All categories

3 years ago

Help please!!!

Mathematics

1 answer:

Maslowich3 years ago

6 0

y varies directly with x.

The constant of variation is k = 7

Step-by-step explanation:

We have to check whether both vary directly with each other or not.

Every pair of x and y will be considered one by one

If y varies directly with x, it should satisfy y = kx or k = yx

So,

For x= -2, y=-14

$-14 = -2k\\k = \frac{-14}{-2}\\k = 7$

For

x=3, y=21

$21 = 3k\\ k = \frac{21}{3}\\k = 7$

For

x=5, y=35

$35 = 5k\\ k = \frac{35}{5}\\k = 7$

As k is same for all pairs of x and y, it can be concluded that:

y varies directly with x.

The constant of variation is k = 7

Keywords: Proportion, variation

Learn more about proportion at:

#LearnwithBrainly

You might be interested in

Ali was swimming along the bottom of his backyard pool at a depth of 6 feet then he pushed off the bottom and rose 4 feet what i

olga nikolaevna [1]

Answer:

2 feets

Step-by-step explanation:

Given that :

Alli's Initial depth = 6 feets

Number of feets in which Alli rose = 4 feets

Alli's new position relative to the surface of the pool:

Difference of Alli's initial depth and feets risen :

6 feets - 4 feets = 2 feets

Hence, Alli is now 2 feets below the surface of the pool.

7 0

3 years ago

What is the value of x in the equation below? -3-(-8)-(-2) = x O-13 O9 O 3 O 7

posledela

Answer:

Step-by-step explanation:

4 0

3 years ago

If you use the addition property of equality , what number would you add to both sides of the equal sign to isolate the variable

kkurt [141]

Answer:

The answer is " $\frac{26}{7}$ "

Step-by-step explanation:

The whole question can be found in the file attached.

$\to x + \frac{5}{7} = \frac{31}{7}\\\\$

Subtracting the $\frac{5}{7}$ from both sides of the equations:

$\to x +\frac{5}{7} - \frac{5}{7} = \frac{31}{7} - \frac{5}{7} \\\\$

$= \frac{31-5}{7} \\\\= \frac{26}{7} \\\\$

5 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

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

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

Applying the coordinates 2,6 and -2 to the basis E we obtain

$2+6t-2t^{2}$

That was the original result of T[e1(t)]

8 0

3 years ago

Molly ordered 12 t-shirts for 14.00 and Teena ordered 23 t-shirts for 14.00 how much did they spend in all? Use the distributive

Cerrena [4.2K]

All together they spent 490

3 0

3 years ago