Consider the two exponential equations shown. Identify the attributes for each equation to complete the table.​

Step-by-step explanation:

a = x^2 - 1

b = 2x

c = x^2 + 1

The Pythagorean theorem states

a^2 + b^2 = c^2

Let's find a^2 and b^2 and add them to get a^2 + b^2:

a^2 = (x^2 - 1)^2 = x^4 - 2x^2 + 1

b^2 = (2x)^2 = 4x^2

a^2 + b^2 = x^4 - 2x^2 + 1 + 4x^2 = x^4 + 2x^2 + 1

Now let's find c^2:

c = x^2 + 1

c^2 = (x^2 + 1)^2 = x^4 + 2x^2 + 1

We see that both a^2 + b^2 and c^2 equal x^4 + 2x^2 + 1, so we have shown that the triangle is a right triangle.

We can see that a² + b² = c² = x⁴ + 2x² + 1, indicating that the triangle is a right triangle.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometric function.

According to Pythagoras, the sum of the squares of two sides equals the square of the longest side.

Given data;

a = x² - 1

b = 2x

c = x² + 1

According to the Pythagorean theorem;

[tex]\rm a^2 + b^2 = c^2[/tex]

Let's find a^2 and b^2 and add them to get a^2 + b^2:

[tex]\rm a^2 = (x^2 - 1)^2 \\\\ a^2 = x^4 - 2x^2 + 1 \\\\ b^2 = (2x)^2 \\\\ b^2 = 4x^2\\\\[/tex]

Left hand side:

[tex]\rm a^2 + b^2 = x^4 - 2x^2 + 1 + 4x^2 \\\\ a^2 + b^2 =x^4 + 2x^2 + 1[/tex]

Right hand side:

[tex]\rm c^2 = (x^2 + 1)^2 \\\\ c^2 = x^4 + 2x^2 + 1[/tex]

L.HS.=R.H.S

Hence,the given triangle is a right angled triangle.

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Answer:

g=6

Step-by-step explanation:

[tex]g^{2} -12=-36\\g^{2} -12+36\\ (g-6)(g-6)\\ g-6=0\\ g=6[/tex]

Answer:

12) 154   squared meters

13) 307  cm^2

Step-by-step explanation:

12) A circle has area pi*r^2

r is half the diameter so half of 14 is 7

pi in this case is 22/7

A=22/7 * (7)^2

A=22/7  * 49

A=22     *49/7

A=22     *7

A=154 squared meters

13)  Area of rectangle is 10(18)=180

      Area of half a circle is .5*pi*r^2=.5*pi*9^2  

       Adding the two areas together would result in a total area of 307.2 squared centimeters

Answer:

2.4

Step-by-step explanation:

tanB = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AC}{BC}[/tex] = [tex]\frac{12}{5}[/tex] = 2.4

Answer:  2.4

Step-by-step explanation:

[tex]tan\theta=\dfrac{opposite}{adjacent}\\\\\\tan\angle B=\dfrac{12}{5}\\\\\\tan\angle B=2.4[/tex]

Answer: alternate exterior angles

Step-by-step explanation:

Answer:  The correct answer is:  " 5% increase " .

_________________________________________

Step-by-step explanation:

_________________________________________

Note:  The particular "percentage change" is a "percent increase" ; since we are going from "20" to "21" which is an "increased value of "1" .

_________________________________________

Note the formula for "percent increase" ; as follows:

_________________________________________

Percent increase = [(new value - original value)/original value] * 100 ;

_________________________________________

So;  let us "plug in" our known values; to solve for the "percentage change"    

                 →  [i.e. "percent increase" (in this case)] :

_________________________________________

 Percent increase  =  [(21 - 20)/20] * 100 ;

                                =  [1/20] * 100 ;

                                = [100/20] ;

                                = 5.

_________________________________________

The correct answer is:  " 5 % increase" .

_________________________________________

Hope this helps!

  Best wishes to you!

_________________________________________

Evaluate 2(x + 1) - 3 when x = 6.

First, plug in x value.

2(6 + 1) -3   ParenthesisEMDAS

2(7) - 3       PEMultiplyDAS

14 - 3          PEMDASubtract

11 ←

Answer:

11

Step-by-step explanation:

just took test

Answer:

13.9 containers or 14 rounded

Step-by-step explanation:

2/7 of a pound is 0.28571429 in decimal form. To solve you have to know how many 2/7 of a pound will go into 4 pounds. So you divide 2/7 of a pound by 4 pounds, and the answer is 14.

Answer:

14

Step-by-step explanation:

He will need 14 containers. 4 times 7/2 is 28/2. You then have to simplify it and will get 14.

Answer:

slope is -5

y-intercept is -5

Step-by-step explanation:

Solve for y to write in y=mx+b

m is slope

b is y-intercept

5x+y=-5

Subtract 5x on both sides

    y=-5x-5

slope is -5

y-intercept is -5

Answer:

6

Step-by-step explanation:

Plug in 3 into both expressions

Then add those results

2(3)+21=6+21=27

3-24             =-21

                    -------

                         6  is the sum of 27 and -21

Answer:

[tex]x^3+1[/tex]

Step-by-step explanation:

[tex] 26(x^3+1)^2-22(x^3+1)-3=0 [/tex]

Comparing to

[tex] A(u)^2+B(u)+C =0 [/tex]

Where A,B,C are constants

You should see that we need to substitute the [tex]x^3+1[/tex] with u.

we can take a peek at two of those lines  hmmm say y = 5x + 3 and y = 5x + 7.

let's notice, those two equations for those lines are in slope-intercept form, so let's solve the system.

since y = y then

5x + 3 = 5x + 7

3  = 7    what the?

well, notice, both lines have the same slope of 5, but different y-intercept, one has it at y = 3 and the other at y = 7, what does that mean?

it means that both lines are parallel to each other, one may well be above the other, but both are parallel, and since a solution to the system is where their graphs intersect, well, parallel lines never touch, so a system with two parallel lines has no solutions.

The two lines are parallel.

We have a girl Deedra who has the equations for lines A and B. When she solved for the point where these two lines intersect, she ended up with the equation 3 = 7.

We have to investigate what it tells about the nature of lines.

The slope intercept form of an equation of line is -

y = mx + c

Let's assume we have two lines with their equations be -

[tex]y_{1} = m_{1} x_{1} + c\\y_{2} = m_{2} x_{2} + d[/tex]

To find the intersecting points of these two lines, then -

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

Therefore -

[tex]m_{1} x_{1} +c =m_{2} x_{2} +d\\[/tex]

Now, in the question she found out that 3 =7 which is same c = d. To fulfill this condition, the slope of these two lines should be equal. Hence, we can conclude that the two lines are parallel.

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Answer:

[tex](x+3)^{2}+(y+5)^{2}=36[/tex]

Step-by-step explanation:

we know that

The equation of a circle in standard form is equal to

[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]

In this problem we have

[tex](h,k)=(-3,-5)[/tex]

[tex]r= 6\ units[/tex]

substitute

[tex](x+3)^{2}+(y+5)^{2}=6^{2}[/tex]

[tex](x+3)^{2}+(y+5)^{2}=36[/tex]

Answer:  Point, Point, Line

Step-by-step explanation:

A plane and a line intersect at a point .  Think of a piece of paper as a plane and a pen as a line.  What happens when you push the pen through the paper?  It creates a point!

Two lines intersect at a point .

Two planes intersect at a line . Think of a piece of paper laid horizontally on a table and another piece of paper standing on it vertically.  What can you draw at the places of intersection? A line!

Answer:

7

Step-by-step explanation:

Blue is 7 and the Red is 7

Answer:

7

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

The only domain problems are going to come from the square root you have there. You only want to square root 0 or positive numbers,. In other words, you want x+2 to be greater than 0 or equal to 0.

x+2>=0

x>=-2

So x has to be greater than ot equal to 0

Answer:

Step-by-step explanation:

Use PEMDAS:

P Parentheses first

E Exponents (ie Powers and Square Roots, etc.)

MD Multiplication and Division (left-to-right)

AS Addition and Subtraction (left-to-right)

[tex]\dfrac{1}{2}\times\underbrace{(6\times4)}_{1}+3+2\\\\=\underbrace{\dfrac{1}{2}\times24}_{2}+3+2\\\\=12+3+2=17[/tex]

Answer:

Practical probability:  9 / 20 = 45%

Theoretical probability: 3 / 6 = 50%

Step-by-step explanation:

So, we have 20 rolls:

1 5 3 2 3 6 5 6 3 3 4 4 1 3 6 5 3 2 2 6

Out of which we have 9 even numbers: 2 6 6 4 4 6 2 2 6

So, the practical probability is 9 / 20 or 45%

The theoretical probability is:

Possible outcomes (6): 1 2 3 4 5 6

Even numbers possible (3): 2 4 6

P = 3 / 6 = 50%

The practical probability is a bit lower (45%) than the theoretical probability (50%) but that's most probably due to the low number of rolls, it's just one roll away from being on target.  With a greater number of rolls, the student would get closer to the theoretical probability.

Answer:

y = x - 6.

Step-by-step explanation:

Do the division:

x + 2 ) x^2 - 4x + 8 (  x - 6 <------- Quotient.

          x^2 + 2x

                    -6x + 8

                    -6x - 12

                     ----------

                              20

Answer:

1/6

Step-by-step explanation:

To find the common ratio, you compare a few pairs of consecutive terms, by dividing an element by its predecessor.

12 / 72 = 1/6

2 / 12 = 1 / 6

1/3 / 2 = 1 / 6

The ratio is constant... so that's your common ratio to go from one term to the next.  

To go from one term to the next, you have to multiply by 1/6.

Answer:

10r(d - 6).

Step-by-step explanation:

The GCF is 10r.

So the answer is:

10r(d - 6).

Answer:

54°

Step-by-step explanation:

Since the triangle is right use the cosine ratio to solve for angle

cos? = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{26}{44}[/tex], hence

? = [tex]cos^{-1}[/tex] ( [tex]\frac{26}{44}[/tex] ) ≈ 54° ( nearest degree )

Answer:

6

Step-by-step explanation:

For both to be chosen the other spot can be taken by any of the other 6 people in the row. So six possibilities

Answer:

A. [tex]^6C_1=6[/tex]

Step-by-step explanation:

Given,

The total number of people = 8,

The number of people have to chosen = 3,

Since, me and my friend both have to be chosen,

So, the remaining number of people = 8 - 2 = 6,

And, the number of remaining number of people have to be chosen = 3 - 2 = 1

Also, the order does not matter,

Hence, the total way of choosing = Total combination of me and my friend × total combination of choosing 1 person out of 6 people

[tex]=^2C_2\times ^6C_1[/tex]

[tex]=1\times ^6C_1[/tex]

[tex]=6[/tex]

Option A is correct.

Hello there!

X = 67°

Answer and work are provided in the image attached.

Answer:

100 Degrees

Step-by-step explanation:

It's correct for Acellus! :-)

The volume of the space outside the pyramid but inside the prism is 250 cubic centimeters.

To find the volume of the space outside the pyramid but inside the prism, we first need to determine the volumes of both the prism and the pyramid.

The prism has a height of 12 centimeters and a square base with sides measuring 5 centimeters. The volume of a rectangular prism is calculated by multiplying the base area by the height. In this case, the base area is 5 cm * 5 cm = 25 square centimeters. Therefore, the volume of the prism is 25 cm² * 12 cm = 300 cubic centimeters.

The pyramid has the same square base as the prism, with sides measuring 5 centimeters. However, its height is half that of the prism, which is 12 cm / 2 = 6 centimeters. The volume of a pyramid is calculated by multiplying the base area by one-third of the height. In this case, the base area is 25 cm², and one-third of the height is 6 cm / 3 = 2 centimeters. Therefore, the volume of the pyramid is 25 cm² * 2 cm = 50 cubic centimeters.

To find the volume of the space outside the pyramid but inside the prism, we subtract the volume of the pyramid from the volume of the prism: 300 cubic centimeters - 50 cubic centimeters = 250 cubic centimeters.

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Answer:

Step-by-step explanation:

Let x - y = A

A^4 - A^2

A^2 ( A^2 - 1)

A^2 (A + 1)(A - 1)

(x - y)^2 (x - y + 1)(x - y - 1)

If I have not thought out the question properly please leave me a note.

Answer: 60 and 80

Step-by-step explanation: Start off with the highest number, which is 10. The numbers between 49 and 95 that can be divided by 10 are 50, 60, 70, 80, and 90. Next, figure out what can be divided by 5. All of them can. Next, find out what numbers can be divided by 4. 50, 70, and 90 can’t because they would end up as a decimals. 60 and 80 can be divided by 4, 5, and 10.

Answer:

V≈4.19ft³

Step-by-step explanation:

The volume of a sphere with a radius of 1 foot is 4.19ft³.

In order to find this:

V=4

3πr3=4

3·π·13≈4.18879ft³

[tex]V=\dfrac{4}{3}\pi r^3\\\\V=\dfrac{4}{3}\cdot3.14\cdot 1^3\approx4.19\text { ft}^3[/tex]