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3 years ago

In the diagram, GB = 2x + 3.. What is GB?

Mathematics

1 answer:

tia_tia [17]3 years ago

6 0

Answer:

GB = 15

Step-by-step explanation:

DC, EB and FA are the medians of the triangle.

The point G where the medians intersect is the centroid.

On each median the distance from the vertex to the centroid is twice as long as the distance from the centroid to the midpoint, hence

FG = 2GA, that is

5x = 2(x + 9)

5x = 2x + 18 ( subtract 2x from both sides )

3x = 18 ( divide both sides by 3 )

x = 6

Hence

GB = 2x + 3 = (2 × 6) + 3 = 12 + 3 = 15

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( HELP PLEASE )

uysha [10]

Answer:

9 6/8, 9 3/4. 9.75

Step-by-step explanation:

1 1/4 would equal 10/8 if she has 10 7/8 then you'd take 7/8 out of 10/8 which would leave you with 2/8 left which you'd take out of the whole number 10 which would leave you with 9 6/8

simplified answer is 9 3/4

or: 9.75

5 0

4 years ago

5. Find the discriminant of 15x2 = 4x – 1 and describe

diamong [38]

Answer:

a) The discriminant of the equation = - 44

b)The nature of the roots will be imaginary.

c) $x = \frac{2 +\sqrt{11} i}{15} or, x = \frac{2 - \sqrt{11} i}{15}$

Step-by-step explanation:

Here, the given expression is $15x^{2} = 4x -1$

or, $15x^{2} - 4x + 1 = 0$

Now the discriminant (D) of a quadratic equation $ax^{2} +b x + c = 0$

D = $b^{2} - 4ac = (-4)^{2} - 4(15) (1) = 16 - (60) = -44$

Hence, the discriminant of the equation = - 44

As D< 0, so the roots will be imaginary.

Now,by quadratic formula : $x = \frac{-b \pm \sqrt{b^{2} - 4ac} }{2a}$

So, here $x = \frac{-(-4) \pm \sqrt{D} }{2a} = \frac{4 \pm \sqrt{(-44 )} }{30}$

So, either $x = \frac{4 + \sqrt{(-44 )} }{30} or, x = \frac{4 - \sqrt{(-44 )} }{30}$

or, $x = \frac{2 +\sqrt{11} i}{15} or, x = \frac{2 - \sqrt{11} i}{15}$

8 0

3 years ago

a segment has and endpoint at (-6, 8). The midpoint is at (-6, 2). What are the coordinates of the other endpoint?

Montano1993 [528]

Answer:

(-6,-4)

Step-by-step explanation:

The first endpoint of the line is (-6,8), we can call

x_1 = -6

and

y_1 = 8

Let the last endpoint have coordinates (x_2,y_2)

Also, the midpoint formula is:

(x_1+x_2)/2 , (y_1+y_2)/2

Now, plugging these values is the formula, we get:

(-6+x_2)/2 = -6

-6+x_2=-12

x_2=-12+6 = -6

x_2 = -6

Also

(8+y_2)/2=2

8+y_2=4

y_2=4-8=-4

y_2 = -4

The coordinates of the other endpoint is (-6,-4)

8 0

3 years ago

Troy drew a triangle with coordinates ( 5 , 6 ) , ( 5 , 4 ) , and ( 8 , 4 ) . He rotated the triangle 180° about the origin. Wha

jenyasd209 [6]

Answer:

The answers are B, C, and D.

Step-by-step explanation:

When you rotate an image 180° about the origin, you are flipping it twice. An easy rule is that an (x, y) pair becomes (-x, -y). Now just reverse the sign of the coordinates. Our rotated shape has the coordinates (-5, -6), (-5, -4), and (-8, -4).

6 0

3 years ago

Read 2 more answers

Kate has a coin collection. She keeps 7 in a box, which is only 5% of her entire collection. What is the total number of coins i

qaws [65]

Answer:

140

Step-by-step explanation:

5%/100 = 7/?

7 times 100 = 700

700 divided by 5 = 140 coins

5 0

3 years ago