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3 years ago

What is the measure of the missing angle? PICTURE BELOW \/

Mathematics

1 answer:

jeka57 [31]3 years ago

6 0

Answer:

The measure of the missing angle is 90°

Step-by-step explanation:

∵ This figure is a quadrilateral

∴ the sum of measures of its angles = 360°

∴ m∠x = 360 - 107 - 72 - 91 = 90°

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Answer:

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3 years ago

The arc of the parabola y = x^2 from (3,9) to (4,16) is rotated about the y-axis. Find the area of the resulting surface. Please

Hitman42 [59]

Answer:

156.5

Step-by-step explanation:

Thinking process:

The area can be calculated using the formula:

$S = \int\limits^4_3 {2\pi x\sqrt{1+}(2x)^{2} } \, dx$

We let the substitution take place.

Therefore, we let $u = 1 + 4x^{2}$

Thus, $du = 8dx.$

So,

$xdx = \frac{1}{8}du$

Also, the interval of the integration changes to [ 37, 65]

Thus,

$S = \int\limits^4_3 {2\pi \sqrt{1+4x^{2} } } \, dx \\= \int\limits^65_35 {2\pi \sqrt{\frac{1}{8}u } } \, dx$

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8 0

3 years ago

Here are three stories:

aev [14]

Answer:

a) 6x+3 = 27

b) x=4

c) We know that x is price of each ticket, so The price of each ticket is $4. They bought 6 tickets, so total cost of ticket = 24 and $3 for parking so, total money spent = $27.

a) 3x + 6 = 27

b) x= 7

c) We know that x is amount of juice poured, so 3 friends of Diego will get 7 ounces of Juice, while Diego will get 6 ounces of juice.

a) 27x + 3 = 6

b) x= 1/9

c) We know that x is time spend on each picture, so Jada spend 1/9 hour on each picture

Step-by-step explanation:

1. A family buys 6 tickets to a show. They also pay a $3 parking fee. They spend $27 to see the show.

a) Decide which equation represents each story. What does x represent in each equation?

Let x be price of one ticket.

The equation will be: 6x+3 = 27

b. Find the solution to each equation. Explain or show your reasoning,

Now solving the equation:

6x+3=27

6x=27-3

6x=24

x=24/6

x=4

So, we get x = 4

c. What does each solution tell you about its situation?

We know that x is price of each ticket, so The price of each ticket is $4. They bought 6 tickets, so total cost of ticket = 24 and $3 for parking so, total money spent = $27.

2. Diego has 27 ounces of juice. He pours equal amounts for each of his 3 friends and has 6 ounces left for himself.

a) Decide which equation represents each story. What does x represent in each equation?

Let x be amount of juice poured.

The equation will be: 3x+6 = 27

b. Find the solution to each equation. Explain or show your reasoning,

Now solving the equation:

3x+6=27

3x=27-6

3x=21

x=21/3

x=7

So, we get x = 7

c. What does each solution tell you about its situation?

We know that x is amount of juice poured, so 3 friends of Diego will get 7 ounces of Juice, while Diego will get 6 ounces of juice.

3. Diego has 27 ounces of juice. He pours equal amounts for each of his 3 friends and has 6 ounces left for himself.

a) Jada works for 6 hours preparing for the art fair. She spends 3 hours on a sculpture and then paints 27 picture frames.

Let x be time spend on each picture frame.

The equation will be: 27x+3=6

b. Find the solution to each equation. Explain or show your reasoning,

Now solving the equation:

27x+3=6

27x=6-3

27x=3

x=3/27

x=1/9

So, we get x = 1/9

c. What does each solution tell you about its situation?

We know that x is time spend on each picture, so Jada spend 1/9 hour on each picture

8 0

3 years ago

Read 2 more answers