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2 years ago

PLEASE HELP ME IN MATH

Mathematics

1 answer:

maks197457 [2]2 years ago

6 0

Answer:

BC= 23.0km (nearest tenth)

Step-by-step explanation:

Please see the attached picture for full solution.

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In Triangle XYZ, measure of angle X = 49° , XY = 18°, and

marissa [1.9K]

Answer:

There are two choices for angle Y: $Y \approx 54.987^{\circ}$ for $XZ \approx 15.193$ , $Y \approx 27.008^{\circ}$ for $XZ \approx 8.424$ .

Step-by-step explanation:

There are mistakes in the statement, correct form is now described:

<em>In triangle XYZ, measure of angle X = 49°, XY = 18 and YZ = 14. Find the measure of angle Y:</em>

The line segment XY is opposite to angle Z and the line segment YZ is opposite to angle X. We can determine the length of the line segment XZ by the Law of Cosine:

$YZ^{2} = XZ^{2} + XY^{2} -2\cdot XY\cdot XZ \cdot \cos X$ (1)

If we know that $X = 49^{\circ}$ , $XY = 18$ and $YZ = 14$ , then we have the following second order polynomial:

$14^{2} = XZ^{2} + 18^{2} - 2\cdot (18)\cdot XZ\cdot \cos 49^{\circ}$

$XZ^{2}-23.618\cdot XZ +128 = 0$ (2)

By the Quadratic Formula we have the following result:

$XZ \approx 15.193\,\lor\,XZ \approx 8.424$

There are two possible triangles, we can determine the value of angle Y for each by the Law of Cosine again:

$XZ^{2} = XY^{2} + YZ^{2} - 2\cdot XY \cdot YZ \cdot \cos Y$

$\cos Y = \frac{XY^{2}+YZ^{2}-XZ^{2}}{2\cdot XY\cdot YZ}$

$Y = \cos ^{-1}\left(\frac{XY^{2}+YZ^{2}-XZ^{2}}{2\cdot XY\cdot YZ} \right)$

1) $XZ \approx 15.193$

$Y = \cos^{-1}\left[\frac{18^{2}+14^{2}-15.193^{2}}{2\cdot (18)\cdot (14)} \right]$

$Y \approx 54.987^{\circ}$

2) $XZ \approx 8.424$

$Y = \cos^{-1}\left[\frac{18^{2}+14^{2}-8.424^{2}}{2\cdot (18)\cdot (14)} \right]$

$Y \approx 27.008^{\circ}$

There are two choices for angle Y: $Y \approx 54.987^{\circ}$ for $XZ \approx 15.193$ , $Y \approx 27.008^{\circ}$ for $XZ \approx 8.424$ .

6 0

2 years ago

Please help!!!<br> 20 points

mrs_skeptik [129]

Answer:

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

HELP ME QUICK: Suppose AB has one endpoint at A(0, 0). If (5, 3) is the midpoint of AB, what are the coordinates of point B?

DiKsa [7]

Answer:

Step-by-step explanation:

If P is midpoint of AB and: $A(0,\,0)\,,\quad P(5,\,3)\,,\quad B(x_B,\,y_B)$

then:

$x_P-x_A=x_B - x_P\qquad\quad\ \wedge\qquad y_P-y_A=y_B - y_P\\\\ 5-0=x_B-5\qquad\quad\wedge\qquad 3-0=y_B -3\\\\ x_B=5+5\qquad\qquad\wedge\qquad\ \ y_B=3+3 \\\\ {}\quad x_B=10\qquad\qquad\wedge\qquad\qquad \ y_B=6$

5 0

2 years ago

Could someone help me finding out the missing answers?

Tema [17]

Answer:

See below.

Step-by-step explanation:

The Slope of PQ is (v - z) / (w - x).

The slope of P'Q' =

(v + b) - (z + b)

--------------------- = (v - z) / (w - x)

(w + a - (x + a)

Both lines have a slope that is (v - z)/ (w - x).

So both lines are parallel.

7 0

2 years ago

Y=4x+1, 2x+y=37 substitution

VLD [36.1K]

Answer:

Step-by-step explanation:

Substitute y = 4x + 1 to the equation 2x + y = 37:

2x + (4x + 1) = 37

(2x + 4x) + 1 = 37 <em>subtract 1 from both sides</em>

6x = 36 <em>divide both sides by 6</em>

x = 6

Pyt the value of x to the first equation:

y = 4(6) + 1

y = 24 + 1

y = 25

4 0

2 years ago