QuestionAnswerA factory uses 1/4 of a barrel of raisins in each batch of granola bars. Yesterday, the factory used 3/4 of a barrel of raisins. How many batches of granola bars did the factory make yesterday?3A water bottle holds 5/6 of a gallon of water. There are 5 5/6 gallons of water in a water tank. How many water bottles can be filled with the water in the tank?7Molly ran 2 laps around the track. If the total distance Molly ran was 3 3/4 miles, how long is each lap around the track?Every day, the Knox Pet Store uses 2 5/6 bags of dog food to feed the dogs. For how many days will 5 2/3 bags of dog food last?Sam grew tomatoes this summer and used them to make 1/2 of a gallon of tomato sauce. He split it into 5 equal portions to freeze for using later. How many gallons was each portion?1/10Kimberly made 2 1/2 quarts of hot chocolate. Each mug holds 1/2 of a quart. How many mugs will Kimberly be able to fill?5Rosa made fancy orange costume decorations for each of the 5 dancers in her year-end dance performance. She cut 5/6 of a yard of ribbon into equal pieces to make the decorations. How long was each piece of ribbon?1/6A factory uses 1/2 of a barrel of raisins in each batch of granola bars. Yesterday, the factory used 1 1/2 barrels of raisins. How many batches of granola bars did the factory make yesterday?3
Answer:
First, a rational number is defined as the quotient between two integer numbers, such that:
N = a/b
where a and b are integers.
Now, the axiom that we need to use is:
"The integers are closed under the multiplication".
this says that if we have two integers, x and y, their product is also an integer:
if x, y ∈ Z ⇒ x*y ∈ Z
So, if now we have two rational numbers:
a/b and c/d
where a, b, c, and d ∈ Z
then the product of those two can be written as:
(a/b)*(c/d) = (a*c)/(b*d)
And by the previous axiom, we know that a*c is an integer and b*d is also an integer, then:
(a*c)/(b*d)
is the quotient between two integers, then this is a rational number.
When a quadratic equation ax^2+bx+c has a double root, the discriminant,
D=b^2-4ac=0
Here
a=2,
b=b,
c=18
and
D=b^2-4ac=b^2-4*2*18=0
solve for b
b^2-144=0
=> b= ± sqrt(144)= ± 12
So in order that the given equation has double roots, the possible values of b are ± 12.
The slope is 3/10, and just graph 2 points ( so like .3,1 and .9,2) and just use Desmos to figure out the line using the y=3/10x+3.64 and just type it in
Answer:
The answer is the second one
im sorry if this is wrong
Step-by-step explanation:
