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3 years ago

What is the total cost of 0.5 pound of peaches selling for $0.80 per pound and 0.7 pound of oranges selling for $0.90 pet pound?

Mathematics

1 answer:

kari74 [83]3 years ago

3 0

The total cost for peaches is $0.40 you get that by (0.5)(0.80) as for oranges (0.7)(.90)=$0.63 so $0.40+$0.63=$1.03

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Is 2 , -5 a solution to this system equation 2x + 5y = -19, 6y - 8x = -54 .? Justify your answer

Andreas93 [3]

The easiest way to solve this problem is to put (2, -5) into both equations and see if it satisfies/works for both of them. 2 = x and -5 = y.

So for 2x + 5y = -19,
2(2) + 5(-5) = -19
4 - 25 = -19
-21 ≠ -19.

You can continue and try it out for 6y - 8x = -54
6(-5) - 8(2) = -54
-30 - 16 = -54
-46 ≠ -54

But since (2, -5) already doesn't work for one equation, it cannot be a solution to the system of equations.

3 0

3 years ago

Solve for x in the diagram below. 15 points :3

OLEGan [10]

Answer: x = 6

Step-by-step explanation:

We know that the angles combined are complementary, meaning they add up to 90 degrees.

Therefore, we can make this equation:

(x + 54) + 5x = 90

Then, combine like terms.

x + 54 + 5x = 90

6x + 54 = 90

Now, subtract the 54 from that side.

6x = 90 - 54

6x = 36

Next, divide!

$\frac{6x}{6}$ = $\frac{36}{6}$

x = 6

4 0

3 years ago

Trinity paid $3.50 in tax on a sweatshirt which cost $40. What tax rate does this represent???

kati45 [8]

Answer:

9% tax rate

Step-by-step explanation:

What you do is 3.50/40 and you will get .0875 which will equal

9% tax rate

3 0

3 years ago

7. A cylindrical tank can hold 2279.64 cubic feet of water. The radius of the tank is 11 feet. What is the height of the tank?

aliina [53]

Answer:

r = 8.12

Step-by-step explanation:

The volume for a cylinder is V=πr^2h therefore,

v = 2279.64

h = 11ft

r = ?

2279.64 = πr^2 * 11

$\frac{2279.64}{11}= {\pi r^2} \\$

207.24 = πr^2

$\frac{207.24}{\pi} =r^2\\\\66 = r^2\\\\\sqrt{66} = r\\\\\\8.12 = r$

3 0

2 years ago

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 $w = \frac{7}{9}$

7 0

3 years ago