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2 years ago

If 1/x + 1/3x equals 4 then what is x

Mathematics

1 answer:

Vikki [24]2 years ago

3 0

Answer:

$\huge\boxed{x=\dfrac{1}{3}}$

Step-by-step explanation:

$\dfrac{1}{x}+\dfrac{1}{3x}=4\\\\\text{Domain:}\ x\neq0\\\\\text{find LCD}=3x\\\\\dfrac{1\cdot3}{x\cdot3}+\dfrac{1}{3x}=4\\\\\dfrac{3}{3x}+\dfrac{1}{3x}=4\\\\\dfrac{3+1}{3x}=4\\\\\dfrac{4}{3x}=\dfrac{4}{1}\qquad\text{cross multiply}\\\\(3x)(4)=(4)(1)\\\\12x=4\qquad\text{divide both sides by 12}\\\\\dfrac{12x}{12}=\dfrac{4}{12}\\\\x=\dfrac{4:4}{12:4}\\\\x=\dfrac{1}{3}\in D$

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What is the horizontal distance between the two points (-7,-4) and (12,-4)? Remember that distance is always positive! Hint: The

RSB [31]

<h3>Answer: 19</h3>

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Explanation:

Draw out a number line. Plot -7 and 12 on the number line. Draw in the tickmarks between them. You should find the distance from -7 to 12 is 19 units since you need to go 19 spaces from either -7 to 12, or vice versa.

You can use subtraction to get

-7-12 = -19

12-(-7) = 12+7 = 19

The final result is made positive since negative distance does not make sense.

So you'd have |-7-12| = |-19| = 19 or |12-(-7)| = |19| = 19.

All of this only works because the two y coordinates are the same, which makes a horizontal line through the two given points.

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2 years ago

Consider the following quadratic function Part 3 of 6: Find the x-intercepts. Express it in ordered pairs.Part 4 of 6: Find the

maksim [4K]

Answer:

The line of symmetry is x = -3

Explanation:

Given a quadratic function, we know that the graph is a parabola. The general form of a parabola is:

$y=ax^2+bx+c$

The line of symmetry coincides with the x-axis of the vertex. To find the x-coordinate of the vertex, we can use the formula:

$x_v=-\frac{b}{2a}$

In this problem, we have:

$y=-x^2-6x-13$

Then:

a = -1

b = -6

We write now:

$x_v=-\frac{-6}{2(-1)}=-\frac{-6}{-2}=-\frac{6}{2}=-3$

Part 3:

For this part, we need to find the x-intercepts. This is, when y = 0:

$-x^2-6x-13=0$

To solve this, we can use the quadratic formula:

$x_{1,2}=\frac{-(-6)\pm\sqrt{(-6)^2-4\cdot(-1)\cdot(-13)}}{2(-1)}$

And solve:

$x_{1,2}=\frac{6\pm\sqrt{36-52}}{-2}$ $x_{1,2}=\frac{-6\pm\sqrt{-16}}{2}$

Since there is no solution to the square root of a negative number, the function does not have any x-intercept. The correct option is ZERO x-intercepts.

Part 4:

To find the y intercept, we need to find the value of y when x = 0:

$y=-0^2-6\cdot0-13=-13$

The y-intercept is at (0, -13)

Part 5:

Now we need to find two points in the parabola. Let-s evaluate the function when x = 1 and x = -1:

$x=1\Rightarrow y=-1^2-6\cdot1-13=-1-6-13=-20$ $x=-1\Rightarrow y=-(-1)^2-6\cdot(-1)-13=-1+6-13=-8$

The two points are:

(1, -20)

(-1, -8)

Part 6:

Now, we can use 3 points to find the graph of the parabola.

We can locate (1, -20) and (-1, -8)

The third could be the vertex. We need to find the y-coordinate of the vertex. We know that the x-coordinate of the vertex is x = -3

Then, y-coordinate of the vertex is:

$y=-(-3)^2-6(-3)-13=-9+18-13=-4$

The third point we can use is (-3, -4)

Now we can locate them in the cartesian plane:

And that's enough to get the full graph:

8 0

4 months ago

Determine the coordinates of the point on the unit circle corresponding to the given central angle. If necessary round your resu

Olenka [21]

Answer:

Option A. (-1, 0)

Step-by-step explanation:

In the figure attached,

Circle O is a unit circle (having radius r = 1 unit)

If a point A with central angles = θ, is lying on the circle then the coordinates of the point A will be,

x = r.cosθ

x = 1.cosθ = cosθ

and y = r.sinθ

y = 1.sinθ = sinθ

Therefore, coordinates representing the point A will be (cosθ, sinθ).

As per question the given point A is lying at P (a point having central angle θ = 180°)

Coordinates of point P will be

(x', y') → (cos180°, sin180°)

→ (-1, 0)

Therefore, Option A will be the answer.

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2 years ago

Evaluate the expression for s = -2.<br> -15s2 - 9-5 + s) =

Fudgin [204]

Answer:

123

Step-by-step explanation:

s=-2

-15s^2-9(-5+s)

=-15s^2+45-9s

=-15s^2-9s+45

=15(-2)^2-9×(-2)+45

=15×4+18+45

=60+18+45

=123

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2 years ago

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lesya [120]

Answer:

A. 30 : 54

Step-by-step explanation:

If you divide 30 by 6 and 54 by 6, you'll get a ratio of 5 : 9, which is the same ratio shown in the problem

Hope this helps :)

5 0

2 years ago