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
Zanzabum
3 years ago
14

Using a graphing utility, find the exact solutions of the system. Round to the nearest hundredth and choose a solution to the sy

stem from the choices below.
y = x² + 3x
y = 2x + 5

(0,4)
(2.79, 0.58)
(1.79, 8.58)
(-0.58, -2.79)

Mathematics
1 answer:
Margaret [11]3 years ago
6 0

Answer:

Part 1) The exact solutions are

(\frac{-1+\sqrt{21}} {2},4+\sqrt{21})   and  (\frac{-1-\sqrt{21}} {2},4-\sqrt{21})

Part 2) (1.79, 8.58)

Step-by-step explanation:

we have

y=x^{2} +3x ----> equation A

y=2x+5 ----> equation B

we know that

When solving the system of equations by graphing, the solution of the system is the intersection points both graphs

<em>Find the exact solutions of the system</em>

equate equation A and equation B

x^{2} +3x=2x+5\\x^{2} +3x-2x-5=0\\x^{2} +x-5=0

The formula to solve a quadratic equation of the form

ax^{2} +bx+c=0

is equal to

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

in this problem we have

x^{2} +x-5=0  

so

a=1\\b=1\\c=-5

substitute in the formula

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

x=\frac{-1\pm\sqrt{21}} {2}

so

The solutions are

x_1=\frac{-1+\sqrt{21}} {2}

x_2=\frac{-1-\sqrt{21}} {2}

<em>Find the values of y</em>

<em>First solution</em>

For x_1=\frac{-1+\sqrt{21}} {2}

y=2(\frac{-1+\sqrt{21}} {2})+5

y=-1+\sqrt{21}+5\\\\y=4+\sqrt{21}

The first solution is the point (\frac{-1+\sqrt{21}} {2},4+\sqrt{21})

<em>Second solution</em>

For x_2=\frac{-1-\sqrt{21}} {2}

y=2(\frac{-1-\sqrt{21}} {2})+5

y=-1-\sqrt{21}+5\\\\y=4-\sqrt{21}

The second solution is the point (\frac{-1-\sqrt{21}} {2},4-\sqrt{21})

Round to the nearest hundredth

<em>First solution </em>

(\frac{-1+\sqrt{21}} {2},4+\sqrt{21}) -----> (1.79,8.58)

(\frac{-1-\sqrt{21}} {2},4-\sqrt{21}) -----> (-2.79,-0.58)

see the attached figure to better understand the problem

You might be interested in
Hey box measures 4" x 8" x 3 / 4 inches find the volume<br><br><br> The volume is blank in3
Maslowich
4*8*(3/4)=3*8=24
the volume is 24.
6 0
3 years ago
How many solutions does the equation have? 0 = -8q + 8q
lawyer [7]
Zeroooo solutions bc i did it earlier
7 0
3 years ago
Read 2 more answers
Explain how you can find 4 times 754 using two different methods.
ludmilkaskok [199]
Method 1:

4(754)

=4(700+50+4)

=2800 + 200 + 16

=3000+16

=3016

-----------------

Method 2:

4(754)

=4(250+250+250+4)

=1000+1000+1000+16

=3016
3 0
3 years ago
Read 2 more answers
Daja is packing her backpack for school. Her textbook weighs 1 ¼ pounds. Her notebooks weigh ¼ pound. Her other supplies weigh ¾
Shalnov [3]

Answer:

2 1/4 or 2.25

Step-by-step explanation:

1 1/4 + 1/4 = 1 2/4

1 2/4 + 3/4 = 2 1/4

6 0
2 years ago
Read 2 more answers
What is the reciprocal of 3/4
Alex73 [517]
The reciprocal of 3/4 is 4/3
5 0
3 years ago
Read 2 more answers
Other questions:
  • The sales tax on a used car is​ $174​, and the sales tax rate is 5​%. Find the purchase price ​(the price before taxes are​ adde
    10·1 answer
  • A dress is on sale for ​$172. What was the original price of the dress if the discount was 1/5 of the original​ price?
    7·1 answer
  • Mr. and Mrs ------ Have a number of children. if 0.83 of the childern are male, what is the least possible number of people in t
    14·1 answer
  • Find x.<br> U<br> X<br> T<br> N 14<br> 49<br> X=<br> I will make you brainlest
    6·2 answers
  • If you can explain it best, and answer them you'll get a brainliest
    10·2 answers
  • In circle Q with the measure of minor arc PR= 48°, find mZPSR.<br> S<br> A<br> R<br> р P.
    14·1 answer
  • Simplify i^7/i x i^3<br><br><br> A. i^4<br> B.i^11<br> C.i^3<br> D. 1
    8·2 answers
  • What is the angle that corresponds to the angle abc​
    7·1 answer
  • Funke gets #2.50 as pocket money. She spends 75 k and saves the rest. What is the ratio of her savings to the amount she spends?
    9·1 answer
  • Could some give the answers AND a good explanation
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!