Which of the following describes the transformations of g(x)--(2)**-2 from the parent function f(x)=2*?
O shift 4 units left, reflect over the x-axis, shift 2 units down
O shift 4 units left, reflect over the y-axis, shift 2 units down
O shift 4 units right, reflect over the x-axis, shift 2 units down
O shift 4 units right, reflect over the y-axis, shift 2 units down

The values of the complex expressions are ✓(x - iy) = a - ib and x² + y² =  (a + ib)²(a - ib)²

From the question, we have the following parameters that can be used in our computation:

✓(x + iy) = a + ib

Changing the signs, we have

✓(x - iy) = a - ib

Multiply both expressions

This gives

✓(x + iy) * ✓(x - iy) =  (a + ib)(a - ib)

Square both sides

So, we have

(x + iy) * (x - iy) =  (a + ib)²(a - ib)²

This gives

x² + y² =  (a + ib)²(a - ib)²

Hence, the values of ✓(x - iy) is a - ib and x² + y² is  (a + ib)²(a - ib)²

Read more about complex expressions at

https://brainly.com/question/10662770

#SPJ1

Answer:

C) 16

Step-by-step explanation:

(3x + 5) + 37 = 90

3x = 90 - 5 - 37

3x = 48

x = 48/3 = 16

Answer:

x = 16°

Step-by-step explanation:

It is 90° angle so their sum must be 90°( complement) .

3x + 5° + 37° = 90°

3x + 42° = 90° ... simplify the like term

3x = 90° - 42°

3x = 48°

3x/3 = 48°/3

x = 16°

So the answer is C, 16

The m<3 is approximately equal to 85.39 degrees.

The sum of the measures of the angles of a triangle is 180 degrees. So, we have:

m<1 + m<2 + m<3 = 180

So, (3x + 12) + (3x + 18) + (7x + 10) = 180

Simplifying and solving for x, we get:

13x + 40 = 180

13x = 140

x = 10.77

Now, we can find m<3 by substituting x in the expression for m<3:

m<3 = 7x + 10

m<3 = 7(10.77) + 10

m<3 = 85.39

Therefore, m<3 is approximately equal to 85.39 degrees.

Learn more about Angle Sum Property here:

https://brainly.com/question/21364160

#SPJ1

The presence of the coefficient "a" in ax^2 + bx + c requires that we look for numbers that have a product of ac

Here we have to determine the difference

From the question, we have the following parameters that can be used in our computation:

ax^2 + bx +c and x^2 + bx +c

The presence of the coefficient "a" in the first expression makes a difference in the factoring process.

When factoring x^2 + bx + c, we are looking for two numbers that multiply to give c and add up to b.

For ax^2 + bx +c , we look for the product of ac and sum of b

Read more about expression at

brainly.com/question/15775046

#SPJ1

Answer:

The zeroes of this function are 2 and -1.

A and C are the correct choices.

A) rectangle

C) parallelogram

D) rhombus

E) rectangle

Answer:

Step-by-step explanation:

a.) When we reflect over xz plane x and z coordinates stay same, y coordinate  changes to same numerical value but opposite sign. Moving front-back is moving over x-axis, moving left-right is moving over y-axis, moving up-down is moving over z-axis.

A(0,0,0)

Reflecting

A(0,0,0)

B(0,5,0)

Reflecting

B(0,-5,0)

C(3,5,0)

Reflecting

C(3,-5,0)

D(3,0,0)

Reflecting

D(3,0,0)

b.)

A(0,0,0)

Moving

A(-2,-3,1)

B(0,-5,0)

Moving

B(-2,-8,1)

C(3,-5,0)

Moving

C(1,-8,1)

D(3,0,0)

Moving

D(1,-3,1)

The total number of ways to arrange all 6 tables is 720

There are 15 ways to choose 4 tables out of 6.

(a) There are 6 options for the first table, 5 options left for the second table, 4 options left for the third table, and so on.

Therefore, the total number of ways to arrange all 6 tables is:

6 x 5 x 4 x 3 x 2 x 1 = 720

(b) To choose 4 tables out of 6, we can use the combination formula:

C(6,4) = 6! / (4! x 2!)

= (6 x 5 x 4 x 3) / (4 x 3 x 2 x 1)

= 15

Therefore, there are 15 ways to choose 4 tables out of 6.

To learn more on Combinations click:

https://brainly.com/question/19692242

#SPJ1

Answer:

Step-by-step explanation:

The problem specifies that you may use a calculator. The formula, as reference, is:

You can use a regular calculator or an online spreadsheet to solve. In sheets, arrange your data and use the =PERCENTILE( ) function. In the parentheses, write the range of your data and the requested percentile as a decimal. So if I type the data (the ages of the signers for this example) in cells A:4 through A:23, I'd write =percentile(A7:A23,0.25).

So the answers:

25th percentile is 34.

80th percentile is 48.4.

The results of each iteration are given as follows:

The iterative formula in the context of this problem is defined as follows:

[tex]x_{n + 1} = \sqrt{8x_n - 5}[/tex]

The first value is given as follows:

[tex]x_1 = 3[/tex]

Hence each value is obtained applying the previous value to the iterative formula.

The second value is given as follows:

[tex]x_2 = \sqrt{8 \times 3 - 5}[/tex]

[tex]x_2 = \sqrt{19}[/tex]

[tex]x_2 = 4.359[/tex]

The third value is then given as follows:

[tex]x_3 = \sqrt{8 \times 4.359 - 5}[/tex]

[tex]x_3 = \sqrt{29.872}[/tex]

[tex]x_3 = 5.466[/tex]

The fourth value is then given as follows:

[tex]x_4 = \sqrt{8 \times 5.466 - 5}[/tex]

[tex]x_4 = \sqrt{38.728}[/tex]

[tex]x_4 = 6.233[/tex]

More can be learned about iterative formulas at https://brainly.com/question/11978795

#SPJ1

The quadratic function f(x) = 2x² - 5x + 3, it is found :

a. The factored function is, f(x) = 2(x - 1)(x - 1.5).

b. The x-intercepts of the function are: x = 1, x = 1.5.

c. The end behavior of the graph is:

As x -> -∞, f(x) -> -∞.

As x -> ∞, f(x) -> ∞.

The quadratic function is :

f(x) = 2x² - 5x + 3.

Hence the coefficients are:

a = 2, b = -5, c = 3.

Using a calculator with these coefficients, the x-intercepts are:

x = 1.

x = 1.5.

Then the factored form of the function;

f(x) = 2(x - 1)(x - 1.5).

Let the leading coefficient of 2 and the x-intercepts.

This is a concave-up parabola, it goes to positive infinity to the left and to the right of the graph.

Hence the end behavior is;

As x -> -∞, f(x) -> -∞.

As x -> ∞, f(x) -> ∞.

To determine the graph, the axis of symmetry is:

x = -b/2a = 5/(2(2)) = 1.25.

The y-coordinate at this point, that is the turning point of the function, is:

f(1.25) = 2(1.25)² - 5(1.25) + 3 = -0.125.

The y-intercept of the function

f(0) = 2(0)² - 5(0) + 3 = 3.

More can be learned about quadratic functions at brainly.com/question/24737967

#SPJ1

Solution:

1. t/5 + 3/4

+4      

___   + 5-3= 20

20

2. Combine fractions w/ common denominator.

3. multiply the #'s.

4. last but not least is: Solution:

4t+15

_____

20

The solution set of the inequality (2/5)*(10x - 15) ≥ 10 is:

[4, ∞)

Here we want to solve the inequality:

(2/5)*(10x - 15) ≥ 10

To solve this we need to isolate the variable x, to do so, we can start multiplying both sides by 5/2

(10x - 15) ≥ 10*(5/2)

10x - 15 ≥ 25

Now add 15 in both sides:

10x ≥ 25 + 15

Now divide both sides by 10.

x ≥ 40/10

x ≥ 4

So the solution set is the set of all real numbers equal or larger than 4.

Learn more about inequalities:

https://brainly.com/question/24372553

#SPJ1

Using the law of sines, the length of b, to the nearest tenth, is: 21.4.

The Law of Sines is a mathematical equation that relates the lengths of the sides of a triangle to the sines of its angles. It states that for any triangle with sides of length a, b, and c and angles A, B, and C (where C is the largest angle), the following relationship holds:

[tex]\sf \dfrac{a}{sin(A)}= \dfrac{b}{sin(B)} =\dfrac{c}{sin(C)}[/tex]

This equation allows you to solve for the unknown sides or angles of a triangle if you know the lengths of its sides and the measure of at least one of its angles. It is often used in geometry and trigonometry to find the unknown parts of a triangle when you have limited information about it.

Given that triangle ABC has the following measures:

[tex]\sf m\angle B = 32^\circ[/tex]

[tex]\sf m\angle C = 38^\circ[/tex]

[tex]\sf a = 22[/tex]

[tex]\sf m\angle A = 180 - 32 - 38 = 110^\circ \ \ [triangle \ sum \ theorem][/tex]

Applying the law of sines, we have:

[tex]\sf \dfrac{38}{sin \ 110} =\dfrac{b}{sin \ 32}[/tex]

Cross multiply:

[tex]\sf (sin \ 110)(b) = (sin \ 32)(38)[/tex]

[tex]\sf b = \dfrac{(sin \ 32 \times38)}{(sin \ 110)}[/tex]

[tex]\sf b = 21.4 \ \ (nearest \ tenth)[/tex].

Learn more about the law of sines on:

brainly.com/question/2807639

Answer:

2m=7. m=7/2. 10x =48. x = 4.8

Step-by-step explanation:

2m

Answer:

a)  7/2 or 3.5

b) 4.8

form equation and solve them

a}n = 17

Step-by-step explanation:

a) 2m + 8 = 15

Subtract 8 from both sides: 2m + 8 - 8 = 15 - 8

Simplify: 2m = 7

Divide both sides by 2: (2m)/2 = 7/2

Simplify: m = 7/2 or 3.5

b) 10x - 3 = 45

Add 3 to both sides: 10x - 3 + 3 = 45 + 3

Simplify: 10x = 48

Divide both sides by 10: (10x)/10 = 48/10

Simplify: x = 4.8

To form and solve an equation for Ashley’s problem, we need to translate the words into mathematical expressions. Here are the steps and solution:

a) Ashley thinks of a number if i double my number and add 6 the answer is 40

Let n be Ashley’s number.

If we double the number, we get 2n.

If we add 6 to the doubled number, we get 2n + 6.

The answer is equal to 40, so we can write an equation: 2n + 6 = 40

To solve for n, we need to isolate it on one side of the equation by using inverse operations.

Subtract 6 from both sides: 2n + 6 - 6 = 40 - 6

Simplify: 2n = 34

Divide both sides by 2: (2n)/2 = 34/2

Simplify: n = 17

Answer:

28.57% chance

Step-by-step explanation:

add them all up which is 14, and if there are 4 white marbles that means its 4/14, which is 28.57 as a percent (2:7 as ratio)

Answer:

51

Step-by-step explanation:

To find the speed, we must divide the distance traveled by the time it took to travel that distance:

[tex]v = \frac{D}{t} = \frac{153\ miles}{3\ hours} = 51\ mph[/tex]

Now that we've found the speed, we must see how fast the car travels in an hour

[tex]D = vt = 51 \ mph * 1 \ h = 51 \ miles[/tex]

Step-by-step explanation:

In the side view diagram, we can see that the tank, the wall, and the floor form a right triangle with the radius of the tank as the hypotenuse. Let x be the distance between the tank and the wall, as shown below:

```

|\

| \

r | \ x

| \

|_ _\

s

```

Using the Pythagorean theorem, we can write:

r^2 = x^2 + s^2

Rearranging this equation, we get:

x^2 = r^2 - s^2

Subtracting r^2 from both sides, we get:

x^2 - r^2 = -s^2

Multiplying both sides by -1, we get:

s^2 - x^2 = 0

Therefore, the equation for the relationship between the two radii is:

s^2 - x^2 = 0

Simplifying this equation, we get:

s^2 = x^2

or

x^2 = s^2

So, there is a zero on one side of the equals sign.

Answer:

Part a)

[tex]MG = \begin{pmatrix}1&k_1+9&4k_2+36\\ 2t_1+4&t_1k_1-17&-19t_1+3k_2-11\\ t_2+1&k_1-4t_2+5&t_2k_2-8\end{pmatrix}[/tex]

Part b)

[tex]t_1 = -2\\\\t_2 = -1\\\\k_1 = -9\\\\k_2 = -9\\[/tex]

Step-by-step explanation:

a) Computing MG

We have
[tex]M = \begin{pmatrix}1&4&5\\ \:t_1&3&-1\\ \:1&t_2&1\end{pmatrix}[/tex]

[tex]G = \begin{pmatrix}2&k_1&-19\\ \:1&-4&k_2\\ \:-1&5&11\end{pmatrix}[/tex]

[tex]MG = \begin{pmatrix}1&4&5\\ \:t_1&3&-1\\ \:1&t_2&1\end{pmatrix}\times \begin{pmatrix}2&k_1&-19\\ \:1&-4&k_2\\ \:-1&5&11\end{pmatrix}[/tex]

[tex]= \begin{pmatrix}1&k_1+9&4k_2+36\\ 2t_1+4&t_1k_1-17&-19t_1+3k_2-11\\ t_2+1&k_1-4t_2+5&t_2k_2-8\end{pmatrix}[/tex]

I am using a matrix calculator to compute the product rather than going through the rather cumbersome multiplication exercise by hand

b) One property of matrices is that if M is a matrix and M⁻¹ is its inverse
M x M⁻¹ is the identity matrix which has a 1 along the primary diagonal (top left - bottom right) and zeros everywhere

Here we are given G = M⁻¹ so M x G is an identity matrix

[tex]MG(1, 2) \\= k_1 + 9 = 0\\= > k_1 = -9\\\\MG(1, 3)\; is\\ 4k_2 + 36 = 0\\k_2 = -36/4 = -9\\\\MG(2, 1) = 2t_1 + 4 = 0\\\implies t_1 = -4/2 = -2\\\\MG(3, 1) = t_2 + 1\\t_2 + 1 = 0\\t_2 = -1\\[/tex]

So the values of the variables are

[tex]t_1 = -2\\\\t_2 = -1\\\\k_1 = -9\\\\k_2 = -9\\[/tex]

To check if these are correct, you can plug in these values into the product matrix MG. You will see that all elements except the diagonal elements are 0; diagonal elements are 1

The apothem and the lateral surface area are 5/2√3 and 210 square units while the surface areas are 210 + 75√3 square units and 339.90 square units

Given that

Side length, s = 5

The apothem is calculated as

a = 1/2√3 * s

Where

Side length, s = 5

So, we have

a = 1/2√3 * 5

Evaluate

a = 5/2√3

The lateral area of the prism is calculated as

LA = 6sh

So, we have

LA = 6 * 5 * 7

LA = 210

This is calculated as

SA = LA + 3√3 s²

So, we have

SA = 210 + 3√3 * 5²

Evaluate

SA = 210 + 75√3

In decimal form, we have

SA = 339.90

Hence, the decimal form of the surface area is 339.90 square units

Read more about surface area at

https://brainly.com/question/26403859

#SPJ1

g is greater than -218,020.041.

We have,

To solve this inequality, we need to simplify the left side first:

9999899(-989789) = -9,899,782,581,211

Next, we can solve for g by dividing both sides by 45,426,663:

-9,899,782,581,211 / 45,426,663 < g

Simplifying the left side:

-218,020.041 < g

Therefore,

g is greater than -218,020.041.

Learn more about inequalities here:

https://brainly.com/question/20383699

#SPJ1

Answer: C

Step-by-step explanation: Polygons are defined as two-dimensional.

Answer:

C

Step-by-step explanation:

A polygon lies entirely in one plane, so it cannot be three dimensional. The rest of the statements are true, so the answer is C

The  greater rate of change is 12.5, which is the rate of change of the first function.

The rate of change of a linear function is the slope of the line, which is represented by the coefficient of x in the equation y = mx + b. Therefore, the rate of change of the first function y = 12.5x + 2 is 12.5.

To find the rate of change of the second function, we can use any two points on the table and use the formula:

rate of change = (change in y) / (change in x)

Let's use the points (-3, -28.5) and (3, 37.5):

rate of change = (37.5 - (-28.5)) / (3 - (-3))

rate of change = 66 / 6

rate of change = 11

Therefore, the greater rate of change is 12.5, which is the rate of change of the first function.

Learn more about Slope here:

https://brainly.com/question/3605446

#SPJ1

The simplified polynomials are:

10. -3(y+1) = -3y - 3

To simplify the expression, we distribute the -3 to both terms inside the parentheses.

11. 5x(3x²-4) = 15x³ - 20x

To simplify the expression, we distribute the 5x to both terms inside the parentheses.

12. 7(-2m²+5m+6) = -14m² + 35m + 42

To simplify the expression, we distribute the 7 to all the terms inside the parentheses.

13. (x+1)(3x-4) = 3x² - x - 4

To simplify the expression, we use the distributive property and multiply x with 3x and 1 with 3x, and then multiply x with -4 and 1 with -4.

14. (-2z²+5z)(-4x-8) = 8z³ + 16z² - 20xz - 40z

To simplify the expression, we use the distributive property and multiply -2z² with -4x and -8, and then multiply 5z with -4x and -8.

15. (9x+5)(-4x-8+10x²) = -40x³ + 45x² - 40x - 72x - 40

To simplify the expression, we use the distributive property and multiply 9x with -4x, -8, and 10x². Then we multiply 5 with -4x, -8, and 10x². Finally, we combine like terms.

Solving for the sum of all coefficients

-3 + (-3) + 15 + (-20) + (-14) + 35 + 42 + 3 + (-1) + (-4) + 8 + 16 + (-20) + (-40) - 40 + 5 + 45 + (-40) + (-40) + (-72) + (-40)

Simplifying, we get:

-148

Therefore, the code to unlock section 3 is -148.

Read more on polynomials here:https://brainly.com/question/4142886

#SPJ1

The value of secβ = (-21√10)/60.

Given that

Cosecβ = 7/3

Cotβ = -(2[tex]\sqrt{10}[/tex])/3

Since,

Cosecβ  =  1/sinβ = 7/3

⇒ sinβ = 3/7

And Cotβ = -(2[tex]\sqrt{10}[/tex])/3

⇒ cosβ/sinβ =  -(2[tex]\sqrt{10}[/tex])/3

⇒ 1/cosβ = -3/[(2[tex]\sqrt{10}[/tex])sinβ]

⇒ secβ = -21/(6√10)

Hence,

⇒ secβ = (-21√10)/60

Learn more about the triangle visit;

brainly.com/question/1058720

#SPJ1

________________________________

________________________________

The two values for x so the points form a right triangle are x = -4 and x = 10

From the question, we have the following parameters that can be used in our computation:

The coordinates of the points are A(5,3), B(5,6) and C(x,3).

The third point is given as

C(x,3)

The value of x can be any real value apart from 5

This is because if x = 5, then it would be the same as point A

So, we can use the following values for x

x = -4 and x = 10

Note that all real values work for x

Read more about right triangles at

https://brainly.com/question/2437195

#SPJ1

Answer:

50(5π + 6) cm²

Step-by-step explanation:

TSA of figure = 1/2 of TSA(Cylinder) + Area of rectangle

= 1/2 of 2πr(h+r) + 20*15

= πr(h+r) + 300

= 10π(15+10) + 300

= 250π + 300 cm²

or 50(5π + 6) cm²

The surface area of the box increases by 67.26 cm² when the height is increased by 0.7 cm.

Recall the formula, Surface Area (SA) of the rectangular prism is given as:

SA = 2lw + 2lh + 2wh

where

l = length,

w = width,

h =  height

From the diagram, we know that:

l = 18cm

w = 6.3cm

h = 30cm

Substituting these values into the surface area formula, we get:

SA₁ = 2(18)(6.3) + 2(18)(30) + 2(6.3)(30) = 2376 cm²

When the height is increased by 0.7cm, the new height becomes:

h' = h + 0.7cm = 30.7cm

The new surface area can be calculated using the same formula:

SA₂ = 2(18)(6.3) + 2(18)(30.7) + 2(6.3)(30.7) = 2443.26 cm²

The increase in surface area is the difference between the new surface area and the original surface area:

SA₂ - SA₁ = 2443.26 cm² - 2376 cm²

= 67.26 cm²

Learn more about rectangular prism here:

https://brainly.com/question/128724

#SPJ1

The value of transformation of f (x) makes f(x) < g(x) is,

⇒ shifts the function 3 units upward.

We know that;

A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

Now, We have;

Functions are,

f (x) = x²

g(x) = x² +3

Hence, The value of transformation of f (x) makes f(x) < g(x) is,

⇒ shifts the function 3 units upward.

Learn more about the transformation visit:

https://brainly.com/question/30097107

#SPJ1