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Sveta_85 [38]
3 years ago
5

What is the cube of 0.5

Mathematics
1 answer:
Arte-miy333 [17]3 years ago
4 0
The answer is 0.125 because all you are doing is just multiplying 5x5x5 and then dividing it by 1000
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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

<u>Solution: </u>

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
3 years ago
You run 18 miles in 2 hours and 45 miles in 5 hours how fast are you running
Lesechka [4]
So let's find the unit rate of these.

18 mi/ 2 hrs = 9 mi/ 1hr

45 mi / 5 hrs = 9 mi/ 1 hr

So you are running 9 miles an hour.

If you have any questions please comment! :)
6 0
3 years ago
Read 2 more answers
I struggle in math, and occasionally I'll confuse the questions I try to answer
Alex17521 [72]
15X=12X+12
Subtract 12X
3X=12
X=4
3 0
3 years ago
Aneesha travels at 50 mph. Morris is traveling at 3 feet per second less than Aneesha. How fast is Morris traveling
vampirchik [111]

Speed of Morris is 47.95 mph

Step-by-step explanation:

  • Step 1: Convert 3 feet per second to miles per hour.

⇒ 3 ft/s = 3/1.467 mph (∵ 1 mph = 1.467 ft/s)

             = 2.05 mph

  • Step 2: Find the speed of Morris.

Speed of Morris = 50 mph - 2.05 mph = 47.95 mph

6 0
3 years ago
Please help ASAP! BRAINLIEST to best/right answer (:
JulsSmile [24]
Just finished doing the math and the correct answer should be B: 5.3  Hope this helps:)
7 0
3 years ago
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