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
Vedmedyk [2.9K]
3 years ago
7

Type the correct answer in each box. Use numerals instead of words.

Mathematics
2 answers:
balu736 [363]3 years ago
5 0

Answer:

System A has 2 real solutions.

System B has 0 real solutions.

System C has 1 real solutions.

Step-by-step explanation:

If the graph of system of equation intersect each other at n points then the system of equation has n real solutions.

System A:

x^2+y^2=17               .... (1)

y=-\frac{1}{2}x             .... (2)

Plot the graph of these equations.

From graph (1) it is clear that the graph of equation (1) and (2), intersect each other at two points, (-3.688,1.844) and (3.688,-1.844).

Therefore, System A has two real solutions.

System B:

y=x^2-7x+10               .... (3)

y=-6x+5             .... (4)

Plot the graph of these equations.

From graph (2) it is clear that the graph of equation (3) and (4), never intersect each other.

Therefore, System B has 0 real solutions.

System C:

y=-2x^2+9               .... (5)

8x-y=-17             .... (6)

Plot the graph of these equations.

From graph (3) it is clear that the graph of equation (5) and (6), intersect each other at one points, (-2,1).

Therefore, System C has 1 real solutions.

lubasha [3.4K]3 years ago
4 0

Answer:

System A has 4 real solutions.

System B has 0 real solutions.

System C has 2 real solutions

Step-by-step explanation:

System A:

x^2 + y^2 = 17   eq(1)

y = -1/2x            eq(2)

Putting value of y in eq(1)

x^2 +(-1/2x)^2 = 17

x^2 + 1/4x^2 = 17

5x^2/4 -17 =0

Using quadratic formula:

x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

a = 5/4, b =0 and c = -17

x=\frac{-(0)\pm\sqrt{(0)^2-4(5/4)(-17)}}{2(5/4)}\\x=\frac{0\pm\sqrt{85}}{5/2}\\x=\frac{\pm\sqrt{85}}{5/2}\\x=\frac{\pm2\sqrt{85}}{5}

Finding value of y:

y = -1/2x

y=-1/2(\frac{\pm2\sqrt{85}}{5})

y=\frac{\pm\sqrt{85}}{5}

System A has 4 real solutions.

System B

y = x^2 -7x + 10    eq(1)

y = -6x + 5            eq(2)

Putting value of y of eq(2) in eq(1)

-6x + 5 = x^2 -7x + 10

=> x^2 -7x +6x +10 -5 = 0

x^2 -x +5 = 0

Using quadratic formula:

x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

a= 1, b =-1 and c =5

x=\frac{-(-1)\pm\sqrt{(-1)^2-4(1)(5)}}{2(1)}\\x=\frac{1\pm\sqrt{1-20}}{2}\\x=\frac{1\pm\sqrt{-19}}{2}\\x=\frac{1\pm\sqrt{19}i}{2}

Finding value of y:

y = -6x + 5

y = -6(\frac{1\pm\sqrt{19}i}{2})+5

Since terms containing i are complex numbers, so System B has no real solutions.

System B has 0 real solutions.

System C

y = -2x^2 + 9    eq(1)

8x - y = -17        eq(2)

Putting value of y in eq(2)

8x - (-2x^2+9) = -17

8x +2x^2-9 +17 = 0

2x^2 + 8x + 8 = 0

2x^2 +4x + 4x + 8 = 0

2x (x+2) +4 (x+2) = 0

(x+2)(2x+4) =0

x+2 = 0 and 2x + 4 =0

x = -2 and 2x = -4

x =-2 and x = -2

So, x = -2

Now, finding value of y:

8x - y = -17    

8(-2) - y = -17    

-16 -y = -17

-y = -17 + 16

-y = -1

y = 1

So, x= -2 and y = 1

System C has 2 real solutions

You might be interested in
?????????????????????????????
nadya68 [22]

Answer:3,7,8,2

Step-by-step explanation:I did this question last night

6 0
2 years ago
Read 2 more answers
BERE
inna [77]

Answer:

  • 2

Step-by-step explanation:

<u>The slope is the ratio of difference of y- coordinates by the difference of x- coordinates:</u>

  • m = 6/3 = 2

3 0
2 years ago
Read 2 more answers
For the function f(x) = - 3x + 7 f(- 8) = _<br> f(-8) = (Simplify your answer)
kodGreya [7K]
31

just substitute -8 for all x

process here:

f(x) = -3x + 7
f(-8)= -3(-8) + 7
3 0
2 years ago
What contribution to geometry is attributed to the work of rene descartes
Verizon [17]

Answer: Analytic geometry

7 0
2 years ago
5+b=25<br> b=20<br> 5+20=25<br> =?
Arisa [49]
The numbers are equal. 25=25
4 0
3 years ago
Read 2 more answers
Other questions:
  • Simplify 9 to the 2nd over 9 to the 7th. 95 1 over 9 to the 9th 1 over 9 to the negative 5th 1 over 9 to the 5th
    8·1 answer
  • (See Image Attachment) Please explain how you got the answer. Thanks.
    5·1 answer
  • You are picking up lumber at a lumber yard for a construction project. In addition to the ten (10) boards you already have, you
    11·2 answers
  • Seven less than twice a number is -19
    5·2 answers
  • What are 4 equivalent fractions for 1/4
    14·2 answers
  • Suppose that your mom gives you $20 to go to the school supplies store. there is a 6% sales tax on supplies. you need to buy the
    15·1 answer
  • Circle the digit in the ones place. Then write even or odd. 36 is?
    5·2 answers
  • Cameron eats 1/4 of a pie. Amy eats 1/2 of what is left. How much of the pie is remaining
    6·1 answer
  • The width of a rectangular sandbox is two less than twice the length. The perimeter of the sandbox is 26 feet. Identify the leng
    15·2 answers
  • How do I Solve this pls help
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!