prove that
[tex] \frac{1 }{ \sin(x) \times \cos(x) } [/tex]
equals 2csc2x
​

Answer:

y = -3x + 7.

Step-by-step explanation:

First find the slope of the given line by converting to intercept form:

3x + y + 2 = 0

y = -3x - 2

So the slope is -3.

Then the line we want has a slope of -3 also (as it is parallel).

y - y1 = m(x - x1)   where m is the slope and (x1, y1) is a point on the line:

m = -3,  x1 = 1 and y1 = 4, so we have:

y - 4 = -3(x - 1)

y = -3x + 3 + 4

y = -3x + 7.

Answer

102.1

Step-by-step explanation:

area of the shaded region is the area of the the whole circle subtract area area of the unshaded minor segment.

Answer:

9. (a) 1/4

   (b) remove 3 alphabet cards

   (c)  add 4 number cards

10.  1/8

Step-by-step explanation:

Question 9

Given:

⇒ total number of cards = 8 + 10 + 6 = 24 cards

[tex]\mathsf{Probability \ of \ an \ event \ occurring = \dfrac{Number \ of \ ways \ it \ can \ occur}{Total \ number \ of \ outcomes}}[/tex]

(a) P(picture card) = 6/24 = 1/4

(b) P(alphabet card) = 10/24 = 5/12

If we remove 3 alphabet cards from the box

⇒ number of alphabet cards = 10 - 3 = 7

⇒ total number of cards = 24 - 3 = 21

Therefore, P(alphabet card) = 7/21 = 1/3

(c)  P(number card) = 8/24 = 1/3

If we add 4 number cards to the box:

⇒ number of number cards = 8 + 4 = 12

⇒ total number of cards = 24 + 4 = 28

Therefore, P(number card) = 12/28 = 3/7

--------------------------------------------------------------------

Question 10

Given:

⇒ area of ΔSDR = area of ΔPRQ = 1/2 × 4 × 4 = 8 cm²

As PR = SD = 4cm

Area of rectangle = (4 + 4) × (12 + 4) = 128 cm²

P(point lies in ΔSDR) = 8/128 = 1/16

P(point lies in ΔPRQ) = 8/128 = 1/16

P(point lies in ΔSDR) OR P(point lies in ΔPRQ) = 1/16 + 1/16 = 2/16 = 1/8

Answer:

15

Step-by-step explanation:

Count the units in the green shape or 3 x 5 = 15

u (-1 ; 0)

t (-3 ; 0)

The cost of painting the rectangular board with a semicircular top is $31.065 to the nearest hundredth.

To find area of the composite figures,

The dimentions of the rectangle is 3 by 4 foot. The area of the rectangle is,

[tex]A_r=3\times4\\A_r=12\rm \;ft^2[/tex]

The radius of the semicircle is 1.5 m. The area of the semicircle is,

[tex]A_{sc}=\dfrac{1}{2}\pi\times(1.5)^2\\A_{sc}=\dfrac{1}{2}(3.14)\times(1.5)^2\\A_{sc}=3.5325\rm\; ft^2[/tex]

The area of the composite figure is,

[tex]A=12+3.5325\\A=15.5325\rm\;ft^2\\[/tex]

The rate of  painting is $2.00 per square foot. Thus the cost to paint the figure is,

[tex]A=15.5325\times2\\A=31.065[/tex]

Hence, the cost of painting the rectangular board with a semicircular top is $31.065 to the nearest hundredth.

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Answer:31

Step-by-step explanation:

The length of all the strings combined is 84 inches, while the length of the smallest string is 6 inches.

A line plot is a graph that shows the frequency of each value by displaying data as points or checkmarks above a number line.

In the given line plot, if we consider each of the options with the plot given to us, we will get to know which of the options are true or not.

A.) A. The difference between the longest length and shortest length is 14 inches.

As given in the plot, the longest string is 14 units while the smallest is 6 units, therefore, the first option is incorrect.

B.) I have twice as many 12-inch strings as I do 8-inch strings.

In the plot since the number of dots represents the number of strings of a particular length, therefore, the number of strings of length 12-inches is 4 and the number of strings of length 8-inches is 2. Thus, the given options are correct.

C.)  The total length of string that I have is 84 inches.

As per the plot, the number of strings of length 6 inches is 1, the number of strings of length 8 inches is 2, the strings of length 12inches is 4, and the number of strings of length 14 inches is 1. Thus, the sum of the length of all the strings is 84 inches.

Hence, the statement is correct.

D.) I cannot determine what the shortest string is by looking at my line plot.

As given in the plot, the length of the smallest string is 6 inches, thus, the statement is incorrect.

E.) Since I need 100 total inches of string for my project, I have enough string.

As the length of all the strings combined is just 84 inches, thus, the statement is incorrect.

Hence, the only option that is correct is 'B' and 'C'.

Learn more about Line plot:

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Answer:

x=21/5

Step-by-step explanation:

5x:9 = 7:3

Turn the ratios into fractions:

5x/9 = 7/3

Then cross mutiply

15x=63

x=21/5

Answer:

He has 4 full boxes

6 Apple pies are leftover

Step-by-step explanation:

42/9 = 4.67 How many full boxes can he fill

9 X 4 = 36 He filled out 4 full boxes

42-36=6 Total - Filled = Remainder

Answer:

she has 4 full boxes of applepies and she has 6 leftover apple pies

Step-by-step explanation:

Answer:

15/28, 15/28, 15/28

Step-by-step explanation:

1. Is simplified

2. Divided

3. Evaluated

(Yes I know there the same but its just in case.)

The volume of a cone with the same radius and height as the cylinder is 40cm³.

A cylinder is a three-dimensional object. It is a prism with a circular base.

Volume of a cylinder = nr^2h

Volume of a cone = 1/3(nr^2h)

The volume of a cone, is 1/3 that of a cylinder.

Volume of the cone = 1/3 x 120 = 40

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Answer:cool

Step-by-step explanation:

iono

Answer:

The answer in percentages is 15%

Answer:

1.53x−14.23

Step-by-step explanation:

simplify:

5.03x−8.03−(3.5x+6.2)

Distribute the Negative Sign:

=5.03x−8.03−1(3.5x+6.2)

=5.03x−8.03−1(3.5x)+(−1)(6.2)

=5.03x−8.03−3.5x−6.2

Combine Like Terms:

=5.03x−8.03+−3.5x−6.2

=(5.03x−3.5x)+(−8.03−6.2)

=1.53x−14.23

(5.03x -8.03) - (3.5x +6.2)=

Answer:

12 units

Step-by-step explanation:

Applying the distance formula, [tex]\sqrt{(x_{2}- x_{1})^{2} + (y_{2}- y_{1})^{2} }[/tex], you get [tex]\sqrt{(2-2)^{2} +(4+8)^{2}}[/tex] = [tex]12[/tex] units.

‎[tex] \qquad\quad\hookrightarrow{\sf { 1000(e-1)}}[/tex]

[tex] \begin{aligned}&\longrightarrow \int_{0} ^{1000} {e}^{ - |x| }dx = \sum_{k = 0}^{999} \int_{k}^{k + 1}e ^{x - |x| }dx \\ \\ &\longrightarrow\int_{0} ^{1000} {e}^{ - |x| }dx = \sum_{k = 0}^{999} \int_{k}^{k + 1}e^{x - k}dx \\\\&\longrightarrow\int_{0} ^{1000} {e}^{ - |x| }dx = \sum_{k = 0}^{999}e^{x - k \big |_{k}^ {k + 1}} \\ \\& \longrightarrow\int_{0} ^{1000} {e}^{ - |x| }dx = \sum_{k = 0}^ {999}(e - 1)\\\\&\longrightarrow\int_{0} ^{1000} {e}^{ - |x| }dx = 1000(e - 1)\end{aligned}[/tex]

Answer:

31.8  cm^2

Step-by-step explanation:

Area of WHOLE circle  = pi r^2

semicircle is 1/2 of this    ( r = 1/2 of the diameter)

  1/2 pi r^2

  1/2 pi  (9/2)^2 =

Hello!

Let's solve this equation:

84=h-8

This is the same as

h-8=84

Add 8 to both sides:

h=84+8

h=92

Hope everything is clear.

Let me know if you have any questions!

#KeepLearning

:-)

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Derivative of tan(x) is sec²x

[tex]\qquad \sf  \dashrightarrow \: \therefore \dfrac{d}{dx} ( \tan(x)) = { \sec}^{2} (x)[/tex]

You can check the first principle method of derivation in attachment

[tex]\rightarrow \sf \dfrac{d}{dx} (tan(x))[/tex]

[tex]\rightarrow \sf \dfrac{d}{dx} ( \ \dfrac{sin(x)}{cos(x)} \ )[/tex]

use the quotient rule

[tex]\rightarrow \sf \dfrac{cos(x) * \dfrac{d}{dx} (sin(x)-sin(x)*\dfrac{d}{dx}(cos(x) }{cos(x)^2}[/tex]

[tex]\rightarrow \sf \dfrac{cos(x) * cos(x)-sin(x)*(-sin(x) )}{cos(x)^2}[/tex]

[tex]\rightarrow \sf \dfrac{cos(x)^2+sin(x)^2}{cos(x)^2}[/tex]

[tex]\rightarrow \sf \dfrac{1}{cos(x)^2}[/tex]

[tex]\rightarrow \sf sec(x)^2[/tex]

used formula's :

Answer:

1/18 x 9 x 1 = .5 cubic yards. Why would you ever waste time asking this....

Step-by-step explanation:

Answer:

Step-by-step explanation:

We have to find the volume. we can use volume of the cuboid formula

l = 1/18 yard

w = 9 yard

h = 1 yard

Volume = l*w*h

             [tex]= \dfrac{1}{18}*9*1\\\\\\= \dfrac{1}{2}\\\\\\= 0.5 \ \sf cubic yard[/tex]

0.5 cubic yards of cement is needed

Answer:

  3 tents hold 2 campers

Step-by-step explanation:

The given relations can be expressed as a single equation in the number of 2-camper tents.

__

Let x represent the number of 2-camper tents. Then the number of 4-camper tents is 6-x, and the total number of campers in tents is ...

  2x +4(6 -x) = 18

  -2x +24 = 18

  -2x = -6 . . . . . . subtract 24

  x = 3 . . . . . . . divide by -2

Exactly 3 tents hold 2 campers.

_____

Additional comment

The other 3 tents hold 4 campers.

Another way to consider this is to assume that all tents hold 2 campers, and then realize there are 18 -6×2 = 6 campers left over. If these are placed 2 per tent, then there will be 6/2 = 3 tents with 4 campers. The remaining 3 tents will have 2 campers.

Answer:

[tex]\frac{1}{36}[/tex]

Step-by-step explanation:

The probability of having 1 is 1/6.

The probability of it happening twice in a row is 1/6 * 1/6 = 1/(6*6)=1/36

Answer:

C. 189 square centimeters

Step-by-step explanation:

Area of a Square/Rectangle is base x height

= 7 X 7 = 49

Area of a triangle = 1/2 Base X Height

= 1/2 X 7 X 10

= 35

There are 4 triangles

35 X 4 = 140

140 + 49 = 189

= 189cm^2

Answer: C. 189 cm²

Step-by-step explanation:

      A rectangle/square is solved for with A = L * W.

The middle square has a (surface) area of:

7 * 7 = 49 cm²

     We then have four triangles. These are solved for with [tex]\frac{B*H}{2}[/tex]. Since all four are congruent, I will multiply one of them by 4.

The triangles have a total (surface) area of:

10 * 7 = 70

70 / 2 = 35

35 * 4 = 140 cm²

     Lastly, we will add the two totals together.

140 cm² + 49 cm² = 189 cm²

         The object has a surface area of C. 189 cm².

Option which does not help Olya to reduce her debt is to skip a month or two paying for her school loan and put the money towards her credit card debt.

Monthly payment is the payment which has to paid against the loan amount or the borrowed money calculated with interest rate.

Olya would like to find a way to reduce her current debt.  The table below shows Olya’s monthly income, expenses and net income.

Olya could spend less on entertainment each month and put the money towards her credit card payment. By this way she can pay the credit card payment faster.

In the second option, she has to skip the montly payment of her school loan which is not possible.

Olya could spend less on food each month and put the money towards her credit card payment. Similar to first option, this way also she  can pay the credit card payment faster.

Hence, the option which does not help Olya to reduce her debt is to skip a month or two paying for her school loan and put the money towards her credit card debt.

Learn more about the monthly payment here;

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Answer:

answer is B

Step-by-step explanation:

Answer:

the answer is B 0.760

Step-by-step explanation:

i did the test.

Answer: The answer is ASA I got it right

Step-by-step explanation:

brainliest pls <3

Answer:

The Formula for Percent Proportion is Parts /whole = percent/100. This formula can be used to find the percent of a given ratio and to find the missing value of a part or a whole.

Answer:

a = 9

Step-by-step explanation:

[tex]\frac{4}{12}[/tex] = [tex]\frac{a}{27}[/tex] ( cross- multiply )

12a = 108 ( divide both sides by 12 )

a = 9