Line segment of length k is divided into 3 equal parts. What is distance between midpoints of first and third segments?A) 2k/3 B) k C) k/6 D) 2k

Answers

Answer 1

Answer:

The distance between the midpoints of the first segment and the third segment is 2k/3. Hence, option A is the right choice.

What is the mid-point of a line segment?

The mid-point of a line segment is the point from which the distance to both ends of the line segment is equal.

How to solve the question?

In the question, we are given a line segment of length k units, which is divided into 3 equal parts.

We are asked to find the distance between the midpoints of the first and third segments.

Firstly, we divide the line segment at points k/3 and 2k/3, to get three equal parts of lengths k/3 each.

Now, the mid-point of the first segment = (0 + k/3)/2 = k/6.

The mid-point of the third segment = (2k/3 + k)/2 = 5k/6

Therefore, the distance between the midpoints of the first segment and the third segment is (5k/6 - k/6) = 4k/6 = 2k/3. Hence, option A is the right choice.

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Answer 2

Answer:

Line segment of length k is divided into 3 equal parts.

so first segment is 0-k/3 and third segment is 2/3k-k

so mid-pt of 1st = k/6 and 3rd = 5/6k

so the distance in between = 5/6k-k/6 = 4/6k = 2/3k

ans is A

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CE is an angle bisector of angle ACB.If m angle ACE = 2x - 15 and m angle ECB = x +5,
determine the value of x.

Answers

The value of x from the angle bisector is: x = 20

How to find the value of the angle bisector?

Angle bisector theorem is a theorem in geometry that states that an angle bisector of a triangle divides the opposite side into two segments that are proportional to the other two sides of the triangle. An angle bisector is a ray that divides a given angle into two angles of equal measures.

Thus, we can say that:

∠ECB = ∠ACE

Thus:

x + 5 = 2x - 15

2x - x = 15 + 5

x = 20

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Answer:

x = 20

Step-by-step explanation:

$\because \overrightarrow {CE}$ is an angle bisector of $\angle ACB.$

$\therefore m \angle ACE = m \angle ECB\n 2x - 15 = x + 5 \n 2x - x = 15 + 5 \n \huge \orange{ x = 20}$

Will a truck that is 10 feet wide carrying a load that reaches 12 feet above the ground clear the semielliptical arch on the one-way road that passes under the bridge shown in the figure on the right? 13 ft --- 52 ft It will clear the arch because the height of the archway of the bridge 5 feet from the center is approximately (Round to two decimal places as needed.) feet.

Answers

Height of the archway 5 feet from the center is required.

The height of the archway 5 feet away from the center is 12.757 feet.

Semi-major axis = $a=(52)/(2)=26\ \text{feet}$

Semi-minor axis = $b=13\ \text{feet}$

The formula for ellipse is

$(x^2)/(a^2)+(y^2)/(b^2)=1\n\Rightarrow (x^2)/(26^2)+(y^2)/(13^2)=1$

At 10 feet is the width of the truck.

The truck is passing through the center so the $x=(10)/(2)=5$

$(5^2)/(26^2)+(y^2)/(13^2)=1\n\Rightarrow y=\sqrt{(1-(5^2)/(26^2))* 13^2}\n\Rightarrow y=12.757\ \text{feet}$

Now $y=12.757\ \text{feet}>12\ \text{feet}$

So, the height of the archway 5 feet away from the center is 12.757 feet.

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Figure is missing, so i have attached it.

Answer:

it will clear the arch because the height of the archway of the bridge 5 feet from the center is approximately 12.76 ft

Step-by-step explanation:

The standard form of equation of an ellipse is;

x²/a² + y²/b² = 1

From the figure in the image attached, we can see that the radius is; a = 52/2 = 26 ft

While the value of b = 13 ft

Thus;

x²/26² + y²/13² = 1

x²/676 + y²/169 = 1

We want to find the height of the archway of the bridge 5 feet from the center.

Thus, we will plug in 5 for x to get;

5²/676 + y²/169 = 1

(25/676) + (y²/169) = 1

Multiply through by 676 to get;

25 + 4y² = 676

4y² = 676 - 25

y² = 651/4

y² = 162.75

y = 12.76 ft

Thus height of the truck is 12 ft and so it will clear the arch because the height of the archway of the bridge 5 feet from the center is approximately 12.76 ft

PLLLLLLLLLLLLLLLZZZZZZ HELP IVE BEEN STUCK ON THIS ONE

Answers

Answer:

yeet device and hope it breaks.

Step-by-step explanation:

Take a picture and say it died

What is the solution to the equation -3(h+5)+2=4(h+6)-9

Answers

Answer:

$h=-4$

Step-by-step explanation:

The equation is $-3(h+5)+2=4(h+6)-9$ we need to find the value of h.

First we are going to distribute the products.

$-3(h+5)+2=4(h+6)-9\n -3h-15+2=4h+24-9\n -3h-13=4h+15$

We have to put the terms with letter h in the left side of the equation and the terms without h in the right side;

$-3h-13=4h+15\n -3h-4h=15+13$

$-7h=28$

Now, for the last step we have to divide both sides of the equation in (-7):

$-7h=28\n ((-7)h)/((-7)) =(28)/((-7)) \n h=-4$

The answer to your question is h=−4

A coin is flipped three times. James is declared the winner if there are at least two tails. Peter is declared the winner if there is a head flipped.a. How many different outcomes are there?
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Answers

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