Identity
An identity is an equation that is true for all values of the variables. For example:
(x+y)^2=x^2+2xy+y^2
The above equation is true for all possible values of x and y, so it is called an identity.
Strictly speaking we should use the "three bar" sign to show it is an
identity as shown below. But it is very common to use the equal sign.
Lily made $75.36 more than Layla did. If Layla raised her price to $1.00, she would still not make more money than Lily.
Use a proportion to find the number of cupcakes Lily makes in 8 hours. She bakes 7 cupcakes in 10 minutes; we want to know how many she makes in 8(60)=480 (since there are 8 hours and each hour is 60 minutes):
7/10 = x/480
Cross multiply:
7*480 = 10*x
3360 = 10x
Divide both sides by 10:
3360/10 = 10x/10
336 = x
Lily bakes 336 cupcakes.
She sells 2/3 of these; 2/3(336) = 2/3(336/1) = 672/3 = 224 cupcakes sold.
Each cupcake is sold for $1.29; 224(1.29) = 288.96
To find the number of cupcakes Layla makes in 8 hours, we set up a different proportion. We know she bakes 8 cupcakes in 12 minutes; we want to know how many she bakes in 8(60) = 480 minutes:
8/12 = x/480
8*480 = 12*x
3840 = 12x
Divide both sides by 12:
3840/12 = 12x/12
320 = x
She bakes 320 cupcakes. She sells 75% of those; 75% = 75/100 = 0.75:
0.75(320) = 240
Each of those 240 cupcakes sells for $0.89:
0.89(240) = 213.60
This means Lily makes 288.96-213.60 = 75.36 more than Layla.
If Layla raised her price to $1.00, she would make 1(240) = $240; this is still less than Lily.
Use distance formula d=sqrt root (y2-y1)^2+(x2-x1)^2. So (-3, 4) and (1, 7). D= sqrt root ( 7-4)^2+(-3+1)^2. So now solve d= sqrt (3)^2+(-2)^2. Now d= sqrt 9+4. D= sqrt 13 or 3.60555
Yo im sorry but I can’t help I’m jus trying to answer questions so I can ask them
