Directions: Solve each problem. Show how you found each answer.
4. Arthur went to bed at 9:30 p.m. and woke up at 6:00 a.m. How many hours was he asleep?

Answer:

y=(x+2)(x-5)

Step-by-step explanation:

The roots of the function (where it touches the x axis) are (0,-2) and (0,5), so you have to pick the equation with those roots. This equation if y=(x+2)(x-5). This is because when y = 0, when you insert those roots as x values the right side also equals zero. For example:

0=(x+2)(x-5)

set x as -2

0=(-2+2)(-2-5)

0=0*-7

0=0

The same would also happen if you inserted 5, showing that this equation is the correct one for this set of roots.

The win-to-loss ratio of 5:3 is a "part-to-part" ratio, so we can represent each part as a fraction of the whole. We can do this by simply adding 3 + 5 = 8 (the "whole") and dividing by that total. This gives us a ratio of Images, which means that the Bombers won Images of their games and lost Images of them. Since they played a total of 120 games, they won Images games and lost Images games.

we know the team has played a total of 24, and we know the wins : losses ratio is 5 : 3, so let's simply divide 24 by (5 + 3) and distribute accordingly.

[tex]\cfrac{wins}{losses}\implies \cfrac{~~5\cdot \frac{24}{5+3}~~}{3\cdot \frac{24}{5+3}}\implies \cfrac{~~ 5\cdot \frac{24}{8}~~}{3\cdot \frac{24}{8}}\implies \cfrac{5\cdot 3}{3\cdot 3}\implies \cfrac{\stackrel{\mathbb{WINS}}{15}}{9}[/tex]

Answer:

2) 50

Step-by-step explanation:

Basically, supplementary is when you add two angles, they should equal 180 degrees. In this picture, we can see that the bottom two rays form a straight line, indicating that it is a 180-degree angle, also. Great way to visualize, by the way. Well, 180 - 130 is 50 degrees, so x is equal to 50 degrees.

Answer:

2) 50

Step-by-step explanation:

x + 130 = 180

  -130     -130

x = 50

I hope this helps!

Answer:

12, 20, 28

Step-by-step explanation:

You simply have to add 4 to the given r-value to reach the s value. 8+4=12, 16+4=20, and 24+4=28.

Answer:

96 square units

Step-by-step explanation:

Add the areas of all of the polygons in the area net which represent the sides of the triangular prism:

SA = 2 small rectangles + 1 big rectangle + 2 small triangles

SA = 2(3 * 7) + (6 * 7) + (6 * 2)

= 42 + 42 + 12

= 84 + 12

= 96 square units

Answer:

Down 13

Step-by-step explanation:

The negative 13 is the b, and the b is on the y axis, negative means down

Answer:

C. $378

Step-by-step explanation:

Total cost of party = food & drink + game tokens + other

                              =  250 + 100 + 70

                              = $420

Deposit = 10% of total cost

              = 10% of $420

              = 0.1 x 420

              = $42

Total cost still to pay = total cost - deposit

                                   = 420 - 42

                                   = $378

Answer:

9 hours

Step-by-step explanation:

75 ----- 3

225 ---- x

[tex]x = \frac{(225)(3)}{75} =\frac{675}{75} =9 h[/tex]

Hope this helps

Answer:

Step-by-step explanation:

Number of Newspaper Published in a day = 300,000

Each news paper must include a Comic section. To check whether each newspaper has comic section or not, the publisher must make a sample Size of 500 or 1,000 will be good . That is , the publisher has to check between Sample size of  either 600 or 300 newspapers ,whether it contain a comic section or not.

So, Just Taking  a newspaper from a  sample size of 600 or 1500 newspapers or 500 or 1000 newspaper and then checking whether it contains Comic section or not will be best way that publisher can adopt.

Time must be kept in mind by the publisher while choosing the sample size.

Answer:

(59-6) × [tex]\sf{(\frac{1}{3})}^{3}[/tex] + 27 ÷ 3

=53 × [tex]\sf\frac{{1}^{3}}{{3}^{3}}[/tex] + 3³ ÷ 3

=53 × [tex]\sf\frac{1}{27}[/tex] + [tex]\sf{3}^{3-1}[/tex]

=[tex]\sf\frac{53\times1}{27}[/tex] + [tex]\sf{3}^{2}[/tex]

=[tex]\sf\frac{53}{27}[/tex] + 9

=9 + [tex]\sf\frac{53}{27}[/tex] + 9

=[tex]\sf\frac{9\times27+53}{27}[/tex]

=[tex]\sf\frac{243+53}{27}[/tex]

=[tex]\sf\frac{296}{27}[/tex]

=[tex]\sf\frac{270}{27}+\frac{26}{27}[/tex]

=[tex]\sf10+\frac{26}{27}[/tex]

=[tex]\sf10\frac{26}{27}[/tex]

[tex]\sf\:[/tex]

8² ÷ 4 × (2 + 3) - 9

=(8×8) ÷ 4 × 5 - 9

=64 ÷ 4 × 5 - 9

=4³ ÷ 4 × 5 - 9

=[tex]\sf{4}^{3-1}[/tex] × 5 - 9

=4² × 5 - 9

=(4×4) × 5 - 9

=16 × 5 - 9

=80 - 9

=71

Answer:

6

Step-by-step explanation:

tell me if I'm wrong:

b-bathroom

s-sweep

《in equation form》

s×3=18

18/3=6

so s=6

《explanation》

^ so you are going to divide 18 by 3 which gives you the answer 6^

Answer:

98,833      98,783   98,587

Step-by-step explanation:

These numbers go up to 99,000 because... the 8 in each of these numbers ask the hundreds place numbers if he can go up.

And if those numbers are 5 and above they can which leads to the 8 going up to 9 making 99,000

for the first one 98,833 it can go up because hundreds place number is a 8 so because of 8  being 5 and above it can go up.

For the second number 98,783 it can go up because the hundreds place number 7 is 5 and above so it can go up.

And for our last number 98,587 it has a 5 in it's hundreds place number so it just makes the cut to go up so those are numbers.

Sorry I'm late but I hope it can still help you actually I'm very very very very very very very very very very very very very very very very very sorry.

Hope it still helps have a great afternoon:)

The height of the shipping container is 7 feet

A volume is the amount of space occupied by a three dimensional shape or object.

Let h represent the height of the shipping container. The volume of the prism is given by:

Volume = length * width * height

1120 = 20 * 8 * h

h = 7 feet

The height of the shipping container is 7 feet

Find out more on volume at: https://brainly.com/question/12410983

Answer:

X = 2(3x + 4)

the rest i dont know sorry D:

Answer:

Im doing the same thing, i dont know the answer, Lol-

Step-by-step explanation:

Answer:

Decimal answer: 0.75 months. Fraction answer: 3/4

Step-by-step explanation: You have to make the 27 months into years, which is 2.25 years. Then subtract 2.25 from 3 and it equals 0.75.

Answer:

1. If it rains tomorrow then the concert will be canceled.

2. If you have two square roots then it's a positive integer.

Step-by-step explanation:

Changing the order of the words and adding if/then

Answer:

Bottom box= 103/210

Middle-right box=19/30

Middle-left box=7/21

Step-by-step explanation:

we can convert 1/7 to 21ths so it will be easier to add.

1/7 = 3/21

so, 3/21 + 4/21 = 7/21

we can now use that to find the box next to it.

The LCM (lowest common multiple) of 21 and 30 is 210.

7/21 = 70/210

29/30 = 203/210

so 203/210-70/210 = 19/30 (simplified)

and finally, we can use this to work out the fraction in the bottom box.

LCM of 30 and 7 is also 210.

so 1/7 = 30/210

19/30 = 133/210

so 133/210 - 30/210 = 103/210.

Answer: No. 8 is a factor of 16, but not a factor of 36.

Step-by-step explanation:

i-Ready

Answer:

a. 493 ft.

b. 269 ft.

Step-by-step explanation:

Please see the attached pictures.

a. Since we are interested in the length of AD, and ∆ABD does not have a right angle, we should think about using sine rule or cosine rule. We are only given two lengths in ∆ABD thus let's find one more angle, ∠ABD.

∠ABD= ∠ABC -∠CBD

∠CBD= 10° (given)

Since the tower should be vertically upright from the ground, we can assume that ∠ABC is 90°.

∠ABD= 90° -10°

∠ABD= 80°

With 2 lengths and 1 angle, we can apply cosine rule to find the length of the 3rd side:

[tex]\textcolor{steelblue}{{ {c}^{2} = {a}^{2} + {b}^{2} - 2abcosC}}[/tex]

(AD)²= 500² +100² -2(500)(100)(cos80°)

After simplifying and taking the square root of both sides, we obtain:

AD= 492.58 (5 s.f.)

AD= 483 (3 s.f.)

Thus, the guy wire has to be [tex]\textcolor{red}{{483 ft}}[/tex].

__________

b. Here, we make the assumption that the 500 ft. is excluding the height of the antenna and each square unit has the same height.

The tower is made up of 12 boxes, while the second guy wire is connected to the 6th box of the tower from the ground.

12 boxes ----- 500 ft

6 boxes ----- 500 ÷2= 250 ft

Pythagoras' Theorem states that in a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides.

Applying Pythagoras' Theorem,

x²= 100² +250²

x²= 72500

Taking the square root of both sides:

x= 269.26 (5 s.f.)

x= 269 (3 s.f.)

Thus, the length of the second guy wire is [tex]\textcolor{red}{{269 ft}}[/tex].

Answer:

a) 493 ft (nearest foot)

b) 269 ft (nearest foot)

Step-by-step explanation:

Part a

The guy wire creates a triangle with the tower with the following:

Therefore, as we have an angle with 2 adjacent side lengths, we can use the cosine rule to find the length of the unknown side opposite the angle.

cosine rule:  c² = a² + b² - 2ab cos C

(where C is the angle, a and b are the sides adjacent the angle, and c is the side opposite the angle)

Substituting given values into the equation and solving for c:

   c² = a² + b² - 2ab cos C

⇒ c² = 500² + 100² - 2(500)(100) cos(80°)

⇒ c² = 260000 - 100000cos(80°)

⇒ c = √[260000 - 100000cos(80°)]

⇒ c = 492.5801277...

Therefore, the length of the guy wire that is connected to the top of the tower and is secured at a point on the sloped side 100 ft from the base of the tower is 493 ft (nearest foot).

Part b

From inspection of the diagram, we can see that the second (left) guy wire is attached halfway up the height of the tower.

This guy wire creates a right triangle with the tower with the following:

Therefore, as we have the length of both legs of a right triangle, we can use Pythagoras' Theorem to find the length of the wire:

Pythagoras' Theorem:  a² + b² = c²

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

Substituting given values into the equation and solving for c:

   a² + b² = c²

⇒ 100² + 250² = c²

⇒ c² = 72500

⇒ c = √(72500)

⇒ c = 269.2582404...

Therefore, the length of the second guy wire is 269 ft (nearest foot)

Answer:

The tree is shorter than 30 feet.

Step-by-step explanation:

The expression x<30 shows that the height of the tree is less than 30 so we can say that the tree's height is less than 30 feet.

Answer:

24.57 Miles

Step-by-step explanation:

Hundredths Place Value

3 + 4 = 7

Put the 7 in Hundredths place

Tenths Place Value

0 + 5 = 5

Put the 5 in Tenths place

Ones Place Value

3 + 1 = 4

Put the 4 in Ones place

Tens Place Value

1 + 1 = 2

Put the 2 in Tens place

Answer:

x+y=30

2x+3y=80

multiplying equation one by -3 and add equation

-3x -3y=-90

2x +3y=80

2(10)+20(3)=80

80=80

Answer:

1 [tex]\frac{3}{7}[/tex]

Step-by-step explanation:

[tex]\frac{10}{7}[/tex]

divide 10 by 7 = 1 remainder 3

the 1 is a whole number and the 3 is the amount of seventh's left , then

[tex]\frac{10}{7}[/tex] = 1 [tex]\frac{3}{7}[/tex]

Answer:

2/3 is the answer

40 minutes is 2/3 of one hour