Answer:
1) The option [tex]c=9-a+b[/tex] is correct.
2) The option x=-2 or x=-3 is correct.
3) The option [tex]c=9-a+b[/tex] is correct.
4) The option [tex]x=\frac{11}{3}[/tex] is correct.
5) The option x=-2 or x=-3 is correct.
Step-by-step explanation:
1) Given equation is [tex]\sqrt{a-b+c}=3[/tex]
Now to solve the equation for c:
[tex]\sqrt{a-b+c}=3[/tex]
Squaring on both sides we get
[tex](\sqrt{a-b+c})^2=3^2[/tex]
[tex]a-b+c=9[/tex]
[tex]c=9-a+b[/tex]
Therefore the option [tex]c=9-a+b[/tex] is correct.
2) Given equation is [tex]\sqrt{3x+10}=x+4[/tex]
Now to solve the equation for x:
[tex]\sqrt{3x+10}=x+4[/tex]
Squaring on both sides we get
[tex](\sqrt{3x+10})^2=(x+4)^2[/tex]
[tex]3x+10=x^2+8x+16[/tex]
[tex]x^2+8x+16-3x-10=0[/tex]
[tex]x^2+5x+6=0[/tex] which is a quadratic equation in x.
We can solve it by finding factors
[tex]x^2+5x+6=(x+2)(x+3)[/tex]
[tex](x+2)(x+3)=0[/tex]
x+2=0 or x+3=0
Therefore x=-2 or x=-3
Therefore the option x=-2 or x=-3 is correct.
3) Given equation is [tex]\sqrt{a-b+c}=3[/tex]
Now to solve the equation for c:
[tex]\sqrt{a-b+c}=3[/tex]
Squaring on both sides we get
[tex](\sqrt{a-b+c})^2=3^2[/tex]
[tex]a-b+c=9[/tex]
[tex]c=9-a+b[/tex]
Therefore the option [tex]c=9-a+b[/tex] is correct.
4) Given equation is [tex]\sqrt{x+3}=2\sqrt{x-2}[/tex]
Now to solve the equation for x:
[tex]\sqrt{x+3}=2\sqrt{x-2}[/tex]
Squaring on both sides we get
[tex](\sqrt{x+3})^2=(2\sqrt{x-2})^2[/tex]
[tex]x+3=2^2(x-2)[/tex]
[tex]x+3=4(x-2)[/tex]
[tex]x+3=4x-8[/tex]
[tex]4x-8-x-3=0[/tex]
[tex]3x-11=0[/tex]
[tex]x=\frac{11}{3}[/tex]
Therefore the option [tex]x=\frac{11}{3}[/tex] is correct.
5) Given equation is [tex]\sqrt{3x+10}=x+4[/tex]
Now to solve the equation for x:
[tex]\sqrt{3x+10}=x+4[/tex]
Squaring on both sides we get
[tex](\sqrt{3x+10})^2=(x+4)^2[/tex]
[tex]3x+10=x^2+8x+16[/tex]
[tex]x^2+8x+16-3x-10=0[/tex]
[tex]x^2+5x+6=0[/tex] which is a quadratic equation in x.
We can solve it by finding factors
[tex]x^2+5x+6=(x+2)(x+3)[/tex]
[tex](x+2)(x+3)=0[/tex]
x+2=0 or x+3=0
Therefore x=-2 or x=-3
Therefore the option x=-2 or x=-3 is correct.
