<u>Given</u>:
The length of a suitcase is 36 inches.
The diagonal of the suitcase is about 51 inches.
We need to determine the width of the suitcase.
<u>Width of the suitcase:</u>
The width of the suitcase can be determined using the Pythagorean theorem.
Thus, we have;
where d is the diagonal, l is the length and w is the width.
Substituting the values, we get;
Squaring the terms, we have;
Subtracting both sides by 1296, we get;
Taking square root on both sides, we get;
Rounding off to the nearest inch, we get;
Thus, the width of the suitcase is 36 inches.
Answer:
The measure of the unknown angle is 15°.
Step-by-step explanation:
Represent this angle by A. Then the complement of A is 90° - A.
"Angle whose complement is five times its measure" would be expressed as
90° - A = 5A
Solve this for A by adding A to both sides:
90° = 6A. Then A = 90°/6, or 15°
$1.49 3ft or $.69 1.5ft
69*2=138
$149 for 3ft or $1.49 1.5ft
options two are better buys
Answer:
Zahara need to add 4 quarts of water to keep the consistency the same
Step-by-step explanation:
Let
x -----> the amount of dry ingredients in quarts
y -----> the mount of water in quarts
we know that
Batch 1
Isolate variable y
----> equation A
Batch 2
For x=10
substitute in the equation A and solve for y
The ratio batch 2 is 
therefore
Zahara need to add 4 quarts of water to keep the consistency the same
<h3>
Answer: D) infinitely many solutions</h3>
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Explanation:
Let's solve the first equation for y
4x - 2y = 6
4x-6 = 2y
2y = 4x-6
y = (4x-6)/2
y = (4x/2) - (6/2)
y = 2x - 3
After doing so, we see that 4x-2y = 6 is equivalent to y = 2x-3
Therefore, the original system of equations is effectively listing the same equation twice (one has a different form compared to the other).
Both equations in this system produce the same graph, which leads to infinitely many solutions. All solutions are on the line y = 2x-3.
You can say that all solutions are in the form (x, 2x-3) where x is any real number you want.
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Here's another approach using substitution
4x - 2y = 6 ... start with the first equation
4x - 2( y ) = 6
4x - 2( 2x-3 ) = 6 .... replace y with 2x-3; ie plug in y = 2x-3
4x - 2(2x) - 2(-3) = 6
4x - 4x + 6 = 6
0x + 6 = 6
0 + 6 = 6
6 = 6
We get a true statement. The last equation is always true regardless of what we plug in for x, so this is another way to see how we get to infinitely many solutions.
Side note: the system is considered dependent since one equation depends on the other. The system is also consistent since it has at least one solution.
