Ask question

Ask question

All categories

3 years ago

9

Martin has a vegetable garden that is 8 feet long and 5 feet wide. Next year, Martin wants to increase both the length and width

of his vegetable garden by 15%. By what percent will the area of Martin’s vegetable garden increase with these changes?

1 answer:

KatRina [158]3 years ago

4 0

Answer:

9.2 feet long and 5.75 feet wide

You might be interested in

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

Find the value of X

olchik [2.2K]

<h3>Answer: 112</h3>

=========================================================

Explanation:

The angle adjacent to the 146 degree angle is 180-146 = 34 degrees.

In other words, the angles 34 and 146 combine to 180. These angles are supplementary.

The tickmarks on this triangle tell us it is isosceles. The angles opposite the congruent sides are congruent angles. So the unmarked interior angles (not marked x) are 34 degrees each.

Now use the fact that any triangle has its interior angles always add to 180

x+34+34 = 180

x+68 = 180

x = 180-68

x = 112

5 0

3 years ago

The value of the varriable which satisfies the equation is called the _______ of the equation

scoray [572]

Answer:

solution

Step-by-step explanation:

solution is the answer

3 0

3 years ago

Which graph represents the equation (x-3)^2 + y^2 =16

Goryan [66]

Answer:

C

Step-by-step

Correct on Edge

6 0

3 years ago

Read 2 more answers

Tony has $12 to buy apples and bananas for a fruit salad. Apples cost $2 per pound and bananas cost $1 per pound. Write and grap

choli [55]

Answer: 2a+b<18

Step-by-step explanation:

6 0

3 years ago