Math help 20 points

Mathematics

1 answer:

kherson [118]3 years ago

3 0

$4)\\\\LM=KN\\\\\text{Therefore we have the equation}\\\\2x-6=x+3\qquad\text{add 6 to both sides}\\\\2x=x+9\qquad\text{subtract x from both sides}\\\\\boxed{x=9}\\\\LM=2x-6\Rightarrow LM=2(9)-6=18-6=12\\\\Answer:\ \boxed{LM=12}$

$5)\\\\m\angle F+m\angle U=180^o\\\\\text{Therefore we have the equation:}\\\\12x-6+11x+2=180\\\\23x-4=180\qquad\text{add 4 to both sides}\\\\23x=184\qquad\text{divide both sides by 23}\\\\\boxed{x=8}\\\\\angle V\cong\angle F\Rightarrow m\angle V=m\angle F\\\\m\angle V=12x-6\Rightarrow m\angle V=12(8)-6=96-6=90\\\\Answer:\ \boxed{m\angle V=90^o}$

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What times what =13?

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faust18 [17]

$6.\\\text{We know}\ 9=3^2.\ \text{Therefore}\\\\9^2=(3^2)^2\\\\\text{use}\ (a^n)^m=a^{nm}\\\\9^2=(3^2)^2=3^{2\cdot2}=3^4\\\\\boxed{3^4=9^2}\\=================$

$7.\\METHOD\ 1:\\\\\sqrt{7^4}=\sqrt{7^{2\cdot2}}\\\\\text{use}\ (a^n)^m=a^{nm}\\\\=\sqrt{(7^2)^2}\\\\\text{use}\ \sqrt{a^2}=a\ \text{for}\ a\geq0\\\\=\boxed{7^2}\\\\METHOD\ 2:\\\\\text{use}\ a^\frac{m}{n}=\sqrt[n]{a^m}\\\\\sqrt{7^4}=7^\frac{4}{2}=\boxed{7^2}\\=================$

$8.\\5^a\times5^b=5^{11}\\\\a)\\\text{use}\ a^n\times a^m=a^{n+m}\\\\5^a\times5^b=5^{a+b}\\\\5^{a+b}=5^{11}\Rightarrow a+b=11\\\\11\ \text{is odd. The sum of even and odd is odd. Therefore}\ a\ \text{and}\ b\ \text{can't be even.}\\--------------------\\\\b)\\5\ \text{solutions}\\\\11=5+6\\11=4+7\\11=3+8\\11=2+9\\11=1+10$