if sinA+cosecA=3 find the value of sin2A+cosec2A​

Answer:

They both will meet each other when they both have been running for 10 seconds

Lauren will run [tex]x=80\ \text{ft}[/tex] and Clara will run [tex]40\ \text{ft}[/tex]

Step-by-step explanation:

Velocity of Lauren

[tex]v_l=\dfrac{24}{3}\\\Rightarrow v_l=8\ \text{ft/s}[/tex]

Velocity of Clara

[tex]v_c=\dfrac{20}{5}\\\Rightarrow v_c=4\ \text{ft/s}[/tex]

Let distance traveled by Lauren be [tex]x[/tex]

As Clara has a 40 feet head start distance she will travel is [tex]x-40[/tex]

[tex]\text{Time}=\dfrac{\text{Distance}}{\text{Speed}}[/tex]

The time that will have passed when they both will meet will be the same for both of them so

[tex]\dfrac{x-40}{4}=\dfrac{x}{8}\\\Rightarrow 8x-320=4x\\\Rightarrow 8x-4x=320\\\Rightarrow 4x=320\\\Rightarrow x=\dfrac{320}{4}\\\Rightarrow x=80\ \text{ft}[/tex]

Time they will meet is [tex]\dfrac{80-40}{4}=\dfrac{80}{8}=10\ \text{s}[/tex].

So, Lauren will run [tex]x=80\ \text{ft}[/tex] and Clara will run [tex]x-40=80-40=40\ \text{ft}[/tex].

Answer:

DF=22.57

DG=26

Step-by-step explanation:

sinF/DG=sinD/FG

sin75/DG=sin48/20

DG*sin48/sin48=20*sin75/sin48

DG=26

D^+F^+G=180(sum of int. angles of triangle)

G^=180-48-75

G^=57

sinG/DF=sinD/FG

sin57/DF=sin48/20

DF*sin48/sin48=20*sin57/sin48

DF=22.57

The value of DF and DG is 22.57 units and 25.9956 units respectively.

Given to us,

∠D = 48°,

∠F = 75°,

FG = 20,

According to sine rule, in a triangle the length of a side of the triangle and the angle opposite to it is always in ratio. therefore,

[tex]\dfrac{A}{sin\alpha}= \dfrac{B}{sin \beta}= \dfrac{C}{sin\gamma}[/tex]

So,

[tex]\dfrac{DF}{sin (G)}= \dfrac{FG}{sin (D)}= \dfrac{GD}{sin(F)}[/tex],

For ∠G,

∠D + ∠F + ∠G = 180°,

48° + 75° + ∠G = 180°,

∠G = 180° - ( 48° +75°),

∠G = 57°,

Now using the sine rule,

[tex]\dfrac{DF}{sin (G)}= \dfrac{FG}{sin (D)}= \dfrac{DG}{sin(F)}\\\\\\\dfrac{DF}{sin (57)}= \dfrac{20}{sin (48)}= \dfrac{DG}{sin(75)}\\\\\\\dfrac{DF}{sin (57)}= \dfrac{20}{sin (48)}\\\\DF = 22.57\ units\\\\\\ \dfrac{20}{sin (48)}= \dfrac{DG}{sin(75)}\\\\DG = 25.9956\ units[/tex]

Hence, the value of DF and DG is 22.57 units and 25.9956 units respectively.

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Answer:

The domain and the range of the function represented by the set of ordered pairs are {-6, -3, -1, 5} and {5, 2, 0, -4}

Step-by-step explanation:

In any set of ordered pairs,

Let us solve the question

∵ The set of ordered pairs is {(-6, 5), (-3, 2), (-1, 0), (5, -4)}

∵ The first number in each ordered pair represents x

∴ x = -6, -3, -1, 5

∵ The set of x is the domain of the function

∴ The domain of the set of ordered pairs = {-6, -3, -1, 5}

∵ The second number in each ordered pair represents y

∴ y = 5, 2, 0, -4

∵ The set of y is the range of the function

∴ The range of the set of ordered pairs = {5, 2, 0, -4}

The domain and the range of the function represented by the set of ordered pairs are {-6, -3, -1, 5} and {5, 2, 0, -4}

Answer:

Domain: {-6,-3,-1,5}

Range: {-4,0,2,5}

Step-by-step explanation:

Answer:

6/7

Step-by-step explanation:

Answer: 6/7

Step-by-step explanation:

Answer:

57.9532

Step-by-step explanation:

Given that:

Wholesale price = 29.95

Markup = 80%

Sales tax = 7.5%

Retail price of the game :

Price before sale tax:

Wholesale price * ( 1 + markup %)

29.95 * (1 + 0.8)

29.95 * (1.8)

$53.91

Sales tax = 7.5%

53.91 * (1 + 0.075)

53.91 * (1.075)

= 57.9532

Hence, $57.9532 will have to be paid

Answer:

Step-by-step explanation:

since the question does not have a given slope you can just put the point into the point slope formula   y-y1 = m(x-x1)  

y-5 = m(x-(-2))

y-5 = m(x+2)

since the slope is not given, leave it like that

.........................

Answer: 54 pounds

Step-by-step explanation:

1. Adressing the variables:

x=number of pounds of type A

y=number of pounds of type B

2. Equations:

x+y=147 pounds

5.15x+4.1y=659.40

3. Subsitution:

y=147-x =>5.15x+4.1(147-x)

4. Solve:

5.15x+602.7-4.1x=659.4

=> 1.05x=56.7 => x=54

5. Solution:

x=54; y=93

Answer:

612

Step-by-step explanation:

you multiply 27 x 12 and 24 x 12, and add up the products, and you get 612

Answer: 612 Treats

Work: To find out how many treats he baked, you do 27 x 12 and 24 x 12. After doing so, you get 324 and 288. Add those up, and you get 612.

I hope this helps, and Happy Holidays! :)

Step-by-step explanation:

By Law of Indices, a^m / a^n = a^(m-n).

Therefore a² / a⁸ = a^(-6).

x = -6.

Answer:

1) x=20 degrees

2) x=25 degrees

Step-by-step explanation:

1) there is 9x if you add all of the angles together and there is 180 degrees in a triangle so 180 divided by 9 equals 20 degrees.

2)there is 7x and 5 dgress in total so we can make an equation:

7x+5=180

7x=175

x=25

Answer:

5: 4

Step-by-step explanation:

original ratio: 3:5

new ratio: 5:4

hope it helps!

Answer:

jacky 12 809 n-t

Step-by-step explanation:

Answer:

he said it not me

Step-by-step explanation:

[tex] {7}^{ - 3} \times {7}^{ - 5} \times 7 {}^{ - 1} [/tex]

[tex] \frac{1}{7 {}^{3} } \times \frac{1}{ {7}^{5} } \times \frac{1}{7 } \\ \frac{1}{ {7}^{3 + 5 + 1 } } \\ \frac{1}{ {7}^{9} } \\ [/tex]

Step-by-step explanation:

[tex] = {7}^{ - 3} \times {7}^{ - 5} \times {7}^{ - 1} [/tex]

[tex] = {7}^{( - 3 - 5 - 1)} [/tex]

[tex] = {7}^{ - 9} [/tex]

[tex] = \frac{1}{ {7}^{9} } [/tex]

Answer:

what does it equal ?? x???

Step-by-step explanation:

Answer:

false 15 is a positive number

Answer:

Option (C)

Step-by-step explanation:

If a point is dilated by a scale factor of 'k' about the origin,

Rule for the dilation,

(x, y) → (kx, ky)

By this rule, if ΔABC is dilated to form image triangle as ΔA'B'C',

A(-2, -2) → A'[2×(-2), 2×(-2)]

B(-1, 2) → B'[2×(-1), 2×(2)]

C(2, 1) → C'[2×(2), 2×(1)]

Therefore, scale factor of the dilation of the dilation will be k = 2

Option (C) will be the answer.

Answer: 25 red marbles

Step-by-step explanation:

Fraction of yellow marbles = 1/3

Fraction of blue marbles = 1/4

Fraction of red marbles = 1 - (1/3 + 1/4) = 5/12

Therefore, the number of red marbles that are there in the bowl would be:

= 5/12 × 60

= 25 red marbles

Answer:

Otieno's age in 4 years: [tex]k+4[/tex]

Kidole's age in 4 years: [tex]k-1[/tex]

Step-by-step explanation:

[tex]k[/tex] = Otieno's age

[tex]k-5[/tex] = Kidole's age

Their ages will increase by 4 years when 4 years pass.

[tex]k+4[/tex] = Otieno's age in 4 years

[tex]k-5+4[/tex] = Kidole's age in 4 years

[tex]k-1[/tex] = Kidole's age in 4 years (after simplifying the expression)

I hope this helps!

Answer:

The value of the entry represented by [tex]c_{41}[/tex] is 12.

Step-by-step explanation:

Let [tex]A = \left[\begin{array}{ccc}-5&3&8\\3&6&-5\\5&-9&0\\7&3&4\end{array}\right][/tex] and [tex]B = \left[\begin{array}{ccc}-7&-8&-5\\7&9&2\\2&5&-7\\2&8&-7\end{array}\right][/tex]. The sum of equal-sized matrices consist in the sum of each pair of corresponding elements. If [tex]C = (A-B)+A[/tex], then:

[tex]C = 2\cdot A -B[/tex] (1)

Then, [tex]c_{41}[/tex] is the element of matrix C located in the fourth row and first column and is defined by the following expression:

[tex]c_{41} = 2\cdot a_{41}-b_{41}[/tex] (2)

If we know that [tex]a_{41} = 7[/tex] and [tex]b_{41} = 2[/tex], then [tex]c_{41}[/tex] is:

[tex]c_{41} = 2\cdot (7)-2[/tex]

[tex]c_{41} = 12[/tex]

The value of the entry represented by [tex]c_{41}[/tex] is 12.

Answer:

1.6 hours / 1 hour 36 minutes

Step-by-step explanation:

105+95=200 miles

This is the distance that the trains could travel in an hour.

320÷200=1.6 hours

Our Answer is 1.6 hours / 1 hour 36 minutes

Given: U.S Flag - rectangle in shape

scale of 0.5 cm = 1 in

length of the scale 2.5 cm

width of the scale 4.75 cm

perimeter of the scale = 2(L+W) = 2(2.5+4.75) =

2(7.25) = 14.5cm

perimeter of the actual flag is:

14.5cm * 1in/0.5cm = 29 inches

hope it helps!

Step-by-step explanation:

Perimeter of scale drawing

= 2 * (Length + Width)

= 2 * (2.5cm + 4.75cm)

= 2 * 7.25cm

= 14.5cm. (C)

Scale length to Actual length = 0.5cm : 1 in

Hence,

Perimeter of actual drawing

=> (1/0.5) * Perimeter of scale drawing

=> (1/0.5) * 14.5cm

=> 29 in. (B)

Answer:

10.

Step-by-step explanation:

6+1/3*12=6+4=10

Answer: 10

Step-by-step explanation:

Answer:

1st option and last option

Answer:

At 4 meters, the potential energy is 800 Joules

At 3 meters, the potential energy is 600 Joules

At 2 meters, the potential energy is 400 Joules

At 1 meter, the potential energy is 200 Joules

Step-by-step explanation:

The given mass of the object = 20 kg

The Potential Energy of an object at a height is. P.E. = m × g × h

Where;

m = The mass of the object

g = The acceleration due to gravity taken as 10 m/s²

h = The height of the object

The potential energy if the height is 4 meters is given as follows;

P.E. = 20 kg × 10 m/s² × 4 m = 800 Joules

The potential energy if the height is 3 meters is given as follows;

P.E. = 20 kg × 10 m/s² × 3 m = 600 Joules

The potential energy if the height is 2 meters is given as follows;

P.E. = 20 kg × 10 m/s² × 2 m = 400 Joules

The potential energy if the height is 1 meter is given as follows;

P.E. = 20 kg × 10 m/s² × 1 m = 200 Joules.

Answer:

9x + 10 = 3

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

Step 1: Define Equation

5 + 2x + 5 + 7x = 3

Step 2: Simplify

Answer:

9x+10=3

Explantion

(2x+7x)+(5+5)=3

= 9x+10=3

[tex] \Large{\boxed{\sf n = 8}} [/tex]

[tex] \\ [/tex]

The perimeter of a rectangle is given by the following formula:

[tex] \Large{\sf P = 2L + 2W } [/tex]

Where:

[tex] \\ [/tex]

[tex] \Large{\boxed{\sf Given \text{:} } \begin{cases} \sf L &=\sf 3n - 9 \\ \sf W &=\sf n + 5 \\ \end{cases} } [/tex]

[tex] \\ [/tex]

Substitute these values into our formula:

[tex] \sf P = 2(3n - 9) + 2(n + 5) [/tex]

[tex] \\ [/tex]

Expand the expression of the perimeter using the following distributive property.

[tex]\green{\begin{gathered}\begin{gathered} \\ \boxed { \begin{array}{c c} \\ \blue{ \sf\boxed{ \sf Distributive \: property \text{ : } }} \\ \\ \sf\star \: \red{ \large{ a (b + c) = ab + ac }} \end{array}}\\\end{gathered} \end{gathered}}[/tex]

[tex] \\ [/tex]

We get:

[tex] \sf P = 2(3n) + 2(-9) + 2n + 2(5) \\ \\ \sf P = 6n - 18 + 2n + 10 \\ \\ \boxed{\sf P = 8n - 8 } [/tex]

[tex] \\ [/tex]

Since the perimeter is equal to 56, the value of n satisfies the following equality:

[tex] \sf 8n - 8 = 56 [/tex]

[tex] \\ [/tex]

To solve this equation, let's add 8 to both sides:

[tex] \sf 8n - 8 + 8 = 56 + 8 \\ \\ \sf 8n = 64 [/tex]

[tex] \\ [/tex]

Now, divide both sides of the equation by 8:

[tex] \sf \dfrac{8n}{8} = \dfrac{64}{8} \\ \\ \\ \boxed{\boxed{\sf n = 8}} [/tex]

[tex] \\ \\ [/tex]

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Answer:

30 minutes

Step-by-step explanation:

Option A.30 minutes.

The change in the amount of time that Alejandro studied on the first day to the amount of time he studied on the last day is 30 minutes.

Step-by-step

The computation of the change in the amount of time is shown below = Number of consecutive ways * number of minutes more each day = 6 days ~ 5 minutes = 30 minutes

Hence, the change in the amount of time is 30 minutes Therefore the correct option is D.

We simply applied the above formula so that the correct value could come, and the same is to be considered(the answer is 30 ).

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Answer:

20%?

Step-by-step explanation: