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bezimeni [28]
3 years ago
13

Which inequality represents the value of x that ensures triangle abc exists?

Mathematics
1 answer:
olasank [31]3 years ago
3 0

Answer:

Option A.

Step-by-step explanation:

According to triangle inequality theorem, a triangle exists if the sum of two sides is greater that third side.

Apply this theorem on each combination.

Case I: (2x+4)+6x>18

8x+4>18

8x>14

x>\dfrac{14}{8}

x>\dfrac{7}{4}      ...(1)

Case II: (2x+4)+18>6x

2x+22>6x

22>4x

\dfrac{22}{4}>x

\dfrac{11}{2}>x     ...(2)

Case III: 6x+18>2x+4

6x-2x>4-18

4x>-14

x>-\dfrac{14}{4}

x>-\dfrac{7}{2}     ...(3)

On combining (1), (2) and (3), we get

\dfrac{7}{4}

Therefore, the correct option is A.

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Find the value of x.<br>(tangent)​
mariarad [96]

Answer:

5\sqrt{2}

Step-by-step explanation:

Special triangle. 1:1:\sqrt{2}

8 0
3 years ago
Read 2 more answers
En una fiesta hay 40 asistentes de los cuales el número de varones que no bailan es el doble que el número de las mujeres que no
Arte-miy333 [17]

Answer:

50%

Step-by-step explanation:

Para resolver este problema vamos a definir 4 variables:

V= número de varones bailando.

M= número de mujeres bailando.

V' = número de varones que no están bailando.

M' = número de mujeres que no están bailando.

Sabemos que hay 40 personas en la fiesta, por lo que podemos construir la siguiente ecuación:

V+M+V'+M'=40

Vamos a suponer que cada mujer que está bailando, está bailando varón respectivamente. (El problema no da más información, entonces podemos suponer esto.)

Entonces si hay 5 mujeres bailando, entonces también hay 5 hombres bailando, por lo que nuestra ecuación se reescribe de la siguiente manera:

5+5+V'+M'=40

y simplificamos:

10+V'+M'=40

V'+M'=40-10

V'+M'=30

Ahora bien, el problem nos dice que el número de varones que no bailan es el doble del número de mujeres que no bailan en un determinado momento. Entonces con esta información podemos construir la siguiente ecuación:

V'=2M'

Y podemos despejar el número de mujeres que no bailan, lo que nos da:

M'=\frac{V'}{2}

Entonces podemos sustituir esto dentro de nuestra ecuación para obtener:

\frac{V'}{2}+V'=30

y podemos entonces despejar V'

\frac{3V'}{2}=30

V'=\frac{2(30)}{3}

V'=20

Entonces hay 20 varones que no están bailando, por lo que la probabilidad de que el varón que se escoge al azar no esté bailando está dada por la siguiente fórmula:

P=\frac{V'}{total}

P=\frac{20}{40}=\frac{1}{2}

P=50%

6 0
3 years ago
Can someone help me with the name of this shape?
Colt1911 [192]

Answer:

<h3>The shape is a Trapezium or trapezoid</h3>

Hope this helps you

6 0
3 years ago
Decrease £13.20 by 15% <br><br> With an explanation (working out) plzzzz
algol [13]

Answer:

£11.22

Step-by-step explanation:

100% = £13.20

50% = £6.60

10% = £1.32

5% = £0.66

so you would add 10% and 5% together which gives you 15% and 15% is £1.98

and then you could to £13.20 - £1.98 which equals to £11.22  

6 0
3 years ago
Rugs sell for 8$ per square foot. Beth bought a 9-foot-long rectangular rug for $432. How wide was the rug?
lawyer [7]
If you know the rugs sell for 8$ per square foot and the total spend was $432. You divide 432 by 8 to find the total number of square foot of the rug. Which is 54. To find total square foot you find the area. So the area of a rectangle is L*W. So 54 = 9*width. So just divide 54 by 9 and you get the width of the rug. The width is 6 foot. Now you check. A nine by 6 rugs square foot is 54. and then times by 8 and you get 432 total. So you know the rug is 6 foot wide. :)
5 0
3 years ago
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