I NEED HELP PLEASE I NEED HELP PLEASE
I NEED HELP PLEASE
I NEED HELP PLEASE
I NEED HELP PLEASE
I NEED HELP PLEASE!!!

1. The width of a rectangle is 5 cm shorter than twice the length. The perimeter is 62 cm. State the
dimensions of this rectangle. (5A, 3C)
2. Stephanie is 3 years older than twice her brother’s age. Two years ago the sum of their ages was 14.
How old will they be next year? (5A, 3C)
3. Find three consecutive integers such that the sum of the smallest and twice the middle integer is 16
more than the largest integer.

1. W=19, L=12

2. Next year Stephanie will be 14 and her Brother will be 6

3. 8, 9, 10

Step-by-step explanation:

1.

(a) W = 2L -5 => W - 2L = -5

(b) 2W + 2L = 62

Making (a)+(b):

3W = 57 => W = 19

from (a): L = (W+5)/2 = 12

2.

Today: S = 2B + 3 => S - 2B = 3 (a),

where S and B are Stephanie and Brother current age

2 years ago: (S-2) + (B-2) = 14,

so S + B = 14 + 4

S + B = 18 (b)

(a) - (b):

-3B = -15 => B = 5

from (a) S = 13

Verification:

2 years ago Stephanie was 11 and Brother was 3, the sum was 14, ok.

Next year Stephanie will be 14 and her Brother will be 6

3. We will find integers: s, m and b:

they are consecutive, so:

m = s+1

b = m+1 = s+2

and:::

s + 2m = b + 16 (a)

In (a) let's express all in terms of s:

s + 2(s+1) = s+2 + 16 =>

2s + 2 = 2 + 16 => s = 8, m=9, b=10

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

well we know there are 4 clubs in 52 cards so it’s replaced so it should be 3/51

step-by-step explanation: