Answer:
Step-by-step explanation:
Let the total amount of water the container can hold be . Currently, there are liters in the container. If Ito adds 10 liters of water, the container will be 60% full. We can express this statement in the following mathematical equation:
Next, we're given that if we add 6 more liters to this, the container will be 75% full.
Therefore, we have:
This is a system of equations:
Subtract both equations to conveniently get rid of :
Combine like terms:
Divide both sides by -0.15:
Now substitute into any equation (I'll choose the first):
Subtract 10 from both sides:
Answer:
c
Step-by-step explanation:
Strong positive because the line is going up and the dots are pretty close together
Answer:
Longer - 20 in and Shorter - 12 in
Step-by-step explanation:
We know that when we subtract the shorter side from longer we get two cuts named x:
2 x = a - b => a - b = 2 x
One of this section ( x ) with height ( h ) and lateral (congruent non parallel) side ( c ) make right triangle, from which we get:
x² = c² - h² and c = 5 in, h = 3 in
x² = 5² - 3² = 25 - 9 = 16 => x = √16 = 4 => x = 4 in
Now we will replace x = 4 in the equation a - b = 2 · 4 = 8 and get first equation of the system.
a - b = 8
We also know that the formula for calculating perimeter is:
P = a + b + 2 c where P = 42 in and c = 5 in
a + b = 42 - 2 · 5 = 42 - 10 = 32
Now we get the second equation of the system:
a + b = 32
a - b = 8
When we add first equation to the second we get:
2 a = 40 => a = 40 / 2 = 20 => a = 20 in
When we replace a = 20 in the first equation we get:
20 + b = 32 => b = 32 - 20 = 12 => b = 12 in
God with you!!!
Answer:
(arranged from top to bottom)
System #3, where x=6
System #1, where x=4
System #7, where x=3
System #5, where x=2
System #2, where x=1
Step-by-step explanation:
System #1: x=4
To solve, start by isolating your first equation for y.
Now, plug this value of y into your second equation.
System #2: x=1
Isolate your second equation for y.
Plug this value of y into your first equation.
System #3: x=6
Isolate your first equation for y.
Plug this value of y into your second equation.
System #4: all real numbers (not included in your diagram)
Plug your value of y into your second equation.
<em>all real numbers are solutions</em>
System #5: x=2
Isolate your second equation for y.
Plug in your value of y to your first equation.
System #6: no solution (not included in your diagram)
Isolate your first equation for y.
Plug your value of y into your second equation.
<em>no solution</em>
System #7: x=3
Plug your value of y into your second equation.