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3241004551 [841]
3 years ago
5

2. One angle of a triangle measures 10 degrees more than the second. The measure of the third angle is twice the sum of the meas

ures of the first two angles. Find the measure of each angle. [Hint: the sum of the three angles in a triangle equals 180°.] PLEASE SHOW YOUR WORK I WILL MAKE BRAINLIST PLEASE!!!!!!!
Mathematics
2 answers:
Yakvenalex [24]3 years ago
5 0

Answer:

first angle = 25 degrees

Second angle = 35 degrees

Third side = 120/degrees

Step-by-step explanation:

Let the size of the second angle be x degrees.

One angle of a triangle measures 10 degrees more than the second. This means that the size of the first angle is ( x+ 10 )degrees.

The measure of the third angle is   twice the sum of the measures of the first two angles. This means that   The third angle = 2( first angle + second angle). So the size of each angle is  

First angle (x + 10) degrees  

Second angle = x degrees

Third angle = 2(x + 10 + x) =  (4x + 20) degrees

Sum of angles in a triangle = 180  degrees. Therefore,  x + 10 + x + 4x + 20 = 180 degrees  6x + 30 = 180

6x = 180 - 30 = 150

x = 150/6 = 25 degrees

First angle = x + 10 = 25 +10 = 35

Third angle = 4x + 20 = 4 × 25 + 20

= 100+ 20 = 120 degrees

Hope this helps

lakkis [162]3 years ago
5 0

Answer:25(1st angle),35(2nd angle),120(3rd angle)

Step-by-step explanation: (/ stands for divide)

180/6=30 (sum of angles/total units=value of one unit, third angle is 4 units as it is twice the sum of first two angles)

30x4=120 (value of unitxnumber of units of 3rd angle=3rd angle)

30x2=60 (value of unitxfirst angle+second angle total units=value of 1st angle+2nd angle)

(60-10)/2=25(1st angle)

25+10=35(2nd angle)

CHECK: 35+25+120=180

hope you get it :)

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Let the two numbers are x and y

Let larger number = x

and smaller number = y

it means

x-y = 0.77

Now it says larger number is increased 5 times

So it now becomes 5x

So second equation becomes

5x -y =77

Now we have to solve these two equations

x-y = 0.77 and 5x-y = 77

multiply first equation by -1 and then add both equations

-x+y = -0.77

Now on adding we get

-x+5x +y -y = 77-0.77

4x = 76.23

Divide both sides by 4

x=19.0575

We get the larger number , now subtract 0.77 from this , we will get the smaller number

y=19.0575-0.77=18.2875

y=18.2875


Hence the larger number = 19.0575

Smaller number = 18.2875

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Answer:

Part 1) The directrix of the parabola is y=-4.25

Part 2) The focus of the parabola is F(1,-3.75)

Step-by-step explanation:

we have

y=x^{2}-2x-3

This is a vertical parabola open upward

we know that

If a parabola has a vertical axis, the standard form of the equation of the parabola is

(x - h)^{2}=4p(y - k)

where

p≠ 0

The vertex of this parabola is at (h, k).

The focus is at (h, k + p).

The directrix is the line y = k - p.

The axis is the line x = h.

step 1

Convert the equation of the parabola in standard form

y=x^{2}-2x-3

y+3=x^{2}-2x

y+3+1=x^{2}-2x+1

y+4=x^{2}-2x+1

y+4=(x-1)^{2}

so

(x-1)^{2}=(y+4) ----> equation in standard form

The vertex is the point (1,-4)

4p=1 ------> p=1/4

step 2

Find the directrix of the parabola

The directrix is the line y = k - p

we have

k=-4

p=1/4

substitute the values

y = k - p

y=-4-(1/4)=-17/4

y=-4.25

step 3

Find the focus of the parabola

we know that

The focus is at (h, k + p).

we have

h=1

k=-4

p=1/4

substitute

F(1,-4+1/4)

F(1,-3.75)

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3 years ago
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