Xian and his cousin Kai both collect stamps, and Kai has 68 stamps. The boys recently joined different stamp collecting clubs. Xian’s club sill send him 12 new stamps per month. Kai’s club will send him 8 new stamps per month. After how many months will Xian and Kai have the same number of stamps? How many stamps will each have?

Answers

Answer 1

Answer: Assuming that Xian starts with 0 stamps, you set the equations equal to each other to find what month they have the same amount of stamps.

(68 from Kai's original stamps) (8 from how many per month)
(0 from Xian's original stamps) (12 from how many per month)
68+8m=0+12m
solve for m in this equation and you get 68=4m
and 68/4 = 17 months

For how many stamps each will have, you plug in 17 into m in Xian's equation (you could do either but Xian's is easier):
0+12m
0+12(17)=204
204 stamps.

Hope this helped, it was kinda long lol

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Segments AP and BP have the same length. If the coordinates of A and P are (-1,0) and (4,12), respectively, which could be the coordinates of B?I. (3/2, 6)

II. (9, 24)

III. (-8,7)

A) I and II only

B) II and III only

C) II only

D) III only

Answers

Answer:

B) II and III only

Step-by-step explanation:

Coordinates of A = (-1,0)

Coordinates of P =(4,12)

Let (x,y) be the coordinates of B

Distance formula : = $√((x_2-x_1)^2+(y_2-y_1)^2)$

AP = BP

$√((4+1)^2+(12-0)^2)=√((4-x)^2+(12-y)^2)$

$(4+1)^2+(12-0)^2=(4-x)^2+(12-y)^2$

$169=16+x^2-8x+144+y^2-24y$

$x^2-8x+y^2-24y-9=0$

I)(3/2,6)

$((3)/(2))^2-8((3)/(2))+6^2-24(6)-9=0\n-126.75 \neq 0$

II)(9,24)

$(9)^2-8(9)+(24)^2-24(24)-9=0$

0= 0

C)(-8,7)

$(-8)^2-8(-8)+(7)^2-24(7)-9=0$

0=0

So, II and III could be the coordinates of B

So Option B is true

II) II and III only

Roger has 4 liters of orange juice. He puts the same amount of juice into each of 5 pitchers. How many liters of orange juice are in 1 pitcher?

Answers

1.25 cuz 5/4 is 1.25 times 4 is 5. I’m Albert Einstein

AB and BA name the same ray.
Always
Never
Sometimes

Answers

Answer:

AB in terms of rays, can never be BA.

Step-by-step explanation:

AB and BA name the same ray.

No, this is never true. A ray starts from a point and move in a single direction to infinity.

So, if starting point is A and ray is moving towards B, so it will continue moving towards the points further from B.

Therefore, AB as in terms of rays, can never be BA.

They are never the same ray. ray AB begins at point A and goes through point B to infinity and ray BA begins at point B and goes through point B to infinity

Tell whether the two rates form a proportion 7 inches 9 hours; 42 inches in 54 hours

Answers

Answer:

They do form a proportion.

Step-by-step explanation:

To determine whether the two rates form a proportion, you can set up a proportion and check if the cross-products are equal.

The two rates you have are:

Rate 1: 7 inches in 9 hours

Rate 2: 42 inches in 54 hours

You can set up a proportion like this:

Rate 1 (inches per hour) / Rate 2 (inches per hour) = Time 1 (hours) / Time 2 (hours)

So, it becomes:

(7 inches / 9 hours) / (42 inches / 54 hours)

Now, let's calculate these fractions:

Rate 1 (inches pr hour) = (7 inches / 9 hours) ≈ 0.7778 inches per hour (rounded to 4 decimal places)

Rate 2 (inches per hour) = (42 inches / 54 hours) ≈ 0.7778 inches per hour (rounded to 4 decimal places)

Now, compare the two rates (rounded to 4 decimal places):

Rate 1 ≈ 0.7778 inches per hour

Rate 2 ≈ 0.7778 inches per hour

Since both rates are approximately equal to 0.7778 inches per hour, they do form a proportion. When two rates are in proportion, their ratios are equal, which is the case here.

Bridget needs an actor. Actor A is offering her services for an initial $250 in additionto $50 per day. Actor B is offering her services for an initial $200 in addition to $60
per day. When will the two actors charge the same amount of money?

Answers

$250 + 50x = $200 + 60x

Get like terms on the same side using subtraction
250 -200 + 50x = 60x
50 + 50x - 50x = 60x -50x
50 = 10x now divide by 10 and get 5 days.

Let's check

Day 1 Actor A is $250 + 50 = $300 Actor B = $200 + 60 = $260
Day 2 Actor A is $250 + 100 = $350 Actor B = $200 + 120 = $320
Day 3 Actor A is $250 + 150 = $400 Actor B = $200 + 180 = $380
Day 4 Actor A is $250 + 200 = $450 Actor B = $200 + 240 = $440
Day 5 Actor A is $250 + 250 = $500 Actor B = $200 + 300 = $500

Answer:

The two actors will have the same amount of money in 5 days.

Step-by-step explanation:

How do you find the radius when the circumference is given?

Answers

Step-by-step explanation:

r = c/2π

The radius of a circle is half of the circumference. So for example if the circumference is 10, the radius would be 5.

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