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2 years ago

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In the diagram, point D divides line segment AB in the ratio of 5:3. If line segment AC is vertical and line segment CD is horiz

ontal, what are the coordinates of point C? Diagram shows a line segment with endpoints A(2, minus 6) and B(10, 2). Point D lies on this line segment. A dashed segment extends up from point A until point C and then extends horizontally to right until point D, forming a right triangle. A. (2, -1) B. (2, -3) C. (5, -3) D. (7, -1) Reset Next

1 answer:

Arlecino [84]2 years ago

7 0

The coordinates of point C that forms the triangle is; (2, -1)

<h3>How to partition a line segment?</h3>

We are told that point D divides line segment AB in the ratio of 5:3.

The line segment division formula is;

(x, y) = (m₁x₂ + m₂x₁)/(m₁ + m₂), (m₁y₂ + m₂y₁)/(m₁ + m₂)

For this question;

x₁ = 2; y₁ = -6; x₂ = 10; y₂ = 2; m₁ = 5; m₂ = 3

Thus, (x, y) gives us;

(5*10 + 3*2)/(5 + 3), (5*2 + 3*-6)/(5 + 3)

D(x, y) = (7, -1)

Now, we need to find the coordinates of C

We will use coordinate system which means the coordinate of x will be the as x coordinate of A since, AC is vertical line

And coordinate of y will be same as y in D since CD is horizontal line. Thus, coordinate of C is; C(2,-1).

Read more about Line segment partition at; brainly.com/question/17374569

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dexar [7]

Answer:

p = 32.32; A = 47.91

Step-by-step explanation:

1. Calculate ∠B

∠A + ∠B + ∠C = 180°

60° + ∠B + 45° = 180°

∠B + 105° = 180°

∠B = 75°

2. Find sides BC and AC

We can use the Law of Sines

$\dfrac{\sin A}{BC} = \dfrac{\sin B}{AC} = \dfrac{\sin C}{AB}$

(i) Find BC

$\dfrac{\sin 75^{\circ}}{AC} = \dfrac{\sin 45^{\circ}}{9}\\\\\dfrac{0.8660}{BC} = \dfrac{0.7071}{9}\\\\BC = 9 \times \dfrac{0.8661}{0.7071} = 11.02$

(ii) Find AC

$\dfrac{\sin 75^{\circ}}{AC} = \dfrac{\sin 45^{\circ}}{9}\\\\\dfrac{0.9659}{AC} = \dfrac{0.7071}{9}\\\\BC = 9 \times \dfrac{0.9659}{0.7071} = 12.29$

3. Find the perimeter

p = AB + AC + BC = 9 + 12.29 + 11.02 = 32.32

4. Find the area of the triangle

A general formula for the area of a triangle is

A = ½ab sinC

If we use ∠A, the formula becomes

A = ½ × 9 × 12.29 × sin60° = 55.30 × 0.8660 = 47.91

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3 years ago

What is the volume of the cylinder below? Use 3.14 for pi and I round to the nearest tenth

Rainbow [258]

Answer:

Option (4).

Step-by-step explanation:

Formula to calculate the volume of a cylinder is,

V = πr²h

Here r = radius of the cylinder

h = Height of the cylinder

From the figure attached,

r = $\frac{13}{2}=6.5$ cm

h = 11 cm

Now we substitute the values of h and r in the formula,

V = π(6.5)²(11)

= 464.75π

= 1459.32

≈ 1459.3 cm³

Therefore, volume of the given cylinder is 1459.3 cm³

Option (4) will be the answer.

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3 years ago

HELPPPPPPP on this question.! I need to pass.

timurjin [86]

9514 1404 393

Answer:

12.25 (or -18.75)

Step-by-step explanation:

If you pay attention to the square of a binomial, ...

(x -a)² = x² -2ax +a²

You see that the constant (a²) is the square of half the x-coefficient. That is, the x-coefficient is -2a, half that is -a, and the square of that is (-a)² = a².

In your equation, the x-coefficient is -7, half that is -3.5, and the square of that is 3.5² = 12.25.

So, you can think of this ambiguous question in a couple of ways.

<u>Concern is only with the x-terms</u>:

x² -7x +31 = (x² -7x +12.25) +31 = 12.25 . . . . . . add 12.25 to both sides

(x -3.5)² +31 = 12.25 . . . . write the x-terms as a square

<u>Concern with the equation overall</u>:

You want the end result to have the x-terms in the form of the square ...

(x -3.5)² = x -7x +12.25

The left side of the equation can be put in that form by adding -18.75 to both sides;

x² -7x +31 -18.75 = -18.75 . . . . . . add -18.75 to both sides

x² -7x +12.25 = -18.75 . . . . . . . . . simplify

(x -3.5)² = -18.75 . . . . . . write the left side as a square

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The short of it is that we're not sure what the question is asking for exactly. The "help video" would probably clarify the intent. Most likely, you're concerned with adding the square of half the x-coefficient, 12.25.

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2 years ago

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Answer:

There is no unique solution to this problem.

There are infinitely many solutions to this problem.

Step-by-step explanation:

Let B denotes broccoli crop

Let S denotes spinach crop

Last year, he grew 6 tons of broccoli per acre and 9 tons of spinach per acre, for a total of 93 tons of vegetables.

Mathematically,

6B + 9S = 93 eq. 1

This year, he grew 2 tons of broccoli per acre and 3 tons of spinach per acre, for a total of 31 tons of vegetables.

Mathematically,

2B + 3S = 31

2B = 31 - 3S

B = (31 - 3S)/2 eq. 2

Substitute eq. 2 into eq. 1

6B + 9S = 93

6[(31 - 3S)/2] + 9S = 93

3(31 - 3S) + 9S = 93

93 - 9S + 9S = 93

- 9S + 9S = 93 - 93

0 = 0

Therefore, there is no unique solution to this problem.

Which means that there are infinitely many solutions to this problem.

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3 years ago

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andrew-mc [135]

Answer:

Multiply vector c by the scalar -1/2.

Step-by-step explanation:

Look at vector c.

It has an x component of 4 and a y component of 4.

You can write vector c as a sum of its components using unit vectors in the x direction (i) and in the y direction (j).

c = 4i + 4j

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d = -2i - 2j

Now ask yourself, what operation do I do to 4 to end up with -2?

One answer is to multiply 4 by -1/2.

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