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3 years ago

Explain I don’t understand

Mathematics

1 answer:

Serggg [28]3 years ago

7 0

So just divide 100 by 25 which equals 4 then divide 120 by 30 which also equals to 4 and if the rest equal 4 then its proportional (1)
And then same for 2 and 3 just divided the bottom by the top and if they all get the same answer they are proportion and if one is not the same then it’s not

For the grids if the dots are line diagonally straight and it starts at the 0 then it’s proportional if not then it’s not

Hope this helps :)

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In an examination 80% students passed. if 15 less have appeared and 10 less have passed, the ratio of passers to failures would

Nina [5.8K]

Answer:

60 students passed, and 75 appeared in examination.

Step-by-step explanation:

Let's say s is the total number of students and p is the number of students who passed.

80% of the students passed, so:

0.8 s = p

If there were 10 less passers, and 15 less students (5 less failures), then the ratio of passers to failures would be 5/1.

(p − 10) / (s − p − 5) = 5 / 1

Simplify the second equation:

p − 10 = 5 (s − p − 5)

p − 10 = 5s − 5p − 25

6p = 5s − 15

Substitute the first equation.

6 (0.8 s) = 5s − 15

4.8 s = 5s − 15

0.2 s = 15

s = 75

p = 0.8 s

p = 60

60 students passed, and 75 appeared in examination.

5 0

3 years ago

Blaize is filling a 20,000-gallon swimming pool. If 7040 gallons have already been filled, and the water is entering the pool at

Svetlanka [38]

We can start with subtracting 7040 from 20,000, getting us 12960 gallons remaining, If 720 gallons per hour are coming, we can make the equation 12960 = 720h, with h as hours. Next, we can divide both sides by 720, getting us 18. It will take 18 hours to fill the pool.

3 0

3 years ago

Consider the linear transformation T from V = P2 to W = P2 given by T(a0 + a1t + a2t2) = (2a0 + 3a1 + 3a2) + (6a0 + 4a1 + 4a2)t

Svet_ta [14]

Answer:

$[T]EE=\left[\begin{array}{ccc}2&3&3\\6&4&4\\-2&3&4\end{array}\right]$

Step-by-step explanation:

First we start by finding the dimension of the matrix [T]EE

The dimension is : Dim (W) x Dim (V) = 3 x 3

Because the dimension of P2 is the number of vectors in any basis of P2 and that number is 3

Then, we are looking for a 3 x 3 matrix.

To find [T]EE we must transform the vectors of the basis E and then that result express it in terms of basis E using coordinates and putting them into columns. The order in which we transform the vectors of basis E is very important.

The first vector of basis E is e1(t) = 1

We calculate T[e1(t)] = T(1)

In the equation : 1 = a0

$T(1)=(2.1+3.0+3.0)+(6.1+4.0+4.0)t+(-2.1+3.0+4.0)t^{2}=2+6t-2t^{2}$

$[T(e1)]E=\left[\begin{array}{c}2&6&-2\\\end{array}\right]$

And that is the first column of [T]EE

The second vector of basis E is e2(t) = t

We calculate T[e2(t)] = T(t)

in the equation : 1 = a1

$T(t)=(2.0+3.1+3.0)+(6.0+4.1+4.0)t+(-2.0+3.1+4.0)t^{2}=3+4t+3t^{2}$

$[T(e2)]E=\left[\begin{array}{c}3&4&3\\\end{array}\right]$

Finally, the third vector of basis E is $e3(t)=t^{2}$

$T[e3(t)]=T(t^{2})$

in the equation : a2 = 1

$T(t^{2})=(2.0+3.0+3.1)+(6.0+4.0+4.1)t+(-2.0+3.0+4.1)t^{2}=3+4t+4t^{2}$

Then

$[T(t^{2})]E=\left[\begin{array}{c}3&4&4\\\end{array}\right]$

And that is the third column of [T]EE

Let's write our matrix

$[T]EE=\left[\begin{array}{ccc}2&3&3\\6&4&4\\-2&3&4\end{array}\right]$

T(X) = AX

Where T(X) is to apply the transformation T to a vector of P2,A is the matrix [T]EE and X is the vector of coordinates in basis E of a vector from P2

For example, if X is the vector of coordinates from e1(t) = 1

$X=\left[\begin{array}{c}1&0&0\\\end{array}\right]$

$AX=\left[\begin{array}{ccc}2&3&3\\6&4&4\\-2&3&4\end{array}\right]\left[\begin{array}{c}1&0&0\\\end{array}\right]=\left[\begin{array}{c}2&6&-2\\\end{array}\right]$