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Gnesinka [82]
3 years ago
12

Solve this equation -k/5=7/10

Mathematics
1 answer:
liberstina [14]3 years ago
4 0
-\dfrac{k}{5}=\dfrac{7}{10}\\
-10k=35\\
k=-3.5
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(x/x+3)-(8/x+2)=(-13x-6)/(x^2+5x+6)​
Fed [463]

Answer:

x = -9

x = 2

Step-by-step explanation:

Given:

\dfrac{x}{x+3}-\dfrac{8}{x+2}=\dfrac{-13x-6}{x^2+5x+6}

First, note that

x^2+5x+6=x^2+2x+3x+6=x(x+2)+3(x+2)=(x+2)(x+3)

Since x+2 and x+3 stay in the denominator, then

x\neq -2\ \text{and}\ x\neq -3

Now add two fractions which stay in the left part. The common denominator is (x+2)(x+3), so multiply the numerator of the first fraction by (x+2) and the numerator of the second fraction by (x+3) and subtract them in the numerator:

\dfrac{x}{x+3}-\dfrac{8}{x+2}=\dfrac{-13x-6}{(x+2)(x+3)}\\ \\\dfrac{x(x+2)-8(x+3)}{(x+2)(x+3)}=\dfrac{-13x-6}{(x+2)(x+3)}\\ \\x(x+2)-8(x+3)=-13x-6\\ \\x^2+2x-8x-24=-13x-6\\ \\x^2+2x-8x+13x-24+6=0\\ \\x^2+7x-18=0\\ \\x^2+9x-2x-18=0\\ \\x(x+9)-2(x+9)=0\\ \\(x+9)(x-2)=0\\ \\x+9=0\ \text{or}\ x-2=0\\ \\x=-9\ \text{or}\ x=2

3 0
3 years ago
Please help <br><br>must show work ​
hjlf

Answer:

b) y=2x-3 y-int.=-3 x= 1/2 (think of rise over run)= up 2 over 1. C) IDK D) y=2/4+3 E)7/2-8

Step-by-step explanation:

<h2>when you solve in slope intercept form ex. 3x+4y=12 move 3x by subtracting  to the other side. 3x-3x=0 cancel then your left with 4y=-3 (you moved to both sides)+ 12  divide the equation by 4. left with 4divided by 4 cancels left with y= -3+12 divided by 4= y=3/4+8</h2><h2 /><h2>Remember if positive subtract if negative number add to both sides.</h2>
3 0
3 years ago
Write an equation in slope-intercept form from the given information.
Bezzdna [24]
Y=3x+1 should be the answer can I get a crown?
3 0
3 years ago
An initial population of 415
slamgirl [31]

Answer:

The exponential function to model the duck population is:

f(n)=415*(1.32)^n, where:

x is the duck population

n is the number of years

Step-by-step explanation:

In order to calculate the duck population you can use the formula to calculate future value:

FV=PV*(1+r)^n

FV=future value

PV=present value

r=rate

n=number of periods of time

In this case, the present value is the initial population of 415 and the rate is 32%. You can replace these values on the formula and the exponential function to model the duck population would be:

f(n)=415*(1+0.32)^n

f(n)=415*(1.32)^n, where:

x is the duck population

n is the number of years

3 0
3 years ago
Worth 25 points!
MrRissso [65]

Answer:

1) \sqrt{-48}=4\sqrt{3} \ i

2) \sqrt{-63}=3\sqrt{7} \ i

3) \sqrt{-72}=6\sqrt{2} \ i

4) \sqrt{-24}=4\sqrt{6} \ i

5) \sqrt{-84}=2\sqrt{21} \ i

6) \sqrt{-99}=3\sqrt{11} \ i

Step-by-step explanation:

We need to simply the following :

<u>Note: For all questions given we know that </u>\sqrt{-1}=i<u> using it in all the given questions.</u>

1) \sqrt{-48}

Factors of 48 are: 2x2x2x2x3

\sqrt{-48}\\=\sqrt{48}\sqrt{-1}  \\=\sqrt{2\times2\times2\times2\times3}\ i\\=  \sqrt{2^2\times2^2\times3}\ i\\=2\times2\sqrt{3} \ i \\=4\sqrt{3} \ i

2) \sqrt{-63}

Factors of 63 are: 3x3x7

\sqrt{-63}\\=\sqrt{63}\sqrt{-1}  \\=\sqrt{3\times3\times7}\ i\\=  \sqrt{3^2\times7}\ i\\=3\sqrt{7} \ i

3) \sqrt{-72}

Factors of 72 are: 2x2x2x3x3

\sqrt{-72}\\=\sqrt{72}\sqrt{-1}  \\=\sqrt{2\times2\times2\times3\times3}\ i\\=  \sqrt{2^2\times3^2\times2}\ i\\=2\times3\sqrt{2} \ i \\=6\sqrt{2} \ i

4) \sqrt{-24}

Factors of 24 are: 2x2x2x3

\sqrt{-24}\\=\sqrt{24}\sqrt{-1}  \\=\sqrt{2\times2\times2\times3}\ i\\=  \sqrt{2^2\times2\times3}\ i\\=2\sqrt{2\times3} \ i \\=2\sqrt{6} \ i

5) \sqrt{-84}

Factors of 84 are: 2x2x3x7

\sqrt{-84}\\=\sqrt{84}\sqrt{-1}  \\=\sqrt{2\times2\times3\times7}\ i\\=  \sqrt{2^2\times3\times7}\ i\\=2\sqrt{21} \ i

6) \sqrt{-99}\\

Prime factors of 99 are: 3x3x11

\sqrt{-99}\\=\sqrt{99}\sqrt{-1}  \\=\sqrt{3\times3\times11}\ i\\=  \sqrt{3^2\times11}\ i\\=3\sqrt{11} \ i \\=3\sqrt{11} \ i

6 0
3 years ago
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