Indicate a general rule for the nth term of the sequence when a1 = 5 and r = √3 .

an = (√3)(5)n + 1
an = (√3)(5)n - 1
an = (5)(√3)n - 1
an = (5)(√3)n + 1

Answer:

Step-by-step explanation:

Let's start by simplifying a little:

g(x) = -2[(x − 1)² + 3]

g(x) = -2(x − 1)² - 6

The negative sign in front means a reflection about the x axis.  The 2 coefficient means a vertical stretch by a factor of 2.  The x−1 means a horizontal shift to the right by 1 unit.  And the -6 means a vertical shift down six units.

So the answer is the third one.

Answer:38

Step-by-step explanation:

Answer:

x = 1

Step-by-step explanation:

Since the triangle is right use Pythagoras' identity to solve for x

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

The hypotenuse is the side opposite the right angle, thus

x² + 1² = ([tex]\sqrt{2}[/tex])²

x² + 1 = 2 ( subtract 1 from both sides )

x² = 1 ( take the square root of both sides )

x = [tex]\sqrt{1}[/tex] = 1

Answer:351.9

Step-by-step explanation:351.9 cm3

V = πr2h

V = π(4)2(7)

V = π(16)(7)

V = 112π

V = 351.858

Final answer:

The volume of the cylindrical container is approximately 352.6 cubic inches.

Explanation:

To find the volume of a cylindrical container, you can use the formula V = πr²h, where V is the volume, r is the radius, and h is the height. In this case, the radius is 4 inches and the height is 7 inches. Plug these values into the formula:

V = 3.14 x (4 inches)² x 7 inches = 3.14 x 16 square inches x 7 inches = 352.64 cubic inches.

Since the question asks for the volume rounded to the nearest tenth, the answer is approximately 352.6 cubic inches.

Answer: 68 total outcomes

Final answer:

To find the total number of outcomes, we multiply the number of options for each class type using the fundamental counting principle, resulting in 5 × 4 × 5 × 3 = 300 total outcomes.

Explanation:

The question asks us to find the total number of outcomes for first-year students at a school who must choose one each of 5 English classes, 4 history classes, 5 math classes, and 3 physical education classes. To calculate the total number of outcomes, we use the fundamental counting principle, which states that if there are m ways to do one thing, and n ways to do another, then there are m × n ways of doing both.

In this scenario, the student can choose:

5 English classes

4 history classes

5 math classes

3 physical education classes

Applying the fundamental counting principle, we multiply the number of options for each subject:

5 (English) × 4 (History) × 5 (Math) × 3 (Physical Education) = 300 total outcomes.

Answer:

B

Step-by-step explanation:

If I have two dollars of debt (negative) and add 2 more dollars of debt (negative), I now owe 4 dollars in debt (negative).

-2+-2=-4

Answer:

B.) Negative 4

Step-by-step explanation:

A negative plus a negative equales a negative, beacause you aren't adding a positive to cancle out some of the numbers. your just adding more negative.

Answer:

The value of x (which is also the height of this triangle) is x = 5 units.

Step-by-step explanation:

The formula for the area of a triangle of base b and height h is

A = (1/2)(b)(h).

Here A = 10 units² = (1/2)(4 units)(x).

Multiplying both sides by 2 yields    20 units² = (4units)(x), and thus

       20 units²

x = ------------------ = 5 units

         4 units

The value of x (which is also the height of this triangle) is x = 5 units.

Answer:

x=5

Step-by-step explanation:

Answer: -4

Step-by-step explanation:

3-9=-6

-6*5=-30

-30-1=-31

6*-31=-186

-186+2=-184

8-2=6

6*7=42

42+4=46.

-184/46=-4

Answer and Step-by-step explanation:

All you have to do is follow the order of operations.

We do everything in the first set of parenthesis, then we work our way out.

[tex]\frac{6(5(3-9)-1) + 2}{7(8-2)+4}[/tex]

First, we would subtract 9 from 3, and 2 from 8.

3 - 9 equals -6

8 - 2 equals 6

[tex]\frac{6(5(-6)-1) + 2}{7(6)+4}[/tex]

Now, we multiply those numbers.

5 times -6 equals -30

7 times 6 is 42

[tex]\frac{6(-30 -1) + 2}{42+4}[/tex]

Now, we simplify.

-30 minus 1 equals -31

42 + 4 equals 46

[tex]\frac{6(-31) + 2}{46}[/tex]

Multiply -31 by 6, then add 2 to the product.

-31 times 6 equals -186

-186 plus 2 equals -184

[tex]\frac{-184}{46}[/tex]

Finally, we divide.

-184 divided by 46 equals

-4

-4 is the answer to the expression.

I hope this helps!

#teamtrees #PAW (Plant And Water)

The transitive property of equality is correctly represented by option A, stating that if WX = XY and XY = YZ, then WX = YZ.

The correct answer is option A.

The transitive property of equality states that if two quantities are equal to a third quantity, then they are equal to each other. Among the given options, the statement that represents the transitive property is:

A) If WX = XY and XY = YZ, then WX = YZ.

This statement adheres to the transitive property because it asserts that if WX is equal to XY and XY is equal to YZ, then it logically follows that WX must be equal to YZ. This principle is fundamental in mathematics and logic, providing a way to establish equality relationships through a chain of equalities.

On the other hand, options B and C do not correctly represent the transitive property:

Option B is a statement about the equality of angles, and it does not involve the transitive relationship between two quantities.

Option C represents the reflexive property (an equality is always equal to itself) rather than the transitive property.

In conclusion, option A accurately represents the transitive property of equality.

The question probable may be:

Which statement represents the transitive property of equality?

A) If WX = XY and XY = YZ, then WX = YZ

B) If mZA = mZB, then mZB = mZA

C) If WX = XY, then XY = WX

Answer:

Step-by-step explanation:

The equation of a circle in standard form:

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

(h, k) - center

r - radius

We have the equation:

[tex](x-3)^2+y^2=8\to(x-3)^2+(y-0)^2=(\sqrt8)^2[/tex]

Therefore

the center: [tex](3,\ 0)[/tex]

the radius: [tex]r=\sqrt8\to r=\sqrt{4\cdot2}\to r=\sqrt4\cdot\sqrt2\to r=2\sqrt2[/tex]

Answer:

The answer is the 1st [tex]\frac{\left[\begin{array}{cc}16&3\\8&1\end{array}\right]}{-8}=1[/tex]

Step-by-step explanation:

Lets revise the Cramer's rule

- If the system of equation is ax + by = c and dx + ey = f

- A is the matrix represent this system of equation

- The first column has the coefficients of x, and

  the second column has the coefficients of y

∴ A = [tex]\left[\begin{array}{cc}a&b\\d&e\end{array}\right][/tex]

- Ax means replace the column of x by the answers of the equation

∴ Ax = [tex]\left[\begin{array}{ccc}c&b\\f&e\end{array}\right][/tex]

- Ay means replace the column of y by the answers of the equation

∴ Ay = [tex]\left[\begin{array}{ccc}a&c\\d&f\end{array}\right][/tex]

- x = Dx/D, where Dx is the determinant of Ax and D is the determinant

 of A

- The determinant of A = ae - bd

- The determinant of Ax = ce - bf

* Now lets solve the problem

∵ x + 3y = 16 and 3x + y = 8

∴ A = [tex]\left[\begin{array}{cc}1&3\\3&1\end{array}\right][/tex]

- Replace the column of x by the answer to get Ax

∴ Ax = [tex]\left[\begin{array}{cc}16&3\\8&1\end{array}\right][/tex]

∵ [tex]x=\frac{Dx}{D}[/tex]

∵ Dx = [tex]\left[\begin{array}{cc}16&3\\8&1\end{array}\right]=(16)(1)-(3)(8)=16-24=-8[/tex]

∵ D = [tex]\left[\begin{array}{cc}1&3\\3&1\end{array}\right]=(1)(1)-(3)(3)=1-9=-8[/tex]

∴ x = [tex]\frac{\left[\begin{array}{cc}16&3\\8&1\end{array}\right]}{-8}=\frac{-8}{-8}=1[/tex]

* x = [tex]\frac{\left[\begin{array}{cc}16&3\\8&1\end{array}\right]}{-8}=1[/tex]

Answer:

The cake costs $30

Step-by-step explanation:

9(10)=90

120-90=30

Answer:  34 kids in all

Step-by-step explanation:

: 40 - 6 = 34

0            6                              34

|------------|----------------------------|

The bus can hold no more than 40 people. 6 are already on so at most, there can be 34 others on board. But the number doesn’t have to be exact.

Answer:

x=3; x=-3; x=√5; x=-√5

Step-by-step explanation:

The equation can be simplified by treating (x^2 - 2) as y. Solving the quadratic equation for y results in y = 4 and y = 7. By substituting these back into the equation and solving for x, we find x = ±sqrt(6) and x = ±sqrt(9). Therefore, one possible solution for x is sqrt(6).

The equation provided is a quadratic in the form of x. In this case, let's take: (x^2 - 2) = y. Therefore the equation can be rewritten as: y^2 - 10y + 21 = 0. In order to find the roots of the equation, we should use the quadratic formula: y = [10 ± sqrt((10)^2 - 4*1*21)] / (2*1), which gives us y = 4 and y = 7. Now we substitute back y = (x^2 - 2). This will form two more quadratic equations: x^2 - 2 = 4 and x^2 - 2 = 7. Solving these, we get x = ±sqrt(6) and x = ±sqrt(9). So, one value of x that is a solution to the equation could be sqrt(6).

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Answer:

3x+2y

Step-by-step explanation:

-3x+2y+x-5x

-5x-3x=-8x+x=-7x

-7x+2y

Answer: [tex]-7x+2y[/tex]

Step-by-step explanation:

You have the expression [tex]-3x +2y + x -5x[/tex]

You can observe that this expresssion has two variables. These are:

"x" and "y"

Then, to simplify the expression given, you need to add the like terms (terms that have the same variable), which are:

[tex]-3x[/tex], [tex]-5x[/tex] and [tex]x[/tex]

Therefore, adding the like terms, you get:

[tex](-3x+x-5x)+2y\\-7x+2y[/tex]

Then, the simplified form of  [tex]-3x +2y + x -5x[/tex] is:

[tex]-7x+2y[/tex]

Answer:

6% x = 8,880 : x = selling price of house.  

x = $148,000 : solve for x

Step-by-step explanation:

The selling price of the house can be calculated by dividing the commission ($8,880) by the commission rate (0.06). This gives a selling price of $148,000.

To solve this problem, you need to understand that the 6% commission the real estate agent received is based on the selling price of the house. You can find the selling price by dividing the commission by the percentage commission expressed as a decimal.

Here's the step-by-step solution:

So, the selling price of the house on which the agent earned an $8,880 commission at a rate of 6% was $148,000.

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it's a.

three more is +3 and it equals 105

that already eliminates c and d

next it says twice the sum of a number and half the number

Answer:

a

Step-by-step explanation:

Answer:

$2680.00

Step-by-step explanation:

We are informed that Faith Franklin sells furniture and earns 8% commission on her total sales. She sold $33,500 last month. We are required to determine her earnings for that month;

We simply evaluate 8% of  $33,500

[tex]\frac{8}{100}*33500=2680[/tex]

Therefore, she earned $2680.00

From the information given, it is true to state that:

"The students in school 1 generally spend more time doing volunteer work than the students in school 2." (Option B)

In statistics, a dot plot, also known as a dot chart is a type of histogram or histogram-like chart that is used to represent data that is relatively small.

It is best used for indicating the statistical relationship between the data and its clusters, outliers, and gaps.

Learn more about dot plots at;
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School 2 students generally spend more time on volunteer work than School 1, while School 1 students tend to spend more time than School 3.

Based on the dot plots representing the number of hours spent on volunteer work by students from three different high schools, we can draw some conclusions about the median values of the data sets.

Firstly, comparing School 1 and School 2, it appears that students in School 2 generally spend more time doing volunteer work. This conclusion is supported by the higher frequency of dots in the higher hour range in School 2 compared to School 1.

Next, comparing School 1 and School 3, it seems that students in School 1 generally spend more time on volunteer work. The dot plot for School 1 shows a higher frequency of dots in the higher hour range compared to School 3.

In summary, students in School 2 generally spend more time doing volunteer work than those in School 1, while students in School 1 tend to spend more time on volunteer work than those in School 3.

Answer:

17.15 cm²

Step-by-step explanation:

The area (A) of a parallelogram is calculated using the formula

A = bh ( b is the base and h the perpendicular height )

here b = AE + EB = 1.4 + 3.5 = 4.9 and h = BF = 3.5, hence

A = 4.9 × 3.5 = 17.15

Answer:

1.  1/6 , 2/9 , 1/4 ,  5/18

2.  1/3 , 4/9 , 1/2 , 5/9

3. 5/12 , 5/9 , 5/8 , 25/36

Hope this helps!

ANSWER

A. (243pi+162) ft^2

EXPLANATION

The area of the shaded region is the sum of the area of the major sector and the area of the isosceles triangle.

Area of major sector

[tex] = \frac{360 - 90}{360} \times \pi \times {18}^{2} [/tex]

[tex] = 243\pi {ft}^{2} [/tex]

The area of the isosceles triangle is calculated using the formula;

[tex] = \frac{1}{2} {r}^{2} \sin( \theta) [/tex]

[tex]= \frac{1}{2} \times {18}^{2} \sin(90 \degree)[/tex]

[tex] = 162 {ft}^{2} [/tex]

The area of the shaded region

[tex] = (243\pi + 162) {ft}^{2} [/tex]

The correct answer is A.

Answer: A

Step-by-step explanation:

1. 49 pic square ft

2. 168 units

3. (4-[tex]\pi[/tex])ft^2

4. 314square ft

5. 22.6 square mm

6. 12 inches

7. 12 [tex]\pi ft^2[/tex]

8. 28.125 [tex]\pi[/tex] square centimeters

9. 22.1 cm

10. (243pi+162) ft^2

Just took the pracitce this will get oyu a 100 hope this helps

[tex]8x - 2y = - 16 \\ \\ 1. \: 2(4x - y) = - 16 \\ 2. \: 4x - y = - \frac{16}{2} \\ 3. \: 4x - y = - 8 \\ 4. \: 4x = - 8 + y \\ 5. \: 4x = y - 8 \\ 6. \: x = \frac{y - 8}{4} [/tex]

D is the answer but I’m not sure

Answer:

34

Step-by-step explanation:

Each of the base angles = x

x + x + 112 = 180                Subtract 112 from both sides. Simplify the left side.

2x + 112 - 112 = 180 - 112    Simplify

2x = 68                              Divide by 2

2x/2 = 68/2                       Simplify

x = 34

Each of the base angles = 34 degrees.

Answer:

83

Step-by-step explanation:

Answer:

4.8 minutes

Step-by-step explanation:

Time = Speed * Distance

Time = 6 mi / 30 min * 24 miles=  1 mi / 5 min * 24 miles = 0,2 mi / min * 24 = 4.8 minutes

Answer:

So if you know that you can complete 6 miles over the course of 30 minutes it is just matter of multipling 30 minutes times 4, this is becasue it takes 4 times your base distance and time to get to yur goal of 24 miles.

30 x 4 equal 120

which you divide by 60 (because you have 60 minutes in one hour)

so it is safe to say that it will take 2 hours of 120 minutes to ski a ditance of 24 miles at a speed of 6 miles per 30 minutes.

Hope this helps!

Answer

The answer is A or 0.20

Step-by-step explanation:

So if you add all the numbers up so (4+4+10+2+5+6+8+1) that would equal=40

8 is the number of girls with brown hair so I would divide 8 by 40

8/40=0.20

Hope this helps!

Answer:

0.20

There are 8 brown-haired girls, out of 40 students.

8

40

Answer:

-3.125

Step-by-step explanation:

Answer: this is the correct answer -3.125

Answer:

x=4 y=10

Step-by-step explanation:

-5y+8x=-18

5y+2x=58

so the first thing you do is cancel out the 5s then you add the 8+2 and -18+58 then you have 10x=40 then you divide both sides by ten. then you plug that four back into an equation so i did 5y+2(4)=58 then 5y+8=58 you subtract 8 from both sides and you have 5y=50 divide both sides by 5 and you get y=10 and that is how you do that

Answer:

D) [tex]x^3+8y^6[/tex]

Step-by-step explanation:

We have been given four choices.

A) [tex]3x^3+8y^6[/tex]

B) [tex]8x^3-27y^6[/tex]

C) [tex]125x^6-9y^3[/tex]

D) [tex]x^3+8y^6[/tex]

Now we need to find about which of the above choices is a sum of cubes.

Basically we need to check which one of the given choices can be represented in cubic form along with addition sign.

3 and 9 can't be written in cubic form unless we use radical numbers.

So the only choice left is D)

D) [tex]x^3+8y^6[/tex]

[tex]=x^3+2^3(y^2)^3[/tex]

[tex]=x^3+(2y^2)^3[/tex]

which is clearly visible as sum of cubes.

The answer is:

D) [tex]x^{3}+8y^{6}[/tex]

We are looking for the expression that can be obtained from a sum of cube factoring, the form of the sum of cubes will be:

[tex]a^{3}+b^{3}=(a+b)(a^{2} -ab+b^{2})[/tex]

The only option that matches with the sum of cubes form is the last option,

D) [tex]x^{3}+8y^{6}[/tex]

and it can be rewritten as the following expression:

[tex]x^{3}+8y^{6}=x^{3}+(2y^{2})^{3}\\\\x^{3}+(2y^{2})^{3}=(x+2y^{2})(x^{2}-2xy^{2}+(2y^{2})^{2})\\\\(x+2y^{2})(x^{2}-2xy^{2}+(2y^{2})^{2})=(x+2y^{2})(x^{2}-2xy^{2}+4y^{4})\\\\(x+2y^{2})(x^{2}-xy^{2}+4y^{4})=x*x^{2}-2x^{2}y^{2}+2xy^{4}+2x^{2}y^{2}-2xy^{4}+8y^{6}\\\\x*x^{2}-2x^{2}y^{2}+2xy^{4}+2x^{2}y^{2}-2xy^{4}+8y^{6}=x^{3}+8y^{6}[/tex]

Therefore, we have that:

[tex]x^{3}+8y^{6}=x^{3}+(2y^{2})^{3}=(x+2y^{2})(x^{2}-2xy^{2}+(2y^{2})^{2})=x^{3}+8y^{6}[/tex]

Hence, the correct answer is:

D) [tex]x^{3}+8y^{6}[/tex]

Have a nice day!