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3 years ago

Which number line represents the solutions to -2/x = -6?

Mathematics

2 answers:

Alex Ar [27]3 years ago

8 0

Step-by-step explanation:

$\\ \sf\longmapsto -2|x|=-6$

$\\ \sf\longmapsto |x|=\dfrac{-6}{-2}$

$\\ \sf\longmapsto |x|=3$

Hence

$\\ \sf\longmapsto x\in (-3,3)$

Option D is correct

anygoal [31]3 years ago

5 0

Answer:

${ \tt{ - 2 |x| = - 6}} \\ \\ { \tt{ |x| = 3}} \\ \\{ \tt{ \{ - 3 \leqslant x \leqslant 3 \}}}$

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Find the value of x. a.17 b.12 c.40 d.18 e.none are correct

Natali5045456 [20]

Answer:

b.12

Step-by-step explanation:

Key skills needed: Interior Angle Measure Theorem, Equation Creation

1) First, we need to classify this shape. It has 7 sides, which means that we can use the Interior angle Theorem to find out the sum of all the interior angle measures

The theorem is: $S = (n - 2)180$

S is the sum of all interior angle measures

n is the number of sides of the polygon

2) With this, we can plug in 7 for "n" (Since the figure has 7 sides) and get:

---> $S = (7-2)180$

---> (7-2) is 5 since 7 - 2 = 5 so --> $S = 5(180)$

---> 5(180) is the same as 5 x 180 which is 900 so --> $S = 900$

This means that the sum of all interior angles is 900 degrees.

3) Now, we have to find out the sum of all the angles that they gave us so:

---> $10x + 10x + 9 + 133 + 9x + 14 + 12x - 9 + 10x + 5 + 136 = 900$

The left side is the sum of all interior angles in the shape, and the right side is what the sum should be when expressed as a number.

4) We have to combine all like terms on the left side:

---> $10x + 10x + 9x + 12x + 10x = 51x$

---> $9 + 133 + 14 -9+5+136 = 288$

5) This means that ---> $51x + 288 = 900$

Subtract 288 from both sides and get:

---> $51x = 612$ (900-288 = 612)

Then divide by 51 from both sides and get:

---> $x = 12$ (612 ÷ 51 = 12)

Therefore b.12 is your answer.

Hope you understood and have a nice day!! :D

8 0

3 years ago

What is congruent of a triangle

Korvikt [17]

Answer:

When two triangles have the exact 3 sides and the same 3 angles

Step-by-step explanation:

In geometry, triangles are congruent when the have the exact same 3 sides and the exact same 3 angles. They can be flipped or reflected, they just have to have same sides and angles

4 0

4 years ago

P=−4b 2 +6b−9 Q=7b 2 −2b−5 P−Q= Your answer should be a polynomial in standard form.

shepuryov [24]

Answer:

−11b^2+8b−4

Step-by-step explanation:

−4b2+6b−9−7b2+2b+5

Simplify by adding terms.

11b2+8b−4

3 0

3 years ago

Factor the trinomial X2-12x +16

wlad13 [49]

2*&/45/+=67364/3/4/32:5,6544 is hothead answer

6 0

3 years ago

How to find the vertex calculus 2What is the vertex, focus and directrix of x^2 = 6y

son4ous [18]

Solution:

Given:

$x^2=6y$

Part A:

The vertex of an up-down facing parabola of the form;

$\begin{gathered} y=ax^2+bx+c \\ is \\ x_v=-\frac{b}{2a} \end{gathered}$

Rewriting the equation given;

$\begin{gathered} 6y=x^2 \\ y=\frac{1}{6}x^2 \\ \\ \text{Hence,} \\ a=\frac{1}{6} \\ b=0 \\ c=0 \\ \\ \text{Hence,} \\ x_v=-\frac{b}{2a} \\ x_v=-\frac{0}{2(\frac{1}{6})} \\ x_v=0 \\ \\ _{} \\ \text{Substituting the value of x into y,} \\ y=\frac{1}{6}x^2 \\ y_v=\frac{1}{6}(0^2) \\ y_v=0 \\ \\ \text{Hence, the vertex is;} \\ (x_v,y_v)=(h,k)=(0,0) \end{gathered}$

Therefore, the vertex is (0,0)

Part B:

A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (directrix)

Using the standard equation of a parabola;

$\begin{gathered} 4p(y-k)=(x-h)^2 \\ \\ \text{Where;} \\ (h,k)\text{ is the vertex} \\ |p|\text{ is the focal length} \end{gathered}$

Rewriting the equation in standard form,

$\begin{gathered} x^2=6y \\ 6y=x^2 \\ 4(\frac{3}{2})(y-k)=(x-h)^2 \\ \text{putting (h,k)=(0,0)} \\ 4(\frac{3}{2})(y-0)=(x-0)^2 \\ Comparing\text{to the standard form;} \\ p=\frac{3}{2} \end{gathered}$

Since the parabola is symmetric around the y-axis, the focus is a distance p from the center (0,0)

Hence,

$\begin{gathered} Focus\text{ is;} \\ (0,0+p) \\ =(0,0+\frac{3}{2}) \\ =(0,\frac{3}{2}) \end{gathered}$

Therefore, the focus is;

$(0,\frac{3}{2})$

Part C:

A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (directrix)

Using the standard equation of a parabola;

$\begin{gathered} 4p(y-k)=(x-h)^2 \\ \\ \text{Where;} \\ (h,k)\text{ is the vertex} \\ |p|\text{ is the focal length} \end{gathered}$

Rewriting the equation in standard form,

Since the parabola is symmetric around the y-axis, the directrix is a line parallel to the x-axis at a distance p from the center (0,0).

Hence,

$\begin{gathered} Directrix\text{ is;} \\ y=0-p \\ y=0-\frac{3}{2} \\ y=-\frac{3}{2} \end{gathered}$

Therefore, the directrix is;

$y=-\frac{3}{2}$

3 0

1 year ago