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
katovenus [111]
3 years ago
11

Part 1

Mathematics
1 answer:
svetlana [45]3 years ago
8 0

Answer:

A: This polynomial has a degree of 2 , so the equation 12x2+5x−2=0 has two or fewer roots.

B: The quadratic equation 12x2+5x−2=0 has two real solutions, x=−2/3 or x=1/4 , and therefore has two real roots.

Step-by-step explanation:

f(x) = 12x^2 + 5x - 2.

Since this is a quadratic equation, or a polynomial of second degree, one can easily conclude that this equation will have at most 2 roots. At most 2 roots mean that the function can have either 2 roots at maximum or less than 2 roots. Therefore, in the A category, 2nd option is the correct answer (This polynomial has a degree of 2 , so the equation 12x^2 + 5x − 2 = 0 has two or fewer roots).

To find the roots of f(x), set f(x) = 0. Therefore:

12x^2 + 5x - 2 = 0. Solving the question using the mid term breaking method shows that 12*2=24. The factors of 24 whose difference is 5 are 8 and 3. Therefore:

12x^2 + 8x - 3x - 2 = 0.

4x(3x + 2) -1(3x+2) = 0.

(4x-1)(3x+2) = 0.

4x-1 = 0 or 3x+2 = 0.

x = 1/4 or x = -2/3.

It can be seen that f(x) has two distinct real roots. Therefore, in the B category, 1st Option is the correct answer (The quadratic equation 12x2+5x−2=0 has two real solutions, x=−2/3 or x=1/4 , and therefore has two real roots)!!!

You might be interested in
Joe needs to buy supplies for a birthday party. At the store, balloons cost $0.50 each and party hats each cost $1.25. If Joe wa
VladimirAG [237]

Answer:

0.50b+1.25h=20

Step-by-step explanation:

Let b be the number of balloons and h be number of party hats.

We have been given that balloons cost $0.50 each, so cost of b balloons will be 0.50b.

We are also told that party hats each cost $1.25, so cost of h party hats will be 1.25h.

Further, Joe wants to spend exactly $20 on the party supplies. We can represent this information in an equation as:

0.50b+1.25h=20

Therefore, the equation 0.50b+1.25h=20 represents the number of balloons ( b) and the number of party hats ( h) that Joe can buy spending exactly $20.

5 0
3 years ago
Henry and Natalie are writing a comic book. Henry writes 12 pages for the comic book, and Natalie writes 16 pages. They want to
Triss [41]

answer: 1736

Step-by-step explanation: big brain

8 0
2 years ago
Read 2 more answers
Use distributive property to rewrite 10(5+14-3)
Allisa [31]
(10x5)+(10x14)+(10x-3)
50+140-30
160
7 0
3 years ago
Three years ago, Ava lent her sister $400 to buy some clothes. Today Ava’s sister paid her loan in full with $454. What simple a
Ostrovityanka [42]
Ava's sister paid a 4.5% annual interest rate

Her sister paid $54 more than she borrowed, divide that by 3 (years till she paid)

54/3 = 18

That's $18 for every year she'd had the $400 loan out, divide it by 4 to get the percentage 

18/4 = 4.5/100 = 4.5%
5 0
3 years ago
Read 2 more answers
The Carter Motor Company claims that its new sedan, the Libra, will average better than 31 miles per gallon in the city. Assumin
Nutka1998 [239]

Answer:

The null hypothesis   H_o :  \mu =  31

The alternative hypothesis H_a :  \mu >  31

Step-by-step explanation:

From the question we are told that

  The population mean is  \mu =  31 \  miles / gallon

Generally

   The null hypothesis is that the company's  new sedan, the Libra, will have an average of   \mu =  31 \  miles / gallon

This mathematically  represented as

The null hypothesis   H_o :  \mu =  31

   The alternative hypothesis is that the company's  new sedan, the Libra, will have an average better than   \mu =  31 \  miles / gallon

This mathematically  represented as

     The alternative hypothesis H_a :  \mu >  31

7 0
3 years ago
Other questions:
  • Write 2.2 as a fraction
    8·2 answers
  • A sequence can be defined by the explicit formula <img src="https://tex.z-dn.net/?f=a_n%3D5-3_n" id="TexFormula1" title="a_n=5-3
    5·1 answer
  • LOAD WEB FONTLOAD WEB FONT LOAD WEB FONT LOAD WEB FONT
    6·2 answers
  • jacks car used 18 gallons of gasoline to go for 68 miles at that rate how many gallons would be used to go 754 miles
    14·1 answer
  • Can someone please help me with this problem<br>​
    12·1 answer
  • What is 7 1/2 - 4 1/4
    11·2 answers
  • What is the inequality to 2w+5&gt;45
    5·1 answer
  • How does starting with a different number change the diagram
    14·1 answer
  • A family went out to eat. The bill is $65.82. The family wants to leave a 20% tip. How much tip will be added on to the cost of
    5·1 answer
  • Triangle DEF has angles that measure
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!