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oee [108]
3 years ago
9

Part 2: Solve the system using the substitution method. Show all work here and indicate the solution for the system as an ordere

d pair.
Part 3: Solve the system using the addition method. Show all work here and indicate the solution for the system as an ordered pair.

x - 2y = 0 
5x + 2y = 24
Mathematics
1 answer:
Rom4ik [11]3 years ago
5 0
Substitution:

Step 1: Choose one of the two equations and solve for either x or y.

     x - 2y = 0
       + 2y  +2y
--------------------------
     x = 2y + 0 

Step 2: Plug in the value you got for x or y into the equation you did not work with in Step 1.

5(2y + 0) + 2y = 24
10y + 0 + 2y = 24
 
12y = 24
------- ------
  12    12

y = 2 

Step 3: Plug in the number you got for y into either equation.

     5x + 2(2) = 24
     5x + 4 = 24
          - 4    - 4
---------------------------
     5x = 20
   ------ ------
      5      5

x = 4

Your final answer should be written as a coordinate pair: (4,2).
____________________________________________________________

Elimination:

Add the two equations together to eliminate y.

     x - 2y = 0
+ 5x + 2y = 24
----------------------
   6x = 24
 ------ ------
    6      6

x = 4

Step 2: Substitute the x value into the original equation to find y.

5(4) + 2y = 24       20 + 2y = 24
                           - 20          - 20
                       --------------------------
                             2y = 4 
                           ------ -----
                              2     2
  
                             y = 2

I hope this answer helps you :D
                         

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Step-by-step explanation:

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Simplifying the equations:

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The boat's rate is 4 mph, and the current's rate is 2 mph.

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Given the function f(x) = 3x + 1, what is the value of f(-2/3)? <br><br>show work <br>​
Marta_Voda [28]

Answer:

f(-2/3) = -1

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

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  4. Multiplication
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Step-by-step explanation:

<u>Step 1: Define</u>

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  1. Substitute:                    f(-2/3) = 3(-2/3) + 1
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If m∠A = 56°, m∠B = 60°, and c = 8, what is the measure of side length b?
Alekssandra [29.7K]

Using the law of sines:

\frac{b}{sin(B)}=\frac{c}{sin(C)}

Solve for b:

\begin{gathered} b=\frac{c\cdot sin(B)}{sin(C)} \\ so: \\ b=\frac{8\cdot sin(60)}{sin(64)} \\ b\approx7.708 \end{gathered}

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7.708

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HELP ME PLZ!!!!! Plz!!!
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Answer:

hi the right answer is option C.112

here's why:

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2 years ago
Dada la ecuacion 25x2 + 4y2 = 100, determina las coordenadas de los vertices, focos, las longitudes de los respectivos ejes mayo
Likurg_2 [28]

Answer:

The given equation is

25x^{2} +4y^{2}=100

Which represents an elipse.

To find its elements, we need to divide the equation by 100

\frac{25x^{2} +4y^{2} }{100} =\frac{100}{100} \\\frac{x^{2} }{4} +\frac{y^{2} }{25} =1

Where a^{2} =25 and b^{2}=4. Remember that the greatest denominator is a, and the least is b. So, we extract the square root on each equation.

a=5 and b=2.

In a elipse, we have a major axis and a minor axis. In this case, the major axis is vertical and the minor axis is horizontal, that means this is a vertical elipse.

The length of the major axis is 2a=2(5)=10.

The length of the minor axis is 2b=2(2)=4.

The vertices are (0,5);(0,-5) and (2,0);(-2,0).

Now, the main parameters of an elipse are related by

a^{2}=b^{2} +c^{2}, which we are gonna use to find c, the parameter of the focus.

c=\sqrt{a^{2}-b^{2} }=\sqrt{25-4}=\sqrt{21}

So, the coordinates of each focus are (0,\sqrt{21}) and (0,-\sqrt{21})

The eccentricity of a elipse is defined

e=\frac{c}{a}=\frac{\sqrt{21} }{5}  \approx 0.92

The latus rectum is defined

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Finally, the graph of the elipse is attached.

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3 years ago
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