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3 years ago

ASAP

Mathematics

1 answer:

Luba_88 [7]3 years ago

4 0

Answer:

The answer is B

Step-by-step explanation:

since the second equation would simplify to y=1/2x-4. If you were to graph those to equations the lines would be parallel

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In the accompanying diagram, what is sin E? A. B. E C. D. 4 G A B С OD

IRINA_888 [86]

Answer:

Sin(E) = $\frac{4}{5}$

Step-by-step explanation:

The full question is as follows :

To find - In the accompanying diagram, what is sin E?

Proof -

We know that,

Sin(theta) = (opposite side) / (hypotenuse)

From the diagram, we can see that,

Base = 3

Perpendicular = 5

Hypotenuse = 5

So,

For angle E,

Opposite side = 4

Hypotenuse = 4

∴ we get

Sin(E) = $\frac{4}{5}$

5 0

3 years ago

-3(2t - 1) = t + t + t + 3

Allisa [31]

T = 0

isolate the variable

4 0

3 years ago

Read 2 more answers

Item 7

Mariulka [41]

Answer:

$A = 74.7^\circ$

$B = 42.5^\circ$

$C = 62.8^\circ$

Step-by-step explanation:

Given

$A = (-1,2) \to (x_1,y_1)$

$B = (2,8) \to (x_2,y_2)$

$C = (4,1) \to (x_3,y_3)$

Required

The measure of each angle

First, we calculate the length of the three sides of the triangle.

This is calculated using distance formula

$d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2$

For AB

$A = (-1,2) \to (x_1,y_1)$

$B = (2,8) \to (x_2,y_2)$

$d = \sqrt{(-1 - 2)^2 + (2 - 8)^2$

$d = \sqrt{(-3)^2 + (-6)^2$

$d = \sqrt{45$

So:

$AB = \sqrt{45$

For BC

$B = (2,8) \to (x_2,y_2)$

$C = (4,1) \to (x_3,y_3)$

$BC = \sqrt{(2 - 4)^2 + (8 - 1)^2$

$BC = \sqrt{(-2)^2 + (7)^2$

$BC = \sqrt{53$

For AC

$A = (-1,2) \to (x_1,y_1)$

$C = (4,1) \to (x_3,y_3)$

$AC = \sqrt{(-1 - 4)^2 + (2 - 1)^2$

$AC = \sqrt{(-5)^2 + (1)^2$

$AC = \sqrt{26$

So, we have:

$AB = \sqrt{45$

$BC = \sqrt{53$

$AC = \sqrt{26$

By representation

$AB \to c$

$BC \to a$

$AC \to b$

So, we have:

$a = \sqrt{53$

$b = \sqrt{26$

$c = \sqrt{45$

By cosine laws, the angles are calculated using:

$a^2 = b^2 + c^2 -2bc \cos A$

$b^2 = a^2 + c^2 -2ac \cos B$

$c^2 = a^2 + b^2 -2ab\ cos C$

$a^2 = b^2 + c^2 -2bc \cos A$

$(\sqrt{53})^2 = (\sqrt{26})^2 +(\sqrt{45})^2 - 2 * (\sqrt{26}) +(\sqrt{45}) * \cos A$

$53 = 26 +45 - 2 * 34.21 * \cos A$

$53 = 26 +45 - 68.42 * \cos A$

Collect like terms

$53 - 26 -45 = - 68.42 * \cos A$

$-18 = - 68.42 * \cos A$

Solve for $\cos A$

$\cos A =\frac{-18}{-68.42}$

$\cos A =0.2631$

Take arc cos of both sides

$A =\cos^{-1}(0.2631)$

$A = 74.7^\circ$

$b^2 = a^2 + c^2 -2ac \cos B$

$(\sqrt{26})^2 = (\sqrt{53})^2 +(\sqrt{45})^2 - 2 * (\sqrt{53}) +(\sqrt{45}) * \cos B$

$26 = 53 +45 -97.67 * \cos B$

Collect like terms

$26 - 53 -45= -97.67 * \cos B$

$-72= -97.67 * \cos B$

Solve for $\cos B$

$\cos B = \frac{-72}{-97.67}$

$\cos B = 0.7372$

Take arc cos of both sides

$B = \cos^{-1}(0.7372)$

$B = 42.5^\circ$

For the third angle, we use:

$A + B + C = 180$ --- angles in a triangle

Make C the subject

$C = 180 - A -B$

$C = 180 - 74.7 -42.5$

$C = 62.8^\circ$

8 0

3 years ago

Find missing measure (No.6)

aalyn [17]

Answer:

Step-by-step explanation:

6 no

1.angle 2=92 degree(being vertically opposite angle)

2.angle 1+33+92=180(sum of interior angles of a triangle)

angle 1+125=180

angle 1=180-125

angle 1=55

3.angle 3+angle 2+115+90=360(sum of four angles is always 360 degree)

angle 3+92+205=360

angle 3+297=360

angle 3=360-297

angle 3=63

6 0

3 years ago

I NEED HELP!!!!!!!!!!!!!!!!

antoniya [11.8K]

Step-by-step explanation:

just think back to the standard circle of radius = 1.

there the trigonometric functions are all represented as sides of right-angled triangles, where the radius is the baseline.

just like the triangle we are seeing here.

the only difference : the baseline (radius) is 17 and not 1.

and that is fine. everything is as in the standard circle, but multiplied by the radius (which is also true for the standard circle, but multiplying by 1 does not change anything, right ?).

angle A is or focus. so, just imagine the triangle turned counterclockwise by 90° (so that AC is horizontal and CB is vertical).

do you see it now ?

sin is the vertical leg, cos the horizontal leg. and the leg lengths here are the standard functions multiplied by the radius.

so,

17 × sin A = 8

sin A = 8/17 = 0.470588235... ≈ 0.47

17 × cos A = 15

cos A = 15/17 = 0.882352941... ≈ 0.88

now B is our focus. imagine the triangle being mirrored at point B, so that B is left, and AC is right. your see it now ?

tan B = sin B / cos B

sin B = 15/17 = 0.882352941... ≈ 0.88

cos B = 8/17 = 0.470588235... ≈ 0.47

tan B = 15/17 / 8/17 = 15/8 = 1.875 ≈ 1.88

cos B = 8/17 = 0.470588235... ≈ 0.47

7 0

3 years ago