The inequality representation of the scenario is :
- 5m + 8c ≤ 25
- m = 1 and c = 1
- Number of mugs = m
- Cost per mug = $5
- Number of ground coffee = c
- Cost per ground coffee = $8
- Total amount to spend = $25
- (Number of mug × cost per mug) + (Number of ground coffee × cost of ground coffee) ≤total amount to spend
- Representing as an inequality : 5m + 8c ≤ 25
Combination of m and c that makes the inequality true :
- Using trial by error :
- m = 1 and c = 1
- 5(1) + 8(1) ≤ 25 ; 13 ≤ 25
Hence, m = 1 and c =1 are valid values for the expression.
Learn more : brainly.com/question/15748955
Answer:
°
Step-by-step explanation:
"Theorem 9-13: The measure of an angle formed by two secants, two tangents, or a secant and a tangent drawn from a point outside the circle is equal to half the difference of the measures of the intercepted arcs."
Basically no matter what other circle, secant or tangent you get, you just use the formula
If you need the outer angle, just put the other angles in and solve
If you need the far or near point angle, re-arrange the formula to get that value.
Answer:
a = √11 and b = 6
Step-by-step explanation:
Refer to attached picture for reference
for an right triangle with angle θ
we are given
cos θ = 5/6 = length of adjacent side / length of hypotenuse
hence
adjacent length = 5 units
hypotenuse length = 6 units
the missing side is the "opposite" length which we can find with the Pythagorean equation. in our case:
hypotenuse ² = adjacent ² + opposite² (rearrange)
opposite ² = hypotenuse ² - adjacent ²
opposite ² = 6² - 5²
opposite = √ (6²-5²) = √11
sin θ = opposite length / hypotenuse (substitute values above)
sin θ = √11 / 6
hence a = √11 and b = 6
It would be positive 4/3 or the inverse would be -3/4
A greatest common factor is the largest number that goes into two or more numbers (in this case two). To find the GCF of two numbers, we have to find the prime factorization (how to express a number as a product of prime numbers) and then see which numbers are common in both of the prime factorizations.
13. The prime factorization of 8 is 2 * 2 * 2. The prime factorization of 26 is 2 * 13. Looking at the prime factorizations, we can see that both of them have 2. That means that the GCF is 1 * 2 which is 2.
12. The prime factorization of 105 is 3 * 5 * 7. The prime factorization of -30 is -5 * 6. We see that the number shared 5. That means that the GCF is 5 * 1 or 5.