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
Nadusha1986 [10]
2 years ago
8

Super urgent can someone help me with this i spent a lot of points and i received a fake answer

Mathematics
1 answer:
Vinvika [58]2 years ago
3 0

Answer:

(a)  3, 2, -3, -7, -12, -18, -25, -33 etc.

(b)  -44, -12, -4, 4, 12, 44

Step-by-step explanation:

<u>Integer</u>: whole numbers (including negatives)

To factor a quadratic in the form ax^2+bx+c

  • Find 2 two numbers (d and e) that multiply to ac and sum to b
  • Rewrite b as the sum of these 2 numbers: d+e=b
  • Factorize the first two terms and the last two terms separately, then factor out the comment term.

<u>Question (a)</u>

Given quadratic:  kx^2+5x+2

\implies a=k, b=5\: \textsf{and}\:c=2

You don't have to do this, but it is helpful to first find the range of k.  To do this, use the discriminant b^2-4ac.

If the quadratic has 2 real roots then b^2-4ac > 0

If the quadratic has 1 real root then b^2-4ac = 0

Therefore, set the discriminant to ≥ 0

\implies 5^2-4(k)(2)\geq 0

\implies 25-8k\geq 0

\implies -8k\geq -25

\implies 8k\leq 25

\implies k\leq 3.125

As k is an integer, k\leq 3

Given quadratic:  kx^2+5x+2

\implies ac=k \cdot 2=2k

\implies d+e=5

So we need to find pairs of numbers that sum to 5 and multiply to a (negative or positive) even number, since ac=2k

2 + 3 = 5  and  2 · 3 = 6   ⇒  2k = 6 ⇒ k = 3

1 + 4 = 5  and  1 · 4 = 4  ⇒  2k = 4 ⇒ k = 2

-1 + 6 = 5  and  -1 · 6 = -6   ⇒  2k = -6 ⇒ k = -3

-2 + 7 = 5  and  -2 · 7 = -14   ⇒  2k = -14 ⇒ k = -7

-3 + 8 = 5  and  -3 · 8 = -24  ⇒  2k = -24 ⇒ k = -12

-4 + 9 = 5  and  -4 · 9 = -36  ⇒  2k = -36 ⇒ k = -18

-5 + 10 = 5  and  -5 · 10 = -50  ⇒  2k = -50 ⇒ k = -25

-6 + 11 = 5  and  -6 · 11 = -66  ⇒  2k = -66 ⇒ k = -33

etc.

Therefore, possible values of k are:

3, 2, -3, -7, -12, -18, -25, -33 etc.

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

<u>Question (b)</u>

Given quadratic:  9x^2+kx-5

\implies a=9, b=k\: \textsf{and}\:c=-5

\implies ac=9 \cdot -5=-45

Find factors of -45:

  • 1 and -45
  • -1 and 45
  • 3 and -15
  • -3 and 15
  • 5 and -9
  • -5 and 9

As a+c=k:

  • 1 + -45 = -44
  • -1 + 45 = 44
  • 3 + -15 = -12
  • -3 + 15 = 12
  • 5 + -9 = -4
  • -5 + 9 = 4

Therefore, all possible values of k are  -44, -12, -4, 4, 12, 44

You might be interested in
Which of the following is the midsegment for A ACE?
11111nata11111 [884]

Answer:

A. DB

Step-by-step explanation:

The line BD is the mid segment because it connects the midpoints of line segment AC and CE

5 0
3 years ago
Write an expression for the situation
MAXImum [283]

Answer:

3b

Step-by-step explanation:

if each brick is 3 inches tall, and there are b bricks, each b is 3, therefore 3b

8 0
3 years ago
Lisa paid 43.95 for 16.1 gallon of gasoline. What was that cost per gallon rounded to the nearest hundredth
djverab [1.8K]

Answer:

2.73

Step-by-step explanation:

It is given that Lisa paid 43.95 for 16.1 gallons of gasoline.

So, the cost of 16.1 gallons of gasoline is 43.95.

Hence, the cost of gasoline per gallon is 43.95/16.1 = 2.7304347.

Now, it is required to round this value to the nearest hundredth.

Therefore, the cost of gasoline per gallon rounded to the nearest hundredth is 2.73. (Answer)

3 0
3 years ago
A family spends 1/3 of its income for the mortgage and 1/6 of its income for food. What proportion of its income remains?
Aloiza [94]

Answer: 1/2

Step-by-step explanation:

1/3 = 2/6 so 2/6 + 1/6 = 3/6

3/6 = 1/2

4 0
2 years ago
Read 2 more answers
A circle has a circumference of 7.85 yards what is the diameter of the well
Vsevolod [243]
2.5 yds
C=2πr
d=2r
Solving ford
d=C
π=7.85
π≈2.
4 0
3 years ago
Other questions:
  • Find the percent change:<br><br> from 80 to 100
    11·1 answer
  • A deck of cards has three yellow cards and five green cards. One green card is drawn from the deck and not replaced. One more ca
    12·2 answers
  • A scout troop is collecting aluminium cans for charity. Their goal is to collect at least the number of cans they collected last
    15·1 answer
  • Alex and leanardo went to the movies a drink cost $4.00 each and a bag of popcorn cost $ 5.00 each how many would they spend of
    15·1 answer
  • 70% of the students applying to a university are accepted. Assume the requirements for a binomial experiment are satisfied for 1
    9·1 answer
  • Change subtraction to addition by adding the
    10·2 answers
  • shalyn went to to the movies. She spent 2/5 of her money on a ticket and 3/7 on popcorn. How much did she spend?
    11·1 answer
  • Assume that the Poisson distribution applies and that the mean number of hurricanes in a certain area is 5.1 per year.
    7·1 answer
  • If 12+15=7 11+14=5 18+25=13 what is 28+36 =?
    11·2 answers
  • Wich number is written in the scientific notation
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!