Select the expression that is equivalent to (x + 6)2.
A. x2 + 12x2 + 36
B. x2 + 6x + 36
C. 2x+ 12x + 12
D. x2 + 12x + 36

The simpliest way is to use the AAS Postulate.

AAS Postulate: If two angles and the non-included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.

From the diagram you have:

1. one pair of angles with measure 40°;

2. one pair of angles with measure 60°;

3. the non-included side of one triangle is congruent to the non-included side of another triangle (their lengths are 10).

Answer: correct choice is D (AAS)

Answer:

AAS postulate :)

Step-by-step explanation:

-36 is the correct answer

The functions for House 1 and House 2 are [tex]\(f_1(x) = 5079.6x + 248900.4\)[/tex] and [tex]\(f_2(x) = 4666.\overline{66}x + 256000\)[/tex] respectively.

After 45 years, House 1 will be valued at $477,555, and House 2 will be valued at $465,000.

Here's the step-by-step solution with complete calculations for the given problem:

Part A: Identifying the Function Type

- House 1:

 - Year 1 to Year 2: [tex]\(259,059.60 - 253,980 = 5,079.60\)[/tex]

 - Year 2 to Year 3: [tex]\(264,240.79 - 259,059.60 = 5,181.19\)[/tex]

- House 2:

 - Year 1 to Year 2: [tex]\(263,000 - 256,000 = 7,000\)[/tex]

 - Year 2 to Year 3: [tex]\(270,000 - 263,000 = 7,000\)[/tex]

The functions are linear because the changes are constant for House 2 and almost constant for House 1.

Part B: Formulating the Equations

- House 1 Equation:

 - Slope (m): [tex]\(5079.6\)[/tex]

 - Y-intercept (c): [tex]\(248900.4\)[/tex]

 - Equation: [tex]\(f_1(x) = 5079.6x + 248900.4\)[/tex]

- House 2 Equation:

 - Slope (m): [tex]\(4666.\overline{66}\)[/tex]

 - Y-intercept (c): [tex]\(256000\)[/tex]

 - Equation: [tex]\(f_2(x) = 4666.\overline{66}x + 256000\)[/tex]

Part C: Calculating Future Values

- House 1 Value at Year 45:

[tex]- \(f_1(45) = 5079.6 \times 45 + 248900.4 = 477555\)[/tex]

- House 2 Value at Year 45:

[tex]- \(f_2(45) = 4666.\overline{66} \times 45 + 256000 = 465000\)[/tex]

These equations predict the values of the houses after 45 years based on the given data. House 1 will be valued at $477,555, and House 2 will be valued at $465,000.

Answer:

The system of equations is

[tex]x+y=15[/tex]

[tex]19x+8y=164[/tex]

Step-by-step explanation:

Let

x------> the number of videos of new releases

y-----> the number of classics videos

we know that

[tex]x+y=15[/tex] ------> equation A

[tex]19x+8y=164[/tex] ------> equation B

Using a graphing tool

Solve the system of equations

Remember that the solution of the system of equations is the intersection point both graphs

The intersection point is [tex](4,11)[/tex]

see the attached figure

therefore

the number of videos of new releases is [tex]4[/tex]

the number of classics videos is [tex]11[/tex]

Answer:

Jerome bought 15 videos from a department store. Some videos were new releases, x,  which cost $19, and some videos were classics, y, which cost $8. He spent a total of $164 on the videos. Which system of equations is set up correctly to model this information?

x + y = 15. 19 x + 8 y = 164.

x + y = 15. 8 x + 19 y = 164.

x + y = 164. 19 x + 8 y = 15.

x + y = 15. 19 x minus 8 y = 164.

ANSWER IS A

Answer:

Option (d) is correct.

The area of triangle is 38.5 square units

Step-by-step explanation:

 Given: An obtuse triangle.

We have to find the area of this obtuse angle.

Consider the given obtuse triangle

Area of triangle = [tex]\frac{1}{2}\cdot b \cdot h[/tex]

where b = Base

h = height

Given : base = 11  units

and height = 7 units

Thus, Area of triangle = [tex]\frac{1}{2}\cdot 11 \cdot 7[/tex]

Simplify, we have,

Area of triangle = 38.5

Thus, The area of triangle is 38.5 square units

Answer: A cosine function would be a simpler model for the situation.

The minimum depth (low tide) occurs at

t = 0. A reflection of the cosine curve also has a minimum at t = 0.

A sine model would require a phase shift, while a cosine model does not.

Step-by-step explanation:

Using a cosine function is simpler to model the tide changes because it starts at the maximum value, aligning with the high tide occurrence.

The depth of the water at the end of a pier changes periodically due to tides. Given that low tides occur at 12:00 am and 12:30 pm with a depth of 2.5 m, and high tides occur at 6:15 am and 6:45 pm with a depth of 5.5 m, we need to model this situation with a periodic function.

Let's align this with a cosine function for simplicity. In general, the cosine function can be modeled as y = A cos(B(t - C)) + D, where:

Therefore, the function becomes: y(t) = 1.5 cos((2π/747.5)(t - 375)) + 4. Using a cosine function is simpler because it starts at the maximum value, which corresponds to the high tide.

Final answer:

The expressions provided are different forms of similar linear expressions, which could potentially describe the measure of angle RST if related algebraically or geometrically. The expression for m∠ RST is 6x - 9

Explanation:

Calculating the measure of angle RST involves understanding that the angles around a point add up to 360°, and the angles on a straight line add up to 180°. Based on the provided expressions, we are likely looking for the expression that adheres to these geometric rules.

The expressions given are: 3x – 9, 6x – 18, 1.5x – 4.5, and 6x – 9. To determine which one correctly represents the measure of angle RST, we would need some context from the problem or a diagram. However, assuming a relationship between the expressions and angle RST using linear or angular sums, we can observe that the expressions 3x – 9 and 6x – 18 are equivalent (by factoring out a 2 from the second expression), and similarly, 1.5x – 4.5 is equivalent to 3x – 9 upon multiplying by 2. The expression 6x – 9 could also be related if RST formed a linear pair with another given angle.

Answer:

he XY is dilated by a scale factor of 1.3 with the origin as the center of dilation to create the X'Y'. So the length of X'Y' is 1.3 times of origin but the slope is the same. The slope is m

Step-by-step explanation:

6 * (4+2)^2 -3^2 =

6 * 6^2 -3^2 =

6* 36-9 =

216-9=

207

Answer is C. 207

The solution of the given quadratic equation will be ( -5, 0 ).

The polynomial having a degree of two or the maximum power of the variable in a polynomial will be 2 is defined as the quadratic equation and it will cut two intercepts on the graph at the x-axis.

Given equation is:-

x²  =   -5x

x²  +   5x  =  0

x  (  x + 5 ) = 0

x  =  0   and   x  =  -5

Therefore the solution of the given quadratic equation will be ( -5, 0 ).

To know more about quadratic equations follow

https://brainly.com/question/1214333

#SPJ2

The solutions to the quadratic equation [tex]\(x^2 = -5x - 3\)[/tex] can be calculated after modifying the quadratic equation and rewriting it to [tex]x^{2} + 5x + 3 = 0[/tex], and then this can be calculated using the quadratic formula. The solutions are x =[tex]\frac{{-5 + \sqrt{13}}}{2}[/tex]and x =[tex]\frac{{-5 - \sqrt{13}}}{2}[/tex] .

To find the solutions to the quadratic equation [tex]\(x^2 = -5x - 3\)[/tex], let's first rewrite it in the standard form:

[tex]\[x^2 + 5x + 3 = 0\][/tex]

Now, we can use the quadratic formula to find the solutions:

[tex]\[x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}\][/tex]

Where a = 1,,b = 5, and c=3.

[tex]\[x = \frac{{-5 \pm \sqrt{{5^2 - 4 \cdot 1 \cdot 3}}}}{{2 \cdot 1}}\][/tex]

[tex]\[x = \frac{{-5 \pm \sqrt{{25 - 12}}}}{2}\][/tex]

[tex]\[x = \frac{{-5 \pm \sqrt{13}}}{2}\][/tex]

So, the solutions are:

x =[tex]\frac{{-5 + \sqrt{13}}}{2}[/tex] and [x = [tex]\frac{{-5 - \sqrt{13}}}{2}[/tex]

Answer:

Its B I just took the test

Answer:

- 6 is the extraneous solution.

Step-by-step explanation:

Given : [tex]\sqrt{-3x -2} = x + 2[/tex].

To find : Which of the following is an extraneous solution .

Solution : We have given that [tex]\sqrt{-3x -2} = x + 2[/tex].

Taking square both sides

-3x - 2 = [tex](x+2)^{2}[/tex].

On applying identity  [tex](a+b)^{2}[/tex] = a² + b² + 2ab

Then ,

-3x -2 =  x² + 2² + 2 * 2 *x

-3x -2 =  x² + 4 + 4x.

On adding both sides by 3x

-2 =  x² + 4 + 4x + 3x

-2 =  x² + 4 + 7x

On adding both sides by 2

0 =  x² + 4 + 7x + 2

On switching sides

x² +7x + 6 = 0

On Factoring

x² +6x + x + 6 = 0

x ( x+ 6 ) +1 (x +6 ) = 0

On grouping

( x +1) ( x +6) = 0

x = -1, -6.

Let check for x = -6

[tex]\sqrt{-3 (-6) -2} = -6 + 2[/tex].

4 =  -4

An extraneous solution is a root of a transformed equation that is not a root of the original equation.

Therefore,  -6 is the extraneous solution.

Answer:

42.06

Step-by-step explanation:

Two points (22,27) and (2,-10)

using distance formula:

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

So, distance between (22,27) and (2,-10) is D

[tex]D=\sqrt{(22-2)^2+(27-(-10))^2}[/tex]

[tex]D=\sqrt{(20)^2+(37)^2}[/tex]

[tex]D=\sqrt{400+1369}[/tex]

[tex]D=\sqrt{1769}[/tex]

[tex]D=42.059[/tex]

Round off two decimal place.

[tex]D=42.06[/tex]

Hence, The distance between the points is 42.06

Final answer:

To find the area of the Mona Lisa in square centimeters, multiply the width and height in inches, then convert to square centimeters using the conversion factor. The area is approximately 4098.97 square centimeters.

Explanation:

To calculate the area of Leonardo da Vinci's Mona Lisa in square centimeters, we start with the given measurements in inches: the painting is 21 inches wide and 30.25 inches tall. Since the area is width multiplied by height, we perform the following calculation:

Area in square inches = width in inches × height in inches

Area in square inches = 21 × 30.25

Area in square inches = 635.25

To convert square inches to square centimeters, we use the conversion factor where 1 square inch = 6.4516 square centimeters.

Area in square centimeters = Area in square inches × 6.4516

Area in square centimeters = 635.25 × 6.4516

Area in square centimeters = 4098.97

Therefore, the area of the Mona Lisa is approximately 4098.97 square centimeters.

Using linear functions, it is found that the store must sell 40 bicycles each month to break even.

A linear function is modeled by:

y = mx + b

In which:

A bicycle store costs $2400 per month to operate, and pays an average of $60 per bike, hence the cost function is given by:

C(x) = 2400 + 60x

The average selling price of each bicycle is $120, hence the revenue function is given by:

R(x) = 120x

It breaks even when cost equals revenue, hence:

R(x) = C(x)

120x = 2400 + 60x

60x = 2400

x = 240/6

x = 40.

The store must sell 40 bicycles each month to break even.

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ2

To determine the number of bicycles the store must sell each month to break even, we can set up a system of equations. The store must sell 40 bicycles each month to break even.

To determine the number of bicycles the store must sell each month to break even, we can set up a system of equations.

Let's say the number of bicycles sold per month is x.

The monthly operating cost of the store is $2400.

The cost of producing each bike is $60, so the total cost to produce x bikes would be $60x.

The average selling price of each bike is $120, so the total revenue from selling x bikes would be $120x.

To break even, the total revenue should equal the total cost, so we can set up the equation:

$120x = $60x + $2400

Simplifying the equation, we get:

$60x = $2400

Dividing both sides by $60, we find:

x = 40

Therefore, the store must sell 40 bicycles each month to break even.

multiply 80 by 1.5

80*1.5 = 120 feet

Answer:  The measure of the fourth angle of the given quadrilateral is 50°.

Step-by-step explanation:  Given that a quadrilateral has three angles that measure 90° , 100° and 120°.

We are to find the measure of the fourth angle of the quadrilateral.

Let x° be the measure of the fourth angle of the quadrilateral.

We know that

The sum of the measures of the four angles of a quadrilateral is 360°.

So, for the given quadrilateral, we have

[tex]90^\circ+100^\circ+120^\circ+x^\circ=360^\circ\\\\\Rightarrow 310^\circ+x^\circ=360^\circ\\\\\Rightarrow x^\circ=360^\circ-310^\circ\\\\\Rightarrow x^\circ=50^\circ.[/tex]

Thus, the measure of the fourth angle of the given quadrilateral is 50°.