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3 years ago

Find the value of x, o is the centroid

Mathematics

1 answer:

Ray Of Light [21]3 years ago

3 0

Answer:

x = 14

Step-by-step explanation:

In the triangle O is the centroid.

Now, we know that the centroid divides the medians in the 2 : 1 ratio that means the distance from the centroid to the vertex and the distance from the centroid to the opposite side remains in 2 : 1 ratio.

So, from the given diagram we can write

$\frac{3x}{2x - 7} = \frac{2}{1}$

⇒ 3x = 4x - 14

⇒ x = 14 (Answer)

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Type the correct answer in each box. If necessary, use / for the fraction bar(s).

Tom [10]

Given:

The values are $a=0.\overline{6},b=0.75$ .

To find:

The values of $ab$ and $\dfrac{a}{b}$ .

Solution:

We have,

$a=0.\overline{6}$

$a=0.666...$ ...(i)

Multiply both sides by 10.

$10a=6.666...$ ...(ii)

Subtracting (i) from (ii), we get

$10a-a=6.666...-0.666...$

$9a=6$

$a=\dfrac{6}{9}$

$a=\dfrac{2}{3}$

And,

$b=0.75$

$b=\dfrac{75}{100}$

$b=\dfrac{3}{4}$

Now, the product of a and b is:

$ab=\dfrac{2}{3}\times \dfrac{3}{4}$

$ab=\dfrac{1}{2}$

The quotient of a and b is:

$\dfrac{a}{b}=\dfrac{\dfrac{2}{3}}{\dfrac{3}{4}}$

$\dfrac{a}{b}=\dfrac{2}{3}\times \dfrac{4}{3}$

$\dfrac{a}{b}=\dfrac{8}{9}$

Therefore, the required values are $ab=\dfrac{1}{2}$ and $\dfrac{a}{b}=\dfrac{8}{9}$ .

6 0

3 years ago

Find the measures of the numbered angles in the isosceles trapezoid. I need help ASP

Novay_Z [31]

Answer:

∠1 = 50°

∠2 = ∠3 = 130°

Step-by-step explanation:

In an isosceles trapezoid, such as this one, the angles at either end of a base are congruent:

∠1 ≅ 50°

∠2 ≅ ∠3

The theorems applicable to transversals and parallel lines also apply to the sides joining the parallel bases. In particular, "consecutive interior angles are supplementary." That is, angles 1 and 2 are supplementary, for example.

∠2 = 180° -∠1 = 180° -50° = 130°

We already know angle 3 is congruent to this.

∠1 = 50°

∠2 = ∠3 = 130°

_____

Additional comment

It can be easier to see the congruence of the base angles if you remove the length of the shorter base from both bases. This collapses the figure to an isosceles triangle and makes it obvious that the base angles are congruent.

Alternatively, you can drop an altitude to the longer base from each end of the shorter base. That will create two congruent right triangles at either end of the figure. Those will have congruent corresponding angles.

5 0

2 years ago

2m+(m-15)=90 solve for m

Ronch [10]

Answer:

m = 35

Step-by-step explanation:

2m + m -15 = 90

3m -15 = 90

+15 +15

3m = 105

/3 /3

m = 35

To check the work just insert 35 for m:

2(35) + 35 -15 = 90

70 + 35 -15 = 90

105 - 15 = 90

90 = 90

5 0

3 years ago

3+1 eqauls what n bhkjcvbsofkhjouidgvgvufg

IRISSAK [1]

3+1=4
As all parents would teach their babies simple math...take three candies and take one more. How many candies do you have now? Four

7 0

3 years ago

Read 2 more answers

A community theater sells about 150 tickets to a play each week when it charges $20 per ticket.

Marta_Voda [28]

Answer:

r = 12.5p(32 -p)
$16 per ticket
$3200 maximum revenue

Step-by-step explanation:

The number of tickets sold (q) at some price p is apparently ...

q = 150 + 25(20 -p)/2 = 150 +250 -12.5p

q = 12.5(32 -p)

The revenue is the product of the price and the number of tickets sold:

r = pq

r = 12.5p(32 -p) . . . . revenue equation

The maximum of revenue will be on the line of symmetry of this quadratic function, which is halfway between the zeros at p=0 and p=32. Revenue will be maximized when ...

p = (0 +32)/2 = 16

The theater should charge $16 per ticket.

Maximum revenue will be found by using the above revenue function with p=16.

r = 12.5(16)(32 -16) = $3200 . . . . maximum revenue

_____

Additional comment

The number of tickets sold at $16 will be ...

q = 12.5(32 -16) = 200

It might also be noted that if there are variable costs involved, maximum revenue may not correspond to maximum profit.

5 0

2 years ago