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
DanielleElmas [232]
3 years ago
5

Match each equation with its solution set.

Mathematics
1 answer:
____ [38]3 years ago
3 0

Answer:

Part 1) a^{2} -9a+14=0 -----> solution set {7,2}

Part 2) a^{2} +9a+14=0 -----> solution set {-2,-7}

Part 3) a^{2} +3a-10=0  -----> solution set {2,-5}

Part 4) a^{2} +5a-14=0   ----> solution set {2,-7}

Part 5) a^{2} -5a-14=0 ----> solution set {-2,7}

Step-by-step explanation:

we know that

The formula to solve a quadratic equation of the form

ax^{2} +bx+c=0

is equal to

x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}

Part 1)

in this problem we have

a^{2} -9a+14=0  

so

a=1\\b=-9\\c=14

substitute in the formula

a=\frac{9(+/-)\sqrt{-9^{2}-4(1)(14)}} {2(1)}

a=\frac{9(+/-)\sqrt{25}} {2}

a=\frac{9(+/-)5} {2}

a=\frac{9(+)5} {2}=7

a=\frac{9(-)5} {2}=2

The solution set is {7,2}

Part 2)

in this problem we have

a^{2} +9a+14=0  

so

a=1\\b=9\\c=14

substitute in the formula

a=\frac{-9(+/-)\sqrt{9^{2}-4(1)(14)}} {2(1)}

a=\frac{-9(+/-)\sqrt{25}} {2}

a=\frac{-9(+/-)5} {2}

a=\frac{-9(+)5} {2}=-2

a=\frac{-9(-)5} {2}=-7

The solution set is {-2,-7}

Part 3)

in this problem we have

a^{2} +3a-10=0  

so

a=1\\b=3\\c=-10

substitute in the formula

a=\frac{-3(+/-)\sqrt{3^{2}-4(1)(-10)}} {2(1)}

a=\frac{-3(+/-)\sqrt{49}} {2}

a=\frac{-3(+/-)7} {2}

a=\frac{-3(+)7} {2}=2

a=\frac{-3(-)7} {2}=-5

The solution set is {2,-5}

Part 4)

in this problem we have

a^{2} +5a-14=0  

so

a=1\\b=5\\c=-14

substitute in the formula

a=\frac{-5(+/-)\sqrt{5^{2}-4(1)(-14)}} {2(1)}

a=\frac{-5(+/-)\sqrt{81}} {2}

a=\frac{-5(+/-)9} {2}

a=\frac{-5(+)9} {2}=2

a=\frac{-5(-)9} {2}=-7

The solution set is {2,-7}

Part 5)

in this problem we have

a^{2} -5a-14=0  

so

a=1\\b=-5\\c=-14

substitute in the formula

a=\frac{5(+/-)\sqrt{-5^{2}-4(1)(-14)}} {2(1)}

a=\frac{5(+/-)\sqrt{81}} {2}

a=\frac{5(+/-)\sqrt{81}} {2}

a=\frac{5(+)9} {2}=7

a=\frac{5(-)9} {2}=-2

The solution set is {-2,7}

You might be interested in
Evaluate each absolute value expression below | 2 | + | 4 | | − 3 | + | 5 | | − 7 | + | − 1 | − | 6 |
Bingel [31]

Answer:

  44

Step-by-step explanation:

The absolute value symbols turn any negative inside of them to a positive, so your expression is ...

  2 + 4·3 +5·7 +1 -6

  = 2 +12 +35 +1 -6

  = 44

4 0
3 years ago
I needed help but then i found the answer
Alenkinab [10]

1/2 × 5 2/3 × 3 = 5

the 2's cancel giving you 5 × 1/3 × 3

then the 3's cancel giving you 5 × 1

and 5 × 1 is 5.

4 0
3 years ago
What percent of discount should be given in a doll costing Rs 180
wolverine [178]

Answer:

11.11%

Step-by-step explanation:

So the question is:

$180 * (x)% = $y

Therefore $180 - $y = $160

Now:

180 - 160 = 20

Therefore; $20 is the discount

Now per cent of discount:

20/180 * 100 = 11.111111111111111111111%

therefore: per cent of discount is 11.11% (rounded to two decimal place)

3 0
3 years ago
Read 2 more answers
What is the area of the obtuse triangle below?
kolezko [41]

Answer:

198

Step-by-step explanation:

just multiply 22 by 8

8 0
3 years ago
A cookie recipe calls for 1/4 cup of brown sugar for one batch of 24 cookies. How many cups of brown sugar would be needed to ba
mixer [17]

Answer:1 1/2

Step-by-step explanation:trust me bro

7 0
3 years ago
Read 2 more answers
Other questions:
  • HELP PLEASE‼️‼️ the questions are on the photo
    9·1 answer
  • 7x²x + 3x3 – 2x²(x² + 2x - 1)​
    15·1 answer
  • Alfred made 21 goals in 3.5 minutes. What is the unit rate?
    5·2 answers
  • The temperature has been going down at a constant rate. In 3 hours it went down 15 degrees. Which expression best shows the temp
    6·2 answers
  • −3(2x+7)=12x<br> what is x?
    9·2 answers
  • A mobile company manufactured 2000 mobiles in the 5th month and 2750 mobiles in the 8th month. Assuming that the production incr
    15·1 answer
  • 6 is the ______ root of 36​
    9·2 answers
  • Hiiiiiiiiiiiiii there
    14·1 answer
  • Am I correct? If not which of the answers is correct?
    10·1 answer
  • Marlene is trying to estimate v 42. She uses this table of values:
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!