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kolbaska11 [484]
3 years ago
9

The measure of the smallest angle of a triangle is ​one-fifthfifth the measure of the largest angle. The measure of the second a

ngle is 51 degrees° less than the measure of the largest angle. Find the measure of the angles of the triangle
Mathematics
1 answer:
Shtirlitz [24]3 years ago
7 0

Answer:

Largest angle is 105°

Smallest angle is 21°

The second angle is 54°

Step-by-step explanation:

Let the largest angle be x°

The smallest angle will be 1/5x°

The second angle will be x° - 51°

Angles in a triangle add up to 180° so;

x + x - 51 + 1/5x = 180

11/5x = 180 + 51 , 11/5x = 231 , x = 105°

Smallest angle is 1/5 × 105 = 21°

The second angle is 105 - 51 = 54°

You might be interested in
How do you do this problem?
umka2103 [35]

Answer:

Step-by-step explanation:

You are going to work entirely on the right, until you can compare what is on the right with what you are given on the left.

a/1 + b/(x + 2) + c/(x - 8)

The first step is to determine the common denominator which is

(x + 2)(x - 8)

Now put each fraction over the common denominator.

<u>a(x + 2)(x - 8) + b(x - 8) + c(x + 2)</u>

             (x + 2)(x - 8)

The denominators on the left and right are the same, so you need only work with the numerators.

Remove the brackets.

a(x^2 - 6x - 16) + bx - 8b + cx + 2c

ax^2 - 6ax - 16a + bx - 8b + cx + 2c

In that whole expression, there is only 1 term that has an x^2 in it and that is the very first term.

a = 2 when you compare it to the left. You do this so you can get a value for  a.

Now put a = 2 in the first three terms on the expression above

2x^2 - 6*2x - 16(2) + bx - 8b + cx + 2c

2x^2 - 12x - 32 + bx - 8b + cx + 2c

The next thing is to get all the terms containing x together.

-12x + bx + cx = - 14x That's the term on the left (-14x). Divide by x

-12 + b + c = - 14          Add 12 to both sides

b + c = -14 + 12

b + c = - 2                    (x)

======================

Now you equate the terms with no x's in them.

-32 - 8b + 2c = - 76      Add 32 to both sides.

-8b + 2c = - 76 + 32

-8b + 2c = - 44             Divide by 2

-4b + c = - 22               (y)

Subtract (y) - (x)

-4b + c = - 22

 <u> b + c = - 2</u>

- 5b = - 20                   Divide by - 5

-5b/-5 = - 20/-5

b = 4

==============

b + c = - 2                     Find c substitute b = 4

4 + c = - 2                     Subtract 4 from both sides

c = - 2 - 4

c = - 6      

===============  

Answer

a = 2

b = 4

c = -6

6 0
3 years ago
Please help will mark Brainly
SIZIF [17.4K]

The solutions of the equation 3x - y = 1 are (-2,-7),(-1,-4) and (3,8) thus option (A),(B) and (D) are correct.

<h3>What is the equation?</h3>

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

In another word, the equation must be constrained with some constraints.

As per the given equation,

3x - y = 1

Substitute, x = -2

3(-2) - y = 1

y = -7 thus  (-2,-7) satisfied.

Similarly (-1,-4) and (3,8) are also satisfied.

Hence "The solutions of the equation 3x - y = 1 are (-2,-7),(-1,-4) and (3,8)".

For more about the equation,

brainly.com/question/10413253

#SPJ1

7 0
1 year ago
A ride-share company has a fee that includes a fixed cost and a cost that depends on both the time spent travelling, in minutes,
zlopas [31]

Answer:

the cost of Roy's ride is $23.05

Step-by-step explanation:

According to the Question,

Let, Cost of per minute charge is 'x' & Cost Of Per Kilometre charge is y .

  • Given, A ride-share company has a fee of the fixed cost of a ride is $2.55 .
  • And, The Total cost of the Ride depends on both the time spent on travelling(in minutes), and the distance travelled(in kilometres) .

⇒ Judy's ride costs $16.75 . but the actual cost after deducting the fixed charge is 16.75-2.55 = $14.20, took 8 minutes & The distance travelled was 10 km. Thus, the equation for the journey is 8x+10y=14.20 ⇒ Equ. 1

⇒ Pat's ride costs $30.35 . but the actual cost after deducting the fixed charge is 30.35-2.55 = $27.80, took 20 minutes & The distance travelled was 18 km. Thus, the equation for the journey is 20x+18y=27.80 ⇒ Equ. 2

Now, on Solving Equation 1 & 2, We get

x=0.4(Cost of per minute charge) & y=1.1(Cost Of Per Kilometre charge)

Now, Roy's ride took 10 minutes & The distance travelled was 15 km . Thus, the cost of Roy's Ride is 10x+15y ⇔ 10×0.4 + 15×1.1 ⇔ $20.5

Hence, the total cost of Roy's ride is 20.5 + 2.55(fixed cost) = $23.05

8 0
3 years ago
A spinner used in a board game is divided into 12 equally sized sectors. Seven of these sectors indicate that the player should
xeze [42]

Answer:

20.8 inches squared

Step-by-step explanation:

Area of spinner:

45.1 is the area of sectors where the token doesn't move, which 5 sectors doesn't move the token (don't forget that the bonus points doesn't move token). Then

45.1/5=9.02

9.02*12=108.24

K=1/2(r^2)sin150

108.24=1/2(r^2)sin150

216.48=(r^2)1/2

432.96=r^2

r=20.8

7 0
4 years ago
Find the sum of the arithmetic sequence 1, 3, 5, 7, … , 99.
bezimeni [28]

The sum of the arithmetic sequence 1, 3, 5, 7, … , 99 is 2525

<h3>What is Sequence?</h3>

Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

Given sequence is 1, 3, 5, 7, … , 99.

It is a arithmetic sequence, the difference between two consecutive terms will be same

d=3-1=2

first term a=1

l=last term =99

We need to find 99 is which term in the sequence

Aₙ = a + ( n - 1 ) d

99=1+(n-1)2

99=1+2n-2

99=2n-1

100=2n

Divide both sides by 2

50=n

Now we need to find the sum of 50 terms

Sₙ=n/2(l+d)

=50/2(99+2)

=25(101)

=2525

Hence, the sum of the arithmetic sequence 1, 3, 5, 7, … , 99 is 2525

To learn more on Sequence click:

brainly.com/question/21961097

#SPJ1

6 0
1 year ago
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