Answer:
![Product = \frac{3}{5}ab](https://tex.z-dn.net/?f=Product%20%3D%20%5Cfrac%7B3%7D%7B5%7Dab)
Step-by-step explanation:
Given
![-\frac{3}{7}a](https://tex.z-dn.net/?f=-%5Cfrac%7B3%7D%7B7%7Da)
![-\frac{21}{15}b](https://tex.z-dn.net/?f=-%5Cfrac%7B21%7D%7B15%7Db)
Required
The product
The product is:
'
Cancel out the negative signs
![Product = \frac{3}{7}a * \frac{21}{15}b](https://tex.z-dn.net/?f=Product%20%3D%20%5Cfrac%7B3%7D%7B7%7Da%20%2A%20%5Cfrac%7B21%7D%7B15%7Db)
Simplify fractions
![Product = \frac{1}{7}a * \frac{21}{5}b](https://tex.z-dn.net/?f=Product%20%3D%20%5Cfrac%7B1%7D%7B7%7Da%20%2A%20%5Cfrac%7B21%7D%7B5%7Db)
![Product = \frac{1}{1}a * \frac{3}{5}b](https://tex.z-dn.net/?f=Product%20%3D%20%5Cfrac%7B1%7D%7B1%7Da%20%2A%20%5Cfrac%7B3%7D%7B5%7Db)
![Product = \frac{3}{5}ab](https://tex.z-dn.net/?f=Product%20%3D%20%5Cfrac%7B3%7D%7B5%7Dab)
Answer:
Step-by-step explanation:
one
FHS is a straight line. Assumption
FHS = 180 Straight lines = 180 degrees
NHF + NHS = 180 degrees NH cuts the line at H. They add to 180
NHF and NHS are supplementary Definitition supplementary
Two
ACE and DCB are straight lines Assumption
They cross at C Given Construction
ACB = DCE Vertical angles are equal
Three
AP = AP Reflexive property.
Four
A is a right angle
B is a right angle
Right angles = 90 degrees
<A = <B
Five
CM bisects AB Given
AM = MB Definition of bisect.
9514 1404 393
Answer:
- 4
- A. 0
Step-by-step explanation:
1. Input 3 for x and do the arithmetic.
z(x) = x+1
z(3) = 3+1 = 4 . . . . . the output is 4
__
2. The expression for n(x) has x in the denominator. The expression will be undefined when the denominator is zero, so x=0 cannot be used.
Given:
at an angle of 45°.
at an angle of 150°.
![w=u+v](https://tex.z-dn.net/?f=w%3Du%2Bv)
To find:
Magnitude and direction angle of w.
Solution:
We have,
![w=u+v](https://tex.z-dn.net/?f=w%3Du%2Bv)
![\theta = 45^\circ, \phi = 150^\circ](https://tex.z-dn.net/?f=%5Ctheta%20%3D%2045%5E%5Ccirc%2C%20%5Cphi%20%3D%20150%5E%5Ccirc)
Now,
![u_x=|u|\cos \theta=10\cos 45^\circ=7.071](https://tex.z-dn.net/?f=u_x%3D%7Cu%7C%5Ccos%20%5Ctheta%3D10%5Ccos%2045%5E%5Ccirc%3D7.071)
![u_y=|u|\sin \theta=u_y=10\sin 45^\circ=7.071](https://tex.z-dn.net/?f=u_y%3D%7Cu%7C%5Csin%20%5Ctheta%3Du_y%3D10%5Csin%2045%5E%5Ccirc%3D7.071)
![v_x=|v|\cos \phi=13\cos 150^\circ=-11.25833](https://tex.z-dn.net/?f=v_x%3D%7Cv%7C%5Ccos%20%5Cphi%3D13%5Ccos%20150%5E%5Ccirc%3D-11.25833)
![v_y=|v|\sin \phi=u_y=13\sin 150^\circ=6.5](https://tex.z-dn.net/?f=v_y%3D%7Cv%7C%5Csin%20%5Cphi%3Du_y%3D13%5Csin%20150%5E%5Ccirc%3D6.5)
Using these information, we get
![R_x=u_x+v_x=7.071-11.25833=-4.18733](https://tex.z-dn.net/?f=R_x%3Du_x%2Bv_x%3D7.071-11.25833%3D-4.18733)
![R_y=u_y+v_y=7.071+6.5=13.571](https://tex.z-dn.net/?f=R_y%3Du_y%2Bv_y%3D7.071%2B6.5%3D13.571)
![\text{Direction angle}=\tan^{-1}(\dfrac{R_y}{R_x})](https://tex.z-dn.net/?f=%5Ctext%7BDirection%20angle%7D%3D%5Ctan%5E%7B-1%7D%28%5Cdfrac%7BR_y%7D%7BR_x%7D%29)
![\text{Direction angle}=\tan^{-1}(\dfrac{13.571}{-4.18733})](https://tex.z-dn.net/?f=%5Ctext%7BDirection%20angle%7D%3D%5Ctan%5E%7B-1%7D%28%5Cdfrac%7B13.571%7D%7B-4.18733%7D%29)
![\text{Direction angle}=-72.8239](https://tex.z-dn.net/?f=%5Ctext%7BDirection%20angle%7D%3D-72.8239)
![\text{Direction angle}=107.1476](https://tex.z-dn.net/?f=%5Ctext%7BDirection%20angle%7D%3D107.1476)
![\text{Direction angle}\approx 107.1](https://tex.z-dn.net/?f=%5Ctext%7BDirection%20angle%7D%5Capprox%20107.1)
Now,
![|w|=\sqrt{(|u|\cos \theta +|v|\cos \phi)^2+(|u|\sin \theta +|v|\sin \phi)^2}](https://tex.z-dn.net/?f=%7Cw%7C%3D%5Csqrt%7B%28%7Cu%7C%5Ccos%20%5Ctheta%20%2B%7Cv%7C%5Ccos%20%5Cphi%29%5E2%2B%28%7Cu%7C%5Csin%20%5Ctheta%20%2B%7Cv%7C%5Csin%20%5Cphi%29%5E2%7D)
![|w|=\sqrt{(10\cos(45)+13\cos 150)^2+(10\sin(45)+13\sin 150)^2}](https://tex.z-dn.net/?f=%7Cw%7C%3D%5Csqrt%7B%2810%5Ccos%2845%29%2B13%5Ccos%20150%29%5E2%2B%2810%5Csin%2845%29%2B13%5Csin%20150%29%5E2%7D)
![|w|=\sqrt{(10(\dfrac{1}{\sqrt{2}})+13(-\dfrac{\sqrt{3}}{2}))^2+(10(\dfrac{1}{\sqrt{2}})+13(\dfrac{1}{2}))^2}](https://tex.z-dn.net/?f=%7Cw%7C%3D%5Csqrt%7B%2810%28%5Cdfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D%29%2B13%28-%5Cdfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%29%29%5E2%2B%2810%28%5Cdfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D%29%2B13%28%5Cdfrac%7B1%7D%7B2%7D%29%29%5E2%7D)
![|w|=14.20236](https://tex.z-dn.net/?f=%7Cw%7C%3D14.20236)
![|w|\approx 14.20236](https://tex.z-dn.net/?f=%7Cw%7C%5Capprox%2014.20236)
Therefore, the correct option is D.
Answer:
-2 < x ≤ 2
Step-by-step explanation: