1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
adell [148]
3 years ago
9

Solve the system by the substitution method. x + y = 2 y= x2 - 6x + 8

Mathematics
1 answer:
ruslelena [56]3 years ago
8 0

Answer:

The solution of the given system is (2,0)

Step-by-step explanation:

Here, the given system of equations is:

x + y = 2    .............. (1)

y= x^2 - 6x +  8  ........  (2)

Now from (1) x = 2 - y

Substitute this value of x = 2- y in (2) ,we get:

y= (2-y)^2 - 6(2-y) +  8\\\implies y = 4 + y^2 - 4y - 12 + 6y + 8\\or, y^2 + y  = 0\\\implies y(y +1) = 0

⇒  y = 0 or,  y = -1

Now, if y = 0, x  = 2

and if x= -1, y = 2-(-1)  = 2+1  = 3, or y = 3

But (x = -1 , y = 3 )is NOT  a solution of (2).

Hence, the solution of the given system is (2,0)

You might be interested in
What number has the same value as 14 tens
tangare [24]
If there are 14 tens, that is 14 multiplied by 10. 14 x 10 = 140.

140 is the answer.

Hope this helps :)
8 0
3 years ago
A researcher drilled a hole in a die and filled it with a lead​ weight, then proceeded to roll it 209 times. The observed freque
ddd [48]

Answer:

Step-by-step explanation:

Given that the observed frequencies for the outcomes as follows:

To check this we can use chi square goodness of fit test.

H_0: equally likely\\H_a: not equally likely

(Two tailed test at 5% significance level)

Assuming equally likely expected observations are found out and then chi square is calculated as (0-E)^2/E

Df = 6-1 =5

Outcome Frequency Expected frequency (Obs-exp)^2/Exp

   

1 36 34.83333333 0.03907496

2 30 34.83333333 0.670653907

3 41 34.83333333 1.091706539

4 40 34.83333333 0.766347687

5 23 34.83333333 4.019936204

6 39 34.83333333 0.498405104

   

209 209          7.086124402

p value =0.214

Since p >alpha, we accept null hypothesis

It appears that the  loaded die does not behave differently than a fair​ die at 5% level of significance

5 0
3 years ago
How many prime numbers are there in between and 60 20​
ladessa [460]

Answer:

hi how are iwant points bye

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
<img src="https://tex.z-dn.net/?f=%20express%20%5C%3A%20%20%5C%3A%20%5Csin%282x%29%20%20-%20%20%5Csqrt%7B3%7D%20%20%5Ccos%282x%2
gizmo_the_mogwai [7]

Answer:

α = π/3

γ = 2

x = -3π/4, -5π/12, π/4, 7π/12

Step-by-step explanation:

Easiest way to do this is in reverse.

γ sin(2x − α)

Angle sum/difference formula:

γ (cos α sin(2x) − sin α cos(2x))

Distribute:

γ cos α sin(2x) − γ sin α cos(2x)

Matching the coefficients:

γ cos α = 1

γ sin α = √3

Solve the system of equations.  Divide to eliminate γ:

tan α = √3

α is between 0 and π/2, so:

α = π/3

γ = 2

sin(2x) − √3 cos(2x) = 1

Using the identity from before:

2 sin(2x − π/3) = 1

Solving:

sin(2x − π/3) = 1/2

2x − π/3 = π/6 + 2kπ or 5π/6 + 2kπ

2x = π/2 + 2kπ or 7π/6 + 2kπ

x = π/4 + kπ or 7π/12 + kπ

x is between -π and π, so:

x = -3π/4, -5π/12, π/4, 7π/12

7 0
3 years ago
What is the next term if the geometric sequence 192,48,12
VladimirAG [237]

the numbers are being divided by 4 so 12/4 =3

 next number is 3

7 0
3 years ago
Read 2 more answers
Other questions:
  • What's the answer to this question
    9·1 answer
  • Help needed please
    15·1 answer
  • Write an expression equivalent to 8(3/4x-1/4)-6(12-x) using the fewest possible terms.
    15·1 answer
  • PLEASE HELPPPPP PLEASEEEE
    11·1 answer
  • What are the partial products of 434 × 310 to find the product
    8·2 answers
  • Ava borrows $600 to buy a bike at a yearly simple interest
    7·1 answer
  • Milk is delivered to a store every 3 days. Bread is delivered to the store every 5 days. Both were delivered today. How many day
    11·1 answer
  • There’s 2 answer options
    14·1 answer
  • D
    10·1 answer
  • 2500 principal earning 4%, compounded quarterly, after 4 years.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!