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
Jillian was asked to translate the expression 9 n into words. She wrote "a number increased by nine. " Which best describes the
statuscvo [17]

A number increased by nine (n + 9) is the same as nine increased by a number (9 + n), the correct option is C.

<h3>What is the pharse in mathematics?</h3>

A mathematical phrase is a set of words or a combination of words and numbers that can be written as a mathematical expression.

Given

Jillian was asked to translate the expression 9 + n into words.

She wrote "a number increased by nine.

The expresion can be written into the two formate which is;

(n+9) and (9+n)

Hence, a number increased by nine (n + 9) is the same as nine increased by a number (9 + n), the correct option is C.

To know more baout pharse click the link given below.

brainly.com/question/22314482

3 0
2 years ago
Soaring Eagles Corp. has total current assets
Andrej [43]

Answer:

1000

Step-by-step explanation:

6 0
2 years ago
Suppose that we don't have a formula for g(x) but we know that g(3) = −1 and g'(x) = x2 + 7 for all x.
Sliva [168]

Answer:

  • g(2.95) ≈ -1.8; g(3.05) ≈ -0.2
  • A) tangents are increasing in slope, so the tangent is below the curve, and estimates are too small.

Step-by-step explanation:

(a) The linear approximation of g(x) at x=b will be ...

  g(x) ≈ g'(b)(x -b) +g(b)

Using the given relations, this is ...

  g'(3) = 3² +7 = 16

  g(x) ≈ 16(x -3) -1

Then the points of interest are ...

  g(2.95) ≈ 16(2.95 -3) -1 = -1.8

  g(3.05) ≈ 16(3.05 -3) -1 = -0.2

__

(b) At x=3, the slope of the curve is increasing, so the tangent lies below the curve. The estimates are too small. (Matches description A.)

4 0
2 years ago
She needs 3/4 cup of water she needs 10 more servings what's the answer A 1/1/5 b 3/1/4 c 7/2/4 d 8/2/3
Eddi Din [679]
<h2><u>Corect option</u> :</h2>

= \color{plum}\tt(C) 7 \frac{2}{4}

<h2><u>Answer with steps</u> :</h2>

Quantity of water she needs = \tt \frac{3}{4} \:  cup

Number of servings she needs = 10

Number of cups of water she will need :

= \tt \frac{3}{4} \:   \times 10

=  \tt\frac{30}{4}

=\tt  7\frac{2}{4} \:  cups

Thus, she needs \tt  7\frac{2}{4} \:  cups of water.

Therefore, the correct option is \color{plum}\tt(C) 7 \frac{2}{4}

7 0
2 years ago
If a fair die is rolled 7 times, what is the probability, rounded to the nearest thousandth, of getting at most 1 two?
hjlf

Answer:

0.67

Step-by-step explanation: From Delta math

4 0
2 years ago
Other questions:
  • Please help me with these problems, I am completely stumped : /
    7·1 answer
  • How do you solve this whole thing please?
    9·1 answer
  • Which statements are true? Check all that apply.
    10·2 answers
  • The Fibonacci numbers are defined by the recursive formula t1 = 0, t2 = 1, tn - 1 + tn - 2 , where n ∈ N and n &gt; 2. What are
    13·2 answers
  • What does z equal in 4z+5=-3z-8
    5·1 answer
  • Simplify i^12. a. 1 b. −1 c. −i d. i
    12·1 answer
  • Has anyone got warned by Katie for nothing
    7·1 answer
  • Solve math problems ​
    13·1 answer
  • Yani buys 4 dozen flyers for $7.25. What is<br> the cost of 12 dozen?<br> helppp now plz
    14·2 answers
  • Please help! 10 POINTS!<br> Please solve<br><br> 2x^2+10+8=0
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!