MATHEMATICS MIDDLE SCHOOL

If 180°<θ<270°, and sin⁡θ=−3/4, what is the value of sin(−θ)?

Answers

Answer 1

Answer:

Answer:

$sin(-\theta)=(3)/(4)$

Step-by-step explanation:

Given:

180°<θ<270° and $sin(\theta)=-(3)/(4)$

We know for any angle $\theta$ ,

$sin(-\theta)=-sin(\theta)$

∴ $sin(-\theta)=-(-(3)/(4))=(3)/(4)$

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The floor of a rectangular meeting room is the same length as the room and is 1/6 the width of the room. What is the width of the raised platform. Length is 7 1/2 and width is 6 2/5.

Answers

Length of floor = length of room = 7.5 units

Width of floor = $(1)/(6)$ * Width of Room = $(1)/(6)$ * $(32)/(5)$

⇒ Width of floor = 1.067 units

Answer:

Width of raised platform = $1(1)/(15)\text{ units}$ = 1.067 units

Step-by-step explanation:

We are given the following information about the room:

Lenght of room = $7(1)/(2)\text{ units}$

Width of room = $6(2)/(5)\text{ units}$

We are given the following information about the raised platform of meeting room.

Length of raised platform = Length of the room = $7(1)/(2)\text{ units}$

Width of the raised platform = $(1)/(6) * \text{Width of the room}$

= $(1)/(6) * (32)/(5)$

= $(16)/(15) \text{ units}$

= $1(1)/(15)\text{ units}$

= 1.067 units

Kate made a box to hold her jewelry collection. She used 42 inches of wood to build the sides of the box. If the box was 9 Inches wide, how long was the box

Answers

We can use the 9 inches wide to determine that 18 inches of the 42 inches are the wide sides. 42 - 18 = 24, so we divide 24 by how many long sides there are, 2. 24 ÷ 2 = 12. The box was 12 inches long.

Earl needs to fill juice cups for his little brother's birthday party. There are 25 juice cups and each juice cup holds 12 fluid ounces. The juice comes in 1-gallon bottles. How many 1-gallon bottles of juice will Earl need to purchase?(1 quart = 32 fluid ounces, 1 gallon = 4 quarts)
a. 1 bottle
b. 2 bottles
c.3 bottles
d. 4 bottles

Answers

Ok so first we need to find how many fluid ounces all the cups hold in totoal.
so 25*12=300
So we have 300 ounces in the cups and 300 ounces is around 2.34 gallons. So we need 2.34 gallons to fill all the cups, and one bottle is one gallon, so if we get two bottles we have 2 gallons, which is a little under the amount we need. So we would need to buy 3 bottles (3 gallons) to have enough to drink.

Hope that helpes:) if it dosn't make sense PM me and I can try to explain better :)

Time(weeks) Lake Depth
(feet)
0 346.0
2 344.8
5 343.0
7 341.8
10 340.0
12 338.8

An environmental agency studying the effects of drought on a lake found that the water level decreased at a constant rate during the first few months of the drought. When the agency began its research, the depth of the lake was 346 feet. The table represents the agency’s susequent observations about the lake's depth.

Which equation represents the depth of the lake, y, based on the number of weeks passed, x?

y = -0.6x + 346

y = -1.2x + 346

y = -0.6x

y = -1.2x

Answers

(0,346)(2,344.8)
slope(m) = (y2 - y1) / (x2 - x1)
slope(m) = (344.8 - 346) / (2 - 0)
slope(m) = -1.2/2 = - 0.6

y = mx + b
slope(m) = - 0.6
(0,346)...x = 0 and y = 346
now we sub
346 = - 0.6(0) = b
346 = b

ur equation is : y = - 0.6x + 346

Jack is 4 times as old as lacy. 4 years ago the sum of their ages was 22. How old are they now

Answers

4 x 22 =?

the question mark is how old they'll be.

Really confused with this problem. It would be great if someone could help

Answers

(2n+12) + (3n+18) = 180
⇒5n+30=180
⇒5n=150
⇒n=30

x=2n+12
=2(30)+12
=72°

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