Answer:
90
Step-by-step explanation:
The first term = 6* 2^0 = 6
The second term = 6 * 2^ (2-1) = 6*2 = 12
The third term = 6* 2^(3-1) = 6*2^2 = 6*4 = 24
The fourth term = 6* 2^(4-1) = 6* 2^3 = 6*8 = 48
S4 is the sum of the 1st four terms
S4 = 6+ 12+24+ 48 = 90
4 x 7.04 ...................................
If angle "a" measures 42° the the other angles that will be congruent to angle "a" and also measure 42° will be angle d, angle e and angle h .
In the question ,
a figure is given ,
From the figure we can see that 2 parallel lines are cut by a transversal .
So ,
angle a = angle d .......because vertically opposite angles .
angle a = angle e ...because corresponding angles are equal in measure
also
angle e = angle h .... because vertically opposite angles .
Therefore , If angle "a" measures 42° the the other angles that will be congruent to angle "a" and also measure 42° will be angle d, angle e and angle h , the correct option is (a) .
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Answer:
![\large\boxed{1.\ f^{-1}(x)=4\log(x\sqrt[4]2)}\\\\\boxed{2.\ f^{-1}(x)=\log(x^5+5)}\\\\\boxed{3.\ f^{-1}(x)=\sqrt{4^{x-1}}}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7B1.%5C%20f%5E%7B-1%7D%28x%29%3D4%5Clog%28x%5Csqrt%5B4%5D2%29%7D%5C%5C%5C%5C%5Cboxed%7B2.%5C%20f%5E%7B-1%7D%28x%29%3D%5Clog%28x%5E5%2B5%29%7D%5C%5C%5C%5C%5Cboxed%7B3.%5C%20f%5E%7B-1%7D%28x%29%3D%5Csqrt%7B4%5E%7Bx-1%7D%7D%7D)
Step-by-step explanation:
![\log_55^{\frac{1}{4}y}=\log_5\left(2^\frac{1}{4}x\right)\qquad\text{use}\ a^\frac{1}{n}=\sqrt[n]{a}\\\\\dfrac{1}{4}y=\log(x\sqrt[4]2)\qquad\text{multiply both sides by 4}\\\\y=4\log(x\sqrt[4]2)](https://tex.z-dn.net/?f=%5Clog_55%5E%7B%5Cfrac%7B1%7D%7B4%7Dy%7D%3D%5Clog_5%5Cleft%282%5E%5Cfrac%7B1%7D%7B4%7Dx%5Cright%29%5Cqquad%5Ctext%7Buse%7D%5C%20a%5E%5Cfrac%7B1%7D%7Bn%7D%3D%5Csqrt%5Bn%5D%7Ba%7D%5C%5C%5C%5C%5Cdfrac%7B1%7D%7B4%7Dy%3D%5Clog%28x%5Csqrt%5B4%5D2%29%5Cqquad%5Ctext%7Bmultiply%20both%20sides%20by%204%7D%5C%5C%5C%5Cy%3D4%5Clog%28x%5Csqrt%5B4%5D2%29)
![--------------------------\\2.\\y=(10^x-5)^\frac{1}{5}\\\\\text{Exchange x and y. Solve for y:}\\\\(10^y-5)^\frac{1}{5}=x\qquad\text{5 power of both sides}\\\\\bigg[(10^y-5)^\frac{1}{5}\bigg]^5=x^5\qquad\text{use}\ (a^n)^m=a^{nm}\\\\(10^y-5)^{\frac{1}{5}\cdot5}=x^5\\\\10^y-5=x^5\qquad\text{add 5 to both sides}\\\\10^y=x^5+5\qquad\log\ \text{of both sides}\\\\\log10^y=\log(x^5+5)\Rightarrow y=\log(x^5+5)](https://tex.z-dn.net/?f=--------------------------%5C%5C2.%5C%5Cy%3D%2810%5Ex-5%29%5E%5Cfrac%7B1%7D%7B5%7D%5C%5C%5C%5C%5Ctext%7BExchange%20x%20and%20y.%20Solve%20for%20y%3A%7D%5C%5C%5C%5C%2810%5Ey-5%29%5E%5Cfrac%7B1%7D%7B5%7D%3Dx%5Cqquad%5Ctext%7B5%20power%20of%20both%20sides%7D%5C%5C%5C%5C%5Cbigg%5B%2810%5Ey-5%29%5E%5Cfrac%7B1%7D%7B5%7D%5Cbigg%5D%5E5%3Dx%5E5%5Cqquad%5Ctext%7Buse%7D%5C%20%28a%5En%29%5Em%3Da%5E%7Bnm%7D%5C%5C%5C%5C%2810%5Ey-5%29%5E%7B%5Cfrac%7B1%7D%7B5%7D%5Ccdot5%7D%3Dx%5E5%5C%5C%5C%5C10%5Ey-5%3Dx%5E5%5Cqquad%5Ctext%7Badd%205%20to%20both%20sides%7D%5C%5C%5C%5C10%5Ey%3Dx%5E5%2B5%5Cqquad%5Clog%5C%20%5Ctext%7Bof%20both%20sides%7D%5C%5C%5C%5C%5Clog10%5Ey%3D%5Clog%28x%5E5%2B5%29%5CRightarrow%20y%3D%5Clog%28x%5E5%2B5%29)
Answer:
35 plants
Step-by-step explanation:
For this case we can make the following rule of three:
4 gallons --------------> 14 plants
x --------------------------> 35 plants
From here, we clear the value of x.
We have then:
therefore, 10 gallons are needed to irrigate 35 plants.
Answer:
it will take 10 gallons to water 35 plants
