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Vanessa uses the expressions (3x2 + 5x + 10) and (x2 – 3x – 1) to represent the length and width of her patio. Which expression

Brut [27]

The area of rectangle with length l and width w is

$A=l\cdot w.$

If the length of rectangle is expressed as $l=3x^2 + 5x + 10$ and the width of rectangle is expressed as $w=x^2-3x-1$ , then the area of rectangle is

$A=(3x^2 + 5x + 10)(x^2-3x-1)=3x^4-4x^3-8x^2-35x-10.$

8 0

3 years ago

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Solve 7r+ 2 = 5(r – 4)

AveGali [126]

Multiply the bracket by 5

I used PEMDAS

P= parenthesis

E= exponents

M=multiplication

D= division

A= addition

S= subtraction

7r+2= 5(r-4)

7r+2= 5r-20

Move 5r to the left hand side . Positive 5r changes to negative 5r

7r-5r+2= 5r-5r-20

2r+2=- 20

2r+2-2= -20-2

Move positive 2 to the right hand side. Changes to negative -2

2r+2-2= -20-2

2r= -22

Divide by 2 for 2r and -22

2r/2= -22/2

r= -11

Answer is r= -11

6 0

3 years ago

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let t : r2 →r2 be the linear transformation that reflects vectors over the y−axis. a) geometrically (that is without computing a

tangare [24]

(a) ( 1, 0 ) is the eigen vector for '-1' and ( 0, 1 ) is the eigen vector for '1'.

(b) two eigen values of 'k' = 1, -1

for k = 1, eigen vector is $\left[\begin{array}{c}0\\1\end{array}\right]$

for k = -1 eigen vector is $\left[\begin{array}{c}1\\0\end{array}\right]$

See the figure for the graph:

(a) for any (x, y) ∈ R² the reflection of (x, y) over the y - axis is ( -x, y )

∴ x → -x hence '-1' is the eigen value.

∴ y → y hence '1' is the eigen value.

also, ( 1, 0 ) → -1 ( 1, 0 ) so ( 1, 0 ) is the eigen vector for '-1'.

( 0, 1 ) → 1 ( 0, 1 ) so ( 0, 1 ) is the eigen vector for '1'.

(b) ∵ T(x, y) = (-x, y)

T(x) = -x = (-1)(x) + 0(y)

T(y) = y = 0(x) + 1(y)

Matrix Representation of $T = \left[\begin{array}{cc}-1&0\\0&1\end{array}\right]$

now, eigen value of 'T'

$T - kI = \left[\begin{array}{cc}-1-k&0\\0&1-k\end{array}\right]$

after solving the determinant,

we get two eigen values of 'k' = 1, -1

for k = 1, eigen vector is $\left[\begin{array}{c}0\\1\end{array}\right]$

for k = -1 eigen vector is $\left[\begin{array}{c}1\\0\end{array}\right]$

Hence,

(a) ( 1, 0 ) is the eigen vector for '-1' and ( 0, 1 ) is the eigen vector for '1'.

(b) two eigen values of 'k' = 1, -1

for k = 1, eigen vector is $\left[\begin{array}{c}0\\1\end{array}\right]$

for k = -1 eigen vector is $\left[\begin{array}{c}1\\0\end{array}\right]$

Learn more about " Matrix and Eigen Values, Vector " from here: brainly.com/question/13050052

#SPJ4

6 0

1 year ago

A dresser contains six pairs of shorts one each in the colors, red, black, blue, green, khaki, and gray. The dresser also contai

marissa [1.9K]

Answer: 1/24

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Work Shown:

A = selects green pair of shorts
B = selects gray t-shirt

P(A) = probability of selecting green shorts
P(A) = (number of green shorts)/(number of shorts total)
P(A) = 1/6
P(B) = probability of selecting gray t-shirt
P(B) = (number of gray t-shirts)/(number of t-shirts total)
P(B) = 1/4

P(A and B) = probability of selecting green shorts AND gray t-shirt
P(A and B) = P(A)*P(B) ... since A and B are independent events
P(A and B) = (1/6)*(1/4)
P(A and B) = (1*1)/(6*4)
P(A and B) = 1/24

Note: The fraction 1/24 is approximately equal to 0.041667

5 0

3 years ago

Calculate the partial sum S for the sequence 243,81,27,....

Llana [10]

Answer:363

Step-by-step explanation:

We have to find partial sum for the sequence 243 , 81 , 27 ..... up to 5 terms(S5 given)

The sequence actually is 3^5,3^4.,3^3.....

Therefore first 5 terms are 1) 3^5 I.e. 243

2) 3^4 I.e. 81

3) 3^3 I.e. 27

4)) 3^2 I.e. 9

5) 3^1 I.e. 3

Adding all those no. we get partial sum of first 5 no. of the sequence

So, 243 + 81 + 27 + 9 + 3

= 363

Hope it helps!!!

4 0

3 years ago

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