The sum identities in trigonometry are cos^2(x)+sin^2(x)=1
sec^2-tan^2(x)=1
cosec^2(x)-cot^2(x)=1
What is Trigonometry?Trigonometry: Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles. Trigonometry is found all throughout geometry, as every straight-sided shape may be broken into as a collection of triangles
Let's prove using the angle addition formula for cosine:
cos(α+β)=cos(α)cos(β)-sin(α)sin(β)
we know that sin(-x)= -sin x and
cos(-x)=cos x
we need to proceed to the proof ,
let α=x and β=-x
cos(x+(-x))=cos(x)cos(-x)-sin(x)sin(-x)
cos(0) = cos(x)cos(x)+sin(x)sin(x)
cos^2(x)+sin^2(x)=1
Hence, it is proved
to prove another identity i.e., sec^2-tan^2(x)=1
start from cos^2(x)+sin^2(x)=1
divide both the sides by cos^2(x)
cos^2(x)/cos^2(x)+sin^2(x)/cos^2(x)=1/cos^2(x)
1+tan^2(x)=sec^2(x)
sec^2-tan^2(x)=1
Hence, it is proved
to prove another identity i.e., cosec^2(x)-cot^2(x)=1
start from cos^2(x)+sin^2(x)=1
divide both sides by sin^2(x)
cos^2(x)/sin^2(x)+sin^2(x)/sin^2(x)=1/sin^2(x)
cot^2(x)+1=cosec^2(x)
cosec^2(x)-cot^2(x)=1
Hence, it is proved
The sum identities in trigonometry are proved
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The formula for the volume V of a sphere with radius r is V = 4/3πr3. If the radius of a spherical rubber ball is 2 3/4 inches, what is its volume, to the nearest cubic inch?
The volume of the spherical rubber ball to the nearest cubic inch is 87.11 cubic inches.
How to find the volume of spherical rubber ball ?The capacity of a sphere is its volume. It is the area that the sphere occupies. Cubic measurements for sphere volume include m^3, cm^3, and in^3.
The formula of volume of the sphere is
V = 4/3πr3
given that the radius of spherical rubber ball is 2 3/4
here the radius is given in improper fraction
now convert it into the decimal by following procedure.
first multiply the 2 with 4
2 X 4 = 8
now add 8 to 3. 8 + 3 = 11
The proper fraction of 2 3/4 is 11/4.
so, the decimal number is 2.75
now put r = 2.75 in formula to get the volume.
V = 4/3 X 3.14 X 2.75 X 2.75 X 2.75
V = 1.33333 X 3.15 X 20.7968
V = 87.11 cubic inches
Hence,the volume of the spherical rubber ball to the nearest cubic inch is 87.11 cubic inches.
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in a box of assorted cookies, 36% contain chocolate and 12% contain nuts. of those, 8% contain both chocolate and nuts. if a cookie is randomly picked, what is the probability that it does not contain chocolate or nuts.
The probability that a cookie is randomly picked and it does not contain chocolate or nuts will be 0.52
As per the question statement, a box of assorted cookies has 36% of them containing chocolate and 12% containing nuts, and of those, again 8% contain both chocolate and nuts, and we are assuming that the rest of the cookies neither contain chocolate, nor nuts.
Based on the conditions and our assumptions provided in the above mentioned statement, we are required to calculate the probability that a cookie is randomly picked and it does not contain chocolate or nuts.
Considering the total number of cookies in the box to be 100%, since 36% of them containing chocolate and 12% containing nuts and the rest of the cookies are assumed to contain neither chocolate, nor nuts,
The probability that a cookie is randomly picked and it does not contain chocolate or nuts will be [{100 - (36 + 12)}/100]
= [(100 - 48)/100]
= (52/100)
= 0.52
Probability: It is a branch of Mathematics, that deals with the numerical descriptions concerning the extent to which an event is likely to occur, or how likely it is for a proposition to be true, and is measured by the ratio of the favorable cases to the whole number of cases possible.
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question on inference method and test statistic - is there evidence that the mean amount of water drank daily by a teenager is more than 1.5 liters? data was collected from a sample of 56 teenagers. the best approach to provide an answer to the question would be:
The best approach to provide an answer to the question would be: Calculate a confidence interval using t*
When do we calculate a confidence interval using t*?The confidence interval is often used to obtain the true population mean. The question asks us to identify evidence that points to the fact that the mean amount of water drank by each teenager is more than 1.5 liters.
We are here searching for the true population mean. We calculate a confidence interval using t when the population variance is not known as is the case here. So, to solve this question, we would calculatethe confidentce interval using t*.
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What is the solution for this system of equations?
Answer: y = x +8
Step-by-step explanation:
Find the measure of FG.
Thank you ;)
The measure of FG is 16 units.
How to find the measure of FG?The measure of FG can be found as follows:
GE is an angle bisector.
An angle bisector is a bisector that bisect angles into two equal halves.
Therefore,
GE bisect ∠FEH
Hence,
FG = GH
FG = x + 11
GH = 3x + 1
x + 11 = 3x + 1
11 - 1 = 3x - x
10 = 2x
x = 10 / 2
x = 5
Therefore,
FG = x + 11 = 5 + 11 = 16 units
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9. Brenna wants an easier way to write 0.0000000000000000587.
0.0000000000000000587 is written as______
x 10____
in scientific notation.
Answer:
5.87 x [tex]10^{-17}[/tex]
Step-by-step explanation:
You need to write the number as 1 or larger than 1, but less than 10. That means that I need to put the decimal between the 5 and the 8. Now I have to count how many places I moved the decimal. I think that I counted right. It was moved 17 places. Since the number in standard form is much smaller than 5.87, the exponent will be negative.
You and your friend, who lives in a different city, are comparing the malls in your respective cities. Your friend describes the locations of some of the ma stores in the following way.
The music store (M) is due north of the bookstore (B) along hallway 1. The shoe store (S) is due east of the music store along hallway 1. The clothing store (C) is northeast of the music store along hallway 2 so that Z MSC is obtuse.
The shoe store and clothing store are on hallway 2. The arcade (A) is southeast of the bookstore along hallway 3
en -
so that _ CSA is acute. The shoe store and arcade are on hallway 3. The food court (F) is due east of the shoe store on hallway 1.
a. Connect S to C and A.
b. The shoe store
c. If a book is a paperback, then it is on sale. If a book is on sale, then its sale price is 20% off the original price.
d. If a book is a paperback, then its sale price is 20% off the original price
What is Location diagram?Any diagram that conveys mathematical concepts is referred to as a math diagram. This includes both simple charts and graphs and complex logic and geometrical diagrams. A visual aid can help you understand math and science concepts.
Two parallel columns make up a mapping diagram. The first column represents a function's domain, and the second column its range. To represent the relationship between any two elements, lines or arrows are drawn from domain to range.
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how many different bracelets have 3 identical orange beads, 3 identical black beads, and 1 teal bead, if rotating or flipping a bracelet does not change it?
10 different bracelets have 3 identical orange beads, 3 identical black beads, and 1 teal bead, if rotating or flipping a bracelet does not change it
What is permutation and combination?Permutations and combinations are the many methods for picking objects from a set to form subsets, usually without replacing them. When the order of selection is a factor, this selection of subsets is known as a permutation; when the order of selection is not a factor, this selection of subsets is known as a combination.
CalculationI think it is only 10 ways.
Put the teal bead on first. It is the marker bead. This takes care of the rotation aspect.
Then you have 2 lots of 3 identical beads. so that is 6!/(3!3!) ways to place them. Which is 20 ways.
But the bracelet can be flipped so I think this will halve the number of possibilities
For instance TOOOBBB is the same as TBBBOOO
So I think the answer is 10 ways.
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Open Ended You are given the point Q(-2,-5), A. Identify a point (x, y,) that along with point Q defines a line with a positive slope.
Slope m is positive when
x₁≥ -2
y₁ ≥ -5
Define slope.Slope, usually referred to as rise over run, is the "steepness" of the line. By dividing the difference in y values between two points by the difference in x values, we may determine slope. The ratio of the increase in elevation between two points to the run in elevation between those same two points is referred to as the slope. A line that is moving up will have a positive slope, and a line that is moving down will have a negative slope, if you view the line from left to right.
Given,
Point (-2. -5)
Slope = [tex]\frac{y_{1}-(-5) }{x_{1}-(-2) }[/tex]
Slope = [tex]\frac{y_{1}+5 }{x_{1}+2 }[/tex]
Slope m is positive when
x₁≥ -2
y₁ ≥ -5
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Evaluate.
72 - 9 ÷ 3 · 2 + 2 =
A) 21
B) 23
C) 44
D) 68
E) 74
Answer:
D) 68
Step-by-step explanation:
PEMDAS
The PEMDAS rule is an acronym representing the order of operations in math:
ParenthesesExponentsMultiplication and Division (from left to right)Addition and Subtraction (from left to right)Given expression:
72 - 9 ÷ 3 · 2 + 2
Following the order of operations, carry out the multiplication and division first, working from left to right.
Divide 9 by 3:
⇒ 72 - 9 ÷ 3 · 2 + 2
⇒ 72 - 3 · 2 + 2
Multiply 3 by 2:
⇒ 72 - 3 · 2 + 2
⇒ 72 - 6 + 2
Now carry out the addition and subtraction, working from left to right.
Subtract 6 from 72:
⇒ 72 - 6 + 2
⇒ 66 + 2
Add 66 and 2:
⇒ 66 + 2
⇒ 68
Solution
72 - 9 ÷ 3 · 2 + 2 = 68
Answer:
d
Step-by-step explanation:
what was the mean number of miles the hiker walked for the 6 days?
Answer:
Incomplete question
...
help pls due tmrw..pls
1) The equation of line is; y = (1/3)x + 1
2) The x - intercept is -3 and the y-intercept is 2
3) Area of CAT is; 6 sq.units
4) Perimeter is; 14.325 units
What is the equation of the Line?
1) The coordinates of the line AC on the graph are;
A(-3, 0) and C(3, 2)
Thus, equation of line is gotten from the formula;
(y₂ - y₁)/(x₂ - x₁) = (y - y₁)/(x - x₁)
(2 - 0)/(3 + 3) = (y - 0)/(x + 3)
2/6 = y/(x + 3)
3y = x + 3
y = (1/3)x + 1
2) The x - intercept is -3 and the y-intercept is 2
3) Area of CAT is;
Area = 1/2 * base * height
Area = 1/2 * 6 * 2
Area = 6 sq.units
4) Perimeter of ACT is gotten by;
AT + CT + AC
AC = √((2 - 0)² + (3 + 3)²)
AC = √40
Thus;
Perimeter = 2 + 6 + √40
Perimeter = 14.325
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An item is regularly priced at $78. Martina bought it at a discount of 80% off the regular price.
Use the ALEKS calculator to find how much Martina paid.
An item is regularly priced at $78. Martina bought it at a discount of 80% off the regular price. Martina paid $15.6
What is Sales Price?Sales price: The price that is paid by the buyer at the time when something is sold: People who sold their homes through real estate agents typically did not get a higher sale price than people who sold their homes themselves
The formula for calculating sales price of an item is:
s=p-(p x d)
where,
s is the sales price (which we are going to calculate in this problem)
p is the regular price of the item which is $78
d is the discount rate which is 80%
which means out of 100 = 80/100
substitute the above values in the formula then we get
s=$78-($78 x 80/100)
s=$78-($6240/100)
s=$78-$62.4
s=$15.6
Martina paid $15.6
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20+ 98075643456=? help me
98,075,643,476
Step-by-step explanation:
I add 20 to 56 and the answer is thos
The area of a circular rug is 78.5ft. What is the diameter of the rug, to the nearest whole foot?
area = 78.5 ft squared
diameter = ?
[tex]\begin{gathered} \text{area of a circular rug=}\pi r^2 \\ 78.5=3.14\times(\frac{d}{2})^2 \\ 78.5=3.14\times\frac{d^2}{4} \\ 78.5=\frac{3.14d^2}{4} \\ \text{cross multiply} \\ 3.14d^2=314 \\ d^2=\frac{314}{3.14} \\ d^2=100 \\ d=\sqrt[]{100} \\ d=10 \end{gathered}[/tex]Solve the equation t − 6 = 13 for t. −7 7 −19 19
I WILL USE THE METHOD OF ADDITIVE INVERSE.
[tex]t - 6 + 6 = 13 + 6 \\ t = 19[/tex]
ATTACHED IS THE SOLUTION
Answer:
Step-by-step explanation:
You need to see what 13 minus 6 is and that the T value then just plug it in. The answer is 7
Stephanie is collecting data on the reaction of bacteria to different antibodies. She did not measure the area of the bacteria in the dish when she began the experiment but measured 20 cm2 of bacteria after 1 hour. She continued to measure the bacteria each hour and entered the data in the table. show the explicit function. How much area would you predict the bacteria to have when measured during the 5th hour?
We take a look at the reduction in the area of the bacteria.
In the first hour, its arae is 20cm2. Following that, it reduces 1.25x, to 16. Then another 1.25x, from 16 to 12.8. And another 1.25x, from 12.8 to 10.24.
So, every hour, the bacteria's area reduces by 1.25x
Therefore, in the 5th hour (prediction probably if this is all a coincidence), the bacteria's area will be : 10.24 : 1.25 = 8.192 cm2.
diseases tend to spread according to the exponential growth model and the early days of AIDS in the growth factor was around 1.9 in 1983 about 1,500 people in the US died of AIDS if this trend had continued unchecked how many people would have died from Aids in 2005
Given the exponential model:
[tex]f(x)=A\cdot b^x^{}[/tex]Where A is the initial condition, b is the growth factor and x is a time-like variable.
We know that the growth factor is 1.9 and that 1500 people died of AIDS in 1983. If we make x to be the years passed since 1983, then 1500 is our initial condition (because 0 years passed). In our model:
[tex]f(x)=1500\cdot1.9^x[/tex]For 2005, x = 22:
[tex]f(22)=1500\cdot1.9^{22}=2035497063[/tex]
(2x+5)(4x-3) find the product
[tex]2x(4x - 3) + 5(4x -3 ) \\ = {8x}^{2} - 6x + 20x - 15 \\ = 8 {x}^{2} + 14x - 15[/tex]
ATTACHED IS THE SOLUTION
Answer:
I think it would be 8x2^ + 14x − 15
please help im literally sobbing
A bus driver makes $14 per hour and works 2,000 hours each year. He
also gets a fee of $50 for each new driver he recruits. If the bus driver
recruits 7 new drivers, what are his total earnings?
The total earnings of the bus driver in a year is $28500.
A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output.
The bus driver works 2000 hours each year and makes $14 per hour.
If the bus driver gets $50 for each new recruit he hired.
Let y be his total earnings and x be the number of new drivers he recruits.
Then his total earnings can be represented by the function:
y = 14 × 2000 + 50 × x
If the bus driver recruits x = 7 new drivers.
y = 28000 + 50 × 7
y = 28000 + 350
y = $28350
The total earnings of the bus driver are $2850.
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a fire department in a rural county reports that its response time to fires is approximately normally distributed with a mean of 22 minutes and a standard deviation of 6.9 minutes. assume that this claim is true.one percent of response times take at least how many minutes?
If this claim is true then one percent of response times take at least [tex]38.077[/tex] minutes.
In the given question,
A fire department in a rural county reports that its response time to fires is approximately normally distributed with a mean of 22 minutes and a standard deviation of 6.9 minutes.
We have to assuming that the claim is true and finding that one percent of response times take at least how many minutes.
From the question,
Mean [tex]\mu=22[/tex] minutes
Standard deviation [tex]\sigma=6.9[/tex] minutes.
Since the given percentage is [tex]1\%[/tex] and percentage means division of [tex]100[/tex] so we can write [tex]1\%=1/100=0.01[/tex]
So the one percent of response times take at least how many minutes is
[tex]P(x\geq a)=0.01[/tex]
[tex]P(x\geq \frac{a-\mu}{\sigma})=0.01[/tex]
As we know the all values. SO putting the values in the formula
[tex]P(x\geq \frac{a-22}{6.9})=0.01\dots\dots[/tex]Equation 1
From the z table
[tex]P(z\geq 2.33)=0.01\dots\dots[/tex]Equation 2
Now from Equation 1 and Equation 2
[tex]\frac{a-22}{6.9}=2.33[/tex]
Multiply by [tex]6.9[/tex] on both side
[tex]\frac{a-22}{6.9}\times6.9=2.33\times6.9[/tex]
Simplifying
[tex]a-22=2.33\times6.9[/tex]
[tex]a-22=16.077[/tex]
Add [tex]22[/tex] on both side
[tex]a-22+22=16.077+22[/tex]
[tex]a=38.077[/tex]
Hence, if this claim is true then one percent of response times take at least [tex]38.077[/tex] minutes.
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if you dilate something by 1 half, what would you have to dilate it to to get it back to the same number.
If I dilate a number by 1 half, then I will have to dilate it again by 2, to get the same to the same number.
As per the question statement, I dilate a number by 1 half.
We are required to calculate that by what should I dilate the result, to reverb back to the same number that I started with.
To solve this question, first we need to understand the concept of Dilation.
Dilation means to create an Image.If dilation of a number or object enlarges it, then it is known as enlargement.On the other hand, if dilation creates a smaller image, then it is known as Reduction.Here, since our first dilation of the original number, say "x" reduces it by 1 half, that is, x becomes (x/2),
To get back to x, we will need to multiply (x/2) by 2 again.
[(x/2) * 2] = x.
Therefore, I will need to enlarge our result with a multiplication with 2 to get back to our original number.
Dilation: Dilation means to change the size of an object without changing its shape, where the size of the object may be increased or decreased based on the scale factor.To learn more about Dilation, click on the link below.
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help me with this pleaseeee
The answer is C y=x+8
Graph of the function
f(x) = -x² - 4x - 1 is the equation of the parabola in the graph.
What is the equation of the graph?From the graph, the parabola passes through point (-1,2) and has a vertex at point (-2,3).
For a parabola with a vertex (h,k), the general equation is expressed as;
y = a( x - h)² + k
First we find 'a', plug in the given coordinates into the equation.
y = a( x - h)² + k
2 = a( -1 - (-2))² + 3
Solve for a
2 = a( -1 + 2 )² + 3
2 = a( 1 )² + 3
2 = a + 3
a = 2 - 3
a = -1
Now substitute the vertex (-2,3 and a ( -1 ) into the general equation.
y = a( x - h)² + k
y = -1( x - (-2))² + 3
Simplify
y = -1( x + 2 )² + 3
Expand using FOIL method
y = -1( (x + 2)(x+2) ) + 3
y = -1( x² + 2x + 2x + 4 ) + 3
y = -1( x² + 4x + 4 ) + 3
Apply distributive property
y = -x² - 4x - 4 + 3
Add like terms
y = -x² - 4x - 1
f(x) = -x² - 4x - 1
Therefore, the equation of the graph is f(x) = -x² - 4x - 1.
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20.86 divided by 0.2 dividing decimals
Answer: 104.3
Step-by-step explanation: To divide a decimal by another decimal: Move the decimal point in the divisor to the right until it is a whole number.
Which dimensions cannot create a triangle?
three angles measuring 10 degrees, 25 degrees, and 145 degrees
three sides measuring 9 m, 15 m, and 9 m
three angles measuring 40 degrees, 70 degrees, and 65 degrees
three sides measuring 6 cm, 8 cm, and 10 cm
Answer:
10,25, and 145
Step-by-step explanation:
to see if it can make a triangle you have to add 2 of the angles together and it has to be more than the other angle
(ex:40+70>65)
a triangle
(ex:10+25<145)
not a triangle
A right circular cone has a radius of x+4 and a height 5 units less than its radius. Express the volume of the cone as a polynomial function. The volume of a cone is V=13πr2h for radius r and height h. Enter π as pi.
Answer:
V(x) = (1/3)π(x + 4)²(x - 1) orV(x) = (1/3)π(x³ + 7x² + 8x - 16)Step-by-step explanation:
GivenRadius of cone = x + 4 units,Height of cone = 5 units less than radius,Volume formula.SolutionWe are given the volume formula:
V = (1/3)πr²hFind the height:
h = r - 5h = x + 4 - 5 = x - 1Substitute all into formula:
V(x) = (1/3)π(x + 4)²(x - 1)You may keep it as is or simplify:
V(x) = (1/3)π(x² + 8x + 16)(x - 1) = (1/3)π(x³ + 8x² + 16x - x² - 8x - 16) = (1/3)π(x³ + 7x² + 8x - 16)The 9th grade class was surveyed about their plans after high school graduation. The table describes the results.
Part A: Find the conditional relative frequency of a student who plans to live at home, given that they plan to attend college. (3 points)
Part B: Is there an association between attending college and living at home? (3 points)
A) The conditional relative frequency of a student who plans to live at home, given that they plan to attend college is; 53.85%
B) Yes, there is an association between attending college and living at home.
What is the Conditional Relative Frequency?
A conditional relative frequency is calculated by dividing a frequency that is not in the Total row or the Total column by the frequency's row total or column total.
A) From the definition above, the conditional relative frequency of a student who plans to live at home, given that they plan to attend college is; 35%/65% = 7/13 = 53.85%
B) Yes there is an association between attending college and living at home because the percentage of students who plans to live at home, given that they plan to attend college over half of those is more than 50%.
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There are 4 Proof and statements that I need. Given AC=BD, and AB and CD bisect each other. Prove:
Given AC=BD.It is also said AB and CD bisect each other.
Since AB and CD bisect each other at O, we can write
AO=OB
CO=OD
Since the three sides of triangle AOC is equal to the corresponding sides of triangle BOD, both the traingles are congruent.
The angles opposite to equal sides of triangles are also equal.
Since AO and
