50 \times h = 2500.75}[/tex]
From here, if we want to, we can find the number of hours worked by simply making h the subject of the equation and evaluating:
h = [tex]\frac{2500.75}{12.50}[/tex]
= 200.6 hours
Answer: 12.50h = 2500.75
Step-by-step explanation:
We know from the question that the student earned $12.50 per hour.
Using this information, we can say that if the student worked for h hours, they would make a total of 12.50 × h dollars.
We also know that the total money they earned is $2500.75.
can someone help? will award brainliest
Answer:
B
Step-by-step explanation:
The beginning temperature is -12 and then it rises 5 degrees each hour at the end of the game it is 32 degrees.
A farmer with 1200 meters of fencing wishes to enclose a rectangular field and then divide it into two plots with a fence parallel to one of the sides. What are the dimensions of the field that produce the largest area
The perimeter of a given figure is a measure of the addition of each individual length of the sides of the figure. Thus the dimensions that would produce the largest area of the field are; length = 300 m, and width = 200 meters.
The perimeter of a given figure is a measure of the addition of each length of the sides of the figure. It always has the unit as that of the given sides of the figure.
So in the given question, the perimeter of the fence required = 1200 meters.
Thus, let the length of the enclosed rectangle be represented by l and its width by w. Thus,
Perimeter = 2l + 3w
1200 = 2l + 3w
Thus, let l be equal to 300, we have;
1200 = 2(300) + 3w
1200 - 600 = 3w
w = 200
Thus the dimensions of the field that would produce the largest area are; length = 300 m and width = 200 m.
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Analysis and observations in these two graphs
By critically observing the graph, we can infer and logically deduce the following points:
The linear function is given by y = 0.0169x + 32.485.The initial temperature for both data is greater than 32°C.The final temperature for both data is less than 33.5°C.Between 1980 and 2020, the temperature for graph 2 (thick-continuous line) was constant.Graph 1 (thin-dashed line) is essentially a linear graph.What is a graph?A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.
What is a linear function?A linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.
This ultimately implies that, the data of a linear graph are directly proportional and as such, as the value on the x-axis increases or decreases, the values on the y-axis also increases or decreases.
By critically observing the graph which models the changes in temperature over a specific period of time (in years), we can infer and logically deduce the following points:
The linear function is given by y = 0.0169x + 32.485.The initial temperature for both data is greater than 32°C.The final temperature for both data is less than 33.5°C.Between 1980 and 2020, the temperature for graph 2 (thick-continuous line) was constant.Graph 1 (thin-dashed line) is essentially a linear graph.In conclusion, there are four (4) points of intersection on this graph.
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QUICK HELP PLSSSS
Find the probabilities of the events described and arrange them in order from the event with the lowest probability of occurrence to the event with the highest probability of occurrence.
The probability of getting red balls is 0.25, probability of getting peaches from fruits is 0.7, probability of getting green tokens is 0.2, probability of getting golf balls is 0.867.
Given A)Number of green marbles=5,number of red marbles=3, number of blue marbles=4,
B) Number of peaches=7,number of apples=3,
C) Number of red token=10, number of blue token=6,green tokens=4,
D)Number of golf balls=13, number of tennis balls=2.
We are required to find the following probabilities:
A) Probability of getting red marble=Number of red marbles/ Total marbles.
=3/12
=1/4
=0.25
B) Probability of getting peaches=Number of peaches/Total fruits.
=7/10
=0.7
C) Probability of getting green tokens=Number of green tokens/Total tokens
=4/20
=1/5
=0.2
D)Probability of getting golf balls= Number of golf balls/ Total balls.
=13/15
=0.867
The sequence will be from C-A-B-D.
Hence the probability of getting red balls is 0.25, probability of getting peaches from fruits is 0.7, probability of getting green tokens is 0.2, probability of getting golf balls is 0.867.
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HELP WANTED!!!!! NEED HELP ASAP!!!!! (02.06; 02.07 MC)
Part A: Michael bought vegetables that weighs 4 and 1 over 8 pounds. How many ounces does the vegetables weigh? Show your work. (5 points)
[16 ounces = 1 pound]
Part B: A running tap dispenses 0.16 gallons of water every second. How many pints of water is dispensed after 25 seconds? Show your work. (5 points)
[1 gallon = 4 quarts, 1 quart = 2 pints]
if you are every so kind.. PLS SHOW ME HOW TO DO THIS PLS!!!!!!!
Using proportions, it is found that:
A. The vegetables weigh 66 pounds.
B. 0.5 pints are dispensed after 25 seconds.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
4 and 1/8 pounds is equivalent to 4.125 pounds. Since each pound has 16 ounces, the weight of the vegetable is of:
W = 16 x 4.125 = 66 pounds.
Every second, 0.16 gallons are dispensed. Hence the amount dispensed in 25 seconds is:
A = 25 x 0.16 = 4 gallons.
Each gallon has 8 pints, hence the number of pints dispensed is:
4/8 = 0.5 pints.
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The navy reports that the distribution of waist sizes among male sailors is approximately normal, with a mean of 32.6 inches and a standard deviation of 1.3 inches. part a: a male sailor whose waist is 34.1 inches is at what percentile? explain your reasoning and justify your work mathematically. (5 points) part b: the navy uniform supplier regularly stocks uniform pants between sizes 30 and 36. anyone with a waist circumference outside that interval requires a customized order. describe what this interval looks like if displayed visually. what percent of male sailors requires custom uniform pants? show your work and justify your reasoning mathematically. (5 points) (10 points)
Using the normal distribution, it is found that:
a. A male sailor whose waist is 34.1 inches is at the 87.5th percentile.
b. 5.7% of male sailors requires custom uniform pants.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable 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.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 32.6, \sigma = 1.3[/tex]
For item a, the percentile is the p-value of Z when X = 34.1, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (34.1 - 32.6)/1.3
Z = 1.15
Z = 1.15 has a p-value of 0.875.
Hence 87.5th percentile.
For item b, the proportion who does not require an special order is the p-value of Z when X = 36 subtracted by the p-value of Z when X = 30, hence:
X = 36:
Z = (36 - 32.6)/1.3
Z = 2.62
Z = 2.62 has a p-value of 0.996.
X = 30:
Z = (30 - 32.6)/1.3
Z = -2
Z = -2 has a p-value of 0.023.
0.996 - 0.023 = 0.943.
Hence the proportion who requires an special order is:
1 - 0.943 = 0.057.
5.7% of male sailors requires custom uniform pants.
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In one game, the final score was Falcons 3, Hawks 1. What fraction and
percent of the total goals did the Falcons score? Show your work in the space
below. Remember to check your solution.
Step-by-step explanation:
3over4 which is 75percentSims waist is 30 inches. He wants to put on more weight and is hoping to gain enough weight to increase his waist size by 8%. How many inches does he want his waist to be?
Answer:
32.4 inches
Step-by-step explanation:
Sam wants the increase to be 8% of 30 inches.
IncreaseThe amount of increase Sam wants in his waist size is ...
8% × 30 in = 0.08×30 in = 2.4 in
Waist sizeAdding the wanted increase to his present size would make Sam's waist size be ...
30 in + 2.4 in = 32.4 in
Sam wants his waist size to be 32.4 inches.
__
Additional comment
The larger size can also be computed from ...
30 +8%×30 = (1 +8%)×30 = 1.08×30 = 32.4 . . . inches
In a hypothesis test, what should we conclude if the data would be very unusual if the original assumption about our parameter were correct?
We conclude the hypothesis test as Alternative Hypothesis if the data would be very unusual if the original assumption about our parameter were correct.
A hypothesis in statistics is a claim or supposition on the properties of one or more variables in one or more populations. There are two hypothesis to choose between because a statement might either be true or wrong.The null hypothesis is the assertion that we (or someone else) consider to be true. Our hypothesis test will come to one of two conclusions: "reject H0" or "do not reject H0." Remember that until data provide evidence to the contrary, we always proceed under the null hypothesis.If the null hypothesis is incorrect, the alternative hypothesis must be true. The hypothesis test can be different in one of three ways: greater than, smaller than, or just different (not equal). As a result, there will always be an inequality requirement in the notation for H.Learn more about Alternative hypothesis here: https://brainly.com/question/17173491
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An interior designer is sketching a rough outline of a
corner room of an office building, as shown above.
If the area of the triangular-shaped room is 1,728
square feet, what is the value of sin(x)?
The measure of the angle x or the value of the x is 53.13 degrees if an interior designer is sketching a rough outline of a corner room of an office building.
What is the triangle?In terms of geometry, the triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.
It is given that:
The area of triangle A = 1728 square feet
The base length of the triangle b = 72 feet
Let h be the height of the triangle
Area = (1/2)b×h
1728 = (1/2)72×h
h = 48 feet
Half of the 72 is 72/2 = 36
As we know,
Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.
Applying trigonometric ratio:
tan(x) = 48/36
tan(x) = 1.333
x = 53.13 degrees
Thus, the measure of the angle x or the value of the x is 53.13 degrees if an interior designer is sketching a rough outline of a corner room of an office building.
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To conduct a test of hypothesis with a small sample, we make an assumption that?
To conduct a test of hypothesis with a small sample, we make an assumption that the population is normally distributed .
What is normal distribution?
A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.
The normal distribution appears as a "bell curve" on a graph.
A probability bell curve is more properly described as the normal distribution.The mean and standard deviation of a normal distribution are 0 and 1, respectively. It has a kurtosis of 3 and zero skew.Not all symmetrical distributions are normal, but all normal distributions are symmetrical.Natural occurrences frequently resemble the usual distribution.To know more about normal distribution........
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What is the volume of the rectangular prism?
2 cm
2 cm
2 cm
Answer:
Step-by-step explanation:
Shira's math test included a survey question asking how many hours students spent studying for the test. The scatter plot below shows the relationship between how many hours students spent studying and their score on the test. A line was fit to the data to model the relationship.
Which of these linear equations best describes the given model?
Answer:
Part 1) Option B. y = 10x + 45
Part 2) The score is 95
Step-by-step explanation:
Linear equation that best describes the given model
Let
x ---> number of hours students spent studying
y ---> their score on the test
Looking at the line that was fit to the data to model the relationship
The slope is positive
The y-intercept is the point (0,45)
For x=1, y=55 ----> point (1,55)
Find the slope
The formula to calculate the slope between two points is equal to
substitute the points (0,45) and (1,55)
Find the equation of the line in slope intercept form
we have
substitute
Part 2) Estimate the score for a student that spent 5 hours studying.
For x=5 hours
substitute in the linear equation and solve for y
Suppose a is jointly proportional to b and c. if a=4 when b=8 and c = 9, then what is a when b=2 and c=18
From the given information, a exists jointly proportional to b and c.
then [tex]$$a \propto b c$[/tex]
Therefore, the value of a exists 2.
What is the value of a?Given, a exists jointly proportional to b and c.
[tex]$$a \propto b c$[/tex]
Taking K as the constant of proportionality.
a = K b c
For b = 8 and c = 9, the value of a = 4
4 = K(8)(9)
4 = 72 K
Dividing the equation by 72, we get
[tex]$K=\frac{1}{18}[/tex]
Using the value of K in the equation:
[tex]$a=\frac{b c}{18}[/tex]
Substitute the values of b = 2 and c = 18, in the above equation
[tex]$a=\frac{2 \times 18}{18} \\[/tex]
a = 2
Therefore, the value of a exists 2.
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. If (5, 7) and (-3, 0) lie on the line ax - by = -20.
i) Find the value of a & b. [IM]
ii) Write the equation of the line in standard form.
iii) Find the coordinate of the point of intersections of the given line with x-axis and y-axis respectively.
iv) Find two more solutions of the given line.
i) The coefficients of the equation of the line are a = 20 / 3 and b = 160 / 21.
ii) The equation of the line in standard form is (20 / 3) · x + (160 / 21) · y = - 20.
iii) The x-intercept and y-intercept of the line are (- 3, 0) and (0, - 21 / 8).
iv) Two alternative solutions of the equation of the line are 20 · x + (160 / 7) · y = - 60 and 140 · x + 160 = 420.
How to derive the equation of a line?
In this problem we know that form of an equation of the line and two points, on which the line pass through. i) We determine the values of the coefficients a and b by solving the following system of linear equations:
5 · a - 7 · b = - 20
- 3 · a = - 20
Whose solution is a = 20 / 3 and b = 160 / 21.
ii) The equation of the line in standard form is (20 / 3) · x + (160 / 21) · y = - 20.
iii) Now we find the coordinates of the intercepts of the line:
x-Intercept
(20 / 3) · x = - 20
x = - 3
y-Intercept
(160 / 21) · y = - 20
y = - 21 / 8
iv) We can find two alternative solutions by using multiples:
20 · x + (160 / 7) · y = - 60
140 · x + 160 = 420
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a. A number is doubled and then increased by 2, the result is equal to 14 more than
5 times the number. What is the number?
Answer:
OK
Let x=the number
2x=double the number
2x+5=the doubled number increased by 5
And we are told that this equals -47
sooooo
2x+5=-47 subtract 5 from each side2x=-47-5=-52
2x=-52
x=-26------the number
CK
2*(-26)=-52
-52 increased by 5=-52+5=-47
-47=-47
Hope this helps- Clara ☆*: .｡. o(≧▽≦)o .｡.:*☆
Step-by-step explanation:
❄ Hi there,
let us start by letting the number be r. The problem tells us that r is doubled and then increased by 2.
This is what it looks like –
[tex]\triangleright \ \sf{2r+2}[/tex]
Also the result is 14 more than 5r.
We end up with an equation that looks like this –
[tex]\triangleright \ \sf{2r+2=14+5r}[/tex]
To find the number we should solve the equation for r –
[tex]\large\begin{gathered} \sf{2r+2=14+5r} . \ Solve \ for \ r: \\ \sf{2r-5r+2=14}\\ \\ \sf{-3r+2=14}\\\sf{-3r=14-2}\\\sf{-3r=12}\\\sf{-r=4}\\\sf{r=-4}\end{gathered}[/tex]
❄
18. A tennis player uses up 800 calories every hour. In 1 hour and 15 minutes, how many calories does this player use? (A) 900 (B) 1000 (C) 1100 (D) 1200
factorise completely
2x²+8+6
Hi there,
please see below for solution steps :
‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
⨠ add 8 and 6
[tex]\sf{2x^2+14}[/tex]
⨠ factor the 2 out
[tex]\sf{2(x^2+7)}[/tex]
Since we cannot simplify this more, we know that we've simplified completely. [tex]\small\pmb{\sf{Frozen \ melody}}[/tex]
‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
all common factors of 24
Answer:
The all common Factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24
A car is traveling at vx = 36 m/s. the driver applies the brakes and the car decelerates at ax = -6. 0 m/s2. what is the stopping distance?
Answer:
6 Meters
Step-by-step explanation:
If the car is driving at a constant velocity of 36 m/s and accelerates at -6.0 m/s ^2 to a stop, then the distance of the car decelerates to a stop in 6 seconds.
a=v/t ->>> 6= 36/t
The side length of each square is 6 units. Find the areas of the inscribed shapes.
By using subtraction of yellow areas from the entire squares, the areas of the inscribed shapes are listed below:
18 units20 units12 units12 unitsHow to calculate the areas of the inscribed shapesThe areas of the inscribed shapes can be easily found by subtracting the yellow areas from the square, in order to find the value of green areas. Now we proceed to find the result for each case by using area formulae for triangles:
Case A
A = 6² - 0.5 · (3) · (6) - 0.5 · (3) · (6)
A = 36 - 18
A = 18 units
Case B
A = 6² - 4 · 0.5 · (2) · (4)
A = 36 - 16
A = 20 units
Case C
A = 6² - 0.5 · 6² - 0.5 · 6 · 2
A = 36 - 18 - 6
A = 12 units
Case D
A = 6² - 2 · 0.5 · 6 · 4
A = 36 - 24
A = 12 units
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does someone mind helping me with this question? Thank you!
Answer:
[tex]\frac{263}{999}[/tex]
Step-by-step explanation:
Find the local maximum and minimum values of f using both the first and second derivative tests. f(x) = 6 9x2 − 6x3 local maximum value local minimum value
The local minimum value of the function f(x) = 6 + 9x² - 6x³ is 6 and the local maximum value of the function f(x) = 6 + 9x² - 6x³ is 9.
For given question,
We have been given a function f(x) = 6 + 9x² - 6x³
We need to find the local maximum and local minimum of the function f(x)
First we find the first derivative of the function.
⇒ f'(x) = 0 + 18x - 18x²
⇒ f'(x) = - 18x² + 18x
Putting the first derivative of the function equal to zero, we get
⇒ f'(x) = 0
⇒ - 18x² + 18x = 0
⇒ 18(-x² + x) = 0
⇒ x (-x + 1) = 0
⇒ x = 0 or -x + 1 = 0
⇒ x = 0 or x = 1
Now we find the second derivative of the function.
⇒ f"(x) = - 36x + 18
At x = 0 the value of second derivative of function f(x),
⇒ f"(0) = - 36(0) + 18
⇒ f"(0) = 0 + 18
⇒ f"(0) = 18
Here, at x=0, f"(x) > 0
This means, the function f(x) has the local minimum value at x = 0, which is given by
⇒ f(0) = 6 + 9(0)² - 6(0)³
⇒ f(0) = 6 + 0 - 0
⇒ f(0) = 6
At x = 1 the value of second derivative of function f(x),
⇒ f"(1) = - 36(1) + 18
⇒ f"(1) = - 18
Here, at x = 1, f"(x) < 0
This means, the function f(x) has the local maximum value at x = 1, which is given by
⇒ f(1) = 6 + 9(1)² - 6(1)³
⇒ f(1) = 6 + 9 - 6
⇒ f(1) = 9
So, the function f(x) = 6 + 9x² - 6x³ has local minimum at x = 0 and local maximum at x = 1.
Therefore, the local minimum value of the function f(x) = 6 + 9x² - 6x³ is 6 and the local maximum value of the function f(x) = 6 + 9x² - 6x³ is 9.
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Area=
Help me please!! Thanks so much :)
Asap
Answer:
16u²
Step-by-step explanation:
It is a regular parallelogram
we have points (3, 4) and (4, 0).
we also have the origin which is (0, 0) and the difference between (0, 0) and (4, 0) on the x axis is 4 and since it is a regular shape, that means the top right corner = (3, 4) + (4, 0), so it is (7, 4). we know the base is 4 now. the vertical height = (7, 4) - (1, 0) which is (6, 4). now we are looking at difference in y. which is between (4, 0) and (6, 4), so the difference is 4.
now we just do 4 x 4 since it is bh and you get 16 units ²
An equilateral is shown inside a square inside a regular pentagon inside a regular hexagon. The square and regular hexagon are shaded.
An equilateral triangle is shown inside a square inside a regular pentagon inside a regular hexagon. Write an expression for the area of the shaded regions.
Shaded area = area of the
– area of the + area of the – area of the
Shaded area = area of the hexagon – area of the pentagon + area of the square – area of the equilateral triangle. This can be obtained by finding each shaded area and then adding them.
Find the expression for the area of the shaded regions:From the question we can say that the Hexagon has three shapes inside it,
PentagonSquareTriangleAlso it is given that,
An equilateral triangle is shown inside a square inside a regular pentagon inside a regular hexagon.
From this we know that equilateral triangle is the smallest, then square, then regular pentagon and then a regular hexagon.
A pentagon is shown inside a regular hexagon.
Area of first shaded region = Area of the hexagon - Area of pentagonAn equilateral triangle is shown inside a square.
Area of second shaded region = Area of the square - Area of equilateral triangleThe expression for total shaded region would be written as,
Shaded area = Area of first shaded region + Area of second shaded region
Hence,
⇒ Shaded area = area of the hexagon – area of the pentagon + area of the square – area of the equilateral triangle.
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Answer:
Regular Hexagon
Regular Pentagon
Square
Equilateral Triangle
Step-by-step explanation:
E2020 Geometry B!! :3
Anna wanted to buy a camera. The first discount store sold her favorite camera for $95. The second store sold the same camera for $115, but it was on sale for 20% off. The third store carried the camera for $105 but offered it at 10% off with a coupon. which store had the better buy?
The second store offered the better buy at the price of $92.00.
What is better buy?
Better buy refers to the lowest price out of the prices offered by the three stores.
In order to determine the lowest price, the no discount price of the first store needs to be compared to the prices of two other stores, bearing that after-discount price is the pre-discount price multiplied by 1 minus the discount rate.
First store price=$95.00
Second store after-discount price=pre-tax discount price*(1-discount rate)
pre-discount price=$115
discount rate=20%
Second store after-discount price=$115*(1-20%)
Second store after-discount price=$92.00
Third store after-discount price=pre-tax discount price*(1-discount rate)
pre-discount price=$105
discount rate=10%
Third store after-discount price=$105*(1-10%)
Third store after-discount price=$94.50
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Prove the identity.
tan^5x = tan x (sec² x - 2 sec² x + 1)
goal:tan^5x=tanx(sec²x-2sec²x+1)
proof: from l.h.s to r.h.s
tan^5x=(tanx)^5=((tanx)(tan²x)(tan²x))
from trigonometry identity
(tan²x)=sec²x-1
tan^5x=(tanx(sec²x-1)(sec²x-1))
=(tanx(sec^4x-sec²x-sec²x+1))
=(tanx(sec^4x-2sec²x+1))
proved
