the function h(x) is a transformation of the square root parent function

Answer:

c

Step-by-step explanation:

First, we can transform this into a matrix. The x coefficients will be the first ones for each row, the y coefficients the second column, etc.

[tex]\left[\begin{array}{cccc}1&-2&3&-2\\6&2&2&-48\\1&4&3&-38\end{array}\right][/tex]

Next, we can define a reduced row echelon form matrix as follows:

With the leading entry being the first non zero number in the first row, the leading entry in each row must be 1. Next, there must only be 0s above and below the leading entry. After that, the leading entry of a row must be to the left of the leading entry of the next row. Finally, rows with all zeros should be at the bottom of the matrix.

Because there are 3 rows and we want to solve for 3 variables, making the desired matrix of form

[tex]\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right][/tex] for the first three rows and columns. This would make the equation translate to

x= something

y= something

z = something, making it easy to solve for x, y, and z.

Going back to our matrix,

[tex]\left[\begin{array}{cccc}1&-2&3&-2\\6&2&2&-48\\1&4&3&-38\end{array}\right][/tex] ,

we can start by removing the nonzero values from the first column for rows 2 and 3 to reach the first column of the desired matrix. We can do this by multiplying the first row by -6 and adding it to the second row, as well as multiplying the first row by -1 and adding it to the third row. This results in

[tex]\left[\begin{array}{cccc}1&-2&3&-2\\0&14&-16&-36\\0&6&0&-36\end{array}\right][/tex]

as our matrix. * Next, we can reach the second column of our desired matrix by first multiplying the second row by (2/14) and adding it to the first row as well as multiplying the second row by (-6/14) and adding it to the third row. This eliminates the nonzero values from all rows in the second column except for the second row. This results in

[tex]\left[\begin{array}{cccc}1&0&10/14&-100/14\\0&14&-16&-36\\0&0&96/14&-288/14\end{array}\right][/tex]

After that, to reach the desired second column, we can divide the second row by 14, resulting in

[tex]\left[\begin{array}{cccc}1&0&10/14&-100/14\\0&1&-16/14&-36/14\\0&0&96/14&-288/14\end{array}\right][/tex]

Finally, to remove the zeros from all rows in the third column outside of the third row, we can multiply the third row by (16/96) and adding it to the second row as well as multiplying the third row by (-10/96) and adding it to the first row. This results in

[tex]\left[\begin{array}{cccc}1&0&0&-5\\0&1&0&-6\\0&0&96/14&-288/14\end{array}\right][/tex]

We can then divide the third row by -96/14 to reach the desired third column, making the reduced row echelon form of the matrix

[tex]\left[\begin{array}{cccc}1&0&0&-5\\0&1&0&-6\\0&0&1&-3\end{array}\right][/tex]

Therefore,

x=-5

y=-6

z=-3

* we could also switch the second and third rows here to make the process a little simpler

Answer:

C

Step-by-step explanation:

EDGE BOY (or girl)

Answer:

[tex]\boxed{\sf x = 7 }[/tex]

Step-by-step explanation:

We are here given a logarithmic equation and we need to solve it out and then find the value of x. The given equation is ,

[tex]\sf\longrightarrow log_6 + log_6 ( x -1) = 1 [/tex]

Here I am assuming that the base of the logarithm is 6 . The equation can be written as ,

[tex]\sf\longrightarrow log_6 1+ log_6 ( x -1) = 1 [/tex]

Recall the property of log as , [tex]\sf log_x a + log_x b = log_x(ab) [/tex] , on using this property we have ,

[tex]\sf\longrightarrow log_6 \{ 1 ( x -1)\} = 1 [/tex]

Simplify ,

[tex]\sf\longrightarrow log_6 ( x -1) = 1 [/tex]

We know that , if [tex]\sf log_a b = c [/tex] then in expotential form it can be expressed as [tex]\sf a^c = b [/tex] . Using this we have ,

[tex]\sf\longrightarrow 6^1 = x - 1[/tex]

Simplify ,

[tex]\sf\longrightarrow 6 = x - 1[/tex]

Add 1 both sides ,

[tex]\sf\longrightarrow x = 6 + 1[/tex]

Therefore ,

[tex]\sf\longrightarrow \boxed{\blue{\sf \quad x = 7\quad }} [/tex]

Hence the value of x is 7 .

Answer:

x=7

Step-by-step explanation:

log6(1) + log6 (x-1) = 1

We know that log (a) * log (b) = log (ab)

log6 (1*(x-1)) = 1

log6 (x-1) = 1

Raising each side to the base of 6

6 ^log6 (x-1)  = 6^1

x-1 = 6

Add 1 to each sdie

x-1+1 = 6+1

x=7

Answer:

the first choice

Step-by-step explanation:

Events A and B are independent if the equation P(A∩B) = P(A) · P(B) holds true.

then it means if the events are independent then the probability is multiplying the probability of each event.

9514 1404 393

Answer:

  C.  f^-1(x) = (x +4)^2; x  ≥ -4

Step-by-step explanation:

The range of the given function f(x) is -4 ≤ f(x). This will be the domain of the inverse function.

We find the inverse function by solving ...

  x = f(y)

  x = √y -4

  x +4 = √y

  (x +4)^2 = y

The inverse function is ...

  f^-1(x) = (x +4)^2 . . . for x ≥ -4

Answer:

2+4/6=1

y-2/x-6=1

y-2=x-6

y=x-4

or y+4=x

Answer:

3rd option

y + 4 = x

Step-by-step explanation:

look,

point A (0, -4) forms the y intercept

(remember the condition for y intercept? the coordinates for which value of x is 0)

so in the equation

[tex]\boxed{ y= mx+c}[/tex]

c being the y intercept is equal to (-4)

finding the slope :-

[tex]m = \frac{ 2 + 4 }{6 - 0} \\ = \frac{6}{6} = 1[/tex]

plugging all these values into the equation

y = 1x - 4

y= x - 4

taking 4 to the other side

y+ 4 = x

Answer:

let:

4x-9=2x+3

4x-2x=3+9

2x=12

x=12/2

x=6 Ans

Answer:

0.9797

Step-by-step explanation:

100*101% = 101

101*0.97% = 97.97% = 0.9797

Answer:

2(x - 3)^2 - 25.

Step-by-step explanation:

2x^2-12x-7

= 2(x^2 - 6x) - 7

= 2[(x - 3)^2 - 9] - 7

= 2(x - 3)^2 - 18 - 7

= 2(x - 3)^2 - 25.

Answer:

b =44

Step-by-step explanation:

We need to use the law of sines to determine b

sin b                     sin 100

----------------  = ----------------

3.6                          5.1

Using cross products

5.1 sin b = 3.6 sin 100

sin b = 3.6 sin 100 / 5.1

Taking the inverse sin of each side

b = arcsin (  3.6 sin 100 / 5.1)

b = 44.03984209

To the nearest degree

n = 44

Answer:

it should be 3 so letter c

Step-by-step explanation:

I hope this help

the answer is in the picture

Answer:

1st option

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 3, 7) and (x₂, y₂ ) = (9, - 1)

m = [tex]\frac{-1-7}{9-(-3)}[/tex] = [tex]\frac{-8}{9+3}[/tex] = [tex]\frac{-8}{12}[/tex] = - [tex]\frac{2}{3}[/tex] , then

y = - [tex]\frac{2}{3}[/tex] x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (9, - 1 ) , then

- 1 = - 6 + c ⇒ c = - 1 + 6 = 5

y = - [tex]\frac{2}{3}[/tex] x + 5 ← equation of line

Step-by-step explanation:

reflection under

x-axis

hope this will help you

The line of reflection is given as  x-axis.

The graph of a function can be transformed by either shifting it in the right, left, up or down.

When the transformation is rightwards, the function becomes as f(x - a).

For left shifting it is f(x + a).

The coordinates of the triangle SKY before and after reflection are given as below,

S(-7, 2) → S'(-7, -2)

K(-1, 8) → K'(-1, -8)

Y(-2, 1) → Y'(-2, -1)

It is clear from the transformed coordinates that the x coordinates are the same but y-coordinate changes.

Thus, the reflection is about x-axis.

Hence, the line of reflection is x-axis.

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Answer:

This would not be 20

Step-by-step explanation:

This question can be thought as a Pythagoras question.

By subtracting 2cm from both the left side ZW, and the right side YX, you will have a right angled triangle WYX (or ZYX, since after subtracting 2cm Z and W are essentially the same point)

I have attached a crude drawing of what the triangle is looking like, we are looking for the unknown value marked with the ?

Pythagoras states that [tex]a^{2} +b^{2} =c^{2}[/tex]

We are given the lengths 2cm and 20cm, which can be thought of as a (or b) and c. Substitute in the values 2 and 20 and solve for the unknown

Answer:

Three times a number minus two times a number

3x-2x

=x

Answer:

11/12 miles Lyon walk.

Step-by-step explanation:

3/4 -> 9/12

1/6 -> 2/12

9 + 2 = 11

The solution is :about  11/12 miles Lyon walk.

Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.

here, we have,

given that,

Lyon walked 3/4 mile from school to the soccer field.

He then walked 1/6 mile home.

now, we have to find that,

About how many miles did Lyon walk

so, we need to add the both distance

i.e.  3/4 + 1/6

so, we have,

3/4 -> 9/12

1/6 -> 2/12

so, we get,

9 + 2 = 11

i.e. 3/4 + 1/6

= 9/12 + 2/12

=11/12

Hence, about  11/12 miles Lyon walk.

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Answer:

6x - 2y > 8

First, solve the inequality (Isolate the y-variable & put it in function format):

[tex]6x - 2y > 8\\-2y > 8 - 6x\\(-1)(-2y) > (-1)(8-6x)\\2y < 6x-8\\y < \frac{6x-8}{2} \\y < 3x - 4[/tex]

Second, graph the function y = 3x - 4 on the graph.

Third, shade in the area below the line(where y-values are smaller).

You can use the same reasoning as I provided on your other question (URL 24277817).

"statistical" has 11 total characters, thus 11! total permutations.

• s, a, and i each appear 2 times

• t appears 3 times

Then the number of distinguishable permutations is

11! / (2! × 2! × 2! × 3!) = 831,600

Answer: 289,952,278

Step-by-step explanation: Big brain

Answer:

A, E, F

Step-by-step explanation:

From the angles given, we can infer that ΔPQR is a 30-60-90 special triangle. In a 30-60-90 triangle, the leg opposite the 30 degree angle is 1/2 the hypotenuse and the leg opposite the 60 degree angle is √3 times the one opposite the 30. Using this, we can say:

PR = 1/2 PQ which is just 2 PR = PQ(E)

PR √3 = QR (A)

We can substitute in PR from the first equation to the second to get:

√3/2 PQ = QR(F)

Answer:

(b) 26.6 days

Step-by-step explanation:

Half life, T =  4 days

initial amount, No = 100 mg

(a) The exponential function is given by

[tex]N = No e^{-\lambda t}\\\\N = No e^{\frac{-0.693t}{T}}\\\\N = No e^{\frac{-0.693t}{4}}\\\\N = No e^{\frac{-0.17325t}{T}}\\\\[/tex]

where, N is the amount left.  

(b) N = 1 mg

[tex]N = No e^{\frac{-0.17325t}{4}}\\\\1 = 100 e^{\frac{-0.17325t}{4}}\\\\4.605 = 0.17325 t \\\\t=26.6 days[/tex]

Answer:

1372/3 π

that's the volume

Answer:

C. 49, x-7

Step-by-step explanation:

(A+B)^2 = A^2 + 2AB + B^2

-14x = 2*A*B

where A=x

Therefore B=-7

and (x-7)^2=x^2-14x+49

Answer:

The x intercept is (8,0)

Step-by-step explanation:

To find the x intercept set y = 0 and solve for x

Y=3/4x - 6

0 =3/4x - 6

6 = 3/4x

4/3 *6 = 4/3*3/4x

8 =x

The x intercept is (8,0)

Answer:

8

Step-by-step explanation:

0 =3/4x - 6

6 = 3/4x

24 = 3x

x = 24/3 = 8

Answer:

C

Step-by-step explanation:

The graph is 5x^2. Hence the option C is correct

The required function g(x) is 5x² for the given graph, which is the correct option (C).

The function is defined as a mathematical expression that defines a relationship between one variable and another variable.

The given function is as follows:

f(x) = x²

Substitute the value of x = 1 in the above equation,

f(1) = 1

As per the given graph, we have

g(1) = 5

Now, we can write the proportion as:

f(x)/g(x) = f(1)/g(1)

Substitute the known values in the above proportion, and solve for g(x):

x²/g(x) = 1/5

Cross-multiplying and we get:

g(x) = 5x²

Therefore, the required function g(x) is 5x².

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Answer:

2a times the sq root of 2a or 2a (2a)**1/2

Step-by-step explanation:

(8a**3)**1/2 =

((2**2 * 2) (a**2) (a))**1/2 then take out and squares

2a (2a)**1/2

or 2a times the sq root of 2a

Answer:

[tex]2 {x}^{2} - 6x - 1 = 0 \\ a = 2 \: \: \: b = - 6 \: \: \: c = - 1 \\ \\ x = \frac{6\binom{ + }{ - } \ \sqrt{ {6}^{2} - 4(2)( - 1)} }{2 \times 2} \\ \\ x = \frac{6 \binom{ + }{ - } \sqrt{44} }{4} \\ x = \frac{6 + \sqrt{44} }{4} \\ \\ or x = \frac{6 - \sqrt{44} }{4} [/tex]

I hope that is useful for you :)