Answer:
Case 1:


Case 2:


Case 3: Not possible
Step-by-step explanation:
Given
See attachment for illustration of each case
Required
Find AB and BC
Case 1:
Using Pythagoras theorem in ANB, we have:

This gives:



Take square roots of both sides


To calculate BC, we consider ANC, where:



Collect like terms


Take square roots


So:



Case 2:
Using Pythagoras theorem in ANB, we have:

This gives:


Collect like terms


Take square roots of both sides


To calculate BC, we consider ABC, where:



Collect like terms


Take square roots


Case 3:
This is not possible because in ANC
The hypotenuse AN (24) is less than AC (40)
This question is incomplete
Complete Question
Tyler went to the supermarket to buy food for a food pantry. He has $36, and can carry up to 20 pounds of food in his backpack. Pasta costs $1 for a 1-pound package. Pasta sauce costs $3 for a 1.5 pound jar. Let x = the number of packages of pasta and y = the number of jars of pasta sauce. One package of pasta is the right amount to go with one jar of pasta sauce. What is the best numbers of packages of pasta and jars of pasta sauce to buy for the food pantry? Explain your reasoning.
Answer:
Eight is the best numbers of packages of pasta and jars of pasta sauce to buy for the food pantry.
Step-by-step explanation:
Let
x = the number of packages of pasta
y = the number of jars of pasta sauce.
He has $36, and can carry up to 20 pounds of food in his backpack. Pasta costs $1 for a 1-pound package. Pasta sauce costs $3 for a 1.5 pound jar.
x + 1.5y ≤ 20....... Equation 1
x = 20 - 1.5y
x × $1 + y × $3 = $36
x + 3y ≤ 36..... Equation 2
20 - 1.5y + 3y = 36
-1.5y + 3y = 36 - 20
1.5y = 16
y = 16/1.5
y = 8
And x = 8
Therefore,
Eight is the best numbers of packages of pasta and jars of pasta sauce to buy for the food pantry.
Let n represent the amount Colin earned on Sunday.
On Sat. he earned n/2; on Sun. he earned n; and on Friday he earned (1/2)(n/2).
Then n/2 + n + n/4 = $70
Mult. all terms by 4 to eliminate fractions:
2n + 4n + n = $280
7n = $280 => n = $40
Colin earned n/2, or $20, on Saturday; n, or $40, on Sunday; and n/4, or $10, on Friday.
Note that $20 and $40 and $10 add up to $70, as they must.
It is the third equation: −512⋅(65⋅13)⋅92=(−512⋅65)⋅(13⋅92)
Associative property means one can group the individual operations arbitrarily without changing the result.
Answer:
Step-by-step explanation:
tan (40) = x/12
x = 12*tan(40)