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11 months ago

Geometry questions....help me someone please

Mathematics

2 answers:

AlekseyPX11 months ago

8 0

Answer:

Triangle 1: x = 80 degrees, acute

Triangle 2: x = 10 degrees, right

Step-by-step explanation:

Triangle 1:

By the Sum of Interior Angles Theorem, all the angles inside the triangle adds up to 180 degrees. So, set up this equation:

$60 + 40 +x = 180$

Solve for x:

$100 + x = 180\\x = 80$

So, x = 80 degrees

Because all the angles are less than 90 degrees, this is an acute triangle.

Triangle 2:

By the Sum of Interior Angles Theorem, all the angles inside the triangle adds up to 180 degrees. So, set up this equation (with the right angle given):

$3x + 60 + 90 = 180$

Solve for x:

$3x + 150 = 180\\3x = 30\\x = 10$

So, x = 10 degrees

Because there is an angle measuring 90 degrees, this is a right triangle.

OLga [1]11 months ago

7 0

Answer:

Triangle 1: x = 80 degrees, acute

Triangle 2: x = 10 degrees, right

By the Sum of Interior Angles Theorem, all the angles inside the triangle adds up to 180 degrees. So, set up this equation:

Solve for x:

So, x = 80 degrees

Because all the angles are less than 90 degrees, this is an acute triangle.

Triangle 2:

By the Sum of Interior Angles Theorem, all the angles inside the triangle add up to 180 degrees. So, set up this equation (with the right angle given):

Solve for x:

So, x = 10 degrees

Because there is an angle measuring 90 degrees, this is a right triangle.

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Help me with this one

Artist 52 [7]

9514 1404 393

Answer:

"complete the square" to put in vertex form

Step-by-step explanation:

It may be helpful to consider the square of a binomial:

(x +a)² = x² +2ax +a²

The expression x² +x +1 is in the standard form of the expression on the right above. Comparing the coefficients of x, we see ...

2a = 1

a = 1/2

That means we can write ...

(x +1/2)² = x² +x +1/4

But we need x² +x +1, so we need to add 3/4 to the binomial square in order to make the expressions equal:

$x^2+x+1\\\\=(x^2+x+\frac{1}{4})+\frac{3}{4}\\\\=(x+\frac{1}{2})^2+\frac{3}{4}$

_____

Another way to consider this is ...

x² +bx +c

= x² +2(b/2)x +(b/2)² +c -(b/2)² . . . . . . rewrite bx, add and subtract (b/2)²*

= (x +b/2)² +(c -(b/2)²)

for b=1, c=1, this becomes ...

x² +x +1 = (x +1/2)² +(1 -(1/2)²)

= (x +1/2)² +3/4

_____

* This process, "rewrite bx, add and subtract (b/2)²," is called "completing the square"—especially when written as (x-h)² +k, a parabola with vertex (h, k).

5 0

2 years ago

Good afternoon!

Vladimir [108]

9514 1404 393

Answer:

5) 112°

6) 40°

Step-by-step explanation:

5) The angle E or ? is half the sum of the intercepted arcs:

? = (130° +94°)/2 = 112°

6) The angle D is half the difference of the intercepted arcs:

? = (135° -55°)/2 = 40°

8 0

2 years ago

Factor the expression completely 8x^2-18 Please help

nirvana33 [79]

Answer:

2 (2x - 3) x (2x + 3)

4 0

3 years ago

usa el teorema de la altura para proponer como se podria construir un segmento cuya longitud sea media proporcional entre dos se

Mrac [35]

Usando el teorema de altura

El teorema de altura relaciona la altura (h) de un triángulo rectángulo (ver figura) y los catetos de dos triángulos que son semejantes al anterior ABC, al trazar la altura (h) sobre la hipotenusa. De manera que en todo triángulo rectángulo, la altura (h) relativa a la hipotenusa es la media geométrica de las dos proyecciones de los catetos sobre la hipotenusa (n y m). Es decir, se cumple que:

 $\frac{n}{h}= \frac{h}{m}$

Dado que el problema establece construir un segmento cuya longitud sea media proporcional entre dos segmentos de 4 y 9 cm, entonces, digamos que n = 4cm y m = 9cm tenmos que:

 $\frac{4}{h}= \frac{h}{9}$

De donde:

$h= \sqrt{(4)(9)}=\sqrt{36}=6cm$

¿Cómo se podria construir si los segmentos son de a cm y b cm?

Si los segmentos son de a y b cm entonces a y b son parámetros que pueden tomar cualquier valor positivo siempre que se cumpla que:

$h= \sqrt{ab}$