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Sholpan [36]
3 years ago
11

How do you do this?

Mathematics
1 answer:
ELEN [110]3 years ago
8 0
Use the Pythagorean Theorem: a² + b² = c².

a and b are the legs of the right triangle, and c is the hypotenuse.

2) 5² + b² = 6²
    25 + b² = 36
    b² = 11
    b = 3.3 cm

3) 7² + b² = 8²
    49 + b² = 64
    b² = 15
    b = 3.9 cm

4) a² + 5² = 13²
     a² + 25 = 169
     a² = 144
     a = 12 cm
You might be interested in
Ben rented a car. It cost $30.00 plus
Neporo4naja [7]

Answer:

2.83

Step-by-step explanation:

85 divided by 30 = 2.83

.25 times 2.83 = .70 cents

8 0
3 years ago
You have been asked to build a tree house with a floor that is twice as long as it is wide. You have only a certain amount of wo
Monica [59]

9514 1404 393

Answer:

  B. Draw a diagram.

Step-by-step explanation:

Most construction starts with a diagram.

_____

<em>Additional comment</em>

You may actually start by finding a pattern you like, then figuring the material required to construct the pattern, then working backward to determine the dimensions you need to use to stay within your material budget. You will probably draw a diagram at many points in the planning process.

4 0
2 years ago
WILL MARK AS BRAINLIEST FOR THESE QUESTIONS.
laiz [17]

1.

Let the sandwich be represented by = x

Let the drink be represented by = y

As given, Joe charges $10.00 for two sandwiches and one drink, so equation becomes 2x+y=10    ....(i)

He charges $6.50 for one sandwich and one drink, so equation becomes x+y=6.50  ....(ii)

Subtracting (ii) from (i) we get

x=3.50

And as x+y=6.50

y=6.50-3.50=3.00

Hence, cost of a sandwich is $3.50 and a drink is $3.00

2.

the question is incomplete. coordinates are missing

3.

Let x represent the number of performances

cost = 8000+300x

revenue = 700x

To break even, the cost must be equal to the revenue.

8000+300x=700x

400x=8000

so x=20

Hence, 20 performances are needed to break even.

4.

Let us take x for 20% material, y for 50% material

\frac{20x+50y}{200}=30

20x+50y=6000    ......... (1)

Accounting for volumes to use, x+y=200 or x=200-y ................ (2)

Putting the value of x in (1)

20(200-y)+50y=6000

4000-20y+50y=6000

4000+30y=6000

30y=2000

y=66.67

x=200-y = 200-66.67 =133.33

Hence, 133.33 ml of 20% acetic acid and 66.67% of 50% acetic acid is needed.





3 0
4 years ago
Solve the system of equations by finding the reduced row-echelon form of the augmented matrix for the system of equations.
Anuta_ua [19.1K]

Answer:

c

Step-by-step explanation:

First, we can transform this into a matrix. The x coefficients will be the first ones for each row, the y coefficients the second column, etc.

\left[\begin{array}{cccc}1&-2&3&-2\\6&2&2&-48\\1&4&3&-38\end{array}\right]

Next, we can define a reduced row echelon form matrix as follows:

With the leading entry being the first non zero number in the first row, the leading entry in each row must be 1. Next, there must only be 0s above and below the leading entry. After that, the leading entry of a row must be to the left of the leading entry of the next row. Finally, rows with all zeros should be at the bottom of the matrix.

Because there are 3 rows and we want to solve for 3 variables, making the desired matrix of form

\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right] for the first three rows and columns. This would make the equation translate to

x= something

y= something

z = something, making it easy to solve for x, y, and z.

Going back to our matrix,

\left[\begin{array}{cccc}1&-2&3&-2\\6&2&2&-48\\1&4&3&-38\end{array}\right] ,

we can start by removing the nonzero values from the first column for rows 2 and 3 to reach the first column of the desired matrix. We can do this by multiplying the first row by -6 and adding it to the second row, as well as multiplying the first row by -1 and adding it to the third row. This results in

\left[\begin{array}{cccc}1&-2&3&-2\\0&14&-16&-36\\0&6&0&-36\end{array}\right]

as our matrix. * Next, we can reach the second column of our desired matrix by first multiplying the second row by (2/14) and adding it to the first row as well as multiplying the second row by (-6/14) and adding it to the third row. This eliminates the nonzero values from all rows in the second column except for the second row. This results in

\left[\begin{array}{cccc}1&0&10/14&-100/14\\0&14&-16&-36\\0&0&96/14&-288/14\end{array}\right]

After that, to reach the desired second column, we can divide the second row by 14, resulting in

\left[\begin{array}{cccc}1&0&10/14&-100/14\\0&1&-16/14&-36/14\\0&0&96/14&-288/14\end{array}\right]

Finally, to remove the zeros from all rows in the third column outside of the third row, we can multiply the third row by (16/96) and adding it to the second row as well as multiplying the third row by (-10/96) and adding it to the first row. This results in

\left[\begin{array}{cccc}1&0&0&-5\\0&1&0&-6\\0&0&96/14&-288/14\end{array}\right]

We can then divide the third row by -96/14 to reach the desired third column, making the reduced row echelon form of the matrix

\left[\begin{array}{cccc}1&0&0&-5\\0&1&0&-6\\0&0&1&-3\end{array}\right]

Therefore,

x=-5

y=-6

z=-3

* we could also switch the second and third rows here to make the process a little simpler

3 0
3 years ago
Out of 350 students, 315 went
larisa [96]

Answer:

350-315=35

(35÷350)×100

=10%

7 0
3 years ago
Read 2 more answers
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