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2 years ago

What is the length of segment BC. ( ) units

Mathematics

2 answers:

weqwewe [10]2 years ago

8 0

Answer:

BC = 144 units

Step-by-step explanation:

It is given a line segment BC.

D is the point on the line segment.

To find the length of BC

BC = 8x

CD = 3x + 8 and BD = 4x + 10

BC = CD + BD

8x = 3x + 8 + 4x + 10

8x = 7x + 18

x = 18

BC = 8x = 8 * 18 = 144 units

Therefore the length of segment BC = 144 units

pentagon [3]2 years ago

4 0

Segment BC is 144 units

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In an attempt to escape a desert island, a castaway builds a raft and sets out to sea. The wind shifts a great deal during the d

nikdorinn [45]

Answer:

R = 7,34 km

Ф = 63,43° north of east

Step-by-step explanation:

Let´s analyze each movement and find its perpendicular components. Then, we are going to add the components along the x and y axes to get the resultant and finally to calculate its magnitude and direction.

To determine the perpendicular components, we will use right triangles trigonometrics ratios.

Please see images for each displacement in attached file.

Displacement A: 2.50 km and 45° north of west

Ax= AcosФ = 2.50cos45° = 1.77 km (neg. direction)

Ay= AsenФ = 2.50sen45° = 1.77 km (pos. direction)

Displacement B: 4.70 km and 60° south of east

Bx= BcosФ = 4.70cos60° = 2,35 km (pos. direction)

By= BsenФ = 4.70sen60° = 4,07 km (neg. direction)

Displacement C: 1.30 km and 25° south of west

Cx= CcosФ = 1.30cos25° = 1,18 km (neg. direction)

Cy= CsenФ = 1.30sen25° = 0.55 km (neg. direction)

Displacement D: 5.10 km due east (0°)

Dx= DcosФ = 5.10 km (pos. direction)

Dy= DsenФ = 0 km

Displacement E: 1.70 km and 5° east of north

Ex= EsenФ = 1.70sen5° = 0,15 km (pos. direction)

Ey= EcosФ = 1.70cos5° = 1.69 km (pos. direction)

Displacement F: 7.20 km and 55° south of west

Fx= FcosФ = 7.20cos55° = 4.13 km (neg. direction)

Fy= FsenФ = 7.20sen55° = 5.90 km (neg. direction)

Displacement G: 2.80 km and 10° north of east

Gx= GcosФ = 2.80cos10° = 2.76 km (pos. direction)

Gy= GsenФ = 2.80sen10° = 0.49 km (pos. direction)

Now, we add the components along the x- and y- axis to find the components of the resultant (R):

Rx = Ax + Bx + Cx + Dx + Ex + Fx + Gx

Ry = Ay + By + Cy + Dy + Ey + Fy + Gy

Therefore,

Rx= (-1.77)+(2.35)+(-1.18)+(5.10)+(0.15)+(-4.13)+(2.76)

Ry= (1.77)+(-4.07)+(-0.55)+(0)+(1.69)+(-5.90)+(0.49)

Note: minus (-) symbol to negative directions

Rx = 3.28 km

Ry = - 6.57 km

Let´s use the Theorem of Pythagoras to find the magnitud ot the resultant:

$R = \sqrt{Rx^{2} +Ry^{2} }$

$R =\sqrt{(3.28)^{2}+(-6.57)^{2} }$

R = 7,34 km

To find the direction of the resultant:

tanФ = $\frac{Ry}{Rx}$

tanФ = $\frac{6.57}{3.28}$

tanФ = 2.00

Ф = tan-1 (2.00)

Ф = 63,43° north of east

Download pdf

3 0

3 years ago

Find the value of x help 10 points

MrRissso [65]

Answer:

x = 5.67

Step-by-step explanation:

We are given a right angled triangle with a length of the hypotenuse 8 with the remaining two sides (base and perpendicular) that are equal to each other.

Assuming the two equal legs of this right angled triangle to be x, we can use the Pythagoras Theorem to find the value of x.

$(x)^2+(x)^2=(8)^2$

$2x^2=64$

Taking square root at both the sides to get:

$\sqrt{2x^2} =\sqrt{64}$

$1.41x=8\\\\x=5.67$

Therefore, x = 5.67.

7 0

2 years ago

What are the coordinates of the image of Q for a dilation with center (0, 0) and scale factor 1/2?

Amanda [17]

The answer would be D. (2,2)
Since the scale factor is 1/2, all you have to do is multiply 1/2 by each of x-coordinate and y-coordinate of Q.
Multiplying by 1/2 is the same as dividing by 2, so you divide the x and y coordinates of Q to get the dilation image of Q as (2,2).

8 0

3 years ago

Jim baked 31 cookies. His family ate m of them. Using m, write an expression for the number of cookies that remained.

Serggg [28]

Answer:

31-m

Step-by-step explanation:

Hope this helps!

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3 years ago

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