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Fudgin [204]
3 years ago
8

If m∠1 = 3x, m∠3 = 2x + 20 and m∠5 = 30, what is the value of x?

Mathematics
1 answer:
Nikolay [14]3 years ago
8 0

Answer:

50 degrees

Step-by-step explanation:

The diagram is attached below.

Theorem: The Exterior angle of a triangle is equal to the sum of two opposite interior angles.

By the theorem stated above:

m∠3+m∠5=m∠1

2x+20+30=3x

3x-2x=50

x=50

The value of x is 50 degrees.

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3(2x + 5) 2 2(x + 6)
puteri [66]

Answer:

i recommend you watch videos on youtuube about equations and take notes.

Step-by-step explanation:

6 0
2 years ago
I can't figure this out
andriy [413]
Suppose that equation of parabola is
y =ax² + bx + c


Since parabola passes through the point (2,−15) then 
−15 = 4a + 2b + c

Since parabola passes through the point (-5,-29), then
−29 = 25a − 5b + c

Since parabola passes through the point (−3,−5), then 
−5 = 9a − 3b + c


Thus, we obtained following system:
4a + 2b + c = −15
25a − 5b + c = −29
9a − 3b + c = −5

Solving it we get that 
a = −2, b = −4, c = 1

Thus, equation of parabola is
y = −2x²− 4x + 1

____________________

Rewriting in the form of 
(x - h)² = 4p(y - k)

i) -2x² - 4x + 1 = y

ii) -3x² - 7x = y - 11
(-3x² and -7x are isolated)

iii) -3x² - 7x - 49/36 = y - 1 - 49/36
(Adding -49/36 to both sides to get perfect square on LHS)

iv) -3(x² + 7/3x + 49/36) = y - 3
(Taking out -3 common from LHS)

v) -3(x + 7/6)² = y - 445/36 

vi) (x + 7/6)² = -⅓(y - 445/36) 
(Shifting -⅓ to RHS)

vii) (x + 1)² = 4(-1/12)(y - 445/36)
(Rewriting in the form of 4(-1/12) ; This is 4p) 


So, after rewriting the equation would be - 

(x + 7/6)² = 4(-⅛)(y - 445/36)

__________________

I hope this is what you wanted.

Regards,
Divyanka♪
__________________
6 0
2 years ago
Read 2 more answers
If the circumference of a circle measures 12π cm, what is the area of the circle in terms of π?
frez [133]
So the formula for the circumference of a circle is π x diameter
Since we know the the circumference already, we just divide that by π:

12π / π = 12

Now we halve the diameter to get the radius:
12 / 2 = 6 

The area of a circle is π x radius²
So the area is:

·π x 6² = 36π·  (or 113 not in terms of π) 
5 0
3 years ago
What is m∠KNL? Enter your answer in the box. ° A horizontal line segment M K intersects with line segment J L at their midpoint
inna [77]

t N.

In the figure shown below

Answer:

A horizontal line segment M K intersects with line segment J L at their midpoint N.

∠J N M =(5x+2)°

∠ LN M=3( x+ 14)°

So, ∠J N M + ∠ LN M =180°[ These two angles form linear pair.Angles forming linear pair are supplementary.]

⇒5 x+ 2+ 3 (x+ 14) =180 [ By Substitution]

⇒ 5 x+2 +3 x+42°= 180°

⇒ 8 x=180°-44°

⇒8 x= 136°

⇒x= 136°÷8

⇒x=17°

So, ∠J N M =5×17 +2=87°

∠ LN M= 3×(17 +14)=3×31=93

∠J N M =∠K N L [Vertically opposite angles]

∠K N L=87°


8 0
3 years ago
Read 2 more answers
The circumference of a circle is 78π cm. Find the diameter, the radius, and the length of an arc of 140°.
jasenka [17]
 The correct answer is the option D, which is: <span>D. 78 cm; 39 cm; 30.3π cm
 The explanation is shown above:
 1-The formula for calculate the circumference of a circle is:
 C=2</span>πr
 78π=2πr
 2- The radius is:
 r=78π/2π
 r=39 cm
 3- The diameter is:
 D=39 cm x 2
 D=78 cm
 4- The arc length is:
 arc length=(140°π/180°)(39 cm)
 arc length=30.3π cm
 
5 0
3 years ago
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