9514 1404 393
Answer:
7 cm, 4.4 cm
Step-by-step explanation:
The side lengths can be found from the law of cosines. Each triangle has legs 3 cm and 5 cm. The angle between these will be 60° or 120°. Then the two sides of the parallelogram are ...
s = √(a² +b² -2ab·cos(C))
s = √(3² +5² -2·3·5·(±1/2)) = √(34 ±15) = {√49, √19}
The two side lengths are 7 cm and about 4.4 cm.
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
Answer:
10
Step-by-step explanation:
To solve this problem you need to create a system of equations. In these equations, use a = 2-seated car and b = 4- seated car
The first equation that you can make can be a + b = 25 because the number of 2-seated cars plus the number of 4-seated cars is going to equal a total of 25 cars.
The next equation you can make is 2a + 4b = 70 because the number of seats provided by the 2-seated cars plus the number of seats provided by the 4-seated cars will equal 70 total seats.
Next, line up the equations and solve:
Step one: Line up the equations
a + b = 25
2a + 4b = 70
Step two: Multiply the top equation by -2 so that you can add both of the equations together
-2(a) + -2(b) = 25(-2) ⇒ -2a - 2b = -50
2a + 4b = 70 ⇒ 2a + 4b = 70
Step three: Add the equations
-2a - 2b = -50
+ 2a + 4b = 70
______________
2b = 20
Step four: Divide both sides by 2 in order to solve for b
2b = 20 ⇒ b = 10
Because b represents the number of 4-seated cars, you now know that there are 10 4-seated cars on the ride.
