Im giving you 30 points just help me :((((((((

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

MAVERICK [17]

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 (a + b + c).

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

$y=ax^2+bx+5$

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

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

Simplify:

$5=a+b$

The point (2, 19) tells us that when x = 2, y = 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 (a + b + c) will be:

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

7 0

3 years ago

Which set of transformations would prove ΔLMN ~ ΔPQR?

weeeeeb [17]

Answer:

dilation

Step-by-step explanation:

Well, you didn't give an option to choose from. I know that the thing in the middle is a similar symbol. Dilations can prove that both shapes are similar. If LMN dilates to a smaller shape PQR then both shapes are SIMILLAR.

7 0

3 years ago

Read 2 more answers

Heeeeeeeelllllpppp why isnt anyone helping me :( find MK

Ne4ueva [31]

Answer:

MK=32.5

Step-by-step explanation:

Hey There!

I believe that these triangles are similar

So to find MK we want to find the scale factor

To do this we divide

66/30=2.2

Now we want to divide 72.5 by 2.2

72.5/2.2=32.5

therefore MK=32.5

hope this helps!

8 0

3 years ago

The cost of each ticket at the carnival was $0.25. Li bought $7.50 worth of tickets. How many tickets did she buy?

Drupady [299]

She bought 30 tickets. Just do 7.50 divide 0.25.

8 0

3 years ago

A survey of a group of seventh graders and a group of teachers at a local middle school asked how many siblings they each have.

mihalych1998 [28]

Answer:

1.5

Step-by-step explanation:

Attached to this answer is the diagram of the box plot described in the question, and the means from the plot are calculated thus;

Students; no. of siblings

student 0 2

student 1 4

student 2 7

student 3 5

student 4 2

Total 20

Mean no. of siblings = (total number of siblings) ÷ (total number of students)

Note that number of students here are the once that had at least one sibling, others without siblings are not used in the calculation, hence 5 students (student-0 to student-4) make up total number of students, while the remaining 4 students (student-4 to student-9) are disregarded.

Therefore, mean = 20 ÷ 5 = 4 siblings.

6 0

3 years ago

Read 2 more answers