Matthew wants to buy a new pair of jeans. If the jeans were originally $65.00, but are on sale with a 10% discount, how much wil
1 answer:
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The equation represent a linear relation with the y-intercept
representing the amount of initial fee.
Correct response:
1. 28 volleyball uniforms
2. Price per uniform
3. Initial flat order fee
4. 10 fewer volleyball uniform
<h3>Methods used for finding the above values</h3>The given equation that represents the relationship between the cost of school volleyball uniform is; C = 20·n + 35
Where;
C = The uniform costs
n = The number of volleyball uniform ordered
The maximum amount the school has to spend = $600
1. The number of uniforms the school can buy is given by setting C = 600 as follows;
- C = 20·n + 35
Therefore;
600 = 20·n + 35
20·n = 600 - 35 = 565
Rounding down to the nearest whole number, we have;
- The number of uniforms the school can buy, n = <u>28 volleyball uniforms</u>.
2. The number 20 represent the additional cost for each extra uniform, which is the unit cost therefore;
- 20 represents a <u>$20 price per uniform</u>.
3. The 35 in the equation represents an initial <u>flat fee</u>, such as an
ordering or initial fee, which is fixed.
Therefore;
- The number 35 represent the <u>fixed cost </u>for producing the uniforms
4. The price per uniform of $30 changes the coefficient of <em>n</em> from 20 to 30 as follows;
C = 30·n + 35
The number of uniforms the school can by with $600 is therefore;
Which gives;
The number of uniforms the school can purchase at $30 per uniform is n = 18 volleyball uniforms
The difference in the number of uniforms purchased = 28 - 18 = 10
Therefore;
- The school can purchase <u>10 fewer uniforms</u> at $30 per uniform
Learn more about linear equations here:
Answer:
s = 16.97 units
Step-by-step explanation:
Since this is a right triangle, we can use trigonometry to figure out the lengths of the sides.
Look at the 45 degree angle. We can use the opposite side (12) and the hypotenuse (s) to solve for s.
Opposite and hypotenuse is sine, so we are using sine. The sine of 45 degrees is 0.70710678118. Make an equation like so:
- 0.70710678118 =
, and we are solving for s.
Put a 1 in the denominator of sine(45 degrees) so you can cross-multiply.
Cross multiply.
- 0.70710678118s = 12
Divide both sides by sine(45 degrees).
- s = 16.97
The length of side s is 16.97 units.
Another way to have done this problem is to use the Pythagorean theorem: a^2 + b^2 = c^2
Substitute 12 for a and b and solve for c, the hypotenuse.
- (12)^2 + (12)^2 = c^2
Evaluate the exponents.
- 144 + 144 = c^2
Add them together.
- 288 = c^2
Square root 288 to solve for c.
c = 16.97, which is the same answer as you got using trigonometry.