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fenix001 [56]
2 years ago
10

Convert y-3=(1/3)(x+1) to slope intercept form

Mathematics
1 answer:
Mekhanik [1.2K]2 years ago
8 0
Slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept.

Here, we first need to distribute the 1/3.

y-3= \frac{1}{3} x+\frac{1}{3}

Next, we add 3 to both sides of the equation.

y= \frac{1}{3} x+\frac{10}{3}
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The nurse needs to mix 2% solution with 10% solution to get 10 ml of the prescribed 6% solution. What amount of each solution do
xenn [34]

<em>Volumes of 2% Solution = </em><em>5 ml</em>

<em>Volumes of 10% Solution = </em><em>5 ml</em>

\texttt{ }

<h3>Further explanation</h3>

Simultaneous Linear Equations could be solved by using several methods such as :

  • <em>Elimination Method</em>
  • <em>Substitution Method</em>
  • <em>Graph Method</em>

If we have two linear equations with 2 variables x and y , then we need to find the value of x and y that satisfying the two equations simultaneously.

Let us tackle the problem!

\texttt{ }

<em>Let:</em>

<em>Volumes of 2% Solution = x</em>

<em>Volumes of 10% Solution = y</em>

\texttt{ }

<em>Total Volume = 10 ml</em>

\boxed{x + y = 10} → <em>Equation 1</em>

\texttt{ }

<em>The nurse needs to mix 2% solution with 10% solution to get 10 ml of the prescribed 6% solution</em>.

2 \% x + 10 \% y = 6 \% (10)

2x + 10y = 6(10)

\boxed{x + 5y = 30} → <em>Equation 2</em>

\texttt{ }

<em>Equation 1 - Equation 2:</em>

( x + y ) - ( x + 5y ) = 10 - 30

-4y = -20

y = -20 \div -4

y = 5 \texttt{ ml}

\texttt{ }

x + y = 10

x + 5 = 10

x = 5 \texttt{ ml}

\texttt{ }

<h2>Conclusion:</h2>

<em>Volumes of 2% Solution = </em><em>5 ml</em>

<em>Volumes of 10% Solution = </em><em>5 ml</em>

\texttt{ }

<h3>Learn more</h3>
  • Perimeter of Rectangle : brainly.com/question/12826246
  • Elimination Method : brainly.com/question/11233927
  • Sum of The Ages : brainly.com/question/11240586

<h3>Answer details</h3>

Grade: High School

Subject: Mathematics

Chapter: Simultaneous Linear Equations

Keywords: Simultaneous , Elimination , Substitution , Method , Linear , Equations

6 0
2 years ago
Wich is the first operation performed in evaluating
stellarik [79]
The first operation performed while evaluating would be to do the parenthesis
3 0
3 years ago
A boat is pulled toward a dock by means of a rope wound on a drum that is located 6 ft above the bow of the boat. If the rope is
Monica [59]

Answer:

Step-by-step explanation:

Given that:

The height of the dock (h) = 6

Let represent d to be the distance between the boat and the dock

Let the length of the rope between the boat and the drum be denoted by (l)

Then, the rate of change for the length of the rope be:

dl/dt = -5 ft/s

Using Pythagoras rule to determine the relationship between these values, we have:

l^2 = h^2 +d^2

l^2 = 6^2 + d^2

l^2 = 36 + d^2

We relate to:  2l * \dfrac{dl}{dt} = 2d* \dfrac{dd}{dt}

From the question;

l = 34,

So to find \dfrac{dd}{dt}, we get;

d = \sqrt{l^2 - 36}

d = \sqrt{34^2 - 36}

d = \sqrt{1156- 36}

d = \sqrt{1120}

d = 33.46

So, we have:

\dfrac{dd}{dt}= \dfrac{l}{d} \times \dfrac{dl}{dt}

\dfrac{dd}{dt}= \dfrac{34}{33.46} \times - 5

\dfrac{dd}{dt}= 1.016 \times - 5

\dfrac{dd}{dt}=-5.08 \ ft/sec

4 0
2 years ago
Simply the square root of negative 50
ZanzabumX [31]

Answer:

5√2

I think, that sign mean square root.. just letting you know.

Hope I helped!

<em>*simplyeliza*</em>

8 0
2 years ago
Find a and b so that f(x) = x^3 + ax^2 + b will have a critical point at (2,3).
Digiron [165]

Using the critical point concept, it is found that a = -3 and b = 7.

<h3>What are the critical points of a function?</h3>
  • The critical points of a function are the values of x for which:

f^{\prime}(x) = 0

In this problem, the function is:

f(x) = x^3 + ax^2 + b

Hence, the derivative is:

f^{\prime}(x) = 3x^2 + 2ax

Then:

f^{\prime}(x) = 0

3x^2 + 2ax = 0

x(3x + 2a) = 0

x = 0

3x + 2a = 0

3x = -2a

x = -\frac{2a}{3}

Since the critical point is at x = 2, we have that:

-\frac{2a}{3} = 2

-2a = 6

2a = -6

a = -3

Then:

f(x) = x^3 - 3x^2 + b

Critical point at (2,3) means that when x = 2, y = 3, then:

3 = 2^3 - 3(2)^2 + b

8 - 12 + b = 3

b = 7

You can learn more about the critical point concept at brainly.com/question/2256078

4 0
1 year ago
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