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
Vadim26 [7]
3 years ago
14

The parabolas defined by the equations y=-x^2-x+1 and y=2x^2-1 intersect at points (a, b) and (c, d), where c>=a. What is c-a

? Express your answer as a common fraction.
Mathematics
1 answer:
Fittoniya [83]3 years ago
3 0

Answer:

c - a = \frac{5}{3}

Step-by-step explanation:

Since the parabolas intersect we can equate them, that is

2x² - 1 = - x² - x + 1 ← subtract terms on right side from terms on left side

3x² + x - 2 = 0

Consider the factors of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 3 × - 2 = - 6 and sum = + 1

The factors are + 3 and - 2

Use these factors to split the x- term

3x² + 3x - 2x - 2 = 0 ( factor the first/second and third/fourth terms )

3x(x + 1) - 2(x + 1) = 0 ← factor out (x + 1) from each term

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

Equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

3x - 2 = 0 ⇒ 3x = 2 ⇒ x = \frac{2}{3}

Since c > a, then

a = - 1 and c = \frac{2}{3}

Thus

c - a = \frac{2}{3} - (- 1) = \frac{2}{3} + 1 = \frac{2}{3} + \frac{3}{3} = \frac{5}{3}

You might be interested in
Two airliners are 1600 miles apart and heading toward each other at different altitudes. The first plane is traveling north at 6
viktelen [127]
In approximately around 2 hours and 10 mins
4 0
3 years ago
Please help thanks ❗​
mojhsa [17]

Answer:

The Two Column Proof is given below.

Step-by-step explanation:

Given:

\overline{MP} \cong \overline{MN}

\overline{PO} \cong \overline{NO}

To Prove:

∠ P ≅ ∠ N

Proof:

In  Δ MPO  and Δ MNO

STATEMENT                                              REASONS  

1. MP ≅ MN                                   1. Given

2. PO ≅ NO                                  2. Given

3. MO ≅ MO                                 3. Reflexive property

4. ΔMPO ≅ ΔMNO                       4. Side-Side-Side congruence test}

5. ∠MPO ≅∠MNO                        5. Corresponding parts of congruent Triangles

i.e ∠ P ≅ ∠ N                                 ..................Proved

3 0
3 years ago
A
LekaFEV [45]

Answer: 31.5 in.

Answer:

the answer is 13 cm

Step-by-step explanation:

3 0
2 years ago
Pumps A, B, and C operate at their respective constant rates. Pumps A and B, operating simultaneously, can fill a certain tank i
jeka94

Let a,b,c be the time it takes for pumps A, B, and C (respectively) to fill 1 tank. Then

\begin{cases}\dfrac1a+\dfrac1b=\dfrac1{\frac65}=\dfrac56\\\\\dfrac1a+\dfrac1c=\dfrac1{\frac32}=\dfrac23\\\\\dfrac1b+\dfrac1c=\dfrac12\end{cases}

Now,

\left(\dfrac1a+\dfrac1b\right)-\left(\dfrac1a+\dfrac1c\right)=\dfrac56-\dfrac23\implies\dfrac1b-\dfrac1c=\dfrac16

Then

\left(\dfrac1b+\dfrac1c\right)+\left(\dfrac1b-\dfrac1c\right)=\dfrac12+\dfrac16\implies\dfrac2b=\dfrac23\implies b=3

This means

\dfrac1a+\dfrac13=\dfrac56\implies\dfrac1a=\dfrac12\implies a=2

and

\dfrac13+\dfrac1c=\dfrac12\implies\dfrac1c=\dfrac16\implies c=6

Working together, all 3 pumps would operate at a rate of

\dfrac1a+\dfrac1b+\dfrac1c=1

or 1 tank in 1 hour, so the answer is D.

8 0
3 years ago
a first class postage stamp was $0.02 in 1885. the same first class postage stamp in 2006 was $0.39. what is the percent of incr
Eddi Din [679]

The price was increased by $0.37 just subtract

5 0
3 years ago
Other questions:
  • Find the slope of line that contains the points (-4,-13) and (8,5).
    12·2 answers
  • A cylindrically shaped space station is rotating about the axis of the cylinder to create artificial gravity. The radius of the
    14·1 answer
  • Please help they’re 2 questions
    11·1 answer
  • Simplify each expression 8x+13-3x+9
    8·1 answer
  • A washer and a dryer cost $800 combined. The washer costs $50 less than the dryer. What is the cost of the dryer?
    9·2 answers
  • Draw and label the final image of △ABC after the given sequence of transformations. Reflect △ABC over the y−axis and then transl
    10·1 answer
  • Pls help me this is due today
    8·2 answers
  • Blank—20.8=41.06 what is it help
    13·1 answer
  • Write the equation of the line that passes<br> through the points (3, 1) and (9,-3)
    15·1 answer
  • Help help help heeeelllpppp
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!