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photoshop1234 [79]
4 years ago
10

Solve for m. y=7m+6solve for b. A=6b

Mathematics
2 answers:
ryzh [129]4 years ago
8 0

y=7m+6

subtract 6 from each side

y-6 = 7m

divide by 7

(y-6)/7 =m


A = 6b

divide by 6

A/6 = b

gladu [14]4 years ago
5 0

7m+6=y\qquad|\text{subtract 6 from both sides}\\\\7m+6-6=y-6\\\\7m=y-6\qquad|\text{divide both sides by 7}\\\\\dfrac{7m}{7}=\dfrac{y-6}{7}\\\\\boxed{m=\dfrac{y-6}{7}}\\--------------------------------------\\\\6b=A\qquad|\text{divide both sides by 6}\\\\\dfrac{6b}{6}=\dfrac{A}{6}\\\\\boxed{b=\dfrac{A}{6}}

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Example 2 Determine the sum of the first 100 terms for the series 2+5+ 8 + ...​
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3 years ago
Read 2 more answers
What is the solution to the equation
Dafna11 [192]
\sqrt{4t+5}=3-\sqrt{t+5}\\\\D:4t+5\geq0\ \wedge\ t+5\geq0\ \wedge\ \sqrt{t+5}\leq3\\\\t\geq-\dfrac{5}{4}\ \wedge\ t\geq-5\ \wedge\ t\leq6

therefore
D:x\in\left< -\dfrac{5}{4};\ 6\right>

\sqrt{4t+5}=3-\sqrt{t+5}\ \ \ |^2\\\\(\sqrt{4t+5})^2=(3-\sqrt{t+5})^2\ \ \ |use:(a-b)^2=a^2-2ab+b^2\\\\4t+5=3^2-2\cdot3\cdot\sqrt{t+5}+(\sqrt{t+5})^2\\\\4t+5=9-6\sqrt{t+5}+t+5\ \ \ \ |-t\\\\3t+5=14-6\sqrt{t+5}\ \ \ \ |-14\\\\3t-9=-6\sqrt{t+5}\ \ \ \ |change\ signs
9-3t=6\sqrt{t+5}\ \ \ \ |:3\\\\3-t=2\sqrt{t+5}\ \ \ \ |^2\\\\(3-t)^2=(2\sqrt{t+5})^2\\\\3^2-2\cdot3\cdot t+t^2=4(t+5)\\\\9-6t+t^2=4t+20\ \ \ |-4t-20\\\\t^2-10t-11=0\\\\t^2+t-11t-11=0\\\\t(t+1)-11(t+1)=0\\\\(t+1)(t-11)=0\iff t+1=0\ \vee\ t-11=0\\\\t=-1\in D\ \vee\ t=11\notin D
Answer: t = -1.


7 0
3 years ago
Read 2 more answers
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