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3 years ago

The perimeter of the triangle is 13 inches. What is the length of the shortest side?

Mathematics

1 answer:

vlabodo [156]3 years ago

6 0

Answer:

3 in

Step-by-step explanation:

Sum of all sides of ∆ = perimeter

Given that it has a perimeter of 13 in, and the following sides: (x - 5) in, x/2 in, and 6 in, therefore:

$x - 5 + \frac{x}{2} + 6 = 13$

Solve to find the value of x

$\frac{2x - 10 + x + 12}{2} = 13$

$\frac{3x + 2}{2} = 13$

Multiply both sides by 2

$\frac{3x + 2}{2}*2 = 13*2$

$3x + 2 = 26$

Subtract 2 from both sides

$3x + 2 - 2 = 26 - 2$

$3x = 24$

Divide both sides by 3

$\frac{3x}{3} = \frac{24}{3}$

$x = 8$

The shortest side = (x - 5) in

Plug in the value of x

= (8 - 5) in

= 3 in

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Weights of different sandwiches in two lengths are shown in the table.

Alexandra [31]

Answer:

Egg salad sandwich is proportional to its length

Step-by-step explanation:

Weight of Sandwiches by Length of Roll

6-inch Roll 12-Inch Roll

Cheese sandwich $\frac{1}{4}$ $\frac{3}{4}$

Chicken salad sandwich $\frac{3}{4}$ $1\frac{3}{4}$

Egg salad sandwich $\frac{2}{3}$ $1\frac{1}{3}$

For cheese sandwich proportion

$\frac{6}{\frac{1}{4}}=\frac{12}{\frac{3}{4}}\\24 \neq 16$

So, Cheese sandwich weight is not proportional to its length

For Chicken salad sandwich proportion

$\frac{6}{\frac{3}{4}}=\frac{12}{\frac{7}{4}}\\8 \neq \frac{48}{7}$

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2 years ago

The greatest factor that two or more numbers have in common is the

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Answer:

"greatest common factor" (GCF) or "greatest common divisor" (GCD)

Step-by-step explanation:

Apparently, you're looking for the term that has the given definition. It is called the GCF or GCD, the "greatest common factor" or the "greatest common divisor."

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The GCF or GCD can be found a couple of ways. One way is to find the prime factors of the numbers involved, then identify the lowest power of each of the unique prime factors that are common to all numbers. The product of those numbers is the GCF.

<u>Example</u>:

GCF(6, 9)

can be found from the prime factors:

6 = 2·3
9 = 3²

The unique factors are 2 and 3. Only the factor 3 is common to both numbers, and its lowest power is 1. Thus ...

GCF(6, 9) = 3¹ = 3

Another way to find the GCD is to use Euclid's Algorithm. At each step of the algorithm, the largest number modulo the smallest number is found. If that is not zero, the largest number is replaced by the result, and the process repeated. If the result is zero, the smallest number is the GCD.

GCD(6, 9) = 9 mod 6 = 3 . . . . . (6 mod 3 = 0, so 3 is the GCD)

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