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3 years ago

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Mathematics

1 answer:

Bogdan [553]3 years ago

3 0

Answer:

Step-by-step explanation:

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mojhsa [17]

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2 years ago

Read 2 more answers

What value of b will cause the system to have an infinite number of solutions?

irga5000 [103]

b must be equal to -6 for infinitely many solutions for system of equations $y = 6x + b$ and $-3 x+\frac{1}{2} y=-3$

Solution:

Need to calculate value of b so that given system of equations have an infinite number of solutions

$\begin{array}{l}{y=6 x+b} \\\\ {-3 x+\frac{1}{2} y=-3}\end{array}$

Let us bring the equations in same form for sake of simplicity in comparison

$\begin{array}{l}{y=6 x+b} \\\\ {\Rightarrow-6 x+y-b=0 \Rightarrow (1)} \\\\ {\Rightarrow-3 x+\frac{1}{2} y=-3} \\\\ {\Rightarrow -6 x+y=-6} \\\\ {\Rightarrow -6 x+y+6=0 \Rightarrow(2)}\end{array}$

Now we have two equations

$\begin{array}{l}{-6 x+y-b=0\Rightarrow(1)} \\\\ {-6 x+y+6=0\Rightarrow(2)}\end{array}$

Let us first see what is requirement for system of equations have an infinite number of solutions

If $a_{1} x+b_{1} y+c_{1}=0$ and $a_{2} x+b_{2} y+c_{2}=0$ are two equation

$\Rightarrow \frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$ then the given system of equation has no infinitely many solutions.

In our case,

$\begin{array}{l}{a_{1}=-6, \mathrm{b}_{1}=1 \text { and } c_{1}=-\mathrm{b}} \\\\ {a_{2}=-6, \mathrm{b}_{2}=1 \text { and } c_{2}=6} \\\\ {\frac{a_{1}}{a_{2}}=\frac{-6}{-6}=1} \\\\ {\frac{b_{1}}{b_{2}}=\frac{1}{1}=1} \\\\ {\frac{c_{1}}{c_{2}}=\frac{-b}{6}}\end{array}$

As for infinitely many solutions $\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$

$\begin{array}{l}{\Rightarrow 1=1=\frac{-b}{6}} \\\\ {\Rightarrow6=-b} \\\\ {\Rightarrow b=-6}\end{array}$

Hence b must be equal to -6 for infinitely many solutions for system of equations $y = 6x + b$ and $-3 x+\frac{1}{2} y=-3$

8 0

2 years ago

Which of these is an exponential parent function?

KATRIN_1 [288]

Did you provide an picture ?!

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1 year ago

Which of the following points does not lie on the graph of y=5x-5? (0-5) (1.0) (-5.0)

mojhsa [17]

Y=5x-5
0=5x-5
-5x=-5

X=1

8 0

2 years ago

A booklet is made from 6 rectangular pieces of paper. Each piece measures 297mm by 420mm. The mass of paper is 80g per m^2. What

liq [111]

Alright, so the area of one paper is 297mm*420mm=124740mm^2. Multiplying that by 6 due to 6 sheets, we get 748440mm^2. Converting mm^2 to m^2, since we know that 1000mm=1m, we simply do (1m/1000m)^2=1m^2/1,000,000mm^2. Our equation is now
748440mm^2*1m^2/1,000,000mm^2=0.748440m^2 by crossing out the millimeters. Lastly, since it's 80g/1m^2, we multiply our number by that to get 59.8752g

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2 years ago