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stealth61 [152]
2 years ago
15

What is 28 % as a fraction?

Mathematics
2 answers:
Aleksandr [31]2 years ago
8 0
28/100 And that can be simplified 14/50 to 7/25 So 7/25 is the most simplified version
IgorLugansk [536]2 years ago
5 0
The answer is 7/25 simplified and if you dont want it to be simplified, it is 28/100
You might be interested in
BRAINLIEST PLUS 30 POINTS
aleksklad [387]

umm I think it =(m)(x+−x)

=(m)(x)+(m)(−x)

=mx−mx

=0

hope it's right and you can download mathpapa

7 0
2 years ago
A shop sells fence panels with a wooden frame going all the way round each panel. The price of each panel is based on the area o
vagabundo [1.1K]

Answer:

a) Each 1m² of fence panel costs: £2

b) I metre of wooden frame costs: £1

Step-by-step explanation:

Let the price of 1 sq.m. of fence panel be x

Let the price of 1 m of wooden frame be y

In Fig 1

Length = 4 m

Breadth = 3 m

Area =Length \times breadth = 4 \times 3 = 12 sq.m.

Cost of 1 sq.m. = x

Cost of 12 sq.m. = 12x

Perimeter =2(l+b)=2(4+3)=14 m

Cost of 1 m of wooden frame = y

Cost of 14 m of wooden frame = 14y

We are given that total cost of framing and fencing is 38

So. 12x+14y=38 ----1

In Fig 2

Length = 6 m

Breadth = 2 m

Area =Length \times breadth = 6 \times 2 = 12 sq.m.

Cost of 1 sq.m. = x

Cost of 12 sq.m. = 12x

Perimeter =2(l+b)=2(6+2)=16 m

Cost of 1 m of wooden frame = y

Cost of 16 m of wooden frame = 16y

We are given that total cost of framing and fencing is 40

So. 12x+16y=40---2

Substitute the value of 12x form 1 in 2

38-14y+16y=40

2y=2

y=1

Substitute the value of y in 2

12x+16=40

12x=24

x=2

So, cost of 1 sq.m. of fence panel is 2 and cost of 1 m of wooden frame is 1

In fig 3

To verify :

Length = 3 m

Breadth = 5 m

Area = Length \times breadth = 3 \times 5 = 15 sq.m.

Cost of 1 sq.m. = 2

Cost of 12 sq.m. =15 \times 2 = 30

Perimeter =2(l+b)=2(3+5)=16 m

Cost of 1 m of wooden frame = 1

Cost of 16 m of wooden frame = 16

So, Total cost = 30+16=46

We are given that cost of fencing and framing is 46

Thus verified

Hence

a) Each 1m² of fence panel costs: £2

b) I metre of wooden frame costs: £1

5 0
3 years ago
Convert the given system of equations to matrix form
yuradex [85]

Answer:

The matrix form of the system of equations is \left[\begin{array}{ccccc}1&1&1&1&-3\\1&-1&-2&1&2\\2&0&1&-1&1\end{array}\right] \left[\begin{array}{c}x&y&w&z&u\end{array}\right] =\left[\begin{array}{c}5&4&3\end{array}\right]

The reduced row echelon form is \left[\begin{array}{ccccc|c}1&0&0&1/4&0&3\\0&1&0&9/4&-4&5\\0&0&1&-3/2&1&-3\end{array}\right]

The vector form of the general solution for this system is \left[\begin{array}{c}x&y&w&z&u\end{array}\right]=u\left[\begin{array}{c}-\frac{1}{6}&\frac{5}{2}&0&\frac{2}{3}&1\end{array}\right]+w\left[\begin{array}{c}-\frac{1}{6}&-\frac{3}{2}&1&\frac{2}{3}&0\end{array}\right]+\left[\begin{array}{c}\frac{5}{2}&\frac{1}{2}&0&2&0\end{array}\right]

Step-by-step explanation:

  • <em>Convert the given system of equations to matrix form</em>

We have the following system of linear equations:

x+y+w+z-3u=5\\x-y-2w+z+2u=4\\2x+w-z+u=3

To arrange this system in matrix form (Ax = b), we need the coefficient matrix (A), the variable matrix (x), and the constant matrix (b).

so

A= \left[\begin{array}{ccccc}1&1&1&1&-3\\1&-1&-2&1&2\\2&0&1&-1&1\end{array}\right]

x=\left[\begin{array}{c}x&y&w&z&u\end{array}\right]

b=\left[\begin{array}{c}5&4&3\end{array}\right]

  • <em>Use row operations to put the augmented matrix in echelon form.</em>

An augmented matrix for a system of equations is the matrix obtained by appending the columns of b to the right of those of A.

So for our system the augmented matrix is:

\left[\begin{array}{ccccc|c}1&1&1&1&-3&5\\1&-1&-2&1&2&4\\2&0&1&-1&1&3\end{array}\right]

To transform the augmented matrix to reduced row echelon form we need to follow this row operations:

  • add -1 times the 1st row to the 2nd row

\left[\begin{array}{ccccc|c}1&1&1&1&-3&5\\0&-2&-3&0&5&-1\\2&0&1&-1&1&3\end{array}\right]

  • add -2 times the 1st row to the 3rd row

\left[\begin{array}{ccccc|c}1&1&1&1&-3&5\\0&-2&-3&0&5&-1\\0&-2&-1&-3&7&-7\end{array}\right]

  • multiply the 2nd row by -1/2

\left[\begin{array}{ccccc|c}1&1&1&1&-3&5\\0&1&3/2&0&-5/2&1/2\\0&-2&-1&-3&7&-7\end{array}\right]

  • add 2 times the 2nd row to the 3rd row

\left[\begin{array}{ccccc|c}1&1&1&1&-3&5\\0&1&3/2&0&-5/2&1/2\\0&0&2&-3&2&-6\end{array}\right]

  • multiply the 3rd row by 1/2

\left[\begin{array}{ccccc|c}1&1&1&1&-3&5\\0&1&3/2&0&-5/2&1/2\\0&0&1&-3/2&1&-3\end{array}\right]

  • add -3/2 times the 3rd row to the 2nd row

\left[\begin{array}{ccccc|c}1&1&1&1&-3&5\\0&1&0&9/4&-4&5\\0&0&1&-3/2&1&-3\end{array}\right]

  • add -1 times the 3rd row to the 1st row

\left[\begin{array}{ccccc|c}1&1&0&5/2&-4&8\\0&1&0&9/4&-4&5\\0&0&1&-3/2&1&-3\end{array}\right]

  • add -1 times the 2nd row to the 1st row

\left[\begin{array}{ccccc|c}1&0&0&1/4&0&3\\0&1&0&9/4&-4&5\\0&0&1&-3/2&1&-3\end{array}\right]

  • <em>Find the solutions set and put in vector form.</em>

<u>Interpret the reduced row echelon form:</u>

The reduced row echelon form of the augmented matrix is

\left[\begin{array}{ccccc|c}1&0&0&1/4&0&3\\0&1&0&9/4&-4&5\\0&0&1&-3/2&1&-3\end{array}\right]

which corresponds to the system:

x+1/4\cdot z=3\\y+9/4\cdot z-4u=5\\w-3/2\cdot z+u=-3

We can solve for <em>z:</em>

<em>z=\frac{2}{3}(u+w+3)</em>

and replace this value into the other two equations

<em>x+1/4 \cdot (\frac{2}{3}(u+w+3))=3\\x=-\frac{u}{6} -\frac{w}{6}+\frac{5}{2}</em>

y+9/4 \cdot (\frac{2}{3}(u+w+3))-4u=5\\y=\frac{5u}{2}-\frac{3w}{2}+\frac{1}{2}

No equation of this system has a form zero = nonzero; Therefore, the system is consistent. The system has infinitely many solutions:

<em>x=-\frac{u}{6} -\frac{w}{6}+\frac{5}{2}\\y=\frac{5u}{2}-\frac{3w}{2}+\frac{1}{2}\\z=\frac{2u}{3}+\frac{2w}{3}+2</em>

where <em>u</em> and <em>w</em> are free variables.

We put all 5 variables into a column vector, in order, x,y,w,z,u

x=\left[\begin{array}{c}x&y&w&z&u\end{array}\right]=\left[\begin{array}{c}-\frac{u}{6} -\frac{w}{6}+\frac{5}{2}&\frac{5u}{2}-\frac{3w}{2}+\frac{1}{2}&w&\frac{2u}{3}+\frac{2w}{3}+2&u\end{array}\right]

Next we break it up into 3 vectors, the one with all u's, the one with all w's and the one with all constants:

\left[\begin{array}{c}-\frac{u}{6}&\frac{5u}{2}&0&\frac{2u}{3}&u\end{array}\right]+\left[\begin{array}{c}-\frac{w}{6}&-\frac{3w}{2}&w&\frac{2w}{3}&0\end{array}\right]+\left[\begin{array}{c}\frac{5}{2}&\frac{1}{2}&0&2&0\end{array}\right]

Next we factor <em>u</em> out of the first vector and <em>w</em> out of the second:

u\left[\begin{array}{c}-\frac{1}{6}&\frac{5}{2}&0&\frac{2}{3}&1\end{array}\right]+w\left[\begin{array}{c}-\frac{1}{6}&-\frac{3}{2}&1&\frac{2}{3}&0\end{array}\right]+\left[\begin{array}{c}\frac{5}{2}&\frac{1}{2}&0&2&0\end{array}\right]

The vector form of the general solution is

\left[\begin{array}{c}x&y&w&z&u\end{array}\right]=u\left[\begin{array}{c}-\frac{1}{6}&\frac{5}{2}&0&\frac{2}{3}&1\end{array}\right]+w\left[\begin{array}{c}-\frac{1}{6}&-\frac{3}{2}&1&\frac{2}{3}&0\end{array}\right]+\left[\begin{array}{c}\frac{5}{2}&\frac{1}{2}&0&2&0\end{array}\right]

7 0
3 years ago
Which statements about the area of the faces of the rectangular prism are true? Select all that apply.
LenaWriter [7]

Answer: The front face has an area of 30 ft2. , The top face has an area of 40 ft2. ,

Step-by-step explanation: SOrry if im wrong

5 0
2 years ago
What is the range of the function graphed below?
Xelga [282]
<h2>Answer:</h2>

Option: B is the correct answer.

The range of the function is:

        B.      5 < y < ∞

<h2>Step-by-step explanation:</h2>

Range of a function--

The range of a function is the set of all the values that is attained by the function.

By looking at the graph of the function we see that the function tends to 5 when x→ -∞ and the function tends to infinity when x →∞

Also, the function is a strictly increasing function.

This means that the function takes every real value between 5 and ∞ .

i.e. The range of the function is: (5,∞)

          Hence, the answer is:

                Option: B

8 0
3 years ago
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