Answer: x=3 ==> 1st option
Step-by-step explanation:
FH=FG+GH
18=4x+2x
6x=18
x=3 ==> 1st option
Answer:
90kg
Step-by-step explanation:
it is so because, to decrease a number by a ratio you have to multiply with the smallest number and divide with the biggest one. For example 117 in the ratio 7:3. 117×3=351 which is divided by 7 and is equal to 50.14.
<span>Cada goma de borrar es $ 5. Primero restar el precio de las revistas ($ 5) del dinero que gastó. Ella ahora tiene $ 20. Luego divida eso entre cuantos borradores compró (4). 20 dividido por 4 es 5. Cada borrador fue de $ 5. ¡Espero que la traducción tenga sentido !!</span>
Given:
![\cos \theta =\dfrac{3}{5}](https://tex.z-dn.net/?f=%5Ccos%20%5Ctheta%20%3D%5Cdfrac%7B3%7D%7B5%7D)
![\sin \theta](https://tex.z-dn.net/?f=%5Csin%20%5Ctheta%20%3C0)
To find:
The quadrant of the terminal side of
and find the value of
.
Solution:
We know that,
In Quadrant I, all trigonometric ratios are positive.
In Quadrant II: Only sin and cosec are positive.
In Quadrant III: Only tan and cot are positive.
In Quadrant IV: Only cos and sec are positive.
It is given that,
![\cos \theta =\dfrac{3}{5}](https://tex.z-dn.net/?f=%5Ccos%20%5Ctheta%20%3D%5Cdfrac%7B3%7D%7B5%7D)
![\sin \theta](https://tex.z-dn.net/?f=%5Csin%20%5Ctheta%20%3C0)
Here cos is positive and sine is negative. So,
must be lies in Quadrant IV.
We know that,
![\sin^2\theta +\cos^2\theta =1](https://tex.z-dn.net/?f=%5Csin%5E2%5Ctheta%20%2B%5Ccos%5E2%5Ctheta%20%3D1)
![\sin^2\theta=1-\cos^2\theta](https://tex.z-dn.net/?f=%5Csin%5E2%5Ctheta%3D1-%5Ccos%5E2%5Ctheta)
![\sin \theta=\pm \sqrt{1-\cos^2\theta}](https://tex.z-dn.net/?f=%5Csin%20%5Ctheta%3D%5Cpm%20%5Csqrt%7B1-%5Ccos%5E2%5Ctheta%7D)
It is only negative because
lies in Quadrant IV. So,
![\sin \theta=-\sqrt{1-\cos^2\theta}](https://tex.z-dn.net/?f=%5Csin%20%5Ctheta%3D-%5Csqrt%7B1-%5Ccos%5E2%5Ctheta%7D)
After substituting
, we get
![\sin \theta=-\sqrt{1-(\dfrac{3}{5})^2}](https://tex.z-dn.net/?f=%5Csin%20%5Ctheta%3D-%5Csqrt%7B1-%28%5Cdfrac%7B3%7D%7B5%7D%29%5E2%7D)
![\sin \theta=-\sqrt{1-\dfrac{9}{25}}](https://tex.z-dn.net/?f=%5Csin%20%5Ctheta%3D-%5Csqrt%7B1-%5Cdfrac%7B9%7D%7B25%7D%7D)
![\sin \theta=-\sqrt{\dfrac{25-9}{25}}](https://tex.z-dn.net/?f=%5Csin%20%5Ctheta%3D-%5Csqrt%7B%5Cdfrac%7B25-9%7D%7B25%7D%7D)
![\sin \theta=-\sqrt{\dfrac{16}{25}}](https://tex.z-dn.net/?f=%5Csin%20%5Ctheta%3D-%5Csqrt%7B%5Cdfrac%7B16%7D%7B25%7D%7D)
![\sin \theta=-\dfrac{4}{5}](https://tex.z-dn.net/?f=%5Csin%20%5Ctheta%3D-%5Cdfrac%7B4%7D%7B5%7D)
Therefore, the correct option is B.
Answer:
Step-by-step explanation:
1) Write 8x+14 as 2(4x+7) and now multiply by 1/2 so that we get 4x+7
2)Subtract 7 from both sides
4x+7=39
-7 -7
4x=32
3) Divide by 8
x=8
Thus we get x=8 as answer
So reasons are
i) Distributive property
ii) Subtraction property of equality
iii) Division property of equality