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In triangle ABC, the measure of angle A is 86 degrees. The measure of angle B is 28 degrees more than three times the measure of angle C. What is the measure, in degrees, of angle C?     

The sum of the interior angles of any triangle is 180^o

so add up the two you know, and subtract that from 180.  

180^o – (86^o + 28^o)  =  66^o the third angle 

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(a²-2)(a²-3)

4(1250-x) = (1490+x)      solve for x

The solutions are $x \in \boxed{[0,2)}$.

1. A + 80 --> 2

    H - 80 --> 1

2. A + 110 --> 3

    H - 110 --> 1

   ----------------------

    A + 80 --> 8

    H - 80 --> 4

    A + 110 --> 9

    H - 110 --> 3

   110 - 80 ÷ 9x - 8x

         30 = 1x

  Total = 12x

          = 12 × 30

          = 360 stamps

R : B+G : T = 5 : 3 : 8 = 35 : 21 : 56

B:G : B+G = 3 : 4 : 7 = 9 : 12 : 21

R:B:G:T = 35 : 9 : 12 : 56

R-G = 35-12 = 23

56×138÷23 = 336

s=3f-24

s+24 = 3f

f = (s+24)/3   = 1/3 s +8

n(n + 1) / 2

900(901)/2 = 405450

none of the above 

CD=8

Slope m, of given line = -2/3        perpindicular slope = - 1/m = 3/2

Point slope form of new line    (y-2) = 3/2 (x+4)    <=====   re-arrange to desired form

(2²)¹⁰ ( 2³)²⁰ (2⁴)³⁰

2²⁰⁰

a =b/c  k       where k  is proportionality constant

ac/b = k

Sub in the values given

  3*9 /5   = 27/5

Sub in the second set of numbers

 4c/3 = 27/5

c = 4.05

h-80 =1/2 (a+80)   

    so    h =1/ 2a +120

then

h-110 = 1/3 (a+110)   

    so    h = 1/3 a + 110/3 + 110

equate the h's

1/2 a+120 = 1/3 a + 110/3 + 110

1/6 a = 110/3 + 110 - 120

a = 160         then    h = 200                   <====== you can add them together

There are   4 x 6 = 24 possible combos of a and b

   the only primes would be   1 * 5     1*7        two out of 24  = 1/12

s/c = 8/5

s = 8/5 c

8/5 c * 20    +     c * 4 = 900

c = 25        then s = 40

If n = 2 (mod 7), find the remainder when (n + 2)(n + 4) is divided by 7.

n==7 + 2 ==9

[9 + 2] * [9 + 4] mod 7 ==[11] * [13] mod 7 ==143 mod 7 ==3 - the remainder.

rate * time = distance

distance / rate = time

The distance Edwyn must ride his steel horse is a constant.

d/10 = (x +1)    d = 10(x+1)

d/15 = (x-1)      d = 15(x-1)           equate the d's

15(x-1) = 10(x+1)

5x = 25

x = 5   hours                         d = 10 ( x+1) = 60 miles

52 members

2x+ 7 = -5   implies x = -6  since this is less than -2 it is a valid solution

-x^2 - x + 1 = -5  can be written as x^2 + x - 6 = 0  which factors as (x-2)(x+3)=0  for which the only solution that is greater than or equal to -2 is x = 2.

Hence the sum of the valid values of x is -6 + 2 = -4

Sorry....I didn't see the ' - ' sign in front of the ' 2 '

-2 ( x^2-9x)     - 15

-2(x - 4.5)²   +  40.5   - 15

-2(x-4,5)²  + 25.5       vertex is at    4.5 , 25,5

Combined, the trains cover ( 80 + 60) = 140 miles per hour

280 miles wil be covered in two hours.....when the trains meet it will be 5:00

See https://web2.0calc.com/questions/please-help_38557#r1

Let Cg = number of girls in Choir club; Cb = number of boys in Choir club

    Rg = number of girls in Robotics club; Rb = number of boys in Robotics club

We are told

Cg = 32

Rg = 19

Cb = Rb*5/7

Cg + Cb = Rg + Rb + 5

Can you take it from here?

Find the base b so that log_b (81)= 1/3.

Hello Guest!

\(log_b (81)= \frac{1}{3}\\ b^{\frac{1}{3}}=81\ |\ power\ of\ 3 \\ b=81^3\)

\(b=531441\)

  !