The simplified expression for cos x csc x tan x is 1 .
Sure, let's simplify the expression step by step:
Given expression:[tex]\( \cos(x) \csc(x) \tan(x) \)[/tex]
We know that:
[tex]- \( \csc(x) = \frac{1}{\sin(x)} \)[/tex]
[tex]- \( \tan(x) = \frac{\sin(x)}{\cos(x)} \)[/tex]
So, we substitute these into the expression:
[tex]\( \cos(x) \cdot \frac{1}{\sin(x)} \cdot \frac{\sin(x)}{\cos(x)} \)[/tex]
Now, we cancel out the common terms:
[tex]\( \frac{\cos(x) \cdot \sin(x)}{\sin(x) \cdot \cos(x)} \)[/tex]
Now, we can see that the numerator and the denominator cancel each other out:
[tex]\( \frac{1}{1} = \boxed{1} \)[/tex]
In conclusion, the simplified expression is ( 1 ).
We start by using the trigonometric identities to express [tex]\( \csc(x) \) and \( \tan(x) \) in terms of \( \sin(x) \) and \( \cos(x) \)[/tex]. Then, we substitute these expressions into the given expression. Next, we cancel out the common terms in the numerator and denominator, resulting in a simplified expression of 1. This simplification demonstrates the relationship between the trigonometric functions and highlights their interconnectedness through fundamental trigonometric identities.
Complete question:
Simplify the expression cos x csc x tan x
A standard bowling ball cannot be more than 27 inches in circumference. What is the maximum volume of such a ball (to the nearest cubic inch) before the holes are drilled?
Answer:
333 in^3
Step-by-step explanation:
Circumference = pi *d
27 = pi*d
Replacing d with 2*r ( 2 times the radius)
27 = pi * 2 * r
Divide each side by 2
27/2 = pi *r
13.5 = pi *r
Divide by pi
13.5/ pi = r
We want to find the volume of a sphere
V = 4/3 pi * r^3
V = 4/3 pi (13.5/pi)^3
= 4/3 pi * (13.5)^3 / (pi^3)
4/3 pi/pi^3 * (13.5)^3
4/3 * 1/ pi^2 *2460.375
3280.5 / pi^2
Let pi be approximated by 3.14
380.5/(3.14)^2
332.7214086 in^3
To the nearest in^3
333 in^3
Answer:
332.384142939 cubic inch, rounded- 332 cubic inches
Step-by-step explanation:
Volume of a sphere is 4/3 pi*r^3
circumference=C = 2 π r
we can simply 27 by 2*pi to get radius-
approx 4.29718346348.
4/3 pi*4.29718346348.^3
4/3* pi*79.3508690311= about 332.384142939
What is 60.38×100 rewritten in equivalent
exspression
Answer:
6038 x 1
or
603.8 x 10
The distance between the two points pictured is d = Use the distance formula to find n. d = n =
Answer:
the answer is 61units
n=61
Step-by-step explanation:
what is the value of 6(2b-4) when b=5
Answer:
36
Step-by-step explanation:
6(2b-4)
Let b = 5
6(2 (5)-4)
Work inside the parentheses out
6(10-4)
6(6)
36
Answer:
36
Step-by-step explanation:
Well, we can do this 2 ways: Distribute first, or do it last.
Distribute First:
12b-24=
12(5)-24=
60-24=
36
Distribute last:
6(2(5)-4)=
6(10-4)=
Now you can take this two ways.
Distribute:
60-24=36
OR
Parenthessess: (I dont know how to spell.)
6(6)=36
What is the area of the kite
Answer:
The area of the kite is 60 square feet
Step-by-step explanation:
The area of a kite is given as half multiplied by the product of the diagonals.
The longer diagonal measures 30 feet.
The shorter diagonal measures 4 feet.
The area of the kite is; [tex]\frac{1}{2}*30*4=60[/tex]
ANSWER
The area of the kite is 60 square feet
EXPLANATION
The area of a kite is half times the product of the diagonals.
The longer diagonal is 10+20=30 feet.
The shorter diagonal is 2+2 =4 feet.
The area of this kite
[tex] = \frac{1}{2} \times 30 \times 4[/tex]
This simplifies to,
[tex] = 60 {ft}^{2} [/tex]
Therefore the area of the kite is 60 square feet
Andy and Jacob work as technicians in a laboratory where gemstones are tested and certified. Andy has already tested 30 gemstones and continues testing at a rate of 30 gemstones per hour. Jacob has already tested 40 gemstones and continues testing at a rate of 25 gemstones per hour. Which function can Andy and Jacob use to determine the total number of gemstones they have tested after x hours? How many gemstones will they have tested after 5 hours? A. The function that describes the total number of gemstones tested by Andy and Jacob in x hours is given by f(x) = 55x + 10. Thus, they will have tested 285 gemstones in 5 hours. B. The function that describes the total number of gemstones tested by Andy and Jacob in x hours is given by f(x) = 70x + 55. Thus, they will have tested 405 gemstones in 5 hours. C. The function that describes the total number of gemstones tested by Andy and Jacob in x hours is given by f(x) = 55x + 70. Thus, they will have tested 345 gemstones in 5 hours. D. The function that describes the total number of gemstones tested by Andy and Jacob in x hours is given by f(x) = 60x + 65. Thus, they will have tested 365 gemstones in 5 hours.
Answer:
Option C is correct.
Step-by-step explanation:
Andy tested gemstones already = 30
Jacob tested gemstones already = 40
Total gemstones tested by Andy and Jacob already = 30+40 = 70
Andy continue to test gemstones per hour = 30
Jacob continue to test gemstones per hour = 25
Total gemstones tested by Andy and Jacob per hour = 30 +25 = 55
The total number of gemstones tested by Andy and Jacob after x hours will be: 55x
So, the equation will be: f(x) = 55x + 70
After 5 hours i.e. x =5
f(5) = 55(5) + 70
f(5) = 275 + 70
f(5) = 345
Andy and Jacob will have tested 345 gemstones in 5 hours.
So, Option C is correct.
Which equation represents a line that passes through (4, ) and has a slope of ?
y – = (x – 4)
y – = (x – 4)
y – = 4(x – )
y – 4 = (x – )
Answer:
the 1st one
Step-by-step explanation:
please help me with this one
Answer:
BF and HG
Step-by-step explanation:
this is because skew lines are lines that are not parrallel but are never going to intercet each other.
Answer:Lines BF and HG are skew.
Step-by-step explanation:
A skew lines are two lines that lie on different planes, will never intersect, and are not parallel.
Janice is buying paint to paint her new apartment. The store sells paint in one-gallon cans. How accurate does her estimate
need to be for the amount of paint needed?
Janice should measure each wall's height and length to determine the square footage needed for painting and divide this by the coverage area of a gallon of paint to estimate the number of gallons she will need, ensuring to round up for any excess needed for touch-ups.
Explanation:Janice's accuracy in estimating the amount of paint needed for her apartment is important to ensure that she neither runs out of paint before completing the job nor wastes money buying too much.
In general, paint cans are sold in one-gallon sizes, and a gallon typically covers around 350 to 400 square feet of wall space.
When calculating the paint needed, Janice should measure each wall's height and length to determine the square footage, considering any deductions for windows and doors.
Once she has the total square footage, she can divide by the coverage area of a gallon of paint to estimate the number of gallons needed. It's usually a good idea to buy a little extra for touch-ups, so round up to the nearest whole number.
As a review, understanding unit conversions is also pertinent.
For example, when converting miles to feet, ounces to pounds, or quarts to gallons, each conversion requires knowledge of the correct factors: 1 mile = 5,280 feet, 1 pound = 16 ounces, and 1 gallon = 4 quarts.
Such conversions are crucial in accurately determining quantities and can help avoid overestimating or underestimating the resources required for a task.
Final answer:
Janice needs to carefully calculate the amount of paint needed for her apartment by considering the square footage and paint coverage, possibly with a margin for extra paint. The painting job timing can be expressed with a linear equation T = 4 + 0.001S, where T is total time and S is square footage.
Explanation:
For Janice to estimate the amount of paint needed accurately, it's important that she does a careful calculation based on the square footage of her apartment walls and the coverage provided by each gallon of paint. The accuracy of this estimation will prevent the wastage of resources and ensure that the work does not halt due to the shortage of paint. However, it's also practical to consider buying an extra can to account for any unforeseen circumstances, as the estimation might have a margin of error.
Regarding the linear equation for the painting job: If it requires four hours of setup time plus one hour per 1,000 square feet, then we can express this as T = 4 + 0.001S, where T is the total time in hours and S is the square footage of the painting area. This linear equation will help to estimate the time needed for any given square footage.
Anyone? i dont understand
Answer:
1725ft^2
Step-by-step explanation:
Hi!
First you have to find your two bases B1 and B2, which are 50 and 65.
Then you find the height, which is 30ft.
Finally, you plug those into the equation 1/2*h*(B1+B2) and solve.
1/2*30*(50+65)
1/2*30*(115)
15*115
1725ft^2 is your answer.
I hope this helps!
Please help right now!!
Check the picture below.
so the figure is really just 3 triangles and one square, we can simply get the area of each shape and sum them up, and that's the area of the composite
[tex]\bf \stackrel{\textit{green triangle}}{\cfrac{1}{2}(9)(3.5)}+\stackrel{\textit{brown triangle}}{\cfrac{1}{2}(2)(2)}+\stackrel{\textit{purple square}}{(2\cdot 2)}+\stackrel{\textit{pink triangle}}{\cfrac{1}{2}(5)(2)} \\\\\\ 15.75+2+4+5\implies 26.75[/tex]
Answer:
26.75Step-by-step explanation:
Look at the picture.
We have
the right traingle with the legs a = 3.5 and b = 2 + 2 + 5 = 9
the trapezoid with the bases b₁ = 2 + 2 + 5 = 9, b₂ = 5 and the height h = 2.
The formula of an area of a right triangle:
[tex]A=\dfrac{ab}{2}[/tex]
Substitute:
[tex]A=\dfrac{(3.5)(9)}{2}=15.75[/tex]
The formula of an area of a trapezoid:
[tex]A=\dfrac{(b_1+b_2)h}{2}[/tex]
Substitute:
[tex]A=\dfrac{(9+2)(2)}{2}=11[/tex]
The area of the shape:
[tex]\bold{A=15.75+11=26.75}[/tex]
find the conplex conjugate of z1 of z1=i+4
Answer:
- i + 4
Step-by-step explanation:
Given a complex number a + bi then the complex conjugate is a - bi
Note the real part remains unchanged while the sign of the imaginary part is negated.
Hence conjugate of i + 4 = - i + 4
the radius of a spherical beach ball is 24 cm.If another spherical beach ball has a raduis 3cm longer, about how much greater is its surface area to the nearest square centimeter ?
Answer:
1923 cm²
Step-by-step explanation:
The surface area of a sphere is A = 4πr².
The first spherical beach ball has a radius of 24 cm:
A = 4π (24)²
A ≈ 7238 cm²
The second spherical beach ball has a radius 3 cm greater, or 27 cm:
A = 4π (27)²
A ≈ 9161 cm²
So the difference in area is:
9161 - 7238
1923 cm²
Answer:
1923 cm²
Step-by-step explanation:
Equation for the surface area of a sphere is 4πr².
The surface area of the bigger ball is (27²×4×π) = 2916π
The surface area of the smaller ball is (24²×4×π) = 2304π
The difference is 2916π-2304π = 612π
This is 1923 cm²
I really need help here ASAP
Answer:
D. [tex]x=\frac{-4-\sqrt{31}}{3}[/tex] or [tex]x=\frac{-4+\sqrt{31}}{3}[/tex]
Step-by-step explanation:
The given equation is:
[tex]3x^2+8x=5[/tex]
Divide through by 3;
[tex]x^2+\frac{8}{3}x=\frac{5}{3}[/tex]
Add the square of half the coefficient of x to both sides.
[tex]x^2+\frac{8}{3}x+(\frac{4}{3})^2=\frac{5}{3}++(\frac{4}{3})^2[/tex]
[tex]x^2+\frac{8}{3}x+\frac{16}{9}=\frac{5}{3}+\frac{16}{9}[/tex]
The left hand side is now a perfect square:
[tex](x+\frac{4}{3})^2=\frac{31}{9}[/tex]
Take square root
[tex]x+\frac{4}{3}=\pm \sqrt{ \frac{31}{9}}[/tex]
[tex]x=-\frac{4}{3}\pm \sqrt{ \frac{31}{9}}[/tex]
[tex]x=-\frac{4}{3}\pm \frac{\sqrt{31}}{3}[/tex]
D. [tex]x=\frac{-4-\sqrt{31}}{3}[/tex] or [tex]x=\frac{-4+\sqrt{31}}{3}[/tex]
Issouf claims that the scale factor is 1/2. which statement about his claim is correct?
A- He is correct because CB is 4 and C' B' is 2. The scale factor is C'B'/CB = 2/4 = 1/2
B- He is correct because he needs to subtract 2 from each side. A reduction has a scale factor that is a fraction, so it must be 1/2
C- He is Incorrect because it is 3. CB is actually 2+4 or 6. So one needs to multiply the pre-image length by 3 to get the image; 3 is the scale factor.
D- He is Incorrect because the scale factor is 1/3. CB is actually 2 + 4 = 6. CB is the pre-image, so the scale factor is C'B'/CB = 2/6 = 1/3.
Answer:
The correct option is D.
Step-by-step explanation:
It is given that Issouf claims that the scale factor is 1/2.
From the given figure it is clear that
[tex]CB'=C'B'=2[/tex]
[tex]B'B=6[/tex]
[tex]CB=CB'+B'B=2+4=6[/tex]
The scale factor of a figure is
[tex]k=\frac{\text{Length of any side of image}}{\text{Length of corresponding side of preimage}}[/tex]
[tex]k=\frac{C'B'}{CB}[/tex]
[tex]k=\frac{2}{6}[/tex]
[tex]k=\frac{1}{3}[/tex]
The scale factor is 1/3 because CB is actually 2 + 4 = 6.
Therefore the correct option is D.
Given: BD is a diameter
m 1 = 100°
m BC= 30°
m DAB
260
180
130
Step-by-step explanation:
1 and 2 share the same line (a line equals 180°) if 1 = 100° then 180°-100°=80°
2=80°
bc and 4 also share a straight line. if bc=30° then 180°-30°=150°
4=150°
this can be checked by adding them all together. a circle is equal to 360°.
100°+80°+30°+150°=360°
San makes up the straight line that makes up 1 and 2 (as you can see I have already answered the question a million times over) and as it is a straight line it is 180° which is backed up by all of the double checked math.
Answer:
180 is correct
Step-by-step explanation:
Of all sixth graders, 70% sent a text message yesterday. Ten trials of a simulation are conducted and the data are recorded below. 62072, 34570, 80983, 04292, 83150, 36330, 96268, 14077, 77985, 13511 The numbers 0 through 6 represent students who sent a text yesterday, and the numbers 7 through 9 represent students who did not send a text yesterday. Based on the simulated data, what is the probability that 3 or more of a group of 5 students randomly selected will send a text today?
Answer:
80%
Step-by-step explanation:
According to the given data, the numbers 0 through 6 represent students who sent a text yesterday while the numbers 7 through 9 represent students who did not send a text yesterday.
Based on this key, we will calculate the number of students who sent the text yesterday and the number of students who did not sent the text yesterday.
The given data is: 62072, 34570, 80983, 04292, 83150, 36330, 96268, 14077, 77985, 13511
For each group we will identify how many students sent the text and how many students did not. According to the key, a number from 0 to 6 will be counted as a student who sent the text and a number from 7 to 9 will be counted as a student who did not send the text. Students who did not sent the text are made bold in the groups below.
62072: 4 students sent the text, 1 did not
34570: 4 students sent the text, 1 did not
80983: 2 students sent the text, 3 did not
04292: 4 students sent the text, 1 did not
83150: 4 students sent the text, 1 did not
36330: All 5 students sent the text
96268: 3 students sent the text, 2 did not
14077: 3 students sent the text, 2 did not
77985: 1 student sent the text, 4 did not
13511: All 5 students sent the text
We need to find the probability that 3 or more of a group of 5 students randomly selected will send a text today.
From the given groups, the number of groups where 3 or more students sent a text = 8
This represents our number of favorable or desired outcomes.
Total number of possible outcomes is the total number of groups = 10
Since, probability is defined as the ratio of number of favorable outcomes to total number of outcomes, based on the simulated data the probability that 3 or more of a group of 5 students randomly selected will send a text today will be = [tex]\frac{8}{10}=0.80=80\%[/tex]
Thus, based on the simulated data there is 80% probability that 3 or more of a group of 5 students randomly selected will send a text today
Answer:
The answer is 80% or 4/5(;
Step-by-step explanation:
Can someone please help me with this?
Answer:
The answer is A; 19
Step-by-step explanation:
4 × (3/4 - 2/4) + 3 × 6
= 4 × 1/4 + 3 × 6
= 1 + 3 × 6
= 1 + 18
= 19
Find the value of x ?
A)67
B)113
C)77
D)57
Answer:
A) 67Step-by-step explanation:
The sum of the angles measures at one side of the parallelogram is 180°.
Therefore we have the equation:
x + 113 = 180 subtract 113 from both sides
x + 113 - 113 = 180 - 113
x = 67
Answer:
67
Step-by-step explanation:
The graphs below have the same shape. f(x) = x^2 what is the equation of the graph of g(x)?
Answer:
A. [tex]g(x)=(x-4)^2[/tex]
Step-by-step explanation:
The graph of [tex]f(x)=x^2[/tex] is transformed to obtain the graph of g(x).
We can see from the diagram that, f(x) is shifted 4 units to the right to obtain the graph of g(x).
Therefore [tex]g(x)=f(x-4)[/tex].
Hence the equation of g(x) is
[tex]g(x)=(x-4)^2[/tex]
The correct answer is A.
The equation of the graph of g(x) is g(x) = (x - 4)²
How to determine the equationFrom the graph shown, we can see that the f(x) = x² as shown is shifted 4 units to the right to obtain the graph of g(x).
Then, we have that this shift can be achieved by replacing x in the equation of f(x) with x - 4 to represent the horizontal shift.
We have the equation of the graph of g(x), to be;
g(x) = (x - 4)²
This equation represents a horizontal shift of the graph of f(x) by by 4 units to the right, as g(x) remains the same shape f(x) but is shifted horizontally to the right by 4 units.
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Find the perpendicular bisector of the points A(3,6) and B(-1,4). Give your answer in the form
ax + by = c.
Answer:
the equation of the perpendicular bisector of segment AB is y = -2x + 7
Step-by-step explanation:
Going from B(-1, 4) to A(3, 6), x increases by 4 and y increases by 2. Thus, the slope of this line is m = rise / run = 2/4, or 1/2.
Any line perpendicular to the one joining A and B has a slope which is the negative reciprocal of 1/2: that'd be -2.
3 - 1 6 + 4
The midpoint of line segment AB is ( --------- , ---------- ), or (1, 5)
2 2
Thus, the perpendicular bisector passes through the midpoint (1, 5) and has slope -2:
Starting from y = mx + b, we get 5 = -2(1) + b, or 7 = b, and so the equation of the perpendicular bisector of segment AB is
y = -2x + 7
Kate is painting a ceramic paperweight shaped like a rectangular prism, as shown here. (dimensions of .8 ft , 1.2 ft, 1.2 ft)She wants to find the surface area of the paperweight so she can determine how much paint she needs.
The area of one of the bases is _____
The area of each lateral rectangular face is _____
The surface area of the paperweight is _____
Answer:
The area of one of the bases is 0.96 ft²
The area of each lateral rectangular face is 4.8 ft²
The surface area of the paperweight is 6.72 ft²
Step-by-step explanation:
we know that
The surface area of the rectangular prism is equal to
SA=2B+LA
where
B is the area of one of the bases
LA is the lateral area of the prism
Find the area of one of the bases B
B=(0.8)(1.2)=0.96 ft²
Find the lateral area LA
The lateral area is the area of each lateral rectangular face
LA=2[(0.8)(1.2)]+2[(1.2)(1.2)]=4.8 ft²
Find the surface area
SA=2(0.96)+4.8=6.72 ft²
Answer: 1.44, 0.96, and then 6.72.
Step-by-step explanation:
the person who answered first is wrong.
the graphs of the linear functions f and g are shown. Enter the solution to the equation f(x)=g(x)
I’m pretty sure the answer is (-4, 4) because when the equations are equal, that is when the points intersect. That happens to be at point (-4,4)
An artist made a 54-inch-tall statue of a former president. If the president was 6 feet tall, what scale did the artist use?
1 foot = 12 inches.
The president is 6 x 12 = 72 inches tall.
54 inch model / 72 inches = 0.75 = 3/4
The model is 3/4 scale.
What is the slope of a line through the points (-3 , 5 ) and ( 1 , -7 ) ?
A 1/2
B -3
C 1/2
D 2
Answer:
B. -3
Step-by-step explanation:
The answer is -3
Because
At a book fair, 1/4 of the people bought 1 book.3/5 of the remaining
people bought 2 books each and the rest of the people bought 3
books each. A total of 4469 books were sold. How many people
were at the book fair?
Answer:
2,180 people
Step-by-step explanation:
Let
x-----> number of people at the book fair
we know that
1) 1/4 of the people bought 1 book each
(1/4)x=(5/20)x
2) 3/5 of the remaining people bought 2 books each
The remaining people is (3/4)x
so
(3/5)(3/4)x=(9/20)x
3) the rest of the people bought 3 books each
The rest of the people is x-(5/20)x-(9/20)x=(6/20)x
The linear equation that represent this situation is
(1)*(5/20)x+(2)*(9/20)x+(3)*(6/20)x=4,469
(5/20)x+(18/20)x+(18/20)x=4,469
(41/20)x=4,469
x=4,469*20/41
x=2,180 people
what is the solution to this equation?
x/5=-20
Answer:
-100
Step-by-step explanation:
Answer:
-100
Step-by-step explanation:
You need to multiply
-20 x 5= -100
Hope this helped please mark me the brainliest answer? Have a good day :)
20. If a sequence is defined recursively by f(0) = 5 and
f(n + 1) = -3f(n) + 2 for n > 0, then f(3) is equal to
(1) 337
(3) 113
(2) -13
(4) -121
Answer:
- 121
Step-by-step explanation:
The recursive formula allows us to find the next term in a sequence from the previous term, thus
f(1) = - 3f(0) + 2 = - 3 × 5 + 2 = - 15 + 2 = - 13
f(2) = - 3f(1) = - 3 × - 13 + 2 = 39 + 2 = 41
f(3) = - 3f(2) + 2 = - 3 × 41 + 2 = - 123 + 2 = - 121
A lifeguard at a swimming pool gives one-hour swim lessons to children in the morning before the pool is open to the public. She earns four dollars per class and fifty cents per swimmer. The minimum wage in her state is $7.25. She hopes to earn more than that amount of money during each class. Write an inequality that models the situation and find the minimum number of students she must teach in each class so that her earnings for that hour exceeds the minimum wage in her state.
Answer:
brainliest ps :)
Step-by-step explanation:
her wage is $4.00 + s*0.5 so 7.25-4> s*.5== 3.25 > s*.5 == 6.5 > s
The inequality for the given information can be written as 6.5 > s.
What is inequality?When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.
A lifeguard at a swimming pool gives one-hour swim lessons to children in the morning before the pool is open to the public. She earns four dollars per class and fifty cents per swimmer. The minimum wage in her state is $7.25.
The inequality can be written as:-
$4.00 + ( s x 0.5 )
7.25-4 > ( s x 0.5 )
3.25 > ( s x 0.5 )
6.5 > s
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What is the standard deviation of the following data set rounded to the nearest tenth?
30, 26, 28, 32, 28, 30
Answer:
Standard Deviation is: 2.09762 or rounded to nearest tenth is 2.1
Step-by-step explanation: