Answer:
58 and 1/2
Step-by-step explanation:
Can someone please help me answer this my grade depends on it!
a. 3 gallons 1 cup
b. 15 cups
Step-by-step explanation:
I'll do the first one as an example.
"What are the coordinates of the point on the directed line segment from K(-5,-4) to L(5,1) that partitions the segment into a ratio of 3 to 2?"
Let's call the point we're trying to find P. Ratio of 3 to 2 means that the distance from K to P divided by the distance from P to L is 3/2.
KP / PL = 3 / 2
Which also means the horizontal distances and vertical distances between the points have a ratio of 3:2.
KxPx / PxLx = 3 / 2
KyPy / PyLy = 3 / 2
First, let's use the x coordinates:
(x − (-5)) / (5 − x) = 3 / 2
(x + 5) / (5 − x) = 3 / 2
2 (x + 5) = 3 (5 − x)
2x + 10 = 15 − 3x
5x = 5
x = 1
And now with the y coordinates:
(y − (-4)) / (1 − y) = 3 / 2
(y + 4) / (1 − y) = 3 / 2
2 (y + 4) = 3 (1 − y)
2y + 8 = 3 − 3y
5y = -5
y = -1
So the point P is at (1,-1).
Answer:
Initial value is 
.
Step-by-step explanation:
Let us assume that the exponential function is 
...... (1)
Now, the point 
will satisfy the above equation.
Now, this point on the graph of the exponential function will be sufficient to find the initial value of the function (1) i.e. a.
Now, putting the value x = 0 and 
in the equation (1) we get,
⇒ 
⇒ 
(Answer)
The value written as 2/7 is a rational number and the other options are irrational numbers.
<h3>What is a rational number?</h3>
A rational number is a number that does not end in a non terminating decimal. Surd forms as well as the value pi are all irrational numbers. We must note that the option that has no surd form or pi as a denominator is a rational number.
Hence; the value written as 2/7 is a rational number and the other options are irrational numbers.
Learn more about rational numbers:brainly.com/question/14297987
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