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2 years ago

What side is the shortest in the picture? A. GF B. DG C. EF D. GE F. DE

Mathematics

1 answer:

igor_vitrenko [27]2 years ago

4 0

Answer:

A. GF

Step-by-step explanation:

The shortest side in a triangle is opposite the smallest angle

<d = 180 -52 -61 =67

The smallest angle is 52 so the smallest side is DG

<f = 180 - 48-85 =50

The smallest angle is 48 so the smallest side is FG

The smallest angle is 48 so the smallest side overall is FG (GF)

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Need help with inscribed angles If M

Cloud [144]

Given:

In the given circle O, BC is diameter, OA is radius, DC is a chord parallel to chord BA and $m\angle BCD=30^\circ$ .

To find:

The $m\angle AOB$ .

Solution:

If a transversal line intersect two parallel lines, then the alternate interior angles are congruent.

We have, DC is parallel to BA and BC is the transversal line.

$\angle OBA\cong \angle BCD$ [Alternate interior angles]

$m\angle OBA=m\angle BCD$

$m\angle OBA=30^\circ$

In triangle AOB, OA and OB are radii of the circle O. It means OA=OB and triangle AOB is an isosceles triangle.

The base angles of an isosceles triangle are congruent. So,

$\angle OAB\cong \angle OBA$ [Base angles of an isosceles triangle]

$m\angle OAB=m\angle OBA$

$m\angle OAB=30^\circ$

Using the angle sum property in triangle AOB, we get

$m\angle OAB+m\angle OBA+m\angle AOB=180^\circ$

$30^\circ+30^\circ+m\angle AOB=180^\circ$

$60^\circ+m\angle AOB=180^\circ$

$m\angle AOB=180^\circ-60^\circ$

$m\angle AOB=120^\circ$

Hence, the measure of angle AOB is 120 degrees.

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2 years ago

Find the exact value of tan 5 π. -1 0 1 undefined

Dimas [21]

Answer:

Step-by-step explanation:

tan 5 π

Remove full rotations of 2 π until the angle is between 0 and 2 π . tan π

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because tangent is negative in the second quadrant. tan 0 The exact value of tan 0 is 0 . Multiply 1 by 0 .

6 0

3 years ago

If 3/4 of a certain number is equal to 41/2 find the number

SSSSS [86.1K]

Answer:

$x = \frac{82}{3}$

Step-by-step explanation:

let $x$ be that number

$(\frac{3}{4} )x = \frac{41}{2}$

$\frac{3x}{4} = \frac{41}{2}$

multiply both sides by $4$

$\frac{3x}{4} * 4 = 4 * \frac{41}{2} \\3x = \frac{41 }{2} * 2 * 2\\3x = 41 *2 \\3x = 82 \\$

divide both sides by 3

$\frac{3x}{3} = \frac{82}{3}$

$x = \frac{82}{3}$

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3 years ago

Find the equation of the line shown

Ganezh [65]

Answer:

y= -0.25x+2

Step-by-step explanation:

$y = mx + b \\ \\ m = \frac{rise}{run} = \frac{ - 1}{4} \\ \\ b = where \: the \: line \: hits \: y \: axis = 2 \\ \\ y = - \frac{1}{4} x + 2$

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2 years ago

Solve using Elimination 3x+y=-9 y=5x+7

valentinak56 [21]

Answer

x=-2 and y=-3

Step-by-step explanation:

Step: Solvey=5x+7for y:

Step: Substitute5x+7 for y in 3x+y=−9:

3x+y=−9

3x+5x+7=−9

8x+7=−9(Simplify both sides of the equation)

8x+7+−7=−9+−7(Add -7 to both sides)

8x=−16

8x/8=−16/8

(Divide both sides by 8)

x=−2

Step: Substitute−2 for x in y=5x+7:

y=5x+7

y=(5)(−2)+7

y=−3(Simplify both sides of the equation)

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2 years ago