Answer:
[tex]\displaystyle \frac{\tan\theta}{\sec\theta - \cos\theta} = \frac{1}{\sin\theta} = \csc\theta[/tex]
Step-by-step explanation:
We have the expression:
[tex]\displaystyle \frac{\tan\theta}{\sec\theta - \cos\theta}[/tex]
And we want to write the expression in terms of sine and cosine and simplify.
Thus, let tanθ = sinθ / cosθ and secθ = 1 / cosθ. Substitute:
[tex]=\displaystyle \frac{\dfrac{\sin\theta}{\cos\theta}}{\dfrac{1}{\cos\theta}-\cos\theta}[/tex]
Multiply both layers by cosθ:
[tex]=\displaystyle \frac{\left(\dfrac{\sin\theta}{\cos\theta}\right)\cdot \cos\theta}{\left(\dfrac{1}{\cos\theta}-\cos\theta\right)\cdot \cos\theta}[/tex]
Distribute:
[tex]\displaystyle =\frac{\sin\theta}{1-\cos^2\theta}[/tex]
Recall from the Pythagorean Theorem that sin²θ + cos²θ = 1. Hence, 1 - cos²θ = sin²θ. Substitute and simplify:
[tex]\displaystyle =\frac{\sin\theta}{\sin^2\theta} \\ \\ =\frac{1}{\sin\theta}[/tex]
We can convert this to cosecant if we wish.
2) The cost of renting a boat for one or more
days is given by the function f(n)=12+20n,
where n = number of days and f(n) = total
cost in dollars.
What is the value of f(7-4)?=
Answer: 3f
Step-by-step explanation:
please anyone give me a answer i need it rn
Answer:
The first option is the right one.
Step-by-step explanation:
7/2. Rate is rise/run
7 is your rise
and 2 is your run
therefore, the answer is 7/2
18-3×5+32÷4
USE BODMAS RULE
the answer should come 11
Answer:
B-bracket
O-of
D-division
M-multiplication
A-addition
S-subtraction
Step-by-step explanation:
18-3×5+32÷4
18-3×5+8 (by dividing 32 by 4 = 8)
18-15+8(by multiplying 3×5=15)
18-7( by -15 +8= 7 )
11
hence proved
11 is the answer by BODMAS rule .
hope this helps you
mrk me braniliest
Two consecutive integers have a sum of 107. Find the integers.
Answer: 53 and 54
Explanation
Let the consecutive numbers be x and x + 1
ATQ
x + x + 1 = 107
2x = 107 - 1
x = 106/2
x = 53
Therefore the numbers are 53 and 54
Must click thanks and mark brainliest
Answer:
x = 53, x + 1 = 54
Step-by-step explanation:
Consecutive integers are two numbers that are after each other. (This is confusing wording, but hopefully this example helps):
Regular consecutive numbers: 1, 2, 3
Even consecutive numbers: 2, 4, 6
Since in this problem the numbers are not given you will use variables.
x + x + 1 = 107
Solve:
x + x + 1 = 107
2x + 1 = 107
-1 -1
----------------
2x = 106
--- -----
2 2
x = 53
x + 1
53 + 1 = 54
Hope this helped.
How would the expression x^2 -9 be rewritten using Difference of Squares?
O A. (x+3)(x - 3)
O B. (X-9)^2
O C. (x +9)(x-9)
O D. (x+3)^2
Answer:
A. (x+3)(x - 3)
Step-by-step explanation:
x^2 -9
Rewriting
x^2 - 3^2
We know that a^2 - b^2 = (a-b)(a+b)
(x-3)(x+3)
Answer:
[tex]\left(x+3\right)\left(x-3\right)[/tex]
Step-by-step explanation:
[tex]x^2 -9[/tex]
To factor an integer, we need to divide it by the ascending sequence of primes (2, 3, 5). The number of times each prime divides the original integer becomes its exponent. [tex]3^{2} =9[/tex]
Now, we need to factor this expression by applying the difference of two squares rule:
[tex]A^{2} -B^{2} =(A+B)(A-B)[/tex]
A= x and B= 3
[tex](x+3)(x-3)[/tex]
OAmalOHopeO
Find the solution set of the inequality. -25 > -5(x + 2.5
Answer:
-25 > -5(x+2.5)
-25 > -5x -12.5
x > 5/2
please click thanks and mark brainliest if you like :)
Answer:
x < 2.5
Step-by-step explanation:
-25>-5(x-12.5)
-25 > -5x -12.5
add 12.5 to both sides
-25+12.5 > -5x -12.5+12.5
-12.5> -5x
divide both sides by -5
(-12.5/-5)> -5x/-5
x>2.5
since we divided by a negative,the inequality sign will flip over
x<2.5
Hii, please help me with this question I keep getting an option that isn't there.
A cylindrical piece of iron pipe is shown below. The wall of the pipe is 1.25 inch thick:
The figure shows a cylinder of height 16 inches and diameter 6 inches.
What is the approximate inside volume of the pipe?
a. 88 cubic inches
b. 49 cubic inches
c. 142 cubic inches
d. 154 cubic inches
The volume of this pipe considering the thickness of the pipe is 154 cubic inches.
How do you calculate the volume of the pipe?The general formula to calculate the volume of a cylindric object such as a pipe is:
V = πd^2h/4In this formula, d represents the diameter and h represents the height.
What is the diameter?The external diameter is 6 inches; however, the pipe is 1.25 inches thick, which implies the real internal diameter is 3.5.
6 inches - 2.5 (1.25 x 2) = 3.5Now, let's calculate the volume:
V = πd^2h/4V= π (12.25 x 16)/4V= π (196)/4V= 615.713 / 4 = 153.93 which can be rounded as 154 cubic inches.Learn more about cylindric in: https://brainly.com/question/14965384
Answer:
D. 154 cubic inches
Step-by-step explanation:
The surface area of a sphere is a function of the radius of the sphere: A = 41182.
Evaluate the function for a basketball with a radius of 11.5 cm.
The value of the function of the surface area of a sphere when the radius is 11.5 cm is approximately 1661.9 cm²
The process of arriving at the above value is as follows;
The known parameter
The function of the radius representing the surface area of a sphere is, f(r) = A = 4·π·r²
The radius of the basketball, r = 11.5 cm
Required;
To evaluate the function, f(r), for the basketball
Method;
The process of evaluating a function, is to find the value of the function at a given value of the input or independent variable of the function
The input variable is the variable that determines the output value of the function, it is the variable which is the function is about
In the question, the function given is dependent on the radius, r
To evaluate the value of the function, we substitute the value of r in the equation of the functionTherefore;
When r = 11.5 cm (the radius of the basketball), from the function, the surface area of the basketball, A = f(11.5) = 4 × π × (11.5 cm)² ≈ 1661.9 cm²
Therefore;
The evaluation of the function which is the value of the function, f(r) = A,
when the radius, r, is 11.5 cm, which is the surface area of the spherical
basketball, is A ≈ 1661.9 cm²
Learn more about evaluation of functions here;
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Guys please help me solve this problem, yes I will mark brainliest
Given that the vertex is at (50, 1000), the max profit is $1000 when 50 items are produced
Please help me solve this quickly!
Answer:
33.80
Step-by-step explanation:
AB = BC = AD√2
AB = BC = 7√2
AD = DC
AC = 2AD
perimeter = AC + AB + BC
= 2AD + 2AB
= 2(7) + 2(7√2)
= 14 + 14√2
≈ 33.80
Answer:
33.8
Step-by-step explanation:
45-45-90 degree triangle rules states that the sides that are opposite the angles measure 45 degrees have the same value. That means that BD has the same value as AD, which is 7. Since triangle BDC is also a 45-45-90 degree triangle, DC is equal to BD, which is 7. We have the value of AC, which is 7+7=14. Now, we can use the Pythagorean theorem to figure out BC and AB. We know that [tex]DC^2+BD^2=BC^2[/tex]. We know that DC and BD is equal to 7, so we can simplify that to [tex]49+49=BC^2[/tex], and we can further simplify that to [tex]BC=\sqrt{98}[/tex]. This is also equal to [tex]7\sqrt{2}[/tex]. Since BC is also equal to AB because of 45-45-90 degree triangle rules, we have the perimeter of the triangle as
[tex]7\sqrt{2} + 7\sqrt{2}+14[/tex], which is equal to [tex]14\sqrt{2} + 14[/tex]. We can simplify 14 times the square root of 2 as 19.8 (rounded to 2 decimal places). We have the answer as 19.8 + 14, which is 33.8.
What is the equation of the graph?
Answer:
In the sciences, many times it is necessary to be able to interpret graphs as well as be able to graph certain equations. Often data is available in a graphical format and you must be able to extract the necessary information. Other times, it may be helpful to plot an equation in order to fully understand a problem. However, graphing can be difficult for some students. The format in this section is a little different. The first part will be simply showing what some special equations look like in graphical form and the second part will be a series of questions to help you understand graphs better.
Step-by-step explanation:
The function f is defined by f(x) = x^2 - 2x - 24. If f(x+3) = x^2 - kx - 21, what is the value of k?
Answer:
k = 4
Step-by-step explanation:
In the equation: x² - 2x - 24
Replace the x with x + 3
(x+3)² - 2(x+3) - 24
x² + 6x + 9 - 2x - 6 -24
Let's rearrange it
x² + 6x -2x - 24 + 9 - 6
x² - 4x - 21
f(x+3) = x² - 4x - 21
The equivalent value of k from the function is k = -4
What is a function rule?The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.
A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Given data ,
Let the function be represented as A
Now , the value of A is
f ( x ) = x² - 2x - 24
Let the second function be represented as B
Now , the value of B is
f ( x + 3 ) = x² - kx - 21
On simplifying , we get
f ( x + 3 ) = ( x + 3 )² - 2 ( x + 3 ) - 24
f ( x + 3 ) = x² + 6x + 9 - 2x - 6 - 24
f ( x + 3 ) = x² + 4x - 21
So , from the equations , we get
-kx = 4x
Divide by -x on both sides , we get
k = -4
Hence , the equation is k = -4
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A textbook store sold a combined total of 240 chemistry and history textbooks in a week. The number of chemistry textbooks sold
was two times the number of history textbooks sold. How many textbooks of each type were sold?
Answer:
160 chemistry books and 80 history books
Step-by-step explanation:
C=chemistry books sold, H=history books sold
C=2H
C+H=240, 3H=240, H=80, C=160
If the graph of f(x) = x^2, how will the graph be affected if it is changed to f(x) = 3r^2?
Answer:
the graph curve will goes above f(x)=x^2.f(x)=3*x^2 curve will also give higher value same value of x .
Step-by-step explanation:
x.(9x-1).(x+2)-x(3x-1).(3x+1)
Answer:
=17x²-x
Step-by-step explanation:
=x.(9x²+18x-x-2)-x.(9x²-1)
=x.(9x²+17x-2-9x²+1)
=x.(17x-1)
=17x²-x
Explain the
The fifth term of a non-linear sequence is 324. The term-to-term rule is ‘multiply by 3?
Work out the second term of the sequence.
Explain the method you used to solve this problem.
Answer:
a2=12 (the second term of the sequence is 12)
Step-by-step explanation:
a5=324
If the term to term rule is multiply by any number, we deal with geometrical sequence
The formula you should use is an= a1*r^(n-1) where n is the number of the term which we know. In our case we know
a5, so use 5 instead of n
Then you have a5=a1*r^4 where r is the number 3 (because each next term is greater than previous in 3 times)
a5=324
324= a1*3^4
324=a1*81
a1=4 (We find the first term of sequence, because having it you can easily search for every term )
Return to the formula an= a1*r^n-1
Now search for the second term using 2 instead of n in the formula
a2= a1*r^1
a2=a1*r, a1=4, r=3
a2=4*3=12
A student states that Figure JKLM is congruent to Figure PQRS. Determine if the student is correct or has made an error. ;D
Answer:
Student has made an error
Step-by-step explanation:
If two figures are said to be congruent, this implies that area of both is same and both as exactly same or copy or each other.
But from the graph, it can be stated that height of figure JKLM is 4 units whereas that of other is 6 unit.
Hence explained !
Please help explanation if possible
that's the answer pls mark as brainliest
Answer:
x = 71 and y = 19
Step-by-step explanation:
Given the 2 equations
x + y = 90 → (1)
x = 14 + 3y → (2)
Substitute x = 14 + 3y into (1)
14 + 3y + y = 90 ( subtract 14 from both sides )
4y = 76 ( divide both sides by 4 )
y = 19
Substitute y = 19 into (1) for value of x
x + 19 = 90 ( subtract 19 from both sides )
x = 71
Larger number x = 71 ; Smaller number y = 19
The population of a city has increased by 27% since it was last measured. If the current population is 38,100, what was the previous population?
=___
Answer:
the previous population was 62,000.
Step-by-step explanation:
The current population of a city = 83,700
The population of a city has increased by 35% since it was last measured.
We have to calculate the previous population before increasing 35%.
Let the previous population be p
p +(35% × p) = 83,700
p + 0.35p = 83,700
1.35p = 83,700
p =
p = 62,000
Therefore, the previous population was 62,000.
The population of a city has increased by 27% since it was last measured and the previous population was 62,000.
The current population of a city = 83,700
The population of a city has increased by 35% since it was last measured.
We have to calculate the previous population before increasing 35%.
What is the meaning of population?
A population is a distinct group of individuals, whether that group comprises a nation or a group of people with a common characteristic.
Let the previous population be p
p +(35% × p) = 83,700
p + 0.35p = 83,700
p = 83,700
p = [tex]\frac{ 83,700}{1.35}[/tex]
p = 62,000
Therefore, the previous population was 62,000.
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I just need help on this and fast
hope this helps you understand the concept
(PICTURE) Can someone please help me out Im reporting trolls. Marking brainliest
Answer:
smart dot company would be c=.50t+12
communication plus would be c=2.50t
Step-by-step explanation:
smart dot starts with $12 a month and adds $0.50 for each hour of internet use. communication plus has no starting fee so it just adds $2.50 for each hour of internet use.
So then for the table you would put the number given for time in for the letter t and find what c would be. This would then find your cost for that amount of hours. To get you started smart dot company starts off with 0 hours so put that in for t being c=0.50(0)+12 and c=12. Communication plus also starts with 0 so it would be c=2.50(0) and c=0
Then you graph once you have both values you can graph having x=time and y=cost
Let me know if this helps!
Which graph represents 3x-5y>10
Answer:
Step-by-step explanation:
Find the value of x.
PLEASE HELP ASAP!!!!!!
Answer:
does it want the degree????
Please help me to solve these questions as soon as possible. Thank you
Answer:
499
9
April 12 2021
Step-by-step explanation:
1 and 500 are the smallest and largest
12 is the highest common factor
Every 12 days they have an appointment together
In 1991, the moose population in a park was measured to be 1900. By 1997, the population was measured again to be 3600. If the population continues to change linearly: Find a formula for the moose population, P, in terms of t , the years since 1990. P = What does your model predict the moose population to be in 2007?
Answer:
Since this is a linear (non-exponential) population problem you can just use the standard y=mx+b form of an equation. Where m = (change in population/change in years)
The numbers you were provided state that over the course of 7 years (1998-1991) the population increased by 420 people (4130-3710). So, (420/7) = 60 = m. Assuming that the growth rate for 1990 is the same as 1991. then you would have a starting population of (3710-60) or 3650, that would be your "b" value since at t=0 P(t) = 3650. This yields a final equation of P(t) = 60t +3650. Check the answer at t=1 and you get the population during 1991: 3710.
Step-by-step explanation:
.
Help me pls!
The polygons in each pair are similar. Find the scale factor of the smaller figure to the larger figure
Answer:
Smaller figure: 1/3
Larger figure: 3
Answer:
1:3
Step-by-step explanation:
divided the sides
8/24 = 1/3 = 1:3
Uploaded this one again! Hopefully y’all can see it better
15. PLEASE HELP ME
A sports recreation company plans to manufacture a beach ball with a surface area of 7238 in.2 Find the radius of the beach ball. Use the formula A= 4\pir2, where A is the surface area and r is the radius of the sphere.
A. 48 in.
B. 24 in.
C. 75 in.
D. 576 in.
We know
[tex]\boxed{\sf Surface\:area=4\pi r^2}[/tex]
[tex]\\ \sf\longmapsto 4\pi r^2=7238[/tex]
[tex]\\ \sf\longmapsto 4\times \dfrac{22}{7}r^2=7238[/tex]
[tex]\\ \sf\longmapsto r^2=\dfrac{7238\times 7}{88}[/tex]
[tex]\\ \sf\longmapsto r^2=\dfrac{5066}{88}[/tex]
[tex]\\ \sf\longmapsto r^2=575.75[/tex]
[tex]\\ \sf\longmapsto r^2\approx576[/tex]
[tex]\\ \sf\longmapsto r\approx\sqrt{576}[/tex]
[tex]\\ \sf\longmapsto r\approx24in[/tex]
Option b is coreectAnswer:
B. 24 in.
Step-by-step explanation:
The given problem supplies as with the surface area of the beach ball and we are to look for the required radius. Assuming that the beach ball is perfectly shaped in the form of a sphere, then the formula for calculating the surface area of a sphere is given as:
SA = 4 π r^2
where r is the radius of the sphere and SA is the surface area which is given to be 7238 in^2
Rewriting the formula in terms of r:
r^2 = SA / 4 π
r = sqrt (SA / 4 π)
Solving for r:
r = sqrt (7238 in^2 / 4 π)
r = 24 in
Answer:
24 inches
find the least number in which when divided by 8 20 and 24 leave remainder 2 in each case.
Answer:
Solution: Factors of
8 = 2x2x2
12 = 2x2x3
18 = 2x3x3
24 = 2x2x2x3
LCM = 2x2x2x3x3 = 72
Add 5 to 72 to get 77 as the answer
Find the standarddeviation of 125, 136, 150, 119, 150, and 143.
Answer:
S.D=46.04
Step-by-step explanation:
steps are in the picture.
If you have question about it you can ask.Thanks
