Angles 1 and 3, angles 2 and 4, angles 5 and 7, and angles 6 and 8. They are also congruent, because vertical angles are congruent.
Answer:
75 pieces
Step-by-step explanation:
1. determine how many pieces per ounce by dividing 45 by 6 (# of pieces in a 6 oz bag)
45/6= 7.5 pieces per ounce
2. multiply 7.5 (for one ounce) by 10
7.5*10 = 75
Answer:
(2, -3)
Step-by-step explanation:
Apparently, the equations are supposed to be ...
The solution for x can be found by subtracting the second equation from the first:
(4x +y) -(3x +y) = (5) -(3)
x = 2 . . . . . . . matches the second answer choice
Y can be found from either equation:
y = 5 - 4x . . . . . subtract 4x from the first equation
y = 5 -4(2) = -3
The solution is (x, y) = (2, -3).
Answer:
A) Independent
B) Dependent
Step-by-step explanation:
A) If we take a marble out and put the marble back, it means we have restored the sample to what it was initially and thus it doesn't affect probability of making another selection.
Thus, this is an independent event.
B) A card is taken from a deck of cards without replacement and set aside. Then after that another card is taken from the first sample, this means that the first sample size has now reduced and thus the first card taken affects the probability of the second card to be picked. Thus, this is a dependent event.
Answer:
height = 12 cm
base length = 4 cm
Step-by-step explanation:
area of a triangle
base length × height / 2
x = height
y = base length
x = y + 8
24 = y × (y + 8) / 2
48 = y × (y + 8) = y² + 8y
squared equation
y² + 8y - 48 = 0
solution
y = (-b ± sqrt(b² - 4ac))/(2a)
a = 1
b = 8
c = -48
y = (-8 ± sqrt(64 - 4×-48))/2 = (-8 ± sqrt(64 + 192))/2 =
= (-8 ± sqrt(256))/2 = (-8 ± 16)/2 = -4 ± 8
y1 = -4 + 8 = 4 cm
y2 = -4 - 8 = -12
but a negative base length did not make any sense, so only y = 4 remains.
x = y + 8 = 4 + 8 = 12 cm
