Mathematics Middle School

(1-sec x)/(1-cos x) = -sec x
I got up to this:
(cos x - 1)/ (cos x(1 - cos x)

Can you help me verify the following identity?

Answers

Answer 1

We are given the trigonometric equation:

(1 - sec x) / (1 - cos x) = - sec x

 

Since the left side has more terms, then let us work on that side to make it exactly like the right side.

We know that sec = 1 / cos, therefore:

(1 – 1 / cos x) / (1 – cos x) = - sec x

[(cos x – 1) / cos x] / (1 – cos x) = - sec x

[- (1 – cos x) / cos x] / (1 – cos x) = - sec x

Cancelling out the term (1 – cos x):

- 1 / cos x = - sec x

- sec x = - sec x

PROVEN!

Related Questions

Jeff takes 20 mins to jog around the race course one time. And 25 mins to jog arpund second time. What is his average speed in kms per hr fpr the whole jog if the course is 3 kms long?

Answers

The main formula used in work-rate, distance-speed problems is:

Work=Rate*Time, or Distance=Speed*Time.


Thus, the time is: [tex]speed= \frac{distance}{time} [/tex].


In our problem, the total distance is 3 km + 3 km = 6 km.

the total time is 20 min + 25 min = 45 min.

60 minutes are 1 hour, then 

45 minutes are [tex] \frac{45min*1h}{60min}= 0.75h[/tex]


Thus, the average speed is : distance/time = 6 km/ 0.75 h = 8 km/h


Answer: 8 km/h

Suppose you buy a movie for $12.98 the sales tax is 6% find the total cost

Answers

So in order to find the tax, you have to multiply 12.98 by 0.06
12.98*0.06=0.7788
Add the tax to 12.98, and you get 13.7588
The total cost is 13.76
hope this helps:)

Use the Distributive Property to simplify each expression:
6(a + 10)
(5 + w)5
14(4f - 8)
2.1(5w -15)
0(3.7x - 4.21)
-(-m + n + 1)

Answers

6a + 60

5w + 25

56 f - 122

10.5 w - 31.5

0

m - n -1


Six less then two thirds of a number is negative ten what is the number

Answers

2/3X-6 = -10

2/3x = -4

x = -4 / 2/3 = -6

X = -6

check:

2/3(-6) - 6 = -4 -6 = -10 TRUE

An architect plans to make a drawing of the room of a house. The segment LM represents the ceiling of the room. He wants to construct a line passing through Q and perpendicular to side LM to represent a wall of the room. He uses a straightedge and compass to complete some steps of the construction, as shown below:

Answers

i believe the answer is c im am stuck on the same problem do you know the answer?

In triangle ∆PQR, C is the centroid.
a. If CY = 10, find PC and PY
b. If QC = 10, find ZC and ZQ
c. If PX = 20, find PQ

Answers

Refer to the redrawn figure below.

Because C is the centroid, 
PZ = ZR;  QY = YR; and PX = XQ.

Part a.
If CY = 10, then PC = 2*CY = 20
PY = PC + CY = 20 + 10 = 30
Answer:
PC = 20
PY = 30

Part b.
If QC = 10, then ZC = QC/2 = 5
ZQ = ZC + QC = 5 + 10 = 15
Answer:
ZC = 5
ZQ = 15

Part c.
Given: PX = 20.
Because the median bisects side PQ, therefore PX = QX = 20
PQ = PX + QX = 40
Answer:
PQ = 40

Define a function f : R → R by the formula
f(x) = 2x − 8.


Prove that f is one-to-one.
Let a, b is in R, and suppose that
f(a) = f(b).
Then
2a − 8 =

Answers

We are given a function f(x) = 2x - 8 and a condition that f (a) = f (b). We are then asked the next terms of 2a - 8 = ______. 

Now, we have to think that the parent function is f(x) = 2x - 8 and f (a) = f (b). This means the value of the function f(a) is if a is substituted to x:

f (a) = 2a - 8, same goes for f (b):

f (b) = 2b - 8.

Since we have a condition that f(a) = f (b), then,

2a - 8 = 2b - 8. 

If we simplify further, 

2a = 2b - 8 + 8
( 2a = 2b ) / 2

the equation becomes:

a = b; this proves that f is a one-to-one function. 


 

What is the sine value of pi over 6?

Answers

The answer is .5 or 1/2

Answer:

The sine value of pi over 6 is:

[tex]\dfrac{1}{2}[/tex]  or 0.5

Step-by-step explanation:

we have to find the value of  [tex]sin\dfrac{\pi}{6}[/tex]

we know that value of  [tex]sin\dfrac{\pi}{6}[/tex]  is [tex]\dfrac{1}{2}[/tex]

Hence, the sine value of pi over 6 is:

[tex]\dfrac{1}{2}[/tex]  or 0.5

Which equation can be used to calculate the area of the shaded triangle in the figure below? A rectangle is shown with a width of 8 ft and a length of 14 ft. There is a diagonal line through the rectangle, and the bottom half is shaded in grey. 2(14 + 8) = 44 square feet 1 over 2.(14 + 8) = 11 square feet 2(14 × 8) = 224 square feet 1 over 2.(14 × 8) = 56 square feet

Answers

If it is a diagonal going from one corner to the other opposite corner about the center, the diagonal simple divides the area by 2.

So:

A=xy/2, and x=8 and y=14 in this case so:

A=(8*14)/2  or as you are probably looking at it (which is the same thing)

(1/2)(8*14)=56 square feet.

Answer:

D) 1 over 2. (14 × 8) = 56 square feet

Step-by-step explanation:

You first need to look at the w x h formula (width x height).

W= 14
H= 8

14 x 8= 112

Then, you have to divide 112 by 2. The reason why is because 112 is the area of the whole rectangle, but you only need the area to the triangle, which is half of the rectangle.

112 ÷ 2= 56 sq. ft.

Therefore, the answer is D. Hope this helped!! <3

Kayla has a tshirt store. she sold three times as many white tshirts as blue tshirts. she sold a total of 48 tshirts. How many white tshirts did kayla sell

Answers

First make the equation:

1. x
2. 3x

x + 3x = 48

Now solve it:
x + 3x = 48
4x= 48
x=12

Now plug in x 
1. x = 12
2. 3x = 36

So Kayla sold 12 blue t-shirts and 36 white t-shirts.


Find the area of the parallelogram shown below

Answers

[tex]A=bh \\ b=7, \ \ h=5 \\ \\ A=7*5=35 \ \text{units}^2 [/tex]
I think its 35 
 
5 * 7 = 
 35 

I WILL GIVE BRAINLIEST please answer both parts

If 365 work days are split among 12 employees evenly

PART: A How can you rewrite this as a fraction?


PART:B What does the fraction represent?

Answers

Q) If 365 work days are split among 12 employees evenly

Part A: To understand this question, you need to read carefully and pick out key words that tells you what to do. All math word / puzzle problems have key words that tell you what you need to do.

For instance, the key word split tells us we need to divide. So, we know we have 365 work days that need to be split among 12 employees. So for Part A: 

365 / 12

For Part B it wants to know what this represents. It represent the number of days each of the 12 employees will get if split evenly among each employee. 

How to show numbers are related to each other

Answers

Human and non-human species possess a mental system of number representations that appear early in the lifespan and that supports approximate number skills, such as numerical estimation or number comparison. With the later acquisition of language and of symbolic numbers, human beings also develop exact number skills that allow using numbers precisely, such as in counting and arithmetic. The current review points out the behavioral data which either support or challenge these contrasting proposals. In an attempt to provide a comprehensive overview of these mixed data, we carefully took into account the heterogeneity of the available studies regarding the kind of tasks, stimuli or ages of assessment. Also, you can show how the numbers are related simply by identifying the tenth place value of each digit.

The singing club keeps sheet music in files. Each file holds 12 sheets. Of all the club's music, 2/3 fit into 3 files. How many sheets of music does the club have?

Answers

1 file -> 12 sheets

Now for 3 files -> 3*12 = 36 sheets, it takes up 2/3 of the total

So the total number of sheets: 36 / (2/3) = 54
Final answer:

The singing club has a total of 36 sheets of music.

Explanation:

To find the total number of sheets of music the club has, we can set up a proportion using the given information. Since 2/3 of the club's music fits into 3 files, this means that 1/3 of the music fits into 1 file. So, if 1/3 represents 12 sheets, then 1 represents 12 * 3 = 36 sheets. Therefore, the club has a total of 36 sheets of music.

Learn more about Total number of sheets of music here:

https://brainly.com/question/34207074

#SPJ2

There are two numbers, which sum up to 53. Three times the smaller number is equal to 19 more than the larger number. What are the numbers

Answers

Let "n" be the smaller number, then
the larger number = 3n-19

n + 3n - 19 = 53
4n = 53 + 19
4n = 72
n = 72/4
n = 18  ←  smaller number

larger number = 53 - 18 = 35

Answer: 18 and 35.
x + y = 53.
Let x be the smaller number; then it'll be 3x = 19 + y

Set the first equation equal to x, then substitute the values and solve.
x + y = 53.
x = 53 - y.
3(53 - y) = 19 + y
x = 18; y = 35
140 - y = y
y = 70.

53 - 70 = -17
x = -17; y = 70.
-17 + 70 = 53; 

Jessie received the following scores on her math tests this year. (45, 65, 70, 80, 85, 100) Suppose the teacher removes the lowest and highest scores. (65, 70, 80, 85) What are the interquartile ranges of Jessie’s original scores and her new scores?

Answers

original scores :
45,65,70,80,85,100
IQR = 85 - 65 = 20

new scores :
65,70,80,85
IQR = (80 + 85)/2 - (65 + 70)/2 = 82.5 - 67.5 = 15

Answer:

Interquartile ranges of Jessie’s original scores = 20

Interquartile ranges of Jessie’s new scores = 15

Step-by-step explanation:

Interquartile range IQR = Higher quartile (Q3) - lower quartile (Q1)

Where Q3 is the mid-value of the second half of a dataset and

Q1 is the mid-value of the first half of a dataset.

Original score = 45, 65, 70, 80, 85, 100

Q1 of original score:

First half of original score = 45, 65, 70

Therefore Q1 = 65

Q3 of original score:

Second half of original score = 80, 85, 100

Therefore Q3 = 85

:. Interquartile range IQR of original score = Q3 of original score - Q1 of original score

:. IQR = 85 - 65 = 20

New score = 65, 70, 80, 85

Q1 of new score:

First half of new score = 65, 70

Therefore Q1 = (65+70)/2 = 67.5

Q3 of new score:

Second half of new score = 80, 85

Therefore Q3 = (80 + 85)/2 = 82.5

:. Interquartile range IQR of new score = Q3 of new score - Q1 of new score

:. IQR = 82.5 - 67.5 = 15

Therefore:

Interquartile ranges of Jessie’s original scores = 20

Interquartile ranges of Jessie’s new scores = 15

a pair of jeans cost 75% as much as a pair of corduroy pants what is the cost of each if the total cost for the jeans and courds is $42

Answers

j= jeans

c= corduroy

jeans = 0.75C

0.75 +c = 42

1.75c = 42

c = 42/1.75 = 24

 jeans cost 24*0.75 = 18

 corduroys cost $24

Jeans cost $18

Answer with Step-by-step explanation:

Let j denote the cost of jeans

and c denotes the cost of corduroy

A pair of jeans cost 75% as much as a pair of corduroy pants.

i.e. j = 0.75c

The total cost for the jeans and corduroy is $42

i.e. j+c=42

⇒ 0.75c+c=42

⇒ 1.75c=42

Dividing both sides by 1.75,we get

c=24

Putting value of c in j= 0.75c gives

j=18

Hence, Cost of jeans=$18

and cost of corduroy=$24

A regular pentagonal prism has a height of 14 in. and a base edge length of 10 in. Identify its lateral area and surface area.
Can anyone help me solve this?

Answers

The lateral faces of the prism are 5 rectangles with dimensions 10 by 14.

So the lateral area = 5 * 10 * 14 =  700 (in squared)


Consider one of the bases of the prism.

As shown in the figure, the pentagon is made up of 5 isosceles triangles.

The vertex of each of these 5 triangles is 360°/5=72°.

Draw the altitude, which forms 2 right triangles with angle measures 36°-54°-90°.
 
Let he hypotenuse be s and the altitude be h in, as shown in the figure.

x*cos54°=5

x=5/(cos54°)=5/(0.588)=8.5

then, 

h=x*sin54°=8.5*(0.8)=6.8 (in)

Thus, the area of one of the 5 congruent isosceles triangles is 

[tex] \frac{1}{2}*10*6.8= 34[/tex] (in squared)

The area of the pentagonal base is 34*5 = 170 (in squared)


Thus the surface area = lateral area + 2 base area
           = 700+2*170 = 700+340 = 1040 (in squared)


Answer: 

lateral area: 700 in squared

surface area: 1040 in squared

Answer:

L = 700 in2 ; S = 1044.1 in2

Step-by-step explanation:

Lucky guess :)

Number 8 please it will help a lot

Answers

well it all depends on the object you are using but in this case lets say remote control cars. You can have an example like "we drove the car around the building twice. the first time it was -8 than how fast it was supposed to go. the second time it was 9. In which round was the car faster?" I dont think i helped very much but i hope i did


If T is the point at a distance 3pi/5 from P(1, 0) on the unit circle with its center at (0, 0), in what quadrant does T lie?

Answers

Since 3pi/5 is not one of the normal points we learn on the unit circle let's reason through this.
We know that 180 degrees on the unit circle is pi, or 5pi/5, which is the same as pi.
So 90 degrees is half of 180 and therefore half of 5pi/5 which is 2.5pi/5.

Since 2.5pi/5 is at the 90 degree mark we know that 3pi/5 has to be past this so it will be in Quadrant II.
I hope this helps.

Final answer:

The point T lies in the second quadrant of the unit circle when it is at an angular distance of 3π/5 from P(1, 0), because this angle falls between π/2 and π radians.

Explanation:

If T is the point at a distance 3π/5 from point P(1, 0) on the unit circle with its center at (0, 0), to determine in what quadrant T lies, we must consider where this angle places T on the unit circle.

Recall that a point on the unit circle has coordinates (x, y) = (cos θ, sin θ), where θ is the angle measured counterclockwise from the x-axis. An angle of 3π/5 radians is more than π/2 radians but fewer than π radians. Therefore, it falls in the second quadrant of the unit circle, where x-coordinates are negative and y-coordinates are positive.

what is 1 and 6/24 simplified as ?

Answers

1 and 1/4 is the answer
[tex] 1\frac{6}{24} = \frac{30}{24} = \frac{5}{4} (a.k.a)1\frac{1}{4} [/tex]

5b-2=13 what does b equal

Answers

5b-2=13  add 2 to both sides

5b=15  divide both sides by 5

b=3

5b-2=13

add 2 to both sides

5b=15

divide both sides by 5

b = 15/5 = 3

b=3

Which expression is equal to 7(1+3)

A.) 7+21

B.) 7+3

C.) 1+21

D.) 7+4

Answers

I would say D. 7+4 because it is the only one that makes since to me


the answer is actually a.) 7+21 because when you distribute the 7 to 1+3, that's what it equals

A pudding recipe makes 4 1/2 cups of pudding. How many 1/3 cup servings does this equal?

Answers

4 1/2 cups  = 9/2 cups

9/2 / 1/3=

9/2 * 3/1 = 27/2 = 13 1/2 servings at 1/3 cup each

 

Answer:

13 1/2

Step-by-step explanation:Just trust

The table shows the number of students in a school who like dodgeball and/or ping pong:



Like Dodgeball
Do Not Like Dodgeball
Total
Like Ping Pong
26
18
44
Do Not Like Ping Pong
24
32
56
Total
50
50
100


What is the relative frequency, by row, of students who like both dodgeball and ping pong?

0.22
0.40
0.48
0.59

PLEASE HELP !!!

Answers

Hi!

I've included the table so it's easier to visualize. 

Divide the amount of students who like ping pong and dodge ball (26, it's highlighted in the image) by the total amount of students that like ping pong (44).

26/44 = 0.59

The answer is 0.59

Hope this helps! :)

Answer:

0.59

Step-by-step explanation:

What is the measure of angle 4?

Answers

<4 + <3 = 180
7x + 23x = 180
30x = 180
    x = 6

m<4 = 7x = 7(6) = 42

answer
B. 42 (Second choice)

Determine the sign of cos pi divided by seven without using a calculator.

Answers

The angle [tex] \frac{\pi}{7} [/tex] is in Quadrant 1 and cos of an angle in quadrant 1 is always positive

Answer:

The [tex]\cos \frac{\pi}{7}[/tex] has positive sign.

Step-by-step explanation:

we need to determine the sign of  [tex]\cos \frac{\pi}{7}[/tex] without using calculator

Cartesian system ( shown in figure -1)

The angle [tex]\cos \frac{\pi}{7}[/tex] lies in quadrant-1 , Where angles are zero (0) to [tex]\frac{\pi}{2}[/tex]

and in first quadrant all trigonometric ratios has positive sign

so,  [tex]\cos \frac{\pi}{7}[/tex] has positive sign.

Three-fourths of the yard is covered in grass but 4/5 of the grass has died. How much of the yard has dead grass?

Answers

multiply the 2 together:

3/4 x 4/5 = 12/20 = 3/5 has dead grass

To find the area of the yard that has dead grass, multiply three-fourths (the grassy area) by 4/5 (the dead portion). Simplifying (3/4) × (4/5) gives us 3/5, which means 3/5 of the yard has dead grass.

To determine how much of the yard has dead grass, we need to calculate the portion of the yard covered in grass and then the fraction of it that has died. Given that three-fourths of the yard is covered in grass, we represent this as 3/4. It is known that 4/5 of this grass has died, hence we multiply the two fractions: (3/4) × (4/5).

Performing the multiplication of these two fractions:

Multiply the numerators: 3 × 4 = 12.Multiply the denominators: 4 × 5 = 20.Combine the products to form the new fraction: 12/20.

Now, simplify the fraction 12/20 by dividing both the numerator and denominator by their greatest common divisor, which is 4:

Divide the numerator: 12 ÷ 4 = 3.Divide the denominator: 20 ÷ 4 = 5.The simplified fraction is 3/5.

Therefore, the correct answer is that 3/5 of the yard has dead grass.

Choose the system of equations which matches the following graph:


A. 5x - y = 7
2x - y = 0

B. 5x - y = 7
2x + y = 0

C. 5x + y = -7
2x + y = 0

D. 5x + y = -7
2x - y = 0

Answers

Answer:

Option B :  [tex]5x - y = 7[/tex]

                 [tex]2x + y = 0[/tex]

Step-by-step explanation:

Intersecting point on the graph = (1,-2)

Substitute this point in the given options .

A. [tex]5x - y = 7[/tex]

   [tex]2x - y = 0[/tex]

Substitute (1,-2)

[tex]5(1) - (-2) = 7[/tex]   and [tex]2(1) -(-2) = 0[/tex]

[tex]7 = 7[/tex] and [tex]4 \neq 0[/tex]

So, this system of equations does not matches the graph.

B. [tex]5x - y = 7[/tex]

   [tex]2x + y = 0[/tex]

Substitute (1,-2)

[tex]5(1) - (-2) = 7[/tex]   and [tex]2(1)+(-2) = 0[/tex]

[tex]7 = 7[/tex] and [tex]0= 0[/tex]

So, this system of equations matches the graph.

C.[tex]5x + y = -7[/tex]

   [tex]2x + y = 0[/tex]

Substitute (1,-2)

[tex]5(1) - (-2) = -7[/tex]   and [tex]2(1)+(-2) = 0[/tex]

[tex]7\neq -7[/tex] and [tex]0= 0[/tex]

So, this system of equations does not matches the graph.

D. [tex]5x + y = -7[/tex]

    [tex]2x - y = 0[/tex]

Substitute (1,-2)

[tex]5(1) - (-2) = -7[/tex]   and [tex]2(1) -(-2) = 0[/tex]

[tex]7\neq -7[/tex] and [tex]4 \neq 0[/tex]

So, this system of equations does not matches the graph.

Answer:

B. 5x - y = 7

2x + y = 0

Step-by-step explanation:

took test

2n2-24n+72 factor completely

Answers

2n^2-24n+72

2(n^2-12+36)

2(n^2-6n-6n+36)

2(n(n-6)-6(n-6))

2(n-6)(n-6)

2(n-6)^2
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