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3 years ago

9

The vertices of a rectangle are given in the columns of the matrix R=[0 0 3 3 0 3 3 0]. If [-1 0 0 1]x R is found to perform a t

ransformation, what are the coordinates of the transformed rectangle?
(0, 0), (0, -3), (-3, -3), (-3,0)
(0,0), (0, 3), (3, 3), (3,0)
(0,0), (0, 3), (-3, -3), (-3,0)
(0,0), (0, 3), (-3, 3), (-3,0)

1 answer:

krok68 [10]3 years ago

7 0

Answer:

(0,0), (0, 3), (-3, 3), (-3,0)

Step-by-step explanation:

The matrix multiplication is shown in the attachment. The transformed coordinates are ...

(0,0), (0, 3), (-3, 3), (-3,0)

_____

You can count the instances of -3 in the result matrix to choose the correct answer.

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What is the range of the equation

a_sh-v [17]

The range of the equation is $y>2$

Explanation:

The given equation is $y=2(4)^{x+3}+2$

We need to determine the range of the equation.

<u>Range:</u>

The range of the function is the set of all dependent y - values for which the function is well defined.

Let us simplify the equation.

Thus, we have;

$y=2 \cdot 4^{x+3}+2$

This can be written as $y=2^{1+2(x+3)}+2$

Now, we shall determine the range.

Let us interchange the variables x and y.

Thus, we have;

$x=2^{1+2(y+3)}+2$

Solving for y, we get;

$x-2=2^{1+2(y+3)}$

Applying the log rule, if f(x) = g(x) then $\ln (f(x))=\ln (g(x))$ , then, we get;

$\ln \left(2^{1+2(y+3)}\right)=\ln (x-2)$

Simplifying, we get;

$(1+2(y+3)) \ln (2)=\ln (x-2)$

Dividing both sides by $\ln (2)$ , we have;

$2 y+7=\frac{\ln (x-2)}{\ln (2)}$

Subtracting 7 from both sides of the equation, we have;

$2 y=\frac{\ln (x-2)}{\ln (2)}-7$

Dividing both sides by 2, we get;

$y=\frac{\ln (x-2)-7 \ln (2)}{2 \ln (2)}$

Let us find the positive values for logs.

Thus, we have,;

$x-2>0$

$x>2$

The function domain is $x>2$

By combining the intervals, the range becomes $y>2$

Hence, the range of the equation is $y>2$

7 0

3 years ago

Old McDonald had a farm. In one pen the old farmer had chickens and bulls together. In that pen there were 40 animals in total,

SVETLANKA909090 [29]

Answer:

There are 15 numbers of chicken and 25 numbers of bulls.

Step-by-step explanation:

The pen had chickens and bulls. The pen contains 40 animals in total. The number of legs in the pen is 130 .

Let

a = number of chicken

b = number of bull

a + b = 40................(i)

A chicken has 2 legs and a bull has 4 legs.

The total legs can be represented as

2a + 4b = 130...........(ii)

combine the equation

a + b = 40................(i)

2a + 4b = 130...........(ii)

a = 40 - b

insert the value of a in equation(ii)

2(40 - b) + 4b = 130

80 - 2b + 4b = 130

80 + 2b = 130

2b = 130 - 80

2b = 50

divide both sides by 2

b = 50/2

b = 25

Insert the value of b in equation (i)

a + b = 40

a + 25 = 40

a = 40 - 25

a = 15

There are 15 numbers of chicken and 25 numbers of bulls.

8 0

3 years ago

20 is what percent of 32 <br> Write as an equation

AlladinOne [14]

20% of 32= 6.4

20% x 32

20 /100 x 32
Reduce the fraction
1 /5× 32
=32/5
=6.4

8 0

3 years ago

In a carnival game, a person wagers $2 on the roll of two dice. if the total of the two dice is 2, 3, 4, 5, or 6 then the pe

Olin [163]

Answer: a loss of 4 cents

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

The probability of rolling a sum of 2, 3, 4, 5, or 6 is $\dfrac{15}{36}$ which earns $2.00

The probability of rolling a sum of 28, 9, 10, 11, or 12 is $\dfrac{15}{36}$ which loses $2.00

The probability of rolling a sum of 7 is $\dfrac{6}{36}$ which loses $0.25

$\bigg(\dfrac{15}{36}\times \$2.00\bigg)+\bigg(\dfrac{15}{36}\times -\$2.00\bigg)+\bigg(\dfrac{6}{36}\times -\$0.25\bigg)=\boxed{-\$0.04}$

6 0

3 years ago

Solve 5x+7 > 17.<br> {x1x<2}<br> O {XIX> 2}<br> O {xIx>-2}<br> O {x1x < -2}

fgiga [73]

Answer:

The answer is $x > 2$

Step-by-step explanation:

to solve this inequality:

$5x+7 > 17$

Put "-7" on both sides

$5x+10$

divide by 5 on both sides

your answer should be 2.

8 0

2 years ago