Find the range of the relation.

A.) {–4, –2, –1, 2}

B.) {–4, 4}

C.) {–3, –2, 0, 2}

D.) {–4, –2, –1, 0, –2}

Starting from -4 and applying a series of moves (+3, -2, +6, -5) sequentially on the number line, the final position of Point x is -2.

The question involves finding the final position of Point x after a series of moves on a number line. Starting from -4, we apply the moves in sequence: adding 3, subtracting 2, adding 6, and finally subtracting 5. The operations are as follows:

Therefore, the final position of Point x on the number line is -2.

A1. Since we have two sides (AC and AB) and the included angle (60°), we are going to use the law of cosines to find the length of BC:

We can conclude that the length of the side BC is .

2. To find the area of triangle ABC we are going to use Heron's formula:  

where

is the area of the triangle 

is the semi-perimeter of the triangle 

But first, we are going to find the semi-perimeter of our triangle using the formula: 

We can infer for our triangle and from our previous calculation that , , and . Lets replace those values to find the semi-perimeter of our triangle:

Answer:

The next number is 127

Step-by-step explanation:

The sequence is the previous number times 2 plus one.

the answer is true hope this helps :)

The symbol 'V' before a number usually implies the square root in mathematics. Therefore, the square root of 65 (V65) is approximately 8.06. Hence, the closest number to V65 is 8.

The symbol 'V' before a number often denotes the square root in mathematics. Thus, 'V65' implies the square root of 65. Calculating this gives an approximate value of 8.06. When you compare this value to the options provided: A. 8, B. 9, C. 32 and D. 64, you can see that the closest number to V65 (the square root of 65) is A. 8.

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First option is correct. The equation of the  is [tex](x-2)^{2} +(y-6)^{2} =16[/tex].

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called "center".

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

where,

(h, k) is the coordinate of the center of a circle

(x, y) are the coordinate points

r is the radius of circle.

According to the question

we have

the center of the circle,  (h, k) = (-2, 6)

and the circle passes through the point (-2, 10)

since, the circle passes through point (-2, 10), the radius(r) of the circle is the distance between the points (-2, 6) and  (-2, 10)

⇒ [tex]r =\sqrt{(-2+2)^{2 }+ (6-10)^{2} }[/tex]

⇒ r = [tex]\sqrt{0^{2}+(-4)^{2} }[/tex]

⇒[tex]r = \sqrt{16}[/tex]

⇒[tex]r = 4unit[/tex]

therefore,

the equation of the circle is given by

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

[tex](x-(-2))^{2} +(y-6)^{2} =16[/tex]

[tex](x+2)^{2} +(y-6)^{2} =16[/tex] ..... (1)

[tex]x^{2} +4+4x+y^{2} +12y+36 = 16[/tex]

[tex]x^{2} +y^{2} +4x+12y+24=0[/tex]

Hence, equation 1 represent the equation of circle i.e. [tex](x+2)^{2} + (y-6)^{2} =16[/tex]

Learn more about the equation of circle here:

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The wrong statement about a circle is c. Every chord is a diameter

Circles are two-dimensional builds which are sets of equidistant points at a point called the center point

The distance of these points to the center is called the radius of the circle. While the circle field is an area which is bounded by a circle

There are terms - terms commonly used in circles:

Let we see the answer choices :

Right, because secant itself is an extension of the chord

Right, because the diameter itself also intersects the circle at two points on the circle, just like secant

Incorrect, because the diameter itself must pass through the center point while the chord does not have to

Right, because each diameter intersects a circle at two different points

So the wrong statement is C. Every chord is a diameter

circumference

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circle transformations

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the arc length of a segment of a circle

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Keywords: circle, secant, diameter, chord

Every chord is a diameter is false. Option (c) is false.

Further explanation:

Given:

The statements are as follows,

(a). Every chord is a part of a secant

(b). Every diameter is a part of secant

(c). Every chord is a diameter

(d). Every diameter is a chord

Explanation:

Diameter is a distance between the points that passes through the center of the circle.

The distance between the two points on the circle is known as the chord. The longest chord is the diameter of the circle.  

Radius is line segment to a point from the center of the circle and the radius is half of the diameter.

Secant is a straight line that intersects two points on the circle.

Every chord is a diameter is false. Option (c) is false.

Statement (a) is true.

Statement (b) is true.

Statement (c) is false.

Statement (d) is true.

Learn more:

Answer details:

Grade: Middle School

Subject: Mathematics

Chapter: Triangles

Keywords: false, chord, part, secant, radius, diameter, Every chord is a part of a secant, Every diameter is a part of secant, Every chord is a diameter, Every diameter is a chord.

Final answer:

A relation where each domain value is mapped to a single, unique range value is considered a function. The relation in question is indeed a function because each domain value corresponds to only one range value, and its correctness is supported by the distinct pairs of the domain and range. The correct answer is option (B)

Explanation:

To determine whether a given relation is a function, we check if each element of the domain maps to exactly one element of the range. The relation in question is composed of the following ordered pairs: (-3, -2), (-1, 0), (1, 0), (5, -2). The domain (which consists of the first elements of the ordered pairs) includes -3, -1, 1, and 5, and the range (the second elements) includes -2, 0.

A crucial aspect of a function is that each domain value is paired with a unique range value. Here, we see that no domain value is repeated; hence, none of them map to more than one range value. This satisfies the criterion for a function. However, it is not a problem that a range value, like -2, appears more than once in the relation as long as it corresponds to different domain values.

Based on this, the correct answer would be "B. yes- only one range value exists for each domain value" because each domain value is associated with one and only one range value, which is the definition of a function.

Answer:

162

Step-by-step explanation:

There are 21 out of 70 people that like the monkey exhibit. So you divide that and get 0.3 or 3/10. Then you have to multiply that by 540. This gets you to 162 which is the answer to your problem.

Answer:

1. x is 7 more than y

meaning

x=y+7

2. x is 1 less than y

meaning

x=y-1

so

the answer:

x = y + 7

x = y – 1