142628281991919182726(35262627282
Answer:
x-int (6.2, 0)
y-int (0, 3.1)
Step-by-step explanation:
x-intercept is found when y = 0.
y-intercept is found when x = 0.
Step 1: Define equation
2x + 4y = 12.4
Step 2: Find x-intercept
<em>Substitute y for 0.</em>
2x + 4(0) = 12.4
2x = 12.4
x = 6.2
(6.2, 0)
Step 3: Find y-intercept
<em>Substitute x for 0.</em>
2(0) + 4y = 12.4
4y = 12.4
y = 3.1
(0, 3.1)
To make it easier, you calculate the volume of the first aquarium.
1st aquarium:
V = L x W x H
V = 8 x 9 x 13
V = 72 x 13
V = 936 in.
Rate: 936 in./2 min.
Now that you've got the volume and rate of the first aquarium, you can find how many inches of the aquarium is filled within a minute, which is also known as the unit rate. To do that, you have to divide both the numerator and denominator by their least common multiple, which is 2. 936 divided by 2 is 468 and 2 divided by 2 is 1.
So the unit rate is 468 in./1 min. Now that you've got the unit rate, you can find out how long it'll take to fill the second aquarium up by finding its volume first.
2nd aquarium:
V = L x W x H
V = 21 x 29 x 30
V = 609 x 30
V 18,270 inches
Calculations:
Now, you divide 18,270 by 468 to find how many minutes it will take to fill up the second aquarium. 18,270 divided by 468 is about 39 (the answer wasn't exact, so I said "about").
2nd aquarium's rate:
18,270 in./39 min.
As a result, it'll take about 39 minutes to fill up an aquarium measuring 21 inches by 29 inches by 30 inches using the same hose. I really hope I helped and that you understood my explanation! :) If I didn't, I'm sorry. I tried. :(
Your answer would be 91.1 units².
We can split this shape into a trapezium and a semicircle, and then find the area of both and add them.
To find the area of a trapezium, the formula is
(a + b)/2 × h, which means we do 14 (the length of AD) + 8 (the length of BC) = 22, and 22/2 = 11. Then we multiply 11 by the height of the trapezium, which is 6 because 10 - 4 = 6. This gives us the area of the trapezium as 66 units².
To find the area of a semicircle, the formula is πr²/2, and the radius is 4 because the diameter is 8 (16 - 8 = 8). This means we do π4²/2 = 16π\2 = 8π = 25.13.
Then we need to add together 66 and 25.13, which equals 91.13, or 91.1 to the nearest tenth.
I hope this helps!
Givens
Sequence 2, - 4, 8, -16, 32 ....
First term = a = 2
Problem
Find the nth term
tn = (-1 )^(n -1) * (a)^n answer or
tn = (-1)^(n - 1) * 2^n
where a is defined as the first term (it usually is given that designation).
Try a few to make sure the formula is correct
<em>n = 1</em>
t1 = (-1)^(1 - 1) * 2^1
t1 = (-1)^0 * 2
t1 = 1 * 2 = 2
<em>n =2</em>
t2 = (-1)^(2 - 1) * 2^2 = (-1)^1 * 4 = -4
