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3 years ago

A line segment has the endpoints C(4,9) and D(8,7). Find the coordinates of its midpoint M

Mathematics

1 answer:

babunello [35]3 years ago

8 0

Answer:

M = (6, 8)

Step-by-step explanation:

To the find the midpoint of a segment you add the x values, then divide by 2, then add the y values and divide by 2. $M = (\frac{x_{1} +x_{2} }{2}, \frac{y_{1} +y_{2} }{y} )$ . Therefore, you would do ((4+8)/2, (9+7)/2). So, you're answer is (12/2, 16/2), which equals (6, 8)

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A jogger runs 140 m due west, then changes direction for the second leg of her run. At the end of the run, she is 374 m away fro

USPshnik [31]

Answer:

The length of her second displacement = 247.12 m.

The direction of her second displacement = 31.24° from west.

Step-by-step explanation:

As per the question,

From the figure as drawn below,

Let the starting point be O. After running 140 m due west, she reached at point A.

∴ OA = 140 m

And At the end of the run, she is 374 m away from the starting point at an angle of 20° north of west.

∴ OP = 374 m

We have to find the distance AP = x.

By using the cosine rule in triangle OAP

$cos \theta = \frac{OA^{2}+OP^{2}-AP^{2}}{2\times OA\times OP}$

After putting the given value, we get

$cos 20= \frac{140^{2}+374^{2}-x^{2}}{2\times 140\times 374}$

$x^{2}=140^{2}+374^{2} - 2\times 140\times 374\times cos 20$

∴ x = 247.12 m

Hence,the length of her second displacement = 247.12 m.

Again,

By using the cosine rule in triangle OAP, we get

$cos \alpha = \frac{OA^{2}+AP^{2}-OP^{2}}{2\times OA\times AP}$

After putting the given value, we get

$cos \alpha = \frac{140^{2}+247.12^{2}-374^{2}}{2\times 140\times 247.12}$

∴ α = 148.759°

Hence, the direction of her second displacement = 180° - α = 180° - 148.759 = 31.24° from west.

8 0

3 years ago

X÷4+9=12 plzzzzzzzzzzzzzzz help step by step

xeze [42]

So we are trying to solve for x so in order to do that we need to get x by itself on one side of the equal sign

first we are going to combine like terms on each side of the equal side

so on the left side we see 4+9 these are booth whole numbers not attached to a variable so we can simplify this by adding these two values together making our equation: x/13 = 12

our x is still not by itself so in order to get it by itself we need to get rid of that 13

we need that x is being divided by 13 so in order to get rid a divided value we have to do the opposite to both sides - multiply by 13 on each side!

x/13 x 13 = x
12 x 13 = 156

so our equation is now:
x = 156

is our x by itself on one side of the equal sign? yes! so our x value is 156

6 0

3 years ago

Select the approximate values of x that are solutions to f(x) = 0, where

irga5000 [103]

A=-2;b=9;c=9;
delta=b^2-4*a*c
root1=(-b+(delta^(0.5)))/(2*a)
<span>root2=(-b-(delta^(0.5)))/(2*a)

delta =153
root1 = -0.8423
root2 =<span> 5.3423

Correct Answer is D</span></span>

3 0

3 years ago

What is the discrimination of the quadratic equation 6x^2-9x-8=0

aleksklad [387]

Answer:

first setup your problem. it should look like this :

6 0

4 years ago

At the soup to nuts cafeteria, larry orders two pieces of toast and a bagel, which comes out to $\$1.30$. Curly orders a bagel a

kotegsom [21]

Let us take costs of a piece of toast = $t, , one bagel cost=$b and a muffin cost=$m.

Larry

Two pieces of toast and a bagel cost = $1.30

2t+b=1.30 -------------equation(1)

Let us solve the equation(1) for t in terms of b, because we need to find one bagel cost.

Subtracting b from both sides we get

2t+b-b=1.30-b

2t= 1.30-b

Dividing by 2 on both sides.

2t/2= (1.30-b)/2

t= (1.30-b)/2

Curly

A bagel and a muffin cost = $2.50.

b + m = 2.50 -------------equation(2)

Solving equation for m in terms of b, we get

m= 2.50-b.

Moe

A piece of toast, two bagels, and three muffins cost = $6.95

t + 2b + 3m = 6.95 ......................equation(3).

Substituting t= (1.30-b)/2 and m= 2.50-b in equation (3)

(1.30-b)/2 + 2b + 3(2.50-b) = 6.95 .

Multiplying each term by 2 to get rid 2 from denominator of (1.30-b).

2*(1.30-b)/2 + 2*2b + 2*3(2.50-b) = 2*6.95

1.30-b + 4b + 6(2.50-b) = 13.90.

1.30 - b + 4b +15 - 6b = 13.90

Combining like terms

-3b +16.30 = 13.90

Subtracting 16.30 from both sides.

-3b +16.30-16.30 = 13.90-16.30.

-3b= -2.4

Dividing both sides by -3.

-3b/-3 = -2.4/-3

b = 0.8

Therefore, cost of one bagel = $0.80.

7 0

3 years ago