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3 years ago

Solve using substitution. x + 3y = -13 5x + 7y = -9

1 answer:

6 0

From equation 1
x = -3y-13
plug this into equation 2:-
5(-3y-13) + 7y = -9
-15y - 65 + 7y = -9
-8y = 56
y = -7
Now plug y = 7 into equation 1
x - 21 = -13
x = -13 + 21 = 8

solution is x = 8 , y = -7

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Solve irrational equation pls

rusak2 [61]

$\hbox{Domain:}\\
x^2+x-2\geq0 \wedge x^2-4x+3\geq0 \wedge x^2-1\geq0\\
x^2-x+2x-2\geq0 \wedge x^2-x-3x+3\geq0 \wedge x^2\geq1\\
x(x-1)+2(x-1)\geq 0 \wedge x(x-1)-3(x-1)\geq0 \wedge (x\geq 1 \vee x\leq-1)\\
(x+2)(x-1)\geq0 \wedge (x-3)(x-1)\geq0\wedge x\in(-\infty,-1\rangle\cup\langle1,\infty)\\
x\in(-\infty,-2\rangle\cup\langle1,\infty) \wedge x\in(-\infty,1\rangle \cup\langle3,\infty) \wedge x\in(-\infty,-1\rangle\cup\langle1,\infty)\\
x\in(-\infty,-2\rangle\cup\langle3,\infty)$

$
\sqrt{x^2+x-2}+\sqrt{x^2-4x+3}=\sqrt{x^2-1}\\
x^2-1=x^2+x-2+2\sqrt{(x^2+x-2)(x^2-4x+3)}+x^2-4x+3\\
2\sqrt{(x^2+x-2)(x^2-4x+3)}=-x^2+3x-2\\
\sqrt{(x^2+x-2)(x^2-4x+3)}=\dfrac{-x^2+3x-2}{2}\\
(x^2+x-2)(x^2-4x+3)=\left(\dfrac{-x^2+3x-2}{2}\right)^2\\
(x+2)(x-1)(x-3)(x-1)=\left(\dfrac{-x^2+x+2x-2}{2}\right)^2\\
(x+2)(x-3)(x-1)^2=\left(\dfrac{-x(x-1)+2(x-1)}{2}\right)^2\\
(x+2)(x-3)(x-1)^2=\left(\dfrac{-(x-2)(x-1)}{2}\right)^2\\
(x+2)(x-3)(x-1)^2=\dfrac{(x-2)^2(x-1)^2}{4}\\
4(x+2)(x-3)(x-1)^2=(x-2)^2(x-1)^2\\$
$
4(x+2)(x-3)(x-1)^2-(x-2)^2(x-1)^2=0\\
(x-1)^2(4(x+2)(x-3)-(x-2)^2)=0\\
(x-1)^2(4(x^2-3x+2x-6)-(x^2-4x+4))=0\\
(x-1)^2(4x^2-4x-24-x^2+4x-4)=0\\
(x-1)^2(3x^2-28)=0\\
x-1=0 \vee 3x^2-28=0\\
x=1 \vee 3x^2=28\\
x=1 \vee x^2=\dfrac{28}{3}\\
x=1 \vee x=\sqrt{\dfrac{28}{3}} \vee x=-\sqrt{\dfrac{28}{3}}\\$

There's one more condition I forgot about
$-(x-2)(x-1)\geq0\\
x\in\langle1,2\rangle\\$

Finally
$x\in(-\infty,-2\rangle\cup\langle3,\infty) \wedge x\in\langle1,2\rangle \wedge x=\{1,\sqrt{\dfrac{28}{3}}, -\sqrt{\dfrac{28}{3}}\}\\
\boxed{\boxed{x=1}}$

3 0

2 years ago

Find the lateral surface area of the prism below in square yards.

denis-greek [22]

Answer:

Step-by-step explanation:

Answer: 14*2 * 3

=> 6 * 14

<h2>=> 84</h2><h2></h2><h2>Please mark as brainliest for further answers :)</h2>

7 0

2 years ago

I need help quick please

kenny6666 [7]

Volume is Length x width x height divided by 3. You have the length and the width. which equals 24. (6x4). The volume that is present is 72... the last thing you do in the equation is divide by three so multiply 72 by 3 and get 216. This is the LxWxH. Like I said before you have the L and the W, which is 24. You would divide 24 from 216. The Height is 9cm.

6 0

3 years ago

Read 2 more answers

Charlotte borrows $9000 to buy a second-hand car. The loan must be repaid

QveST [7]

Answer:

$13,400

Step-by-step explanation:

Simple Interest = principal × rate × time

principal= $9000

Rate= 12/100=0•12

Time=5years

Simple interest =PRT

= 9000× 0•12 × 5

= 5400

Total amount to be paid = 9000 + 5400

= $13400

8 0

3 years ago

2. What is the variable in the expression:<br> 13x3 +7<br> (Select one answer)<br> 7<br> 3<br> 13

sdas [7]

I think it would be 3

3 0

2 years ago