If sin (x) =2/5 and tan(x) > 0, what is sin(2x)?

Answer:

sin2x = [tex]\frac{4\sqrt{21} }{25}[/tex]

Step-by-step explanation:

Given sinx = [tex]\frac{2}{5}[/tex] = [tex]\frac{opposite}{hypotenuse}[/tex]

Then the third side, the adjacent is found using Pythagoras' identity, that is

adj² + opp² = hyp²

adj² + 2² = 5²

adj² + 4 = 25 ( subtract 4 from both sides )

adj² = 21 ( take the square root of both sides )

adj = [tex]\sqrt{21}[/tex] , then

cosx = [tex]\frac{adj}{hyp}[/tex] = [tex]\frac{\sqrt{21} }{5}[/tex]

Using the double angle identity

sin2x = 2sinxcosx

         = 2 × [tex]\frac{2}{5}[/tex] × [tex]\frac{\sqrt{21} }{5}[/tex]

         = [tex]\frac{4\sqrt{21} }{25}[/tex]

Juan cuts a piece of rope that is 16 meter long into 2 equal pieces.

What is the length of each shorter piece of rope?

Enter your answer as a fraction in simplest form by filling in the boxes

Ashley practiced the piano for 41 minutes. She practiced 13 minutes less than(means subtraction) her brother did. Write and solve an equation to determine how long her brother practiced the piano.(identify the question)

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Theo wants to use a cookie recipe
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HELPPPPPP
Keisha is working to complete her summer reading in one week so she can relax for the remainder of the summer. She read (2x2 + 5x – 3) pages on Monday, (5x – 3) pages on Tuesday, and (6x2+ 2) pages on Wednesday. How many pages did she read in three days?

Find the slope of the line that passes through (1, 1) and (-3, -5)

Find the value of each trigonometric ratio. Write your answer as a fraction in simplest form. (Example: If the answer is one-half, type 1/2.)

PLS HEL P ASAP NOT THAT HARD!! CONVERT TO ENTIRE RADICAL FORM

i need help urgently lease :D

234 students in 9 different classrooms. What is the ratio of students to classrooms?

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I NEED HELP WITH THIS ASAP!!!!

Lillian is in the business of manufacturing phones.
She must pay a daily fixed cost to rent the building and equipment, and also pays a cost per phone produced for materials and labor.

Let CC represent the total cost, in dollars, of producing pp phones in a given day.

The table below has select values showing the linear relationship between pp and C.C.

Determine the fixed cost for rent and equipment.

P C
2 1200
4 1600
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Which inequality is equivalent to -m ≥ 15?

A. m ≥ 15
B. m ≥ -15
C. m ≤ -15
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1. Carlos tiene un terreno de 30.000 m2, él
vende 3/5 del total del terreno y recibe por
la venta $27.000.000.000; en 1/3 del
terreno restante va a construir una piscina
que tiene de profundidad desde 1,2 metros
hasta 1,8 m en forma descendente; en el
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De la información, se puede decir que Carlos
vendió cada m2 por un valor de
A. $1.500.000
B. $1.800.000
C. $2.100.000
D. $2.400.000
PROCEDIMIENTO:

​

Three people attend a concert for $155. Ten attend the same concert for $470. Find the rate of change.

A program was created to randomly choose customers at a shoe store to receive a discount. The program claims 15% of the receipts will get a discount in the long run. The manager of the shoe store is skeptical and believes the program's calculations are incorrect. She selects a random sample and finds that 12% received the discount. The confidence interval is 0.12 ± 0.05 with all conditions for inference met.


Part A: Using the given confidence interval, is it statistically evident that the program is not working? Explain.


Part B: Is it statistically evident from the confidence interval that the program creates the discount with a 0.15 probability? Explain.


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1. The surface area of a cube whose edges have lengths of 5 inches each is equal to which of the
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(1) 25 square inches
(2) 75 square inches
(3) 125 square inches
(4) 150 square inches
5 in
5 in
5 in

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2
7
8
4​

The resale value of a certain car when purchased new is $20,000. The car is expected to lose 10% of its value each year.
Which graph shows the predicted value of the car over time?
HELPPPP I’M GIVING 18 points ASAP




The graph that shows the predicted value of the car over time is the
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b. Blue graph, g
c. Green graph, h
d. Orange graph, k

This makes sense because it’s y-intercept is at
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b. 20,000

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b. Decreases

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True or False??

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Solve for z.
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the question is in the picture. it’s math.

I need help with this question

Find the area of the figure.
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6 cm
2 cm
2 cm
2 cm
2 cm
2 cm
2 cm
2 cm

Please help me !!!!!