Answer:
It is an acute triangle.
Step-by-step explanation:
It would be much easier for you to see where I'm getting at if you draw a diagram.
Assume this triangle is labelled ABC where a = 14, b = 21, and c = 16.
cos A = (16^2 + 21^2 - 14^2)/(2(16)(21))
∠A = cos^-1(0.82291...)
∠A ≅ 34.6°
cos B = 16^2 + 14^2 - 21^2)/(2(16)(14))
∠B = cos^-1(0.024...)
∠B ≅ 56.8°
∠C = 180 - (∠A + ∠B)
∠C ≅ 56.8°
Since there is no right-angle nor is there an obtuse angle,
Therefore the triangle is an acute triangle.
Circle b:
Diameter = x
Radius =

Area =

Circle a:
Diameter =

Radius =

Area =

Thus,
Area of circle b to area of circle a
=

÷

=

×

= 4
Hence, the area of circle b is
4 times the area of circle a.
The amount of drinks is a linear function of the number of drinks. The maximum amount that can be purchased is 100 soft drinks.
Let
amount of drinks
number of drinks
For drinks not more than 50

For drinks more than 50.

For a purchase of $85, it means that:

So, we solve for x in both equations.


Collect like terms


Divide through by 0.8

--- approximated


Collect like terms


Divide by 0.7

By comparing both values:



Hence, the maximum amount that can be purchased is 100
Read more about functions at:
brainly.com/question/20286983
Answer:
y = -18
General Formulas and Concepts:
<u>Pre-Algebra</u>
- Order of Operations: BPEMDAS
- Equality Properties
<u>Algebra I</u>
- Solving systems of equations using substitution/elimination
Step-by-step explanation:
<u>Step 1: Define systems</u>
y = 5x - 3
3x - 2y = 27
<u>Step 2: Rewrite systems</u>
- Define: 3x - 2y = 27
- Add 2y on both sides: 3x = 2y + 27
- Divide 3 on both sides: x = 2/3y + 9
<u>Step 3: Redefine</u>
y = 5x - 3
x = 2/3y + 9
<u>Step 4: Solve for </u><em><u>y</u></em>
- Substitute in <em>x</em>: y = 5(2/3y + 9) - 3
- Distribute 5: y = 10/3y + 45 - 3
- Combine like terms: y = 10/3y + 42
- Subtract 10/3y on both sides: -7/3y = 42
- Divide -7/3 on both sides: y = -18