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vfiekz [6]
3 years ago
14

Help asappppp hbshhshshhshshsshshshs

Mathematics
1 answer:
SVEN [57.7K]3 years ago
8 0

9 on the top as well so 9 x 2 18 3x2 6 3

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Graph a system of equations to approximate the
SIZIF [17.4K]

Answer: B

Step-by-step explanation:

8 0
2 years ago
Find x so that the points (x,x+1), (x+2,x+3) and (x+3,2x+4) form a right-angled triangle.
azamat

Let <em>a</em>, <em>b</em>, and <em>c</em> be vectors each starting at the origin and terminating at the points (<em>x</em>, <em>x</em> + 1), (<em>x</em> + 2, <em>x</em> + 3), and (<em>x</em> + 3, 2<em>x</em> + 4), respectively.

Then the vectors <em>a</em> - <em>b</em>, <em>a</em> - <em>c</em>, and <em>b</em> - <em>c</em> are vectors that point in directions parallel to each of the legs formed by the triangle with these points as its vertices.

If this triangle is to contain a right angle, then exactly one of these pairs of vectors must be orthogonal. In other words, one of the following must be true:

(<em>a</em> - <em>b</em>) • (<em>a</em> - <em>c</em>) = 0

<em>or</em>

(<em>a</em> - <em>b</em>) • (<em>b</em> - <em>c</em>) = 0

<em>or</em>

(<em>a</em> - <em>c</em>) • (<em>b</em> - <em>c</em>) = 0

We have

<em>a</em> - <em>b</em> = (<em>x</em>, <em>x</em> + 1) - (<em>x</em> + 2, <em>x</em> + 3) = (-2, -2)

<em>a</em> - <em>c</em> = (<em>x</em>, <em>x</em> + 1) - (<em>x</em> + 3, 2<em>x</em> + 4) = (-3, -<em>x</em> - 3)

<em>b</em> - <em>c</em> = (<em>x</em> + 2, <em>x</em> + 3) - (<em>x</em> + 3, 2<em>x</em> + 4) = (-1, -<em>x</em> - 1)

Case 1: If (<em>a</em> - <em>b</em>) • (<em>a</em> - <em>c</em>) = 0, then

(-2, -2) • (-3, -<em>x</em> - 3) = (-2)×(-3) + (-2)×(-<em>x</em> - 3) = 2<em>x</em> + 12 = 0   ==>   <em>x</em> = -6

which would make <em>a</em> - <em>c</em> = (-3, 3) and <em>b</em> - <em>c</em> = (-1, 5), and their dot product is not zero. Then the triangles vertices are at the points (-6, -5), (-4, -3), and (-3, -8).

Case 2: If (<em>a</em> - <em>b</em>) • (<em>b</em> - <em>c</em>) = 0, then

(-2, -2) • (-1, -<em>x</em> - 1) = (-2)×(-1) + (-2)×(-<em>x</em> - 1) = 2<em>x</em> + 4 = 0   ==>   <em>x</em> = -2

which would make <em>a</em> - <em>c</em> = (-3, -1) and <em>b</em> = (-1, 1), and their dot product is also not zero. The vertices are the points (-2, -1), (0, 1), and (1, 0).

Case 3: If (<em>a</em> - <em>c</em>) • (<em>b</em> - <em>c</em>) = 0, then

(-3, -<em>x</em> - 3) • (-1, -<em>x</em> - 1) = (-3)×(-1) + (-<em>x</em> - 3)×(-<em>x</em> - 1) = <em>x</em> ² + 4<em>x</em> + 6 = 0

but the solutions to <em>x</em> here are non-real, so we throw out this case.

So there are two possible values of <em>x</em> that make a right triangle, <em>x</em> = -6 and <em>x</em> = -2.

3 0
3 years ago
For the questions, imagine a segment in a plane. Use that information to help you answer the questions.
Mars2501 [29]
1 a
2 c
3 a

Hope this help :)
7 0
3 years ago
4. A mail carrier earns time and a half for any overtime hours. If her
nata0808 [166]

Answer:

$14.70

Step-by-step explanation:

If she get paid the time and a half you would first divide $9.80 by 2 which is $4.90. Now that you have the half price you add the original time to it. $9.80+$4.90= 14.70 so that’s the answer

4 0
11 months ago
X² - 6x + y² + 2y = -1<br> find center &amp; Radius
Fofino [41]

Answer:

The answer to your question is Center = (3 , -1), radius = 3

Step-by-step explanation:

Equation

                       x² - 6x + y² + 2y = -1

-Process

1.- Leave a space between the like terms

                     x² - 6x           + y² + 2y          = -1

2.- Divide the middle term of each group by 2 and write the result to the power of 2 in both sides of the equation.

                     x² - 6x + (3)² + y² + 2y + (1)² = -1 + 3² + 1²

3.- Simplification

                     x² - 6x + 9 + y² + 2y + 1 = -1 + 9 + 1

4.- Factor

                     (x - 3)² + (y + 1)² = 9

5.- Find the center and the radius

     Center = (3 , -1)

     Radius = √9 = 3

                   

                     

8 0
3 years ago
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