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3 years ago

Examine triangle ABC. What is the value of x? 37 48 127 138

Mathematics

1 answer:

Flura [38]3 years ago

4 0

The outside angle of B needs to equal 180 - 79 = 101 degrees.

The 3 outside angles of a triangle need to equal 360 degrees.

Set up the equation with what we know:

X + (x+5) + 101 = 360

Simplify:

2x + 106 = 360

Subtract 106 from both sides:

2x = 254

Divide both sides by 2:

x = 254 / 2

x = 127

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How many solutions does the equation have, x1 + x2 + x3 = 10 , where x1 , x2, and x3 are non-negative integers?

MAVERICK [17]

Non-negative integers are positive integers or zero.

1. When $x_1=0,$ then there are such possible cases for $x_2$ and $x_3:$

$x_2=0,\ x_3=10;$
$x_2=1,\ x_3=9;$
$x_2=2,\ x_3=8;$
$x_2=3,\ x_3=7;$
$x_2=4,\ x_3=6;$
$x_2=5,\ x_3=5;$
$x_2=6,\ x_3=4;$
$x_2=7,\ x_3=3;$
$x_2=8,\ x_3=2;$
$x_2=9,\ x_3=1;$
$x_2=10,\ x_3=0.$

In total 11 solutions for $x_1=0.$

2. For $x_1=1,$ there are such possible cases for $x_2$ and $x_3:$

$x_2=0,\ x_3=9;$
$x_2=1,\ x_3=8;$
$x_2=2,\ x_3=7;$
$x_2=3,\ x_3=6;$
$x_2=4,\ x_3=5;$
$x_2=5,\ x_3=4;$
$x_2=6,\ x_3=3;$
$x_2=7,\ x_3=2;$
$x_2=8,\ x_3=1;$
$x_2=9,\ x_3=0.$

In total 10 solutions for $x_1=1.$

3. This process gives you

for $x_1=2$ - 9 solutions;
for $x_1=3$ - 8 solutions;
for $x_1=4$ - 7 solutions;
for $x_1=5$ - 6 solutions;
for $x_1=6$ - 5 solutions;
for $x_1=7$ - 4 solutions;
for $x_1=8$ - 3 solutions;
for $x_1=9$ - 2 solutions;
for $x_1=10$ - 1 solution.

4. Add all numbers of solutions:

$11+10+9+8+7+6+5+4+3+2+1=66.$

Answer: there are 66 possible solutions (with non-negative integer variables)

8 0

3 years ago

Read 2 more answers

Please help ILL MARK BRAINLIEST(17 points too)

jonny [76]

Answer:

5, 10, 15, 20, 25, 30

6, 12, 18, 24, 30

Answer: 30

3, 6, 9, 12, 15, 18, 21, 24

Answer: 24

14, 28

4, 8, 12, 16, 20, 24, 28, 32

Answer: 28

Hoped it helped :)

3 0

3 years ago

If two angles of a triangle measure 50 degrees and 85 degrees what is the measure of the third angle

Dvinal [7]

I think it's 45 because 50+85=135

*Remember in total the sum of all angles must be equal to 180
So in order to find the missing angle subtract 180-135=45.

45 is the measure of the 3rd angle.

Hope I helped :)

6 0

3 years ago

In XYZ, mX=90 and mY=30.In TUV,mU= 30 and mV=60. Which is true about the two triangles? XYZ=TUV, XYZ= VUT,No congruency statemen

Flauer [41]

Answer:

No congruency statement can be made because the side length are unknown.

Step-by-step explanation:

The sum of the measures of all interior angles in a triangle is always 180°.

In triangle XYZ,

$m\angle X=90^{\circ}\\ \\m\angle Y=30^{\circ},$

then

$m\angle X+m\angle Y+m\angle Z=180^{\circ}\Rightarrow m\angle Z=180^{\circ}-90^{\circ}-30^{\circ}=60^{\circ}$

In triangle TUV,

$m\angle U=30^{\circ}\\\\m\angle V=60^{\circ},$

then

$m\angle T+m\angle U+m\angle V=180^{\circ}\Rightarrow m\angle T=180^{\circ}-30^{\circ}-60^{\circ}=90^{\circ}$

We have two triangles with congruent angles but we have no information about side lengths. Therefore, can not be made because the side length are unknown. Correct option is last option.

6 0

3 years ago

Read 2 more answers

Train X is traveling at a constant speed of 30 miles per hour and Train Y is traveling at a constant speed of 40 miles per hour.

topjm [15]

Answer:

3.5 hours

Step-by-step explanation:

Speed of train X=30 mph

Speed of train Y=40 mph

Relative speed When the two trains travelling in same direction

Relative speed=40-30=10 mph