The Pythagorean theorem states that if two side lengths of a(n) _____ triangle are known, the length of the third side can be found.

To prove the converse of the Pythagorean theorem, it must be assumed that the Pythagorean theorem is true. This assumption is fundamental to the proof. Option A is correct answer.

The proof of the converse of the Pythagorean theorem.

To prove the converse of the Pythagorean theorem, it is important to start by assuming that the Pythagorean theorem itself holds true.

Therefore, option A is the correct answer: It must be assumed that the Pythagorean theorem is true.

This fundamental assumption is crucial since the converse states that if the sum of the squares of two sides of a triangle is equal to the square of the third side, then the triangle is a right triangle.

This is a direct implication assuming the Pythagorean theorem's validity.

An essential part of a mathematical proof, especially in geometry, involves using established theorems and logical deductions.

It's also worth mentioning Euclid's proposition that states, "Any two sides of a triangle are together greater than the third side." While this proposition is relevant to the properties of triangles, it is not a component of the proof for the converse of the Pythagorean theorem.

Answer:

5/2 Hope this helped

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

It still has a solution, just not a solution with whole or exact numbers.

A system of equations would only have no solution if there were no points of intersection at all.

Answer:

D. square root of 2

Step-by-step explanation:

The square root of 2 is an irrational number because it cannot be written as a ratio of two integers.

Final answer:

Choice D, square root 2, is an example of an irrational number. Unlike the other options, it cannot be expressed as a fraction with an integer numerator and denominator.

Explanation:

An irrational number is a number that cannot be expressed as a simple fraction, meaning its decimal form is non-terminating and non-repeating. Among the options given, choice D, which is square root 2 (written as √2), is an example of an irrational number. Option A is 74/99, a fraction that simplifies to a rational number; option C is 3/4, also a rational number; and the option B is missing from the context provided.

To determine between which two consecutive integers an irrational number like √2 lies, we first identify the perfect squares nearest to the number we are taking the square root of. For √2, the perfect squares are 1 (√1) and 4 (√4), which correspond to the integers 1 and 2. √2 lies between these two integers because 2 is greater than 1 and less than 4, and since the square root function is increasing, √2 is more than 1 and less than 2.

Answer:

C = 26π inches

In 10 rotations, the bicycle tire travels 260π inches, or about 816.8 inches.

Answer: C. 10 cm

Step-by-step explanation:

the hypotenuse of a right triangle will always be longer than the other 2 sides.  So 10 cm

To solve this you must use Pythagorean theorem:

[tex]a^{2} +b^{2} =c^{2}[/tex]

a and b are the legs (the sides that form a perpendicular/right angle)

c is the hypotenuse (the side opposite the right angle)

In this case...

a = 8 cm

b = 6 cm

c = x

^^^Plug these numbers into the theorem

[tex]8^{2} +6^{2} =x^{2}[/tex]

simplify

64 + 36 = [tex]x^{2}[/tex]

100 = [tex]x^{2}[/tex]

To remove the square from x take the square root of both sides to get you...

√100 = x  

Which is when simplified:

(choice C)

10 cm  

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

its (x,y)(-y,-x)

Step-by-step explanation:

Answer:

(x ,y) ---> (x ,-y)

Step-by-step explanation:

:)

Answer:

  1413.7 ft^3

Step-by-step explanation:

The volume of a cylinder is given by ...

  V = πr^2·h

After emptying part of container A into container B, the empty space in container A will be exactly the volume of container B:

  V = π(5 ft)^2·(18 ft) ≈ 1413.7 ft^3

Answer:

Step-by-step explanation:true

Answer:

True

Step-by-step explanation:

Yes, this is in standard form

Answer:

The first one is a right triangle.  The second one is C. (13,9)

Step-by-step explanation:

For each ordered pair, go over first, then up.  For the first question, if all points are plotted, it makes a right triangle.

With the second question, the point must be the same distance from Q as P is already.  That's 3 lines over and 7 lines up and down.  It could stay at (__,9), so 3 spaces over is (13,9).  

Answer:

Find the volume of a triangular prism by using the formula

✔ V = Bh

.

Use the base and height to calculate the area of the

✔ triangle

base, B.

The volume of the tent is

✔ 96

ft3.

Step-by-step explanation:

Find the volume of a triangular prism by using the formula

Volume of a triangular prism = area of base triangle × length of the prism .

Use the base and height to calculate the area of the triangular base, B.

The volume of the tent is 96 ft3.

A triangular prism is a polyhedron made up of two triangular bases and three rectangular sides. It is a three-dimensional shape that has three side faces and two base faces, connected to each other through the edges. If the sides are rectangular, then it is called the right triangular prism else it is said to be an oblique triangular prism.

Based on the given information, the tent is a right triangular prism.

The dimensions of the rectangles are:

two of the rectangles have the dimension [tex]8ft \times 5ft[/tex]

the base rectangle has the dimension [tex]8ft \times 6ft[/tex]

The dimensions of the triangles are:

base = 6ft

height = 4 ft

Volume of a triangular prism = area of base triangle × length of the prism

[tex]V=\frac{1}{2} \times b\times h \times l\\\\V=\frac{1}{2} \times 6\times 4 \times 8\\\\V=96[/tex]

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Answer:

See Explanation

Step-by-step explanation:

5/4 = 1.25

1.25 / 4 = 0.3125 (this step separated the whole thing into quarters)

[tex]\frac{0.3125}{10000}=\frac{5}{16}[/tex]

Tony should use 5/16 of the salt.

Answer:

see explanation

Step-by-step explanation:

Under a reflection in the line y = - x

a point (x, y ) → (- y, - x ), thus

S(- 2, - 10 ) → (10, 2 )

T(- 2, - 3 ) → T'(3, 2 )

U(3, - 3 ) → U'(3, - 3 )

V(3, - 10 ) → V'(10, - 3 )

Answer:

-20

Step-by-step explanation:

The first thing is to define each one:

Polynomial: expression made with constants, variables and exponents, which are combined using addition, subtraction and multiplication. Exponents can only be natural numbers and the polynomial cannot have an infinite number of terms.

Example:

This is a:  [tex]5x^{3} + 4x^{2} -99x +20[/tex]

Degree: It is the exponent with the highest degree. If a monomial of those that are forming the polynomial has two unknowns, each with its exponent, these add up since we would be doing a multiplication of monomials.

Example: [tex]5x^{3} + 4x^{2} -99x +20[/tex]

The degree of this polynomial is 3 because it is the largest exponent.

Linear term coefficient: is the number that multiplies the variable with the highest exponent

Example: [tex]5x^{3} + 4x^{2} -99x +20[/tex]

In this case it is 5 because [tex]x^{3}[/tex] is the variable with the highest exponent

Constant term coefficient: is one that is found in a polynomial alone, that is, without multiplying the x or another unknown.

Example:  [tex]5x^{3} + 4x^{2} -99x +20[/tex]

In this case it is 20 because it is the one found without multiplying any linear term (x)

Attached image with example of this.

Answer: y=4x

Step-by-step explanation: 2 times 4 is 8, 3 times 4 is 12, etc.

Answer:

y= kx

k= y/x = 8/2= 4

Therefore, k= 4

Answer:

2

Step-by-step explanation:

It would be 2. You can find this by putting 1 finger up and then another finger up then count your fingers :)

Answer:

Open circle

Step-by-step explanation:

If the inequality has < or > it is an open circle.

If the inequality has =< or >= it is closed

Have A Great day

Answer:

Open circle. You only use a closed circle if it is greater/less than or equal to (which is the greater/less than sign with a line under it to indicate the "or equal to" part)

Step-by-step explanation:

Segment AC is twice as long as segment A''C''.

The relationship between segment AC and segment A''C'' is that segment AC is a dilation of segment A''C'' by a scale factor of 2 from the origin. This means that segment AC is twice as long as segment A''C''.

Answer:

  see below (first table shown)

Step-by-step explanation:

All of the frequency tables have the same numbers in the first and last categories, so choosing the correct table can be done by counting instances in any of the middle three categories.

We note there are 5 who biked to school, so the first table is indicated as being correct.

_____

If you complete a frequency table, you find that it matches the first table shown.

Answer:

#1

Step-by-step explanation:

Answer:

C. k = -3

Step-by-step explanation:

First of all please try and understand math, cheating will never get you anywhere :)

So we can deduce that the value k is -3 for the following reasons:

If k is greater than 1, it will become narrower

If k is negative, it will shift right

Therefore we can conclude that k = -3

(I might be wrong but we will see)

The function g(x) transformed to f(x) by 3 unit on right side.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

We have the graph

g(x) = f(k x)

Here k represent the transformation or we can say shifting.

If  k is greater than 1 then the graph will become narrower

and, if  k is negative or less than then it will shift right.

From the graph the function g(x) is shifted to f(x) by 3 units.

Thus, the value of k is -3 ( Right side shifting)

Learn more about Transformation here:

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Answer:

b=41

Step-by-step explanation:

180=19v-41+(180-(20v+39))+17v

v=5

180=19v-41+b+17v

180=19(5)-41+b+17(5)

b=41

Answer: 1 1/2 yards of yarn

Step-by-step explanation: For this problem, we will simply be multiply 1/2 yard by 3 to get the amount of yard that Ahlam will need.

1/2 x 3/1 = 3/2 or 1 1/2 yards of yarn. Basically you multiply the top of the fractions first (1 x 3) = 3 Then, you multiply the bottom of the fractions second  (2 x 1) = 2    (3/2 or 1 1/2)

Answer:

1.5 yards

Step-by-step explanation:

Salma: ½ yard

Ahlam: 3 × ½ = 1.5

Answer:

undefined.  

Step-by-step explanation:

so there is a point at the origin, and from there there are two rays coming off it.  One goes along the positive x axis, so it goes straight right, then the other goes through point (0,1).  That point is right above the origin.  So it makes an l shape.  what sort of polygon could you fit into the corner of an L?  Well, a square or rectangle, and the corners of a square and rectangle are all 90 degrees is theta.

Now it wants tan of 90 degrees.  tangent is sine divided by cosine, so let's find those.

sine of 90 is the y value on the unit circle at 90 degrees.  Since the unit circle has a radius of 1 then when it points straight up or down the y value is either 1 or -1 respectively.  Similarly cosine is 1 when pointing to the right, at 0 degrees or 360 degrees, and -1 at 180 degrees.  For sine straight up is of course 90 degrees and down is 270 degrees.

Now, sine of 90 is 1 and cosine of 90 is therefore 0.  so now we want sine divided by cosine.  this is 1/0.  Well you can't divide by 0, so it is undefined.  

Answer:

the answer is D undefined

Step-by-step explanation:

took the test on edg.

Answer:

43120 yards

Step-by-step explanation:

You would just need to convert miles to yards, 1 mile = 1760 yards

Just do 24.5 * 1760

Answer:

43,120 yards

Step-by-step explanation:

24.5 x 1760 = 43,120

When converting from miles to yard, take the miles mulitplied by 1,760.

- Hope this helps! Please let me know if you need a further explanation.

Answer: The radius of the circle is 7.75 m (approximately)

Step-by-step explanation: The area of a sector is determined as follows;

Area of sector = (∅/360) x πr²

The area has been given as 10π, and the angle subtended by the sector has been given as 60. Substituting for known values we now have;

10π = (60/360) x πr²

10π = (1/6) x πr²

By cross multiplication we now have;

(10π/π) x 6 = r²

10 x 6 = r²

60 = r²

Add the square root sign to both sides of the equation

√60 = √r²

7.7459 = r

The radius of the circle is approximately 7.75 meters

Look at the attached picture⤴

Look at the attached picture⤴Hope it will help u....:)

Answer:

y = - [tex]\frac{1}{4}[/tex] x - 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, - 3) and (x₂, y₂ ) = (4, - 4) ← 2 points on the line

m = [tex]\frac{-4+3}{4-0}[/tex] = - [tex]\frac{1}{4}[/tex]

Note the line crosses the y- axis at (0, - 3) ⇒ c = - 3

y = - [tex]\frac{1}{4}[/tex] x - 3 ← equation of line