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3 years ago

If sin(2x)=cos (x+30°), what is the value of x?

Mathematics

1 answer:

denis23 [38]3 years ago

5 0

Step-by-step explanation:

$\sin(2x)= \cos (x+30°) \\ \\ \therefore \: \cos(90 \degree - 2x)= \cos (x+30°)\\ \{\because \sin \theta = \cos(90°-\theta)\} \\ \\ \therefore \: 90\degree - 2x = x+30° \\ \\ \therefore \: 90\degree - 30\degree = x + 2x \\ \\ \therefore \: 60\degree =3 x\\ \\ \therefore \: x = \frac{60\degree}{3} \\ \\ \huge \red{ \boxed{ \therefore \: x = 20 \degree }}$

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Lines a and bare perpendicular. If the slope of line a is - 2/3 is the slope of line b?

Elena-2011 [213]

Answer:

B. 3/2

Step-by-step explanation:

The slopes of perpendicular lines are negative reciprocals

The negative reciprocals of -2/3

is 3/2

5 0

2 years ago

Heather is making a blanket for her baby and is going to put a ribbon border around it. The blanket will be 3 feet by 5 feet. Th

mote1985 [20]

Answer:

The approximate total cost for the blanket is $10.08 ⇒ B

Step-by-step explanation:

The formula of the area of a rectangle is A = L × W

The formula of the perimeter of a rectangle is P = 2(L + W)

where:

L is the length of the rectangle
W is the width of the rectangle

∵ The baby blanket shaped a rectangle

∵ The dimensions of the blanket are 3 feet and 5 feet

- Find the area of the blanket

∵ A = 3 × 5 = 15 feet²

- Change feet to yard because the cost is by square yard

∵ 1 foot = $\frac{1}{3}$ yard

∴ 1 foot² = $(\frac{1}{3})^{2}=\frac{1}{9}$ yard²

∴ 15 feet² = 15 × $(\frac{1}{9})$ = $\frac{5}{3}$ yards²

∴ The area of the blanket is $\frac{5}{3}$ yards²

∵ The fabric cost of the blanket is $1.25 per square yard

∴ The fabric cost = $\frac{5}{3}$ × 1.25

∴ The fabric cost = 2.08333 dollars

∵ Heather is going to put a ribbon border around it

- The length of the ribbon is equal to the perimeter of the blanket

∵ P = 2(3 + 5) = 16 feet

∴ The length of the ribbon is 16 feet

∵ The cost of the ribbon is $0.5 per foot

∴ The cost of the ribbon = 16 × 0.5

∴ The cost of the ribbon = 8 dollars

Now add the fabric cost to the ribbon cost to find the total cost of the blanket

∵ The total cost = 2.08333 + 8

∴ The total cost = 10.08333

- Round it to the nearest cent

∴ The total cost = 10.08 dollars

The approximate total cost for the blanket is $10.08

7 0

3 years ago

Mrs. Ham is planning a party for students who have met their goal of reading seven books during the most recent eight weeks of v

djyliett [7]

Answer:

8 pizzas and 32 drinks

Step-by-step explanation:

12 times 8 equals 96

0.50 times 32 equals 16

96 plus 16 equals 112

7 0

3 years ago

Find the other endpoint of the line segment with the given endpoint and midpoint.

Shtirlitz [24]

Answer:

endpoint is (29, -13)

Step-by-step explanation:

Formula for midpoint is $(\frac{x_{1} + x_{2} }{2} ,\frac{y_{1} + y_{2} }{2} )$

So, let $(x_{2} , y_{2} )$ be the coordinates of the endpoint you are looking for.

$x_{1} = -9$ and $y_{1} = 7$

$(\frac{-9 + x_{2} }{2} , \frac{7 + y_{2} }{2} )$ = (10, -3)

$\frac{-9 + x_{2} }{2} = 10$ $\frac{7 + y_{2} }{2} = -3$

-9 + $x_{2}$ = 20 7 + $y_{2} = -6$

$x_{2} = 29$ $y_{2} = -13$

endpoint is (29, -13)

6 0

2 years ago

A helicopter travels 240 miles every 2 hours. The vehicle travels miles.

S_A_V [24]

is this the whole question because there's nothing to find?

5 0

2 years ago