Answer:
![x=-0.75](https://tex.z-dn.net/?f=x%3D-0.75)
Step-by-step explanation:
The given equation is
![4^{-5x-7}=6^{2x-1}](https://tex.z-dn.net/?f=4%5E%7B-5x-7%7D%3D6%5E%7B2x-1%7D)
We take logarithm of both sides to base 10.
![\log(4^{-5x-7})=\log(6^{2x-1})](https://tex.z-dn.net/?f=%5Clog%284%5E%7B-5x-7%7D%29%3D%5Clog%286%5E%7B2x-1%7D%29)
![(-5x-7)\log(4)=(2x-1)\log(6)](https://tex.z-dn.net/?f=%28-5x-7%29%5Clog%284%29%3D%282x-1%29%5Clog%286%29)
We expand the brackets to get;
![-5x\log(4)-7\log(4)=2x\log(6)-\log(6)](https://tex.z-dn.net/?f=-5x%5Clog%284%29-7%5Clog%284%29%3D2x%5Clog%286%29-%5Clog%286%29)
Group similar terms;
![-7\log(4)+\log(6)=2x\log(6)+5x\log(4)](https://tex.z-dn.net/?f=-7%5Clog%284%29%2B%5Clog%286%29%3D2x%5Clog%286%29%2B5x%5Clog%284%29)
![-7\log(4)+\log(6)=(2\log(6)+5\log(4))x](https://tex.z-dn.net/?f=-7%5Clog%284%29%2B%5Clog%286%29%3D%282%5Clog%286%29%2B5%5Clog%284%29%29x)
![\frac{-7\log(4)+\log(6)}{(2\log(6)+5\log(4))}=x](https://tex.z-dn.net/?f=%5Cfrac%7B-7%5Clog%284%29%2B%5Clog%286%29%7D%7B%282%5Clog%286%29%2B5%5Clog%284%29%29%7D%3Dx)
![x=-0.752478](https://tex.z-dn.net/?f=x%3D-0.752478)
To the nearest hundredth.
![x=-0.75](https://tex.z-dn.net/?f=x%3D-0.75)
Answer:
1.8 units.
Step-by-step explanation:
The questions which involve calculating the angles and the sides of a triangle either require the sine rule or the cosine rule. In this question, the two sides that are given are adjacent to each other and the given angle is the included angle. This means that the angle is formed by the intersection of the two lines. Therefore, cosine rule will be used to calculate the length of the largest side of the triangle. The cosine rule is:
b^2 = a^2 + c^2 - 2*a*c*cos(B).
The question specifies that a=0.5, B=120°, and c=1.5. Plugging in the values:
b^2 = 0.5^2 + 1.5^2 - 2(0.5)(1.5)*cos(120°).
Simplifying gives:
b^2 = 3.25.
Taking square root on the both sides gives b = 1.8 (rounded to the nearest tenth).
This means that the length of the third side is 1.8 units!!!
she can use all of the flowers. she cut down 9 and bought 18.
The answer is a (three eights over three fifths= five eights)
Please, see the offered decision:
1) common equation for lines is y=kx+b. If k₁=k₂ (for line 1 and line 2) ⇒ 'line 1' || 'line 2'.
2) for line 3x+5y=6 k= -3/5. It means (according to item 1) for unknown line k is the same (-3/5).
3) using points (0;3) it is easy to find parameter b (x=0, y=3) via y=kx+b:
3=0*(-3/5)+b ⇔ b=3.
4) finaly (k=-3/5; b=3):