Given the function: f(x)=−(x−3)2+3. Describe the transformations in the order in which they occur.

Answer:

range is the y part and domain is the x so the range is the y coordinates

-6,-3,-2,-2,1,4

Step-by-step explanation:

If these vectors are to be linearly independent, then there exists some not-all-zero choice for scalars [tex]c_1,c_2,c_3,c_4[/tex] such that

[tex]c_1(1,1,0,-1) + c_2(1,k,1,1) + c_3(5,1,k,1) + c_4(-1,1,1,k) = (0,0,0,0)[/tex]

We can recast this as a system of linear equations,

[tex]\begin{bmatrix}1&1&5&-1\\1&k&1&1\\0&1&k&1\\-1&1&1&k\end{bmatrix}\begin{bmatrix}c_1\\c_2\\c_3\\c_4\end{bmatrix} = \begin{bmatrix}0\\0\\0\\0\end{bmatrix}[/tex]

This system has a solution if the coefficient matrix on the left side is not singular. So we attempt to find k such that it *is* singular, i.e. the determinant is zero:

• A cofactor expansion along the first column gives

[tex]\begin{vmatrix}1&1&5&-1\\1&k&1&1\\0&1&k&1\\-1&1&1&k\end{vmatrix} = \begin{vmatrix}k&1&1\\1&k&1\\1&1&k\end{vmatrix} - \begin{vmatrix}1&5&-1\\1&k&1\\1&1&k\end{vmatrix} + \begin{vmatrix}1&5&-1\\k&1&1\\1&k&1\end{vmatrix}[/tex]

• Cofactor expansions along the first columns of the remaining 3x3 matrices give

[tex]\begin{vmatrix}k&1&1\\1&k&1\\1&1&k\end{vmatrix} = k \begin{vmatrix}k&1\\1&k\end{vmatrix} - \begin{vmatrix}1&1\\1&k\end{vmatrix} + \begin{vmatrix}1&1\\k&1\end{vmatrix} = k^3-3k+2[/tex]

[tex]\begin{vmatrix}1&5&-1\\1&k&1\\1&1&k\end{vmatrix} = \begin{vmatrix}k&1\\1&k\end{vmatrix} - \begin{vmatrix}5&-1\\1&k\end{vmatrix} + \begin{vmatrix}5&-1\\k&1\end{vmatrix} = k^2-4k+3[/tex]

[tex]\begin{vmatrix}1&5&-1\\k&1&1\\1&k&1\end{vmatrix} = \begin{vmatrix}1&1\\k&1\end{vmatrix} - \begin{vmatrix}5&-1\\k&1\end{vmatrix} + \begin{vmatrix}5&-1\\1&1\end{vmatrix} = -k^2 - 6k + 7[/tex]

It follows that

[tex]\begin{vmatrix}1&1&5&-1\\1&k&1&1\\0&1&k&1\\-1&1&1&k\end{vmatrix} = (k^3-3k+2) - (k^2-4k+3) + (-k^2 - 6k + 7) \\\\ \begin{vmatrix}\cdots\end{vmatrix} = k^3 - 2k^2 - 5k + 6 = (k-3)(k-1)(k+2)[/tex]

which makes the coefficient matrix singular if k = 3, k = 1, or k = -2.

Then the four vectors are linearly independent for

[tex]\left\{ k\in\mathbb R \mid k\not\in\{-2,1,3\}\right\}[/tex]

Answer:

hope it is helpful

Step-by-step explanation:

68,020-

6= 60,000

8= 8,000

0=0

2= 20

0=0

Multiply the amount owed by 20% by changing the percent to a decimal.

20% = 0.20

200 x 0.20 = 40

The late fee is $40

Answer:

Step-by-step explanation:

A function can be defined as two variables (independent and dependent) which cannot have more than one output for each input.

Step-by-step explanation:

1. the first mapping is a function

2. the second mapping is not a function, because: B has 2 relations, C & E have no relations.

3. the third mapping is a function

4. the fourth mapping is not a function, because B has no relation.

Answer:

R(-1,-9) But I know if the answer is correct or not

Step-by-step explanation:

Answer:

153.86 ft^2

Step-by-step explanation:

π=3.14

r=7ft

πr^2=3.14*7*7

=153.86 ft^2

Area of circle = π r²

Here , We have

Area of circle = 3.14 × (7)²

Area of circle = 3.14 × 49 ft²

Area of circle = 153.86 ft²

Answer:

The equation is

[tex]{ \underline{ \sf{y = - 2 {e}^{ - 2x} + 7 }}}[/tex]

Step-by-step explanation:

[tex]{ \sf{ {e}^{2x} \frac{dy}{dx} = 1}} \\ \\ { \sf{dy = {e}^{ - 2x} dx}}[/tex]

integrate:

[tex]{ \sf{ \int dy = \int { - e}^{2x} dx}} \\ { \sf{y = - 2 {e}^{ - 2x} + c}}[/tex]

c is a constant.

when y is 5, x is 0:

[tex]{ \sf{y = { - 2e}^{ - 2x} + c}} \\ { \sf{5 = - 2 {e}^{( - 2 \times 0)} + c }} \\ { \sf{5 = - 2 {e}^{0} + c }} \\ { \sf{5 = ( - 2 \times 1) + c}} \\ { \sf{5 = - 2 + c}} \\ { \sf{c = 7}}[/tex]

therefore, equation:

[tex]y = - 2 {e}^{ - 2x} + 7[/tex]

Answer:

1. (-∞ , -10]

2. [0, ∞ )

3. [12.566, 4.242]

4. [15, 50]

5. (-∞ , 5]

6. [18, ∞)

Step-by-step explanation:

Answer:

1. The set of all numbers less than negative ten.

2. The set of all positive real numbers.

3. The set of all numbers less than 4.242 and greater than 12.566.

4. The set of all numbers that are greater than 15 and less than 50.

5. The set of all numbers that are at most 5.

6. The set of all numbers that are at least 18.

Answer:

-11 - z

(-11) - (-11)

= 0

I hope I have helped.

Answer:

33.33%

Step-by-step explanation:

Decrease in price= Original price -- New price

= $6 - $4

= $2

Percentage decrease= $2÷$6 × 100

= 33.33%

Answer:

1000

Step-by-step explanation:

10³

= 1000

Answer:

10 * 10 * 10

Step-by-step explanation:

Cubing a number just means you are multiplying that number 3 times to itself. Since we have 10^3, we multiply 10 to itself three times.

Best of Luck!

Answers:

The coordinates of the vertices are

These coordinates are from the red points shown in the diagram below.

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

Explanation:

Because the center of dilation is at the origin, we'll multiply each coordinate of each point by the scale factor.

Specifically, we'll double the coordinate values since the scale factor is 2.

and so on

The diagram is shown below. The original preimage is in blue while the dilated enlarged image is in red. Your teacher only wants the location of the red corner points.

9514 1404 393

Answer:

  √8

Step-by-step explanation:

8 is between 2² = 4 and 3² = 9. 12 is not.

√8 falls between 2 and 3.

__

Your calculator can help with this.

  √8 ≈ 2.828 . . . . . between 2 and 3

  √12 ≈ 3.464 . . . . not between 2 and 3 (between 3 and 4)

Answer:

-33

Step-by-step explanation:

this math equation looks relatively simple so i assume the actual equation is -2/3x - 8 = 14

add 8

-2/3x =22

multiply by -3/2

answer is -33

Answer:

a = 5, b = - 13

Step-by-step explanation:

The Remainder theorem states that the remainder when f(x) is divided by (x - a) is equal to f(a)

Thus the remainder for division by (x + 2) is zero , then by substituting x = - 2 into the expression.

2(- 2)³ + a(- 2)² + b(- 2) - 30 = 0

2(- 8) + 4a - 2b - 30 = 0

- 16 + 4a - 2b - 30 = 0

- 46 + 4a - 2b = 0 ( add 46 to both sides )

4a - 2b = 46 → (1)

----------------------------------------------------

Similarly when f(x) is divided by (cx - a) the remainder is f([tex]\frac{c}{a}[/tex] )

The remainder on dividing by (2x - 1) is - 35, then by substituting x = [tex]\frac{1}{2}[/tex]

2([tex]\frac{1}{2}[/tex] )³ + a([tex]\frac{1}{2}[/tex] )² + [tex]\frac{1}{2}[/tex] b - 30 = - 35

2([tex]\frac{1}{8}[/tex] ) + [tex]\frac{1}{4}[/tex] a + [tex]\frac{1}{2}[/tex] b - 30 = - 35 ( add 30 to both sides )

[tex]\frac{1}{4}[/tex] + [tex]\frac{1}{4}[/tex] a + [tex]\frac{1}{2}[/tex] b = - 5 ( multiply through by 4 to clear the fractions )

1 + a + 2b = - 20 ( subtract 1 from both sides )

a + 2b = - 21 → (2)

Solve (1) and (2) simultaneously )

Add (1) and (2) term by term to eliminate b

5a = 25 ( divide both sides by 5 )

a = 5

Substitute a = 5 into (2)

5 + 2b = - 21 ( subtract 5 from both sides )

2b = - 26 ( divide both sides by 2 )

b = - 13

According to the remainder theorem, when a polynomial P(x) is divided by (x-t) then the remainder of the division is equal to P(t). The value of a and b are 5 and -13, respectively.

According to the remainder theorem, when a polynomial P(x) is divided by (x-t) then the remainder of the division is equal to P(t). If P(t)=0, then the (x-t) is the factor of the polynomial.

Using the remainder theorem we can write,

f(x) = 2x³+ ax² + bx - 30

f(-2) = 2(-2)³ + a(-2)² + b(-2) - 30 = 0

-16 + 4a - 2b - 30 = 0

4a - 2b = 46   ........ equation 1

f(x) = 2x³+ ax² + bx - 30

f(1/2) = 2(1/2)³ + a(1/2)² + b(1/2) - 30 = -35

(1/4) + a(1/4) + b(1/2) = -35 + 30

(1+a+2b)/4 = -5

1 + a + 2b = -5 × 4

a + 2b = -21   .......... equation 2

Adding the two equations,

4a + 2b + a - 2b = 46 - 21

5a = 25

a = 25/5

a = 5

Substitute the value of a in any one of the equation,

a + 2b = -21

5 + 2b = -21

2b = -21 - 5

2b = -26

b = -26/2

b = -13

Hence, the value of a and b are 5 and -13, respectively.

Learn more about the Remainder Theorem here:

https://brainly.com/question/13264870

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Step-by-step explanation:

[tex] \frac{ \frac{8}{9} }{ - 4} \\ \frac{8}{9} \times \frac{1}{ - 4} \\ \frac{8 \times 1}{9 \times - 4} \\ \frac{8}{ - 36} \\ \frac{2}{ - 9} \\ - 0.22[/tex]

Answer:

B. [tex] - \frac{2}{9} [/tex] (second option)

Step-by-step explanation:

[tex] \frac{ \frac{8}{9} }{ - 4} [/tex]

[tex] \frac{8}{9} \div 4 = \frac{8}{9} \times \frac{1}{4} [/tex]

[tex] \frac{8 \times 1}{9 \times 4} = \frac{8}{9 \times 4} [/tex]

[tex] - \frac{2}{9} [/tex] ✅

Answer:

10

Step-by-step explanation:

It 10 bucks each ticket

Answer:

R = V/I

Step-by-step explanation:

I = V/R

Multiply both sides by r

IR = V

Divide both sides by I

R = V/I

Ex:

2 = 6/3

3 = 6/2

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Step-by-step explanation:

solution :

cost of 18 drinks (is)=52

Answer: x=41

Step-by-step explanation:

Let x be the number missing

Given expression

x - 14 = 9 × 3

Simplify by multiplication

x - 14 = 27

Add 14 on both sides

x - 14 + 14 = 27 + 14

[tex]\boxed {x=41}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Step-by-step explanation:

[tex]x - 14 = 9 \times 3 \\ x - 14 = 27 \\ x = 27 + 14 \\ x = 41 \\ thank \: you[/tex]

Answer:

8 tickets

Step-by-step explanation:

To find how many tickets he bought, we can divide.

66 / 8.25 = 8

Best of Luck!

Answer:

8

Step-by-step explanation:

66 divided by 8.25, bringing it to 8.

Answer:

Step-by-step explanation:

There are many ways this could be done, but the simplest way is to divide 18 into 72. That gives 4. So each plot is 4 * 20 = 80 m^2

If you are willing to use fractions, the answer could be 20*72 / 18 = 8 * 10  which is more feasible and still gives 80, but the land may not permit it. However math will.

It's hard to give an exact answer when it is this open ended.

Answer:

1.3

Step-by-step explanation:

I guess it's 1.8 - 0.5

Answer:

to find midpoint add both"X" coordinates and divide by 2

also add "Y" coordinates and divide by 2

then for line of segment use distance formula which is D=√[(x2-x1)²+(y2-y1)²]

Midpoint is the average of x and y coordinates of the endpoint while the length of a line segment is given by the formula [tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex].

A line section that can connect two places is referred to as a segment.

In other words, a line segment is just part of a big line that is straight and going unlimited in both directions.

The line is here! It extends endlessly in both directions and has no beginning or conclusion.

To determine the midpoint of two coordinates (x₁,y₁) and (x₂,y₂ )

Midpoint = [ (x₁ + x₂)/2 + (y₁ + y₂)/2 ]

The distance between two points (x₁,y₁) and (x₂,y₂ )

[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]

Hence "Midpoint is the average of x and y coordinates of the endpoint while the length of a line segment is given by the formula [tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]".

For more about line segment,

https://brainly.com/question/25727583

#SPJ2

Answer:

6.875

Step-by-step explanation:

7- (1/2)^3​ = 7-1/8 = 6.875

Answer:

solution -2/5+1/2 =-2*2+1*5/5*2 =-4+5/10 =1/10

Answer:

Step-by-step explanation:

All real number