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Finger [1]
2 years ago
13

What is a sketch and description for each locus of points in a plane? The points in the interior of ∠ABC and equidistant from th

e rays of ∠ABC
Mathematics
1 answer:
Thepotemich [5.8K]2 years ago
4 0

The circumcenter (O) is the point in the interior of ∠ABC that's equidistant from all the rays (vertices) of triangle ABC.

<h3>What is a locus?</h3>

In Geometry, a locus can be defined as a set of points which all meets and satisfies a stated condition for a geometrical figure (shape). This ultimately implies that, the locus of points defines a geometrical figure (shape) in geometry.

<h3>What is a circumcenter?</h3>

A circumcenter can be defined as the point where perpendicular bisectors (right-angled lines to the midpoint) of the sides of a triangle meet together or intersect.

In this context, we can infer and logically deduce that the circumcenter of any triangle is always equidistant from all the rays (vertices) of that triangle.

In triangle ABC (see attachment), the circumcenter can be determined by drawing the perpendicular bisectors (right-angled lines to the midpoint) of both sides AC and CB.

By critically observing the diagram (see attachment) of these triangles, we can logically deduce that point O is where these perpendicular bisectors meet together or intersect.

In conclusion, the circumcenter (O) is the point in the interior of ∠ABC that's equidistant from all the rays (vertices) of triangle ABC:

OA = OB = OC.

Read more on the locus of points here: brainly.com/question/3678578

#SPJ1

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A farmer sells 8.9 kilograms of apples and pears at the farmer's market. 3 /4 of this weight is apples, and the rest is pears. H
aleksandrvk [35]

Answer: 2.225 kg

Step-by-step explanation:

You know that:

- The total weight the farmer sold was 8.9 kilograms.

- 3/4 of this weight is apples, and the rest is pears.

Therefore, to calculate the amount of kilograms of pears   she sold at the farmer's market (which you can call x), you need to apply the following proccedure.

Thefore, you obtain the following result:

x=8.9kg-(8.9kg*\frac{3}{4})\\x=2.225kg

4 0
3 years ago
Read 2 more answers
Sum of cubes: (a b)(a2 – ab b2) = a3 b3 Difference of cubes: (a – b)(a2 ab b2) = a3 – b3 Which products result in a sum or diffe
valentina_108 [34]

By comparing all the options with the formula of sum of cubes and difference of cubes we get that  (x+4)\left(x^{2}-4 x+16\right)  is sum of cubes

<h3>What is formula of sum of cubes and difference of cubes?</h3>

Formula of sum of cubes and difference of cubes are following

(a+b)(a^2 -ab +b^2) = a^3+ b^3 \\\\\\(a - b)(a^2+ ab+ b^2) = a^3 - b^3

(a)

(x-4) \left(x^{2}+4 x-16\right)\\=(x-4) \left(x^{2}+4 x-4^2\right)\\\\

by comparison with formula we can say that this is neither sum or nor difference of cubes.

(b)

(x-1)\left(x^{2}-x+1\right)\\=(x-1)\left(x^{2}-x+1^2\right)

by comparison with formula we can say that this is neither sum nor difference of cubes.

(c)

(x+1)(x-1)=x^{2}-1^{2}\\

we can say that this is neither sum  nor difference of cube as it's difference of squares.

(d)

(x+4)\left(x^{2}-4 x+16\right)\\\\(x+4)\left(x^{2}-4 x+4^2\right)

by comparison with formula this is equal to

x^{3}+4^{3}\\

Hence this is sum of cubes

(e)

(x+4)\left(x^{2}+4 x+16\right)\\(x+4)\left(x^{2}+4 x+4^2\right)

by comparison with formula we can say that this is neither sum  nor difference of cubes.

By comparing all the options with the formula of sum of cubes and difference of cubes we get that  (x+4)\left(x^{2}-4 x+16\right) is sum of cubes

To know more about cubes visit: brainly.com/question/107100

8 0
2 years ago
About 57 people rent skates at the skating rink each day. It cost $4.25 to rent skates. About how much does the Rink make in ska
seraphim [82]

Answer:1695.75

Step-by-step explanation:

We know that there are 7 days in a week. Since 57 people rent skates each day, we know that 57*7=399 skates are rented each week. Since one skate cost 4.25, we know that 399*4.25 is the cost, which is 1695.75. (If you are not allowed to use a calculator, you can do 400*4.25-4.25, to make it easier to compute)

4 0
3 years ago
What do you need to know?
cupoosta [38]

Answer:

incorrect

Step-by-step explanation:

the volume of a cube = s³ ( where s is the length of the side )

to find s take the cube root

s = \sqrt[3]{27} = 3

since 3 × 3 × 3 = 27


4 0
3 years ago
A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. Four hu
castortr0y [4]

<em>Answer: h = 120 ft;    w = 80 ft </em>

<em></em>

<em>A = 9600 ft^2</em>

<em />

<em>Step-by-step explanation: Let h and w be the dimensions of the playground. The area is given by:</em>

<em></em>

<em>A = h*w   (eq1)</em>

<em></em>

<em>The total amount of fence used is:</em>

<em></em>

<em>L = 2*h + 2*w + w    (eq2)    (an extra distance w beacuse of the division)</em>

<em></em>

<em>Solving for w:</em>

<em></em>

<em>w = L - 2/3*h = 480 - 2/3*h   (eq3)  Replacing this into the area eq:</em>

<em></em>

<em></em>

<em></em>

<em>We derive this and equal zero to find its maximum:</em>

<em></em>

<em>   Solving for h:</em>

<em></em>

<em>h = 120 ft.  Replacing this into eq3:</em>

<em></em>

<em>w = 80ft</em>

<em></em>

<em>Therefore the maximum area is:</em>

<em></em>

<em>A = 9600 ft^2</em>

<em />

5 0
3 years ago
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