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SVEN [57.7K]
3 years ago
10

A science teacher has 15 ounces of vinegar to divide

Mathematics
1 answer:
Gelneren [198K]3 years ago
6 0

Answer:

Its wrong, you should divide the amount of the objects you have by the amount of students

Step-by-step explanation:

Think of division as how many times you can subtract from a number so for 15/8, you can subtract 1.875 ounces equally 8 times to get 15

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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
Now that the party is over, it’s time to help your friend write the thank you notes. You have $24 to purchase and mail 32 thank
Tasya [4]
0.75 Jordan went to the pond and died soon
6 0
3 years ago
What is the simplified form of StartRoot StartFraction 72 x Superscript 16 Baseline Over 50 x Superscript 36 Baseline EndFractio
aalyn [17]

Answer:

  StartFraction 6 Over 5 x Superscript 10 Baseline EndFraction

Step-by-step explanation:

Apparently you want to simplify ...

  \sqrt{\dfrac{72x^{16}}{50x^{36}}}

The applicable rules of exponents are ...

  (a^b)(a^c) = a^(b+c)

  1/a^b = a^-b

  (a^b)^c = a^(bc)

__

So the expression simplifies as ...

  \sqrt{\dfrac{72x^{16}}{50x^{36}}}=\sqrt{\dfrac{36}{25x^{36-16}}}=\sqrt{\dfrac{36}{25x^{20}}}\\\\\sqrt{\left(\dfrac{6}{5x^{10}}\right)^2}=\boxed{\dfrac{6}{5x^{10}}}

9 0
2 years ago
Use substitution to determine which of the following points is a solution to the standard form equation below. 2y = 5
sashaice [31]
The question is incomplete.

This is the complete question as I found in internet:

<span>Use substitution to determine which of the following points is a solution to the standard form equation below 5x-2y = 10

these are the points:
</span>
-1,5

1,5

0,-5

0,5

Answer: (0, -5)

Explanation:


point          x           y        5x - 2y = 10 ?


-1,5         -1           5         5(-1) - 2(5) = - 5 - 10 = - 15 ≠ 10 ⇒ not a solution

1,5            1          5         5(1) - 2(5) = 5 - 10 = 5 ≠ 10 ⇒ not a solution
 
0,-5           0        -5           0 -2(-5) = 10 ⇒ a solution

0,5             0         5          0 - 2(5) = - 10 ≠ 10 ⇒ not a solution

7 0
3 years ago
What is the result of 6 divided by 3/8?<br> Please help I’ll give brainliest
worty [1.4K]

Answer:

16

Step-by-step explanation:

5 0
3 years ago
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