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3 years ago

3 Prove thatcos130°+cos 110+ cos10=0

Mathematics

1 answer:

Evgesh-ka [11]3 years ago

5 0

We know, cos A + cos B = 2cos(C+D)/2 × cos(C - D)/2

So,

cos 130 + cos 110 + cos 10

cos 130 + 2cos (110+10)/2 × cos( 110-10)/2

cos 130 + 2cos 60 × cos 50

cos ( 180 - 50 ) + 2cos60 cos 50

We know, cos ( 180 - A ) = -cos A

2cos 60 cos 50 - cos 50

Also, cos 60 = 0.5

2×0.5 cos 50 - cos50

cos 50 - cos 50

0 = RHS.

Hence proved

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Help. Solving Multi Step Ratio Problems!

Romashka-Z-Leto [24]

Answer:

Part 1) $30\ coupons$

Part 2) $12\ sandwiches$

Part 3) $60\ push-ups$

Part 4) $96\ minutes$

Part 5) $\$95$

Part 6) $1\frac{7}{8}\ cups\ of\ pretzel$

Step-by-step explanation:

Part 1) we know that

At the Green House of Salad , you get a $1 coupon for every 3 salads you buy

Using proportion

Find out the number of salads you could buy to get $10 in coupons

$\frac{1}{3}=\frac{10}{x} \\\\x=3(10)\\\\x=30\ coupons$

Part 2) we know that

Kim orders catering for $35

She spend $5 on a large order of potato salad and the rest on turkey sandwiches

Each sandwich is $2.50

How many sandwiches does Kim buy?

step 1

Find out how many Kim spent on turkey sandwiches

Subtract $5 from $35

35-5=$30

step 2

Using proportion, find out the number of sandwiches

$\frac{1}{2.50}=\frac{x}{30}\\\\x=30/2.50\\\\x= 12\ sandwiches$

Part 3) we know that

Molly does 10 push-ups at the same time as Liza does 15 push-ups

Using proportion

Find out how many push-ups Liza does when Molly does 40 push-ups

$\frac{10}{15}=\frac{40}{x}\\\\x=15(40)/10\\\\x=60\ push-ups$

Part 4) we know that

A shark swim at a speed of 25 miles per hour

The shark rest after 40 miles

How long in minutes, does the shark swim before resting?

Using proportion

Find out how long in minutes the shark swim 40 miles

Remember that

$1\ h=60\ min$

$\frac{25}{60}\ \frac{miles}{minutes}=\frac{40}{x}\ \frac{miles}{minutes}\\\\x=60(40)/25\\\\x=96\ minutes$

Part 5) we know that

For every bar of soap that Aly sells, she earns $5

For every mug that Janet sells, she earns twice as much as Aly

Aly sells 5 bars of soap and Janet sells 7 mugs

How much money did they make altogether?

step 1

Find out the amount earned by Aly

using proportion

$\frac{1}{5}=\frac{5}{x}\\\\x=5(5)\\\\x=\$25$

step 2

Find out the amount earned by Janet

Remember that

For every mug that Janet sells, she earns twice as much as Aly

For every mug that Janet sells, she earns 2($5)=$10

using proportion

$\frac{1}{10}=\frac{7}{x}\\\\x=10(7)\\\\x=\$70$

step 3

Adds the amount earned by Aly plus the amount earned by Janet

$25+70=\$95$

Part 6) we know that

Ted is making trail mix for a party

He mixes 1 1/2 cups of nuts, 1/4 cup of rising and 1/4 cup of pretzel

How many cups of pretzel does Ted need to make 15 cups of trail mix?

Adds the quantities

$1\frac{1}{2}+\frac{1}{4} +\frac{1}{4}=2\ cups\ of \ trail\ mix$

That means

For every 2 cups of trail mix we need 1/4 cup of pretzel

using proportion

Find out how many cups of pretzel does Ted need to make 15 cups of trail mix

$\frac{2}{(1/4)}=\frac{15}{x}\\\\x=15(1/4)/2\\\\x=\frac{15}{8}\ cups\ of\ pretzel$

Convert to mixed number

$\frac{15}{8}=\frac{8}{8}+\frac{7}{8}=1\frac{7}{8}\ cups\ of\ pretzel$

6 0

4 years ago

What are the zeros of f(x) = x^2 + x - 20?

kvv77 [185]

X² + x - 20
= (x+5)(x-4)

x + 5 = 0
x = -5

x - 4 = 0
x = 4

hence the answer is C

3 0

3 years ago

Does anyone understand this.

saw5 [17]

Easy. There is a pattern on the graph. Each baseball card set costs $4. If you add $4 to the $16 (because that is what she will have left after buying 1 baseball card set), you will get $20. So the answer is $20

6 0

3 years ago

Read 2 more answers

Find the coordinates of the orthocenter for XYZ with X(-5,-1) Y(-2,4), Z(3,-1)

V125BC [204]

9514 1404 393

Answer:

(-2, 2)

Step-by-step explanation:

The orthocenter is the intersection of the altitudes. The altitude lines are not difficult to find here. Each is a line through the vertex that is perpendicular to the opposite side.

Side XZ is horizontal, so the altitude to that side is the vertical line through Y. The x-coordinate of Y is -2, so that altitude has equation ...

x = -2

Side YZ has a rise/run of -1/1 = -1, so the altitude to that side will be the line through X with a slope of -1/(-1) = 1. In point-slope form, the equation is ...

y -(-1) +(1)(x -(-5))

y = x +4 . . . . . . . . subtract 1 and simplify

The orthocenter is the point that satisfies both these equations. Using the first equation to substitute for x in the second, we have ...

y = (-2) +4 = 2

The orthocenter is (x, y) = (-2, 2).

4 0

3 years ago

Pls help pls pls pls

Darya [45]

Answer:

12/4 i really hope this helps i took the test and got a 100

Step-by-step explanation:

3 0

3 years ago

3 Prove thatcos130°+cos 110+ cos10=0​

3 Prove thatcos130°+cos 110+ cos10=0