The expression 14y⁴x³ * 12x³y² * 5x²y² is equivalent to 840 y⁸x⁸ .
<h3>What is an Expression ?</h3>
An expression is defined as the mathematical statement which consists of variables , constant s and mathematical Operators simultaneously.
It is given that the expression
14y⁴x³ * 12x³y² * 5x²y²
By exponent theorem
![\rm a^m * a^n = a^{m+n}](https://tex.z-dn.net/?f=%5Crm%20a%5Em%20%2A%20a%5En%20%3D%20a%5E%7Bm%2Bn%7D)
Therefore 14* 12 * 5 * y⁴⁺²⁺² x ³⁺³⁺²
840 y⁸x⁸
The expression 14y⁴x³ * 12x³y² * 5x²y² is equivalent to 840 y⁸x⁸ .
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Answer:
StartFraction f minus v Over t
EndFraction =a
Step-by-step explanation:
The equation for acceleration is a= f-v
-----
t
Rearrange f=v+at
solve for a
f= v+at minus v
-v -v
get a by itself. multiplication is happening a between and t so divide
f-v=at
--- ---
t t
a= f-v
----
t
Given:
![y=-2](https://tex.z-dn.net/?f=y%3D-2)
![y=\sqrt{3}x-1](https://tex.z-dn.net/?f=y%3D%5Csqrt%7B3%7Dx-1)
To find:
The obtuse angle between the given pair of straight lines.
Solution:
The slope intercept form of a line is
...(i)
where, m is slope and b is y-intercept.
The given equations are
![y=0x-2](https://tex.z-dn.net/?f=y%3D0x-2)
![y=\sqrt{3}x-1](https://tex.z-dn.net/?f=y%3D%5Csqrt%7B3%7Dx-1)
On comparing these equations with (i), we get
![m_1=0](https://tex.z-dn.net/?f=m_1%3D0)
![m_2=\sqrt{3}](https://tex.z-dn.net/?f=m_2%3D%5Csqrt%7B3%7D)
Angle between two lines whose slopes are
is
![\tan \theta=\left|\dfrac{m_2-m_1}{1+m_1m_2}\right|](https://tex.z-dn.net/?f=%5Ctan%20%5Ctheta%3D%5Cleft%7C%5Cdfrac%7Bm_2-m_1%7D%7B1%2Bm_1m_2%7D%5Cright%7C)
Putting
and
, we get
![\tan \theta=\left|\dfrac{\sqrt{3}-0}{1+(0)(\sqrt{3})}\right|](https://tex.z-dn.net/?f=%5Ctan%20%5Ctheta%3D%5Cleft%7C%5Cdfrac%7B%5Csqrt%7B3%7D-0%7D%7B1%2B%280%29%28%5Csqrt%7B3%7D%29%7D%5Cright%7C)
![\tan \theta=\left|\dfrac{\sqrt{3}}{1+0}\right|](https://tex.z-dn.net/?f=%5Ctan%20%5Ctheta%3D%5Cleft%7C%5Cdfrac%7B%5Csqrt%7B3%7D%7D%7B1%2B0%7D%5Cright%7C)
![\tan \theta=\pm \sqrt{3}](https://tex.z-dn.net/?f=%5Ctan%20%5Ctheta%3D%5Cpm%20%5Csqrt%7B3%7D)
Now,
and ![\tan \theta=-\sqrt{3}](https://tex.z-dn.net/?f=%5Ctan%20%5Ctheta%3D-%5Csqrt%7B3%7D)
and ![\tan \theta=\tan (180^\circ-60^\circ)](https://tex.z-dn.net/?f=%5Ctan%20%5Ctheta%3D%5Ctan%20%28180%5E%5Ccirc-60%5E%5Ccirc%29)
and ![\theta=120^\circ](https://tex.z-dn.net/?f=%5Ctheta%3D120%5E%5Ccirc)
, so it is an obtuse angle and
, so it is an acute angle.
Therefore, the obtuse angle between the given pair of straight lines is 120°.
Answer2 bags of stone only
Step-by-step explanation:
so you need to times up the amount the bags weight to the ones he already has 25*8=200 and 22.5*19=427.5 and 50*20=1000 the you subtract what he needs to use like he doesn’t need any cement bags nor sand he only needs 2 bags of stone
Answer:
(C)
Step-by-step explanation:
If can't have a meaning as something can't decrease more than 100% of itself.