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
slega [8]
2 years ago
7

The graph shows the amount of gas that Dario's car uses to travel different distances.

Mathematics
1 answer:
sergeinik [125]2 years ago
8 0
It’s a graph that provides information
You might be interested in
Find the partial fraction decomposition of the rational expression with prime quadratic factors in the denominator
SpyIntel [72]
\dfrac{5x^4-7x^3-12x^2+6x+21}{(x-3)(x^2-2)^2}=\dfrac{a_1}{x-3}+\dfrac{a_2x+a_3}{x^2-2}+\dfrac{a_4x+a_5}{(x^2-2)^2}
\implies 5x^4-7x^3-12x^2+6x+21=a_1(x^2-2)^2+(a_2x+a_3)(x-3)(x^2-2)+(a_4x+a_5)(x-3)

When x=3, you're left with

147=49a_1\implies a_1=\dfrac{147}{49}=3

When x=\sqrt2 or x=-\sqrt2, you're left with

\begin{cases}17-8\sqrt2=(\sqrt2a_4+a_5)(\sqrt2-3)&\text{for }x=\sqrt2\\17+8\sqrt2=(-\sqrt2a_4+a_5)(-\sqrt2-3)\end{cases}\implies\begin{cases}-5+\sqrt2=\sqrt2a_4+a_5\\-5-\sqrt2=-\sqrt2a_4+a_5\end{cases}

Adding the two equations together gives -10=2a_5, or a_5=-5. Subtracting them gives 2\sqrt2=2\sqrt2a_4, a_4=1.

Now, you have

5x^4-7x^3-12x^2+6x+21=3(x^2-2)^2+(a_2x+a_3)(x-3)(x^2-2)+(x-5)(x-3)
5x^4-7x^3-12x^2+6x+21=3x^4-11x^2-8x+27+(a_2x+a_3)(x-3)(x^2-2)
2x^4-7x^3-x^2+14x-6=(a_2x+a_3)(x-3)(x^2-2)

By just examining the leading and lagging (first and last) terms that would be obtained by expanding the right side, and matching these with the terms on the left side, you would see that a_2x^4=2x^4 and a_3(-3)(-2)=6a_3=-6. These alone tell you that you must have a_2=2 and a_3=-1.

So the partial fraction decomposition is

\dfrac3{x-3}+\dfrac{2x-1}{x^2-2}+\dfrac{x-5}{(x^2-2)^2}
7 0
3 years ago
Which experiment describes a binomial experiment?
marshall27 [118]
Answer: the last option.
A binomial experiment is an experiment with only two possible outcomes.

In the first option, there is three possible outcomes (i.e. A, B, C)
In the second option, there is four poissible outcomes (i.e. ace, king, queen, jack)
The third option has six possible outcomes (i.e. six faces of a die)
In the last option, there are two possible outcomes (i.e. '2 number cubes')
6 0
3 years ago
Ab (3a-5b) equals to?
Aleks04 [339]

Answer:

3a^2b-5ab^2

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
You buy tomatoes in 25-pound cases.
julsineya [31]
For a single 25 pound case you can make 133 servings, As a single pound of tomatoes equals 16 ounces; and 16x25 is 400, and when you divide that be 3 it turns into 133.3333333- and goes on, but you round that down to 133 for your answer.
6 0
3 years ago
What expression is equivalent to (5z^2+3z+2)^2
statuscvo [17]
The answer is, 25z^4+30z^3+29z^2+12z+4
Or z(z(z(25z+30)+29)+12)+4
6 0
2 years ago
Other questions:
  • Lila makes bags of stickers that are exactly the same for 5 friends. She uses a total of 45 stickers. Each bag has 2 butterfly s
    5·1 answer
  • A prism has total surface area of 360 m2 and volume of 60 m3.
    10·2 answers
  • What is the inverse of the function f(x) = 2x + 1?
    6·2 answers
  • Another one i need help with
    8·1 answer
  • Nadia has £5 to buy pencils and rulers. Pencils are 8p each. Rulers are 30p each. She says “I will buy 15 pencils. Then I will b
    7·1 answer
  • H.<br> 1.<br> 9<br> 2 8 8<br> 6<br> 3 3<br> 64<br> 37
    5·1 answer
  • Find the inverse of the following function. A. B. C. D.
    5·2 answers
  • Unit 7 polynomials and factoring homework 7 factoring trinomials answer key
    7·1 answer
  • What is 0.167 times 180
    6·2 answers
  • Sam has $372 and Mark has $12.26. What is the difference? Who has more?
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!