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2 years ago

Is UVW=Xyz?if so, name the postulate that applies

Mathematics

1 answer:

aivan3 [116]2 years ago

4 0

By critically observing the two triangles, we can deduce that they: B. might not be congruent.

<h3>The properties of similar triangles.</h3>

In Geometry, two triangles are said to be similar when the ratio of their corresponding sides are equal in magnitude and their corresponding angles are congruent.

By critically observing the two triangles, we can logically deduce that the three angles of both triangles are congruent in accordance with AAA similarity postulate:

<U ≅ <X

<V ≅ <Y

<W ≅ <Z

However, AAA isn't a congruence postulate and as such all similar triangles might not be congruent.

Read more on congruency here: brainly.com/question/11844452

#SPJ1

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Will give brainliest to correct answer.

Kobotan [32]

Note that c is the hypotenuse of the blue triangle, and that the Pyth. Thm. states that (length of one leg)^2 + (length of the other leg)^2 = (hyp)^2.

Therefore, (hyp)^2 = c^2 = [2sqrt(x^2+3x)]^2 + 3^2, or
= 4(x^2+3x) + 9, or
= 4x^2 + 12x + 9 = (2x+3)^2
Taking the sqrt of both sides, c = plus or minus (2x+3). Eliminate -(2x+3) because the middle term of the square of this would be negative, in conflict with the given +12x.

c=2x+3 is the correct answer.

8 0

4 years ago

A regular decagon has a radius of 14'. Determine the length of the apothem. Then determine the perimeter of the decagon

pav-90 [236]

Answer:

Part 1) The length of the apothem is 13.32'

Part 2) The perimeter of the decagon is 86.5'

Step-by-step explanation:

we know that

A regular decagon has 10 equal sides and 10 equal interior angles

A regular decagon can be divided into 10 congruent isosceles triangle

(they are isosceles since their two sides are the radii of the polygon and the unknown side is the side of the polygon)

The vertex angle of each isosceles triangle is equal to

$\frac{360^o}{10}=36^o$

To find out the side length of the decagon, we can use the law of cosines

$c^2=a^2+b^2-2(a)(b)cos(C)$

where

c is the length side of decagon

a and b are the radii

we have

$a=14'\\b=14'\\C=36^o$

substitute the values

$c^2=14^2+14^2-2(14)(14)cos(36^o)$

$c^2=392-(392)cos(36^o)$

$c=8.65'$

To fin out the perimeter of decagon multiply the length side by 10

$P=8.65(10)=86.5'$

To find out the apothem we can apply the Pythagorean Theorem in one isosceles triangle

see the attached figure to better understand the problem

$r^2=a^2+(c/2)^2$

substitute the given values

$14^2=a^2+(8.65/2)^2$

solve for a

$a^2=14^2-(8.65/2)^2$

$a=13.32'$

8 0

3 years ago

Find M < A the diagram is not to scale

hichkok12 [17]

Answer:

107 i think

Step-by-step explanation:

3 0

3 years ago

Can someone please help me with these two?? (With a clear answer please)

suter [353]

Try this solution:
rule: the volume of any cylinder can be calculated with formula: V=πr²h, where r - the radius of the base, h - height of the cylinder.
Using the formula written above:
5. V=π*25*6=150*3.1415≈471.2389≈471.2 cm³;
6. V=π*64*4=256*3.1415≈804.2477≈804.3 cm³

4 0

4 years ago

The initial cost of an office fax machine is $100. After 1 year, its value becomes $80. Which is the correct linear depreciation

Elis [28]

Answer:

$y=100-20x$

Step-by-step explanation:

Let the x-axis be the time (in years) and the y-axis the value of the fax machine (in dollars).

We know that the initial value of the fax machine is $100; in other words, when the time is zero years, the value is $100, or as an ordered pair (0, 100). We also know that after 1 year the value decreases to $80, so (1, 80).

Now we can find the slope of the line passing through those two points using the slope formula

$m=\frac{y_2-y_1}{x_2-x_1}$