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grigory [225]
3 years ago
9

What is an equation for the linear function whose graph contains the points (-1,-2) and (3,10) enter your answers in the boxes

Mathematics
1 answer:
mr Goodwill [35]3 years ago
6 0

The equation for the linear function whose graph contains the points (-1, -2) and (3, 10) is y = 3x + 1

<h3><u>Solution:</u></h3>

Given that linear function whose graph contains the points (-1, -2) and (3, 10)

We have to find the equation of line

Any function of the form f (x) = m x + b, where m is not equal to 0 is called a linear function

So let us use the slope intercept form

<em><u>The slope intercept form is given as:</u></em>

y = mx + c

Where "m" is the slope of line and "c" is the y - intercept

Let us first find slope of line containing points (-1, -2) and (3, 10)

<em><u>The slope of line is given as:</u></em>

m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}

\text {Here } x_{1}=-1 \text { and } y_{1}=-2 \text { and } x_{2}=3 \text { and } y_{2}=10

m=\frac{10-(-2)}{3-(-1)}=\frac{12}{4}=3

Thus the slope of line is "m" = 3

Substitute m = 3 and (x, y) = (-1, -2) in y = mx + c

-2 = 3(-1) + c

-2 = -3 + c

c = -2 + 3 = 1

Now substitute c = 1 and m = 3 in slope intercept form to get equation of line

y = 3x + 1

Thus the equation for the linear function is found out

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tigry1 [53]

Answer:

Her son is 10 years old.

Step-by-step explanation:

Let son be x

Ellie is 4x

In 5 years time: Her son = x + 5

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Solve x: 4x + 5 = 3(x + 5) ,4x + 5 = 3x + 15

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Step-by-step explanation:

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2 years ago
Graph the data in the table below. Which kind of function best models the data? write an equation to model the data.
harina [27]

Answer:

A quadratic function.

y=2.5x^{2}

Step-by-step explanation:

If you plot the points given in the table, you obtain the graph shown in the figure attached.

As you can see, it is a parabola, therefore, the function that best models the data is a quadratic function.

By definition, the parent function of a quadratic function is:

y=x^{2}

You can compress or stretch it in the y-direction by multiplying the function by a constant C:

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If 0, then the function is compressed.

If C>1, then the function is stretched.

You can find the constant of the function asked as following:

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y=(1)^{2}=1

Then the point is (1,1)

- As you can see, with x=1 you obtain y=1 in the parent function, and in the function given in the table when x=1, y=2.5, therefore, the function is multiplied by 2.5. Therefore the constant is:

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3 years ago
What is the total resistance of a parallel circuit that has two loads? Load one has a resistance of 10 ohms. Load two has a resi
Romashka-Z-Leto [24]

Answer:

The total resistance is 7.0588\Omega

Step-by-step explanation:

Attached please find the circuit diagram. The circuit is composed by a voltage source and two resistors connected in parallel: R_1=10\Omega and R_2=24\Omega.

First step: find the total current

For finding the current that the voltage source can provide, you must find the current consumed by each load and then add both. To do that, take first into account that the voltage is the same for both resistors (R_1 and R_2).

  • I_{R_1}=\frac{V_S}{R_1}
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The total current is:

I_{TOTAL}=I_{R_1}+I_{R_2}=\frac{V_S}{R_1}+\frac{V_S}{R_2}=\frac{R_2\cdot V_S+R_1\cdot V_S}{R_1\cdot R_2}

I_{TOTAL}=V_S\cdot \frac{R_1+R_2}{R_1\cdot R_2}

Now, the total resistance (R_{TOTAL}) would be the voltage divided by the total current:

R_{TOTAL}=\frac{V_S}{I_{TOTAL}}

If you replace I_{TOTAL} by the expression obtained previously, the total resistance would be:

R_{TOTAL}=\frac{V_S}{V_S\cdot \frac{R_1+R_2}{R_1\cdot R_2}}

After simplifying the terms you should get:

R_{TOTAL}=\frac{R_1\cdot R_2}{R_1 + R_2}}

Now, you must replace the values of the resistors:

R_{TOTAL}=\frac{(10\Omega )\cdot (24\Omega)}{10\Omega + 24\Omega}}=\frac{120}{17}\Omega=7.0588\Omega

Thus, the total resistance is 7.0588\Omega

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