All categories

2 years ago

Given RT below, if S lies on RT such that the

Mathematics

1 answer:

defon2 years ago

6 0

Answer:

(-2, -3)

Step-by-step explanation:

If a segment having extreme ends as $(x_1,y_1)$ and $(x_2,y_2)$ is divided by a point (x, y) in the ratio of m:n,

x = $\frac{mx_2+nx_1}{m+n}$

y = $\frac{my_2+ny_1}{m+n}$

Since, a line RT has extreme ends as R(-5, 3) and T(-1, -5) then a point S(x, y) which divides RT in the ratio of 3 : 1 will be,

x = $\frac{3(-1)+1(-5)}{3+1}$

= $\frac{-8}{4}$

= -2

y = $\frac{3(-5)+1(3)}{3+1}$

= $-\frac{12}{4}$

= -3

Therefore, coordinates of the point S will be (-2, -3).

You might be interested in

Find the vector x determined by the given coordinate vector [x]B and the given basis B.

iren2701 [21]

[3-13 16] is the answer

7 0

2 years ago

Ahmad just put some money into a cd that pays 11.3% interest compounded semiannually according to the rule of 72 in approximatel

lilavasa [31]

The "rule of 72" says that the doubling time in years is approximately 72 divided by the interest rate in percent. To make the money grow by a factor of 4 requires that it double twice, so will take twice as long as the period to double once.
2×72/11.3 ≈ 12.7 . . . . years

_____
The "rule of 72" is an approximation. The actual quadrupling time for this interest rate and compounding is about 12.6 years. (The actual product of doubling time and nominal interest rate is about 71.25.)

5 0

2 years ago

Which classification best represents a triangle with side lengths 6 cm, 10 cm, and 12 cm? acute, because 62 + 102 < 122 acute

maw [93]

The Pythagoras theorem states that
the sum of squares of the shorter sides (legs) of a right triangle equals the square of the third side.

A corollary from the same theorem helps us solve this problem:
If the sum of the squares of the shorter sides of a triangle is greater than the square of the third side, the included angle is acute. ..... (case 1)
Conversely, if the sum of the squares of the shorter sides of a triangle is less than the square of the third side, the triangle is obtuse. .....(case 2)

Here we have
6^2+10^2 = 36+100=136 <12^2=144
Therefore case 2 applies, and the triangle is obtuse.

7 0

2 years ago

Read 2 more answers

This line plot shows something about trails in a state park. What is true about the data in this line plot?

Zepler [3.9K]

Answer:

The total length of the Dogwood Trail is 24 kilometers

The difference between the lengths of the trails is 6 kilometers

Step-by-step explanation:

The complete and correct question is

The diagram shows two different nature trails in a state park. The solid line shows the Dogwood Trail. The dashed line shows the Elm Trail.

Which of the following statements are true about the lengths of the trails? Check all that apply.

1.The total length of the Dogwood Trail is 16 kilometers.

2.The total length of the Dogwood Trail is 24 kilometers.

3.The Elm Trail is longer than the Dogwood Trail.

4.The difference between the lengths of the trails is 2 kilometers.

5.The difference between the lengths of the trails is 6 kilometers.

The picture in the attached figure

step 1

Find the value of a

Applying the Pythagorean Theorem in the right triangle ABC

$13^2=a^2+5^2\\a^2=169-25\\a^2=144\\a=12\ km$

step 2

Find the value of b

Applying the Pythagorean Theorem in the right triangle CDE

$5^2=b^2+3^2\\b^2=25-9\\b^2=16\\b=4\ km$

step 3

Find the total length of the Dogwood Trail (solid blue line)

The total length is equal to

$AD=AB+BC+CE+ED$ ---> by segment addition postulate

substitute the given values

$AD=a+5+b+3=(a+b+8)\ km$

substitute the value of a and b

$AD=(12+4+8)=24\ km$

step 4

Find the total length of the Elm Trail (dashed red line)

The total length is equal to

$AD=AC+CD$ ---> by segment addition postulate

substitute the given values

$AD=13+5=18\ km$

Verify the following statements

Part 1) The total length of the Dogwood Trail is 16 kilometers

The statement is false

Because

The total length of the Dogwood Trail is 24 kilometers (see the explanation)

Part 2) The total length of the Dogwood Trail is 24 kilometers

The statement is true (see the explanation)

Part 3) The Elm Trail is longer than the Dogwood Trail

The statement is false

Because

The Elm Trail is smaller than the Dogwood Trail

$18\ km < 24\ km$

Part 4) The difference between the lengths of the trails is 2 kilometers

The statement is false

Because

The difference is equal to

$24-18=6\ km$

Part 5) The difference between the lengths of the trails is 6 kilometers

The statement is true

Because

The difference is equal to

$24-18=6\ km$

4 0

2 years ago

Read 2 more answers

Can someone help me with this

Anvisha [2.4K]

Answer:

D. $\frac{{7}^{11} }{ {4}^{11} }$

Step-by-step explanation:

$( \frac{7}{4}) {}^{11} = \frac{7 {}^{11} }{4 {}^{11} }$

Since we are multiplying an exponential number to a fraction the answer is going to be

$\frac{7 {}^{11} }{4 {}^{11} }$

Hope this helps ❤❤❤ ;)

7 0

2 years ago

Read 2 more answers