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Vlad [161]
3 years ago
14

How many real solutions does this system of equations have? xy = 9 y = 3x - 1

Mathematics
1 answer:
tekilochka [14]3 years ago
6 0

Answer:

two real, unequal roots

Step-by-step explanation:

y is definied as y = 3x - 1.  Substitute 3x - 1 for y in xy = 9, obtaining:

x(3x - 1) = 9.  Then:

3x^2 - x - 9 = 0.  In this quadratic, the coefficients are a = 3, b = -1 and c = -9.

Calculating the discriminant b^2 - 4ac, we get (-1)^2 - 4(3)(-9), or 1 + 108, or 109.  Because the discriminant is positive, we have two real, unequal roots.

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aniked [119]
The difference is 6. Each number increases by 6 in the sequence.
2 + 6 = 8
8 + 6 = 14
14 + 6 = 20
20 + 6 = 26
Etc.
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6 0
2 years ago
Read 2 more answers
A cashier has 26 bills consisting of three times as many ones as fives, one less ten than fives, and the rest twenties. If the v
monitta
Let number of  fives = x then number of ones = 3x  and number of tens = x - 1

so we can create the equation 

x + 3x +  x-1 + y = 26  where y = number of twenties
so
5x + y = 27

also we have the equation 

5x + 3x + 10(x - 1) + 20y = 120

18x + 20y = 130..................................(1)
5x    + y    = 27     multiply  by -20:-
-100x - 20y = -540..............................(2)
Adding equation (1) and (2)
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Now plug x = 5 into equation 1:-
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3 years ago
Change 5 5/16 into a decimal and show work
Alex Ar [27]

to convert a fraction to a decimal, like say a/b is really simply the quotient of a ÷ b.


now, let's first convert the mixed fraction to improper, and then do the division.


\bf \stackrel{mixed}{5\frac{5}{16}}\implies \cfrac{5\cdot 16+5}{16}\implies \stackrel{improper}{\cfrac{85}{16}}\\\\[-0.35em] \rule{31em}{0.25pt}\\\\ \cfrac{85}{16}\implies 85\div 16\implies 5.3125

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Simplify the expression using the order of operations. 10^2/4 x 3
Setler [38]

Answer:

10^2 is exponent so do it first - 100

100/4=25

25x3=75

75

Parentheses

Exponents

Multiply - Multiply and Divide are interchangeable

Divide

Add - Adding and subtracting are interchangeable

Subtract

Step-by-step explanation:

6 0
2 years ago
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