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3 years ago

The angles in a triangle are in the ratio 1:2:3. Show that the triangle is a right - angled triangle.

Mathematics

1 answer:

Alja [10]3 years ago

4 0

Answer:

Angles in a triangles add up to 180°

Respectively 1 : 2 : 3 is going to be 1 x , 2 x and 3 x so,

1 x + 2 x + 3 x = 180°

⇒ Simplify

6 x = 180°

⇒ Divide by 6 on both sides to isolate x

x = 30°

Since the ratio was 1 x : 2 x : 3 x and x is 30°,

30 : 60 : 90

And since there is a 90° angle, it is a right - angled triangle

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Can someone help me how to solve this?

Assoli18 [71]

Answer:

x > -5 in the answer

Step-by-step explanation:

(5 - 3x) / 4 < 5

multiplying both sides by 4:-

5 - 3x < 20

-3x < 15

x > 15/-3

x > -5 (Note the inequality sign is flipped because we are dividing by a negative number)

8 0

3 years ago

(1 point) Linear System - Three Variables Solve the following system of equations using Gaussian elimination method. If there ar

EastWind [94]

Answer:

$x=\frac{-363}{70}$ ≈ -5.1857

$y=\frac{-192}{35}$ ≈ -5.4857

$z=\frac{313}{84}$ ≈ 3.7262

Step-by-step explanation:

Rewrite the equation system as:

$6x+8y=-75$

$-3x+6y+6z=5$

$2x-9y=39$

Now, write the system in its augmented matrix form:

$\left[\begin{array}{cccc}6&8&0&-75\\-3&6&6&5\\2&-9&0&39\end{array}\right]$

applying row reduction process to its associated augmented matrix:

Swap R1 and R3, and then Swap R1 and R2:

$\left[\begin{array}{cccc}-3&6&6&5\\2&-9&0&39\\6&8&0&-75\end{array}\right]$

R3+2R1

$\left[\begin{array}{cccc}-3&6&6&5\\2&-9&0&39\\0&20&12&-65\end{array}\right]$

3R2+2R1

$\left[\begin{array}{cccc}-3&6&6&5\\0&-15&12&127\\0&20&12&-65\end{array}\right]$

15R3+20R2

$\left[\begin{array}{cccc}-3&6&6&5\\0&-15&12&127\\0&0&420&1565\end{array}\right]$

Now we have a simplified system:

$-3x+6y+6z=5\\0-15y+12z=127\\0+0+420z=1565$

$-3x+6y+6z=5\hspace{5 mm}(1)\\0-15y+12z=127\hspace{3 mm}(2)\\0+0+420z=1565\hspace{3 mm}(3)$

From (3):

$z=\frac{313}{84}$ (4)

Replacing (4) in (2)

$y=\frac{-192}{35}$ (5)

Finally replacing (5) and (4) in (1)

$x=\frac{-363}{70}$

7 0

3 years ago

Lisa store collect 5% sales tax on every item sold if she collected $22 and sold thanks what was the cost of the items her store

Bumek [7]

8 divide by 5 X=4-3 and that's the right answer Thank you

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3 years ago

I need help with b. please

aniked [119]

Its 1/5,

35/100 - 15/100 = 20/100

for 20, 40, 60, 80, 100
1, 2, 3, 4, 5

so 20/100 = 1/5

8 0

2 years ago

I need help I’m having so much trouble with this

sergeinik [125]

Answer: Decimal Form: 4.47213595 …

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3 years ago