Which one of the following is not a way to represent the solution of the inequality 2(x-1)>-12

"Three times a number increased by eleven is seventeen" translates to which of the following equations?

ololo11 [35]

3x + 11 = 17 i think

7 0

2 years ago

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Which is better Financial manager or accountant?

Umnica [9.8K]

Answer:

Financial manager sounds more professional.

Step-by-step explanation:

7 0

2 years ago

In triangle abc, the perimeter is 36, and ab=ac. line ad is perpendicular to bc at the point d, and triangle abd's perimeter is

Musya8 [376]

Let x=ab=ac, and y=bc, and z=ad.

Since the perimeter of the triangle abc is 36, you have:

Perimeter of abc = 36
ab + ac + bc = 36
x + x + y = 36
(eq. 1) 2x + y = 36

The triangle is isosceles (it has two sides with equal length: ab and ac). The line perpendicular to the third side (bc) from the opposite vertex (a), divides that third side into two equal halves: the point d is the middle point of bc. This is a property of isosceles triangles, which is easily shown by similarity.

Hence, we have that bd = dc = bc/2 = y/2 (remember we called bc = y).

The perimeter of the triangle abd is 30:

Permiter of abd = 30
ab + bd + ad = 30
x + y/2 + z =30
(eq. 2) 2x + y + 2z = 60

So, we have two equations on x, y and z:

(eq.1) 2x + y = 36
(eq.2) 2x + y + 2z = 60

Substitute 2x + y by 36 from (eq.1) in (eq.2):

(eq.2') 36 + 2z = 60

And solve for z:

36 + 2z = 60 => 2z = 60 - 36 => 2z = 24 => z = 12

The measure of ad is 12.

If you prefer a less algebraic reasoning:

- The perimeter of abd is half the perimeter of abc plus the length of ad (since you have "cut" the triangle abc in two halves to obtain the triangle abd).

- Then, ad is the difference between the perimeter of abd and half the perimeter of abc:

ad = 30 - (36/2) = 30 - 18 = 12

4 0

3 years ago

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How to solve <br><img src="https://tex.z-dn.net/?f=%20%5Csqrt%7B4%7D%20x%20%7B%7D%5E%7B2%7D%20%20%3D%20x%20%2B%202" id="TexFormu

Vikentia [17]

Answer:

➩ $x=2,-\frac{2}{3}$

Step-by-step explanation:

$\sqrt{4x^2}=x+2$

➨ We can also solve by completing both squares, however. Since we can pull out the square root.

$\sqrt{4x^2}=|2x|$ ➩ Define of Absolute Value/Square Root

➩ $\sqrt{x^2}=|x|$

Thus, our new equation is ➩ $|2x|=x+2$

To solve an absolute-value equation, let there be two conditions.

➨ Where x ≥ 0

$2x=x+2\\$

Move x to another side

$2x-x=2\\x=2$

➨ Where x < 0

$-2x=x+2\\-2x-x=2\\-3x=2\\x=\frac{2}{-3}\\x=-\frac{2}{3}$

3 0

2 years ago

Angles

coldgirl [10]

<h3>Answer: XWY and STR</h3>

I tend to think of parallel lines as train tracks (the metal rail part anyway). Inside the train tracks is the interior region, while outside the train tracks is the exterior region. Alternate exterior angles are found here. Specifically they are angles that are on opposite or alternate sides of the transversal cut.

Both pairs of alternate exterior angles are shown in the diagram below. They are color coded to help show how they pair up and which are congruent.

A thing to notice: choices B, C, and D all have point W as the vertex of the angles. This means that the angles somehow touch or are adjacent in some way due to this shared vertex point. However, alternate exterior angles never touch because parallel lines never do so either. We can rule out choices B,C,D from this reasoning alone. We cannot have both alternate exterior angles on the same exterior side of the train tracks. Both sides must be accounted for.

4 0

3 years ago