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3 years ago

Complete the proof by providing the missing statement and reasons

Mathematics

1 answer:

Fittoniya [83]3 years ago

3 0

Answer:

2. angle bisector splits into even halves

Step-by-step explanation:

that's all i can assist with sorry, proofs still confuse me!

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Find the equation of the sphere in standard form centered at (−6,10,5) with radius 5.

Dovator [93]

Answer:

The equation of the sphere in standard form is

$x^{2} +y^{2}+z^{2} +12 x-20 y-10 z+136=0$

Step-by-step explanation:

Step 1:-

The equation of the sphere having center and radius is

$(x-h)^{2} +(y-k)^{2} +(z-l)^{2} = r^{2}$

Given centered of the sphere is (-6,10,5) and radius r=5

$(x-(-6))^{2} +(y-10)^{2} +(z-5)^{2} = 5^{2}$

on simplification,we get

$using (a+b)^{2} =a^{2} +2 a b+b^{2}$

$using (a-b)^{2} =a^{2} -2 a b+b^{2}$

simplify , we get

$x^{2} +y^{2}+z^{2} +12 x-20 y-10 z+136=0$

8 0

3 years ago

Find the area. 20 ft 12 ft 5 ft

andriy [413]

The area of what? if those are the dimensions of a triangle, you would do base times height divided by 2.

7 0

3 years ago

You can draw a quadrilateral with two sets of parallel lines and no right angles?

bonufazy [111]

Yes you can. The quadrilateral that you would get is called parallelogram. It has 2 paris of parallel lines. and 2 pairs of equal angles. one pair is angles that are less than 90 degrees and other one is where 2 angles are greater than 90 degrees each. Therefore there isnt any right angle there and you got yourself quadrilateral. of these 2 parallel lines are of equal lenght than you get something called rhombus.

8 0

3 years ago

Evaluate the expression without using a calculator Tan(arccos3/4)

julia-pushkina [17]

9514 1404 393

Answer:

(√7)/3

Step-by-step explanation:

The relationship between tangent and cosine is ...

tan(α) = √(1/cos(α)² -1)

The cosine of the angle is given as 3/4, so the tangent is ...

tan(arccos(3/4)) = √(1/(3/4)² -1) = √(16/9 -1) = √(7/9)

tan(arccos(3/4)) = (√7)/3

6 0

3 years ago

Prove that if r is any rational number, then 3r2 − 2r + 4 is rational. The following properties may be used in your proof. Prope

ziro4ka [17]

Given:

Expression is

$3r^2-2r+4$

To prove:

If r is any rational number, then $3r^2-2r+4$ is rational.

Step-by-step explanation:

Property 1: Every integer is a rational number. It is Theorem 4.3.1.

Property 2: The sum of any two rational numbers is rational. It is Theorem 4.3.2.

Property 3: The product of any two rational numbers is rational. It is Exercise 15 in Section 4.3.

Let r be any rational number.

We have,

$3r^2-2r+4$

It can be written as

$3(r\times r)-2r+4$

Now,

3, -2 and 4 are rational numbers by property 1.

$r^2=r\times r$ is rational by Property 3.

$3r^2\text{ and }-2r$ are rational by Property 3.

$3r^2+(-2r)+4$ is rational by property 2.

So, $3r^2-2r+4$ is rational.

Hence proved.

6 0

3 years ago