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oee [108]
3 years ago
12

Need help ASAP !!!!!!!

Mathematics
1 answer:
Anestetic [448]3 years ago
5 0
First we distribute \frac{1}{5} into n and -\frac{1}{7}.

\frac{1}{5} * n =  \frac{1}{5} n
\frac{1}{5}  *  -\frac{1}{7}  = - \frac{1}{35}

That makes the left side of the equation 

\frac{1}{5} n -  \frac{1}{35} =  \frac{1}{6} n

Now we subtract \frac{1}{5}n from \frac{1}{6} n, which makes \frac{1}{30}

Now the equation is 

-\frac{1}{35} =  -\frac{1}{30n}

Our goal is to isolate n, so we both sides by 30

30* -\frac{1}{35} = - \frac{1}{30}n * 30 

That will make the equation 

- \frac{30}{35} = -n

We multiply -1 on both sides of the equation:

\frac{30}{35} = n

Finally we simplify \frac{30}{35}, which makes \frac{6}{7}

So the answer is n =  \frac{6}{7}
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The length of a rectangular garden is 4 less than twice the width find the perimeter and area of the garden
sergeinik [125]

Answer:

Let w be the width. Then the length is 2w-4. So:

w(2w-4)=96

2w²-4w-96=0

w²-2w-48=0

(w-8)(w+6)=0

w=8 or -6

Throwing out the negative value for w, we get a width of 8 yds, and a length of 12 yds. ☺☺☺☺

4 0
2 years ago
In the triangle pictured, let A, B, C be the angles at the three vertices, and let a,b,c be the sides opposite those angles. Acc
Troyanec [42]

Answer:

Step-by-step explanation:

(a)

Consider the following:

A=\frac{\pi}{4}=45°\\\\B=\frac{\pi}{3}=60°

Use sine rule,

\frac{b}{a}=\frac{\sinB}{\sin A}
\\\\=\frac{\sin{\frac{\pi}{3}}
}{\sin{\frac{\pi}{4}}}\\\\=\frac{[\frac{\sqrt{3}}{2}]}{\frac{1}{\sqrt{2}}}\\\\=\frac{\sqrt{2}}{2}\times \frac{\sqrt{2}}{1}=\sqrt{\frac{3}{2}}

Again consider,

\frac{b}{a}=\frac{\sin{B}}{\sin{A}}
\\\\\sin{B}=\frac{b}{a}\times \sin{A}\\\\\sin{B}=\sqrt{\frac{3}{2}}\sin {A}\\\\B=\sin^{-1}[\sqrt{\frac{3}{2}}\sin{A}]

Thus, the angle B is function of A is, B=\sin^{-1}[\sqrt{\frac{3}{2}}\sin{A}]

Now find \frac{dB}{dA}

Differentiate implicitly the function \sin{B}=\sqrt{\frac{3}{2}}\sin{A} with respect to A to get,

\cos {B}.\frac{dB}{dA}=\sqrt{\frac{3}{2}}\cos A\\\\\frac{dB}{dA}=\sqrt{\frac{3}{2}}.\frac{\cos A}{\cos B}

b)

When A=\frac{\pi}{4},B=\frac{\pi}{3}, the value of \frac{dB}{dA} is,

\frac{dB}{dA}=\sqrt{\frac{3}{2}}.\frac{\cos {\frac{\pi}{4}}}{\cos {\frac{\pi}{3}}}\\\\=\sqrt{\frac{3}{2}}.\frac{\frac{1}{\sqrt{2}}}{\frac{1}{2}}\\\\=\sqrt{3}

c)

In general, the linear approximation at x= a is,

f(x)=f'(x).(x-a)+f(a)

Here the function f(A)=B=\sin^{-1}[\sqrt{\frac{3}{2}}\sin{A}]

At A=\frac{\pi}{4}

f(\frac{\pi}{4})=B=\sin^{-1}[\sqrt{\frac{3}{2}}\sin{\frac{\pi}{4}}]\\\\=\sin^{-1}[\sqrt{\frac{3}{2}}.\frac{1}{\sqrt{2}}]\\\\\=\sin^{-1}(\frac{\sqrt{2}}{2})\\\\=\frac{\pi}{3}

And,

f'(A)=\frac{dB}{dA}=\sqrt{3} from part b

Therefore, the linear approximation at A=\frac{\pi}{4} is,

f(x)=f'(A).(x-A)+f(A)\\\\=f'(\frac{\pi}{4}).(x-\frac{\pi}{4})+f(\frac{\pi}{4})\\\\=\sqrt{3}.[x-\frac{\pi}{4}]+\frac{\pi}{3}

d)

Use part (c), when A=46°, B is approximately,

B=f(46°)=\sqrt{3}[46°-\frac{\pi}{4}]+\frac{\pi}{3}\\\\=\sqrt{3}(1°)+\frac{\pi}{3}\\\\=61.732°

8 0
3 years ago
What is the log 5x=log (2x+9)
Ray Of Light [21]
5x = 2x + 9, where 5x > 0 and 2x + 9 > 0 ;
Then, 3x = 9 ;
Then, x = 3 ;
Verify : 5 × 3 = 2 × 3 + 9 ;correct !
            5 × 3 > 0 ; correct !
            2 × 3 + 9 > 0; correct !
8 0
3 years ago
The ratio of width to length of baily's television screen is 3:4. what is the width of the screen if the length is 32 inches
Yuri [45]
If the length is 32 and the ratio is 3:4, you'd do 32 ÷ 4 = 8. The answer is 3 × 8, which is 24 inches. I hope this helps!
5 0
2 years ago
What is the inverse operation of subtraction? How do you "undo" subtraction?
son4ous [18]
The inverse operation of subtraction is A . Addition
8 0
3 years ago
Read 2 more answers
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