What is the common ratio of the geometric sequence below?

–96, 48, –24, 12, –6, ...

The required answers are 1) \($$A = x^2 + 28x + 192$$\) 2) 300000 3) \($$x^2 + 28x + 192 = (x + 14 - 2\sqrt{19})(x + 14 + 2\sqrt{19})$$\).

area of the land purchased is given as 480m², and the dimensions of the land are (x+12)mx(x+16)m. Therefore, the area of the land can be expressed as:

\($$A = (x+12)(x+16)$$\)

Expanding this expression, we get:

\($$A = x^2 + 28x + 192$$\)

Hence, the area of the land purchased is given by the polynomial expression \($x^2 + 28x + 192$\).

The total budget for the expenses is Rs. 5,00,000. If Mr. Chand's daughter is ready to share 3/5 of the expenses, then the fraction of the expenses she will pay is:

\($\frac{3}{5}=\frac{x}{500000}$$\)

Simplifying this expression, we get:

\($x = \frac{3}{5}\times 500000 = 300000$$\)

Therefore, Mr. Chand's daughter will pay Rs. 3,00,000 towards the expenses.

We can solve the polynomial \($x^2 + 28x + 192$\) into different factors by using the quadratic formula:

\($x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$\)

Here, the coefficients of the polynomial are:

\($$a = 1, \quad b = 28, \quad c = 192$$\)

Substituting these values in the quadratic formula, we get:

\($x = \frac{-28 \pm \sqrt{28^2 - 4\times 1 \times 192}}{2\times 1}$$\)

Simplifying this expression, we get:

\($$x = -14 \pm 2\sqrt{19}$$\)

Therefore, the polynomial \($x^2 + 28x + 192$\) can be factored as:

\($$x^2 + 28x + 192 = (x - (-14 + 2\sqrt{19}))(x - (-14 - 2\sqrt{19}))$$\)

or

\($$x^2 + 28x + 192 = (x + 14 - 2\sqrt{19})(x + 14 + 2\sqrt{19})$$\)

So, we have factored the polynomial into two factors.

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Answer:

1. ∧A and ∧B

2. ∧A and ∧C

3. ∧E and ∧O

Answer: \(cosx =- \sqrt{ 1 - sin^2x}\)

Step-by-step explanation:

Generally speaking; \(cos^2x + sin^2x = 1\)

rearranging this gives us all sorts of cool things.

for now, we will use: \(cosx = \sqrt{ 1 - sin^2x}\)

This however, is general.

In the third quadrant, cosine is negative. So cosx in QIII will be:

\(cosx =- \sqrt{ 1 - sin^2x}\)

and thats the answer :)

x = 28/3

y = 7/3

Step-by-step explanation:

If the triangles are congruent, then corresponding sides are equal.

x = 4y

x + 1 = y + 8

Solve the system of equations using substitution or elimination.  Using substitution:

4y + 1 = y + 8

3y = 7

y = 7/3

Solving for x:

x = 28/3

:D

Answer:

4.5 hours

Step-by-step explanation:

fbdjdbercyTxxivdu

Answer:

Basically You are asking how many hours we need to reach 7:00, if we are at 2:30, so: we need 4hours, to reach 6:30, and and extra 30minutes to reach 7:00pm. The answer is 4hours and 30minutes.

Answer:7/15

Step-by-step explanation:

The expression "F = {(x, y) : φ(x, y, p)}" represents a set of ordered pairs (x, y) that satisfy a condition defined by the function φ. The interpretation and nature of the set F depend on the specific function φ and the parameter p, which determine the relationship between the variables x, y, and p.

The expression "F = {(x, y) :  φ(x, y, p)}" represents a set F consisting of ordered pairs (x, y) that satisfy a particular condition defined by the function  φ, which takes the variables x, y, and p as inputs.

To fully understand the meaning of F, we need to delve into the function  φ and its relationship with the variables x, y, and p. The function φ could represent a wide range of mathematical relationships or conditions that determine the inclusion of certain pairs (x, y) in the set F.

For instance, let's consider a specific example where vraphi(x, y, p) is defined  φ(x, y, p) = \(x^2 + y^2 - p^2.\)In this case, F = {(x, y) : \(x^2 + y^2 - p^2\)= 0} represents a set of ordered pairs (x, y) that satisfy the equation \(x^2 + y^2 - p^2 = 0.\) This equation represents a circle with radius p centered at the origin (0, 0). Consequently, F corresponds to all the points lying on the circumference of this circle.

It is important to note that the specific meaning and implications of F heavily rely on the nature of the function  φ and the parameter p. Different functions and parameters will yield distinct sets F with their own unique characteristics and interpretations.

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Answer:

Polygon A: A, D, E

Polygon B: F, G, H

Polygon C: K, L, M, N, O

Polygon D: S, T

Step-by-step explanation:

Answer:

10-1/3x=4

Step-by-step explanation:

10 minus is 10-

1/3 of a number is 1/3x

is 4 means =4

10-1/3x=4

each box costs $3 : The cost of one box = $3

12 boxes of cookies : The total number of boxes = $12

For the total cost of 12 boxes : Multiply the cost of one box by the number of boxes

The total cost of 12 boxes = 12 x $3

The cost of 12 boxes = $36

The cost of 12 boxes of cookies ia $36

Answer : $36

The answer is: x is 0

Answer:

True

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

Answer:

B false

Step-by-step explanation:

The Theorem states that for a right triangle,

a^2 + b^2 = c^2

where c is the hypotenuse and a and b are the two shorter sides.

So does our given lengths work? Let's see:

16^2+30^2=35^2

256+900=1225

1156=1225

1156≠1225

And as we can see, the two sides do not equal each other, so this means the sides do not make a right triangle.

Answer:

23.5 inches^2

Step-by-step explanation:

Area of triangle = 1/2 * base * height

area = 1/2 * (5+2) * (5+4)

area = 31.5 in^2

Area of rectangle = length * breadth

area = 4 * 2

area = 8 in^2

Area of figure = area of triangle - area of rectangle

area = 31.5 - 8

area =23.5 in^2

Answer:

Step-by-step explanation:

The ratio here would be 1 foot to every 10 inches, or without any units: 1/10

Answer:

False, the computer can hold 10,000 pictures.

Step-by-step explanation:

(2x10^9) divided by (2x10^5) is exactly 10,000

Answer:

0.85

Step-by-step explanation:

1.37-0.52=0.85

All rational numbers have the following in common:

1. They can be expressed as a fraction

2. They can be represented on a number line.

3. They can be added, subtracted, multiplied, and divided.

4. They can be written as terminating or repeating decimals.

1. Fractional representation: All rational numbers can be expressed as a fraction, where the numerator is an integer and the denominator is a non-zero integer.

2. Number line representation: All rational numbers can be represented on a number line.

3. Arithmetic operations: All rational numbers can be added, subtracted, multiplied, and divided.

4. Decimal representation: All rational numbers can be written as terminating or repeating decimals.

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Answer:

14

Step-by-step explanation:

Step 1:

1/2x - 3 = 25

Step 2:

1/2x = 28

Answer:

x = 14

Hope This Helps :)

The system of equations has an infinite number of solutions.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 8 is an equation.

We have,

3x + 2y = 6 ____(1)

6x + 4y = 12 _____(2)

Applying the substitution method.

3x + 2y = 6

x = (6 - 2y)/3 in (2)

6 (6 - 2y)/3 + 4y = 12

2 (6 - 2y) + 4y = 12

12 - 4y + 4y = 12

12 = 12

This means,

It has an infinite number of solutions.

Thus,

An infinite number of solutions.

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The complete question is:

Graph the system of equations

3x + 2y = 6

6x + 4y = 12

and find the solution to the system.

Answer:

Positive

Step-by-step explanation:

There are a couple ways we can go about this.

First, we can see that as x increases, so does y, so that means its positive

For perspective, if x is the amount of time and y is the number of sales, we can see that the sales are going up and not going down or staying at the same place

If you wanna check your work on that, you can plot two points and find the slope using y1-y1/x1-x2 and the slope will be positive.

We can also use the process of elimination, we know it can't be zero because it's not a straight, horizontal line and we know its not undefined because it isn't a straight vertical line, so it's between negative and positive, and since the line is going up, that means that it's positive.

The form of the equation of the circle is

(h, k) is the center

r is the radius

Let us compare it with the given equation to find the center and the radius

From the comparing

h = -1

k = 1

r^2 = 36

Find the square root of 36 to get r

The center is (-1, 1) and the radius is 6

Answer:

(cot)x always hold

Step-by-step explanation:

Answer: C 92) = 0.0625(4)

Step-by-step explanation:

it iz

Answer:

1/2x +2

Step-by-step explanation:

If we start at (0,2), to the next point you rise 1 run 2, so 1/2 slope. You can see the 2 is the y intercept.

The equation X^2/2 - 8 = 2X - 2 has two solutions, X = 6 and X = -2. These are the values of X that satisfy the equation and make both equations Y = X^2/2 - 8 and Y = 2X - 2 intersect on the graph.

To find the solutions to the equation X^2/2 - 8 = 2X - 2, we need to set the two equations equal to each other and solve for X.

The equation is:

X^2/2 - 8 = 2X - 2

To simplify the equation, let's multiply both sides by 2 to eliminate the fraction:

X^2 - 16 = 4X - 4

Next, we rearrange the equation to have all terms on one side:

X^2 - 4X - 12 = 0

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. Let's use factoring in this case:

(X - 6)(X + 2) = 0

Setting each factor equal to zero gives us two possible solutions:

X - 6 = 0 --> X = 6

X + 2 = 0 --> X = -2

So the solutions to the equation X^2/2 - 8 = 2X - 2 are X = 6 and X = -2.

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Answer:

p = 6 , q = 43

Step-by-step explanation:

x² + 12x - 7

using the method of completing the square

add/subtract ( half the coefficient of the x- term )² to x² + 12x

=x² + 2(6)x + 36 - 36 - 7

= (x + 6)² - 43 ← in the form (x + p)² - q

with p = 6 and q = 43