Answer:
31 laps
Step-by-step explanation:
Take the total distance and divide by the distance each lap is
7.75 ÷ .25
31
Amanda jogged 31 laps
Z / -4 < 2....multiply both sides by -4, cancelling out the -4 on the left. And dont forget to change the inequality sign because of multiplying by a negative.
z > 2 * -4
z > -8
Answer:
13 ingredients
Step-by-step explanation:
The number of different recipes that can be made from 2 ingredients = 78
Since there are no two recipes that share the exact same two ingredients ;
The number of recipes in Mark's kitchen is:
nCk = 78
k = Number of ingredients per recipe = 2
n = total number of ingredients in kitchen
Total recipes made = 78
n! / (n-r)!r! = 78
n! / (n - 2)!2! = 78
n(n-1)(n-2)! / (n-2)! * 2 * 1 = 78
n(n - 1) / 2 = 78
n(n-1) = 156
n² - n = 156
n² - n - 156 = 0
Factorize :
n² - 13n + 12n - 156 = 0
n(n - 13) +12(n-13) = 0
(n-13) = 0 ; (n+12) = 0
n = 13 or n = - 12
n cannot be negative
Hence, n = 13
Number of ingredients is 13
Answer:
m∠4 = 40°
Step-by-step explanation:
Using the vertical angle theorem we can find that...
m∠6 ≅ m∠7
Using this, we know that angle 6 and 8 are supplementary so...
m∠6 + m∠8 = 180°
140° + m∠8 = 180°
m∠8 = 40°
Then, we can use the corresponding angle theorem to find that...
m∠8 ≅ m∠4
m∠4 = 40°
