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Komok [63]
2 years ago
13

In ∆ABC, Angle A is 4 times angle B. and angle C is 5 times that of angle B Find the measure of each angle.​

Mathematics
1 answer:
Liula [17]2 years ago
3 0

Step-by-step explanation:

Let angle b be x

Let angle a be 4x

Let angle c be 5x

Then,

      4x+x+5x=180(sum of angle of a triangle is 180)

   or,10x=180

   or,x=180/10

      x=18

angle a=4x=4*18=72

angle b=18

angle c=5x=5*18=90

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X - 3y +3=0
Arte-miy333 [17]

Answer:

We know that for a line:

y = a*x + b

where a is the slope and b is the y-intercept.

Any line with a slope equal to -(1/a) will be perpendicular to the one above.

So here we start with the line:

3x + 4y + 5 = 0

let's rewrite this as:

4y = -3x - 5

y = -(3/4)*x - (5/4)

So a line perpendicular to this one, has a slope equal to:

- (-4/3) = (4/3)

So the perpendicular line will be something like:

y = (4/3)*x + c

We know that this line passes through the point (a, 3)

this means that, when x = a, y must be equal to 3.

Replacing these in the above line equation, we get:

3 = (4/3)*a + c

c = 3 - (4/3)*a

Then the equation for our line is:

y = (4/3)*x + 3 - (4/3)*a

We can rewrite this as:

y = (4/3)*(x -a) + 3

now we need to find the point where this line ( y = -(3/4)*x - (5/4)) and the original line intersect.

We can find this by solving:

(4/3)*(x -a) + 3 =  y = -(3/4)*x - (5/4)

(4/3)*(x -a) + 3  = -(3/4)*x - (5/4)

(4/3)*x - (3/4)*x = -(4/3)*a - 3 - (5/4)

(16/12)*x - (9/12)*x = -(4/3)*a - 12/4 - 5/4

(7/12)*x = -(4/13)*a - 17/4

x = (-(4/13)*a - 17/4)*(12/7) = - (48/91)*a - 51/7

And the y-value is given by inputin this in any of the two lines, for example with the first one we get:

y =  -(3/4)*(- (48/91)*a - 51/7) - (5/4)

  = (36/91)*a + (153/28) - 5/4

Then the intersection point is:

( - (48/91)*a - 51/7,  (36/91)*a + (153/28) - 5/4)

And we want that the distance between this point, and our original point (3, a) to be equal to 4.

Remember that the distance between two points (a, b) and (c, d) is:

distance = √( (a - c)^2 + (b - d)^2)

So here, the distance between (a, 3) and ( - (48/91)*a - 51/7,  (36/91)*a + (153/28) - 5/4) is 4

4 = √( (a + (48/91)*a + 51/7)^2 + (3 -  (36/91)*a + (153/28) - 5/4 )^2)

If we square both sides, we get:

4^2 = 16 =  (a + (48/91)*a + 51/7)^2 + (3 -  (36/91)*a - (153/28) + 5/4 )^2)

Now we need to solve this for a.

16 = (a*(1 + 48/91)  + 51/7)^2 + ( -(36/91)*a  + 3 - 5/4 + (153/28) )^2

16 = ( a*(139/91) + 51/7)^2 + ( -(36/91)*a  - (43/28) )^2

16 = a^2*(139/91)^2 + 2*a*(139/91)*51/7 + (51/7)^2 +  a^2*(36/91)^2 + 2*(36/91)*a*(43/28) + (43/28)^2

16 = a^2*( (139/91)^2 + (36/91)^2) + a*( 2*(139/91)*51/7 + 2*(36/91)*(43/28)) +  (51/7)^2 + (43/28)^2

At this point we can see that this is really messy, so let's start solving these fractions.

16 = (2.49)*a^2 + a*(23.47) + 55.44

0 = (2.49)*a^2 + a*(23.47) + 55.44 - 16

0 = (2.49)*a^2 + a*(23.47) + 39.44

Now we can use the Bhaskara's formula for quadratic equations, the two solutions will be:

a = \frac{-23.47  \pm  \sqrt{23.47^2 - 4*2.49*39.4}  }{2*2.49} \\\\a =  \frac{-23.47  \pm  12.57 }{4.98}

Then the two possible values of a are:

a = (-23.47 + 12.57)/4.98  = -2.19

a = (-23.47 - 12.57)/4.98 = -7.23

4 0
2 years ago
There are 100 teachers in a school. 60 teach science, 25 teach humanities, 15 teach both science and humanities. Find the number
UkoKoshka [18]

Answer:

15

Step-by-step explanation:

The total number of teachers in the school is 100.

The number who teach Science is 60

The who teach humanities is 25.

The number that teach both humanities and Science is 15.

We want to find the number who teach Science but not Humanities.

We obtain this by subtracting the number of teachers who teach both subjects from the number that teach Science.

= 60 - 15 = 45

Therefore 25 teaches science but not Humanities

8 0
3 years ago
helppppp please James has $32 and earns $10 per week for his allowance. What is the initial value for the scenario described? (4
telo118 [61]

Answer:

Anwser is **42** Because if you add 32 and 10 you end up with 42

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
The instructions on your aspirin bottle say take two 200-milligram aspirin. How many grams is the total dose?
REY [17]

Answer:

[see below]

Step-by-step explanation:

There are 0.001 grams in a milligram. (1,000 milligrams in a gram.)

\frac{200}{1000}=0.2

The total dose should be 0.2 grams.

Hope this helps.

7 0
2 years ago
How would I solve for the area of this triangle? Please help
Lyrx [107]
You would solve it by multiplying the sides of the triangle
4 0
2 years ago
Read 2 more answers
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