for each of the following find, if possible, a whole number that makes the equation true. a. 3+ z=12 b. 36 = 18 + 3 •Z

How is a straightedge and compass used to make basic constructions?

IgorLugansk [536]

compass.

The idealized ruler, known as a straightedge, is assumed to be infinite in length, have only one edge, and no markings on it. The compass is assumed to have no maximum or minimum radius, and is assumed to "collapse" when lifted from the page, so may not be directly used to transfer distances. (This is an unimportant restriction since, using a multi-step procedure, a distance can be transferred even with collapsing compass; see compass equivalence theorem.) More formally, the only permissible constructions are those granted by Euclid's first three postulates.

It turns out to be the case that every point constructible using straightedge and compass may also be constructed using compass alone.

The ancient Greek mathematicians first conceived straightedge and compass constructions, and a number of ancient problems in plane geometry impose this restriction. The ancient Greeks developed many constructions, but in some cases were unable to do so. Gauss showed that some polygons are constructible but that most are not. Some of the most famous straightedge and compass problems were proven impossible by Pierre Wantzel in 1837, using the mathematical theory of fields.

In spite of existing proofs of impossibility, some persist in trying to solve these problems.[1] Many of these problems are easily solvable provided that other geometric transformations are allowed: for example, doubling the cube is possible using geometric constructions, but not possible using straightedge and compass alone.

In terms of algebra, a length is constructible if and only if it represents a constructible number, and an angle is constructible if and only if its cosine is a constructible number. A number is constructible if and only if it can be written using the four basic arithmetic operations and the extraction of square roots but of no higher-order roots.

5 0

3 years ago

Please answer this correctly

Phoenix [80]

Answer:

Heather

Step-by-step explanation:

Because it says that Heather lives FARTHER away from the park than Bryant and that Eva lives CLOSER to the park than Bryant

So since Heather lives even farther away than Bryant she definitely lives farther away than Eva because she's closer than Bryant

5 0

3 years ago

Solve. 3x2 + 4x = –5 <br> using quadratic equation ...?

cupoosta [38]

3x^2 + 4x - 5 = 0
x = [-b ±√(b^2 - 4ac)]/2a

a = 3
b = 4
c = -5

x = [-4 ±√(16 + 60)]/6
x = [-4 ±√76]/6
x = [-4 ±√(2^2 * 19)]/6
x = [-4 ±2√19]/6
x = [-2 ±√19]/3

x = [-2 + √19]/3
x = [-2 + 4.35]/3
x = 2.35/3
x = 0.78 (rounded to the nearest hundredth)

x = [-2 - ±√19]/3
x = [-2 - 4.35]/3
x = -6.35/3
x = -2.12 (rounded to the nearest hundredth)

<span>∴ x = -2.12 , 0.78 (rounded to the nearest hundredth)</span>

6 0

3 years ago

Bharat types 20 words/min. How many words can he type in each length of time? a) 5 min b) 30 min c) 23 min

e-lub [12.9K]

Bharat can type words in lengths of time as 100 words, 600 words, and 460 words in 5 minutes, 30 minutes, and 23 minutes respectively.

<h3>What are Arithmetic operations?</h3>

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

* Multiplication operation: Multiplies values on either side of the operator

For example 12×2 = 24

Bharat types 20 words per minute which are given in the question.

To determine the number of words can he type in each length of time

We have to multiply the time by his typing speed.

The number of words that can be typed by Bharat in 5 minutes :

⇒ 20 × 5

⇒ 100

The number of words that can be typed by Bharat in 30 minutes :

⇒ 20 × 30

⇒ 600

The number of words that can be typed by Bharat in 23 minutes :

⇒ 20 × 23

⇒ 460

Therefore, He can type words in lengths of time as 100 words, 600 words, and 460 words in 5 minutes, 30 minutes, and 23 minutes respectively.

Learn more about Arithmetic operations here:

brainly.com/question/25834626

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3 0

2 years ago

Write the equation of the perpendicular bisector of if A(–6, –4) and B(2, 0).

mart [117]

Answer:

(-2 , -2)

Step-by-step explanation:

Here,

(-6,-4)=(x1,y1)

(2,0)=(x2,y2)

Mid point formula,

(x,y)=(x1+x2/2 , y1+y2/2)

=(-6+2/2 , -4+0/2)

=(-2 , -2)

3 0

3 years ago