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anygoal [31]
4 years ago
5

Which is the approximate solution to the system y = 0.5x + 3.5 and y = − 2/3 x + 1/3 shown on the graph? (–2.7, 2.1) (–2.1, 2.7)

(2.1, 2.7) (2.7, 2.1)
Mathematics
2 answers:
Volgvan4 years ago
6 0

Answer:

(–2.7, 2.1)

Step-by-step explanation:

edg. 2020 unit test

AlekseyPX4 years ago
5 0

Answer:

The approximate solution to the system is (-2.7, 2.1).

Step-by-step explanation:

To solve the system of equations \begin{bmatrix}y=0.5x+3.5\\ y=-\frac{2}{3}x+\frac{1}{3}\end{bmatrix} you must:

\mathrm{Rationalize\:equations}\\\\\begin{bmatrix}y=\left(\frac{1}{2}\right)x+\left(\frac{7}{2}\right)\\ y=-\frac{2}{3}x+\frac{1}{3}\end{bmatrix}

\mathrm{Subsititute\:}y=-\frac{2}{3}x+\frac{1}{3}\\\\\begin{bmatrix}-\frac{2}{3}x+\frac{1}{3}=\frac{1}{2}x+\frac{7}{2}\end{bmatrix}

\mathrm{Isolate}\:x\:\mathrm{for}\:-\frac{2}{3}x+\frac{1}{3}=\frac{1}{2}x+\frac{7}{2}\\\\-\frac{2}{3}x=\frac{19}{6}+\frac{1}{2}x\\\\-\frac{7}{6}x=\frac{19}{6}\\\\6\left(-\frac{7}{6}x\right)=\frac{19\cdot \:6}{6}\\\\-7x=19\\\\x=-\frac{19}{7}\approx-2.7

\mathrm{For\:}y=-\frac{2}{3}x+\frac{1}{3}\\\\\mathrm{Subsititute\:}x=-\frac{19}{7}\\\\y=-\frac{2}{3}\left(-\frac{19}{7}\right)+\frac{1}{3}\\\\y=\frac{15}{7}\approx 2.1

The approximate solutions to the system of equations are:

x=-2.7 ,\:y=2.1

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Solve and express the solution set in simplest form.
oee [108]

Answer:

\frac{11}{6}

Step-by-step explanation:

The equation to be solve is

4x−1/3=7/1

We can go about this by first adding 1/3 to both sides.

4x -  \frac{1}{3}  + \frac{1}{3} = \frac{7}{1} +  \frac{1}{3}

\implies \ 4x = \frac{7}{1} +  \frac{1}{3}

We then simplify the the right hand side of the equation

\implies 4x =  \frac{21 + 1}{3}

\implies 4x =  \frac{22}{3}

To find x, we multiply through by 1/4

\implies  \frac{1}{4}  \times 4x = \frac{22}{3} \times  \frac{1}{4}

\implies x = \frac{22}{12}

\implies x = \frac{11}{6}

Hence the solution set in the simplest form for the expression is

{x=11/2}

6 0
3 years ago
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mars1129 [50]

Answer:

5

Step-by-step explanation:

t-u/v

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3 0
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The depth (inches) of water that accumulates in the spring soil from melted snow can be determined by dividing the cumulative wi
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Answer:

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Step-by-step explanation:

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6 0
3 years ago
I need help please, i dont understand
jenyasd209 [6]

9514 1404 393

Answer:

  (a)  none of the above

Step-by-step explanation:

The largest exponent in the function shown is 2. That makes it a 2nd-degree function, also called a quadratic function. The graph of such a function is a parabola -- a U-shaped curve.

The coefficient of the highest-degree term is the "leading coefficient." In this case, that is the coefficient of the x² term, which is 1. When the leading coefficient of an even-degree function is positive, the U curve has its open end at the top of the graph. We say it "opens upward." (When the leading coefficient is negative, the curve opens downward.)

This means the bottom of the U is the minimum value the function has. For a quadratic in the form ax²+bx+c, the horizontal location of the minimum on the graph is at x=-b/(2a). This extreme point on the curve is called the "vertex."

This function has a=1, b=1, and c=3. The minimum of the function is where ...

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This value is not listed among the answer choices, so the correct choice for this function is ...

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The attached graph of the function confirms that the minimum is located at x=-1/2

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<em>Additional comment</em>

When you're studying quadratic functions, there are few formulas that you might want to keep handy. The formula for the location of the vertex is one of them.

8 0
3 years ago
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