The combinations of batches that Rebecca can use are the solutions of:
120 ≤ 15*x + 12*y ≤ 360
One example is x = 10 and y = 0.
<h3>What combination of batches of each could Rebecca make?</h3>
Let's define the variables:
- x = number of batches of cookies.
- y = number of batches of cupcakes.
We know that she makes batches of 15 cookies and batches of 12 cupcakes, then the total number of baked goods that she makes is:
15*x + 12*y
And we know that she wants to make at least 120 and no more than 360, then we can write the inequality:
120 ≤ 15*x + 12*y ≤ 360
So any pair of values of x and y that make the inequality true, is a combination of batches that Rebecca could use.
An example is x = 10 and y = 0.
120 ≤ 15*10 + 12*0 ≤ 360
120 ≤ 150 ≤ 360
If you want to learn more about inequalities:
brainly.com/question/24372553
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Answer:
see explanation
Step-by-step explanation:
f(x) is valid for all real values of x , so
domain is x ∈ R
Since the coefficient of the x² term < 0 , then
f(x) has a maximum vertex at (0, 5 )
range is ( - ∞ , 5 ]
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.
Divide both sides by sine(45 degrees).
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.
Evaluate the exponents.
Add them together.
Square root 288 to solve for c.
c = 16.97, which is the same answer as you got using trigonometry.
Answer:
67.2
Step-by-step explanation:
The easiest way to do this is by taking your original number 112, and multiply it by the percentage. The way to do that is
112 x .6
This gets you 67.2