Describe the relationship between the segments made when secant lines intersect outside a circle. Use the following image as reference.

Answer: C:6

Step-by-step explanation:

I just got it right on the quiz

Option (c) represents an inconsistent system of equations, as the constant terms are not proportional, while the coefficients of x are. This system (y=4x-3, y=4x+3) has no solutions.

In mathematics, specifically in algebra, an inconsistent system is a system of equations that has no solutions. To check which system is inconsistent from the options you've given, we need to compare the coefficients of each equation within a system. An inconsistent system will have proportional coefficients of x and y between the two equations, but the constant terms will not be proportional.

Looking at each option:

Option (a): y=x+4 and y=2x+4
Option (b): y=x and y=−x
Option (c): y=4x−3 and y=4x+3
Option (d): y=2x−3 and 2y=4x−6

From here, we can see that option (c): y=4x-3, y=4x+3 is inconsistent. In this system, the coefficients of x are proportional (4), but the constant terms (-3 and +3) are not proportional.

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The equation of a line perpendicular to the x-axis passing through the point (5,1) is x = 5. This is because a vertical line crossing the x-axis at a specific point will have the same x-coordinate for all its points.

In mathematics, a line perpendicular to the x-axis is a vertical line that crosses the x-axis at a specific point. All points on this line will share the same x-coordinate. Therefore, a line that is perpendicular to the x-axis, and passes through the point (5,1) will have the equation x = 5. This equation represents a line that is vertical and intercepts the x-axis at the point where x equals 5. This is because in each point on the line, x remains constant, which is the characteristic of a vertical line in a Cartesian Coordinate System.

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In adults, the arm span is approximately 5 cm greater than the height in adult males and 1.2 cm in adult females. To calculate the arm span for the heights given, we add 5cm to their height. The following are the results:

Height                   Arm Span Length (in cm)

4’10                        152.32

4’11                        154.86

5’0                          157.4

5’4                          167.56

5’5                          170.10

5’7                          175.18

5’8                          177.72

5’9                          180.26

5’10                        182.80

5’11                        185.34

6’0                          187.88

To add, the total measurement of the length from the furthermost part of an individual's arms to the other end when raised equidistant to the ground at shoulder height at a 90º angle is called the arm span or wingspan.

The surface area of the given cone is 747.32.

"The total surface area of a cone is defined as the total area of the cone occupied in a three-dimensional area. It is equal to the sum of the curved surface and the base of the cone. "

Surface area of the cone is [tex]\pi*r(l+r )[/tex]

[tex](22/7)*7*(27+7)[/tex]

= 747.32

The surface area of the cone is 747.32

Hence, option C is correct.

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The exact solution to the equation [tex]4^{(12 - 4x)[/tex] = 256 is x = 2. By recognizing that 256 is 4 raised to the fourth power, we equate the exponents and solve for x.

To solve this problem, we need to recognize that 256 is a power of 4. 4⁴ = 256. With this insight, the equation can be rewritten as:

[tex]4^{(12 - 4x)[/tex] = 4⁴

Since the bases are the same, we can equate the exponents:

12 - 4x = 4

Now, we'll isolate the variable x:

Subtract 12 from both sides: -4x = 4 - 12

-4x = -8

Divide both sides by -4: x = 2

Thus, the exact solution to the given equation is x = 2.

The measures of angles B and D are 110° and 70° respectively.

The rule of cyclic quadrilateral states that, the sum of the opposite is supplementary i.e 180°

Therefore, applying this rule, Angle B and D are supplementary

Then, B+D=180°

Given that, B=3x-4 and D= 2x-6

Thus, (3x-4)+(2x-6)=180°

3x-4+2x-6=180°

3x+2x-4-6=180°

5x-10=180°

5x=180°+10

5x=190°

Then, x =190/5

x=38°

Then solving for B and D;

B=3x-4

B=3(38)-4

B=114-4

B=110°

Also, D=2x-6

D=2(38)-6

D=76-6

D=70°

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The value of the [tex]\rm ^6p_2[/tex] is 30.

The value of  P(6,2).

According to the question

The value of the [tex]\rm ^6p_2[/tex] is determined by using permutation.

The probability of selecting an ordered set of 'r' objects from a group of 'n' number of objects.

The order of objects matters in the case of permutation.

The formula to find [tex]\rm ^np_r[/tex] is given by:

[tex]\rm ^np_r = \dfrac{n!}{(n-r)!}[/tex]

Substitute n = 6 and r = 2 in the formula;

[tex]\rm ^np_r = \dfrac{n!}{(n-r)!}\\ \\ \rm ^6p_2 = \dfrac{6!}{(6-2)!}\\ \\ \rm ^6p_2= \dfrac{6 \times 5\times 4 \times 3\times2 \times 1}{4!}\\ \\ ^6p_2= \dfrac{6 \times 5\times 4 \times 3\times2 \times 1}{4\times 3 \times2 \times 1}\\ \\ ^6p_2= 6 \times 5}\\ \\ ^6p_2= 30[/tex]

Hence, The value of the [tex]\rm ^6p_2[/tex] is 30.

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The average rate of change can be found using a discrete graph by calculating the slope between two points on the graph. This provides insight into how the dependent variable changes as the independent variable varies.

The average rate of change can be found using a discrete graph by calculating the difference in the y-values of two points and dividing it by the difference in the x-values of those same points. This will give you the slope of the line connecting the two points, which represents the average rate of change between those two points. For example, if you have two points (x1, y1) and (x2, y2), the average rate of change can be calculated as:

(y2 - y1) / (x2 - x1)

By finding the average rate of change at different intervals on the graph, you can analyze how the dependent variable changes in relation to the independent variable.

The easiest way to answer this is to try all choices, plug in values for the 1st term and 2nd term then check if the answer matches with 5 and 2. (n = 1 and n = 2)

We know that n starts with 1 because that is our 1st term, we do not have 0th term, therefore that leaves us with 2 choices.

Choice 1: an = 5 − 2(n − 1); all integers where n ≥ 1

n = 1

a1 = 5 – 2 (1 – 1) = 5 – 2 (0)

a1 = 5

n = 2

a2 = 5 – 2 (2 – 1) = 5 – 2 (1)

a2 = 3   (FALSE!)

Choice 2: an = 5 − 3(n − 1); all integers where n ≥ 1

n = 1

a1 = 5 – 3 (1 – 1) = 5 – 3 (0)

a1 = 5

n = 2

a2 = 5 – 3 (2 – 1) = 5 – 3 (1)

a2 = 2   (TRUE)

Therefore the correct answer is:

an = 5 − 3(n − 1); all integers where n ≥ 1

Answer:

A is INCORRECT

Step-by-step explanation:

Just finished the FLVS test

Answer:

Graph 1

Step-by-step explanation:

Here, the given equation is,

[tex]f(x)=x^2+3x+2-----(1)[/tex]

For x-intercept, f(x) = 0

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

[tex]x^2+2x+x+2=0[/tex]

[tex]x(x+2)+1(x+2)=0[/tex]

[tex](x+1)(x+2)=0[/tex]

[tex]\implies x=-1\text{ or } -2[/tex]

So, the x-intercept of the function are (-1,0) and (-2,0)

Since, the line must has at least one x-intercept.

⇒ Graph 2 and Graph 4 can not be the graph of the given function,

Also, for y-intercept,

Put x = 0 in equation (1),

We get, f(x) = 2,

Hence, the y-intercept of the given function is (0,2),

But in Graph 3 the y-intercept of the function = (0,1)

⇒ Graph 3 can not be the graph of the given function,

Therefore, Graph 1 is the correct graph of the given function.

Answer: The answer is (d) Find the slopes and show that their product is -1.

Step-by-step explanation:  Given in the question and shown in the attached figure that the vertices of the quadrilateral PQRS are P(0, 0), Q(a + c, 0), R(2a + c, b), and S(a, b). We are asked to use geometry to show that the diagonals PR and QS are perpendicular to each other.

We know that the two lines are perpendicular if the product of their slopes is --1.

So, first we will find the slopes of PR and QS, multiply them, and check the value.If the value is -1, then the diagonals are perpendicular to each other.

That is, if 'm' and 'p' are the slopes of the diagonals PR and QS, and if m × p = -1, then the two diagonals are perpendicular.

Thus, the correct answer is (d).

The coordinate point of the other endpoint, G is (-1, 3)

The given parameters;

the midpoint = M(-2, 5)

one end point = H(-3,7)

To find:

Let the coordinate point of the other endpoint = G(x, y)

The coordinate point of the other endpoint, G will be calculated using midpoint formula.

[tex]M(-2, 5) =( \frac{x + (-3)}{2} , \frac{y + 7}{2} )\\\\-2 = \frac{x - 3}{2} \ \ \ and \ \ 5 = \frac{y+ 7}{2} \\\\x-3 = 2(-2)\\\\x - 3 = -4\\\\x = -4 + 3\\\\x = -1\\\\y+ 7 = 2(5)\\\\y + 7 = 10\\\\y = 10 -7\\\\y = 3\\\\G= (-1, 3)[/tex]

Thus, the coordinate point of the other endpoint, G is (-1, 3)

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Given:

f(0) = 2

So first of all, we let x = 2012, y = 0: 

Then, F(2012) = 2012 + f(0)

Since f(0) = 2, then f(2012) = 2012 + 2 = 2014.

To add, the process that relates an input to an output is called a function.

There are always three main parts of a function, namely:

Input

The Relationship

The Output

The classic way of writing a function is "f(x) = ... ".

What goes into the function is put inside parentheses () after the name of the function: So, f(x) shows us the function is called "f", and "x" goes in.

What a function does with the input can be usually seen as:

f(x) = x2 reveals to us that function "f" takes "x" and squares it.

Answer:3s+2,000

Step-by-step explanation:

Answer:

286°28'44

Step-by-step explanation: