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3 years ago

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A triangle has side lengths of (1.3f+2.9g)(1.3f+2.9g) centimeters, (1.1f-7.7h)(1.1f−7.7h) centimeters, and (2.3h+1.5g)(2.3h+1.5g

) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?

1 answer:

VikaD [51]3 years ago

8 0

Answer:

Perimeter of the triangle = (2.4f+4.4g-5.4h) centimeters.

Step-by-step explanation:

It is given that, a triangle has side lengths of (1.3f+2.9g) cm, (1.1f-7.7h)cm, and (2.3h+1.5g) cm.

We have to find the expression which represents the perimeter, in centimeters, of the triangle.

Perimeter of a triangle = Sum of its all the sides.

$Perimeter=(1.3f+2.9g)+(1.1f-7.7h)+(2.3h+1.5g)$

On combining like terms, we get

$Perimeter=(1.3f+1.1f)+(2.9g+1.5g)+(-7.7h+2.3h)$

$Perimeter=2.4f+4.4g+(-5.4h)$

$Perimeter=2.4f+4.4g-5.4h$

Therefore, the perimeter of the triangle is (2.4f+4.4g-5.4h) centimeters.

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The perimeter of a triangle is 27 feet. One side is 3 feet longer than the shortest side, and the longest side is twice as long

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Answer:

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Step-by-step explanation:

Let s be the shortest side. Using the information you're given, you can create an equation. 27= s + s+3 + 2s. Now just solve the equation. Subtract 3 from both sides. 24=4s. Divide by 4 on both sides. 6=s. So the shortest side is 6 feet long, so we add 3 to that for the one that is neither the shortest or the longest. That side is 9 feet long. We double s to get 12, which is the longest side.

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3 years ago

Read 2 more answers

Use Gaussian elimination to write each system in triangular form

Feliz [49]

Answer:

To see the steps to the diagonal form see the step-by-step explanation. The solution to the system is $x = -\frac{1}{9}$ , $y= -\frac{1}{9}$ , $z= \frac{4}{9}$ and $w = \frac{7}{9}$

Step-by-step explanation:

Gauss elimination method consists in reducing the matrix to a upper triangular one by using three different types of row operations (this is why the method is also called row reduction method). The three elementary row operations are:

Swapping two rows
Multiplying a row by a nonzero number
Adding a multiple of one row to another row

To solve the system using the Gauss elimination method we need to write the augmented matrix of the system. For the given system, this matrix is:

$\left[\begin{array}{cccc|c}1 & 1 & 1 & 1 & 1 \\1 & 1 & 0 & -1 & -1 \\-1 & 1 & 1 & 2 & 2 \\1 & 2 & -1 & 1 & 0\end{array}\right]$

For this matrix we need to perform the following row operations:

$R_2 - 1 R_1 \rightarrow R_2$ (multiply 1 row by 1 and subtract it from 2 row)
$R_3 + 1 R_1 \rightarrow R_3$ (multiply 1 row by 1 and add it to 3 row)
$R_4 - 1 R_1 \rightarrow R_4$ (multiply 1 row by 1 and subtract it from 4 row)

$R_2 \leftrightarrow R_3$ (interchange the 2 and 3 rows)

$R_2 / 2 \rightarrow R_2$ (divide the 2 row by 2)
$R_1 - 1 R_2 \rightarrow R_1$ (multiply 2 row by 1 and subtract it from 1 row)
$R_4 - 1 R_2 \rightarrow R_4$ (multiply 2 row by 1 and subtract it from 4 row)
$R_3 \cdot ( -1) \rightarrow R_3$ (multiply the 3 row by -1)
$R_2 - 1 R_3 \rightarrow R_2$ (multiply 3 row by 1 and subtract it from 2 row)
$R_4 + 3 R_3 \rightarrow R_4$ (multiply 3 row by 3 and add it to 4 row)
$R_4 / 4.5 \rightarrow R_4$ (divide the 4 row by 4.5)

After this step, the system has an upper triangular form

The triangular matrix looks like:

$\left[\begin{array}{cccc|c}1 & 0 & 0 & -0.5 & -0.5 \\0 & 1 & 0 & -0.5 & -0.5\\0 & 0 & 1 & 2 & 2 \\0 & 0 & 0 & 1 & \frac{7}{9}\end{array}\right]$

If you later perform the following operations you can find the solution to the system.

$R_1 + 0.5 R_4 \rightarrow R_1$ (multiply 4 row by 0.5 and add it to 1 row)
$R_2 + 0.5 R_4 \rightarrow R_2$ (multiply 4 row by 0.5 and add it to 2 row)
$R_3 - 2 R_4 \rightarrow R_3$ (multiply 4 row by 2 and subtract it from 3 row)

After this operations, the matrix should look like:

$\left[\begin{array}{cccc|c}1 & 0 & 0 & 0 & -\frac{1}{9} \\0 & 1 & 0 & 0 & -\frac{1}{9}\\0 & 0 & 1 & 0 & \frac{4}{9} \\0 & 0 & 0 & 1 & \frac{7}{9}\end{array}\right]$

Thus, the solution is:

$x = -\frac{1}{9}$ , $y= -\frac{1}{9}$ , $z= \frac{4}{9}$ and $w = \frac{7}{9}$

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Explanation how solve step by step 2/7m-1/7=3/14

Drupady [299]

Answer:

m = 25/28

Step-by-step explanation:

It's best to enclose fractional coefficients inside parentheses to eliminate ambiquity: 2/7m-1/7=3/14 => (2/7(m - (1/7) = (3/14).

The LCD is 14; each of the denominators {7, 14} divides evenly into 14. Hence our equation becomes

(4)(m - 1/7) = 3

... after multiplying every term by 14.

Let's multiply each side by 7 to eliminate the remaining fraction:

4(7m - 1) = 21, or

28m - 4 = 21, or

28m = 25.

Hence, m = 25/28.

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4 years ago

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castortr0y [4]

Answer:

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Step-by-step explanation:

1. First, we need to find which digits √(113) is between, and that would be 10 and 11.

2. Okay, so √(113) is between 10 and 11, meaning 113 is between 100 and 121.

3. Since 113 is a little over half between 100 and 121, let's multiply 10.6 by 10.6 to see how close we are to 113:

$10.6 * 10.6$
$112.36$

4. 112.36 is pretty close to 113, therefore, the dot on the number-line should be placed at 10.6.

7 0

3 years ago