All categories

3 years ago

What are the coordinates of point G ,which divides DE un the ratio 2:3?

Mathematics

1 answer:

klemol [59]3 years ago

4 0

Answer:

(5, 7.8)

Step-by-step explanation:

There are several ways to solve this problem, but all of them involve similar triangles and ratios.

See the attached image.

The horizontal distance between points D and E is 11 - 1 = 10. If a segment 10 units long is divided in the ratio 2:3 (as shown by the two smaller segments of length a and b), then

$\frac{a}{b}=\frac{2}{3}\\\frac{a}{a+b}=\frac{2}{2+3}\\\frac{a}{10}=\frac{2}{5}$

"Cross-multiply" to get

5a = 20

a = 4

To get the x-coordinate of point G, add 4 to 1, the x-coordinate of D.

The x-coordinate of G is 1 + 4 = 5.

The same idea can be used on the second coordinate of G.

The vertical distance from D to E is 15 - 3 = 12.

$\frac{a}{b}=\frac{2}{3}\\\frac{a}{a+b}=\frac{2}{2+3}\\\frac{a}{12}=\frac{2}{5}$

5a = 24

a = 24/5 = 4.8

The y=coordinate of G is 3 + 4.8 = 7.8

You might be interested in

A stone dropped from a bridge strikes the water 2.2 s later. How high is the bridge above thewater

vivado [14]

Let the only force acting on the ball is the gravity (free-failing) and the ball was initially stationary
vo = 0

s = vot + 1/2 gt^2

s = 1/2 x 10 x (2.2) ^2 = 24.2 m

3 0

3 years ago

Read 2 more answers

A cash register contains $10 bills and $20 bills with a total value of $520. If there are 32 bills total, then how many of each

ohaa [14]

12 is the number of $10 bills

20 is the number of $20 bills

Step-by-step explanation:

Hello,

Let's note

a the number of $10 bills

b the number of $20 bills

The total value is $520 so we can write the first equation (1)

$\boxed{\sf 10a \ + \ 20b \ = \ 520 }$

We know that there are 32 bills in total so we can write the second equation (2)

$\boxed{\sf a \ + \ b \ = \ 32 }$

(1) - 10*(2) gives

10a + 20b - 10(a+b) = 520 - 320 = 200

10a + 20b - 10a - 10b = 10b = 200

So b = 200/10=20

and then from (2) a = 32 - 20 = 12

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

7 0

3 years ago

Name the smallest even number divisible by 6 and 9.

Step2247 [10]

Answer:

Step-by-step explanation:

5 0

2 years ago

He cost, in millions of dollars, of building a three-story high school in new york state was estimated to be c(x) = 2.1 + 0.12x

ratelena [41]

Given cost function is

c(x) = $2.1 + 0.12x - 0.0001x^2$ (20 ≤ x ≤ 400)

where x is the number of thousands of square feet

total revenue will be $0.2 million dollars per thousand square feet

Revenue is 0.2 millions per thousand square feet. we know x is the number of thousand of square feet

So R(x) = 0.2x

We know Profit = Revenue - Cost

P(x) = R(x) - C(x)

$P(x) = 0.2x - (2.1 + 0.12x - 0.0001x^2)$

$P(x) = 0.2x - 2.1 - 0.12x + 0.0001x^2)$

combine like terms

$P(x) =-2.1 + 0.08x + 0.0001x^2$

Profit function is

$P(x) =0.0001x^2 + 0.08x - 2.1$

5 0

3 years ago

A crate that is 10 inches long, 8 inches wide, and 3 inches high is shown above. The floor and the four walls are all one inch t

miskamm [114]

Answer:

Step-by-step explanation:

The exterior of the crate is 10 inches long, meaning that the inside measurement is 8 inches. Next, the 8 inch width corresponds to 6 inches inside. Finally, the 3 inch height corresponds to 1 inch interior height.

Thus the inside floor of the box is 8 by 6 inches, or 48 square inches.

Since the inside height is only 1 inch, this means that 48 one-inch cubical blocks will fit inside the crate.

7 0

4 years ago

What are the coordinates of point G ,which divides DE un the ratio 2:3?​

What are the coordinates of point G ,which divides DE un the ratio 2:3?