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
SVETLANKA909090 [29]
3 years ago
14

The graph of $y=ax^2+bx+c$ passes through points $(0,5)$, $(1,10)$, and $(2,19)$. Find $a+b+c$.

Mathematics
1 answer:
MAVERICK [17]3 years ago
7 0

Answer:

a+b+c=10

Step-by-step explanation:

We are given that the graph of the equation:

y=ax^2+bx+c

Passes through the three points (0, 5), (1, 10), and (2, 19).

And we want to find the value of (<em>a</em> + <em>b</em> + <em>c</em>).

First, since the graph passes through (0, 5), its <em>y-</em>intercept or <em>c</em> is 5. Hence:

y=ax^2+bx+5

Next, since the graph passes through (1, 10), when <em>x</em> = 1, <em>y</em> = 10. Substitute:

(10)=a(1)^2+b(1)+5

Simplify:

5=a+b

The point (2, 19) tells us that when <em>x</em> = 2, <em>y</em> = 19. Substitute:

(19)=a(2)^2+b(2)+5

Simplify:

14=4a+2b

This yields a system of equations:

\begin{cases} 5 = a + b \\ 14 = 4a + 2b\end{cases}

Solve the system. We can do so using elimination (or any other method you prefer). Multiply the first equation by negative two:

-10=-2a-2b

Add the two equations together:

(-10)+(14)=(-2a+4a)+(-2b+2b)

Combine like terms:

4 = 2a

Hence:

a=2

Using the first equation:

5=(2)+b\Rightarrow b=3

Therefore, our equation is:

y=2x^2+3x+5

Thus, the value of (<em>a</em> + <em>b</em> + <em>c</em>) will be:

a+b+c = (2) + (3) + (5) = 10

You might be interested in
Brent has a $400 console with a credit card that has 25% APR is minimum payment is $10 per month will he pay more and less than
Afina-wow [57]

Answer:

he will pay more

Step-by-step explanation:

in totoal he will pay 413.40 because apr is interest

his interest total will be 13.40$

3 0
2 years ago
How to simplyfy 2x+2x
VladimirAG [237]

Answer:

Your answer is 4x.

Step-by-step explanation:

Add 2+2

Combine your x's (like terms)

then you got 4 from 2+2

Add the leftover x so it makes 4+x then add it will give you 4x.

4 0
2 years ago
Plz help me am being timed right now
artcher [175]

Answer:

11.8 meter below

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
THIRTY FIVE POINTS.
son4ous [18]

Answer: 31500 to 38500

Step-by-step explanation:

Lets find lower limit of guess

35000 - ( 35000 * 10% )

= 31500

Upper limit of guess

35000 + ( 35000 * 10% )

= 38500

So your guess can be anything between these two values.

3 0
3 years ago
working together two mathletes solve 32 math problems in a certain amount of time how many problems will 3 mathletes solve if th
dexar [7]

If they together at the same rate for the same amount of time, they will solve 48 math problems,

From the question, we can see that two mathletes solve 32 math problems in a certain amount of time, this can be written as:

  • 2 mathletes = 32 math problems

In order to determine the number of problems for 3 mathletes, this is expressed as:

  • 3 mathletes = x

DIvide both expressions:

  • 2/3 = 32/x

Cross multiply

2x = 3* 32

x = 3 * 16

x = 48math problems

Hence if they together at the same rate for the same amount of time, they will solve 48 math problems,

Learn more on proportion here: brainly.com/question/1496357

6 0
2 years ago
Other questions:
  • The stock is worth at least $14.50
    5·1 answer
  • Which of the following is a step in simplifying the expression-
    14·2 answers
  • Rectangle swim pool was 9 meters wide with surface area of 90 square meters. What's length of the pool?
    15·2 answers
  • What is the greatest common factor 10 and 20 have in common?
    8·1 answer
  • How to evaluate 3ac if a=4 and c=7
    9·2 answers
  • If the spread of data on one side of the median of a data set is much greater than the spread of data on the other side, then wh
    11·1 answer
  • Will give brainliest
    5·2 answers
  • Just number three pls give right answer and will give brainless
    12·1 answer
  • Solve for x: -2x+14=20
    14·2 answers
  • A new car is purchased for 23700 dollars. The value of the car depreciates at
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!