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faltersainse [42]

2 years ago

14

Is .07 closer to 1/2,0 or 1

1 answer:

Nikitich [7]2 years ago

7 0

0, because 1/2 = 0.50. therefore .07 is more closer to 0

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Write the equation of the quadratic function that passes through the points (-1, 1), (1, 5), and (2,10).

Serjik [45]

Answer:

$\displaystyle f(x)=x^2+2x+2$

Step-by-step explanation:

<u>System Of Linear Equations </u>

In this problem, we'll need to solve a 3x3 system of linear equations because we have three unknowns and three conditions.

We are required to find the equation of the quadratic function that passes through the points (-1, 1), (1, 5), and (2,10)

The general quadratic function can be written as

$\displaystyle f(x)=ax^2+bx+c$

We need to find the values of a,b, and c. Let's use the first condition, i.e. f(-1)=1

$\displaystyle f(-1)=a(-1)^2+b(-1)+c$

$\displaystyle f(-1)=a-b+c$

$\displaystyle a-b+c=1.....[eq\ 1]$

Now we use the second condition f(1)=5

$\displaystyle f(1)=a(1)^2+b(1)+c$

$\displaystyle f(1)=a+b+c$

$\displaystyle a+b+c=5.......[eq\ 2]$

Finally, we use the third condition f(2)=10

$\displaystyle f(2)=a(2)^2+b(2)+c$

$\displaystyle f(2)=4a+2b+c$

$\displaystyle 4a+2b+c=10....[eq\ 3]$

We put together eq 1, eq 2, and eq 3 to form the system

$\displaystyle \left\{\begin{matrix}a-b+c=1\\ a+b+c=5\\ 4a+2b+c=10\end{matrix}\right.$

Adding the first two equations we have

$\displaystyle 2a+2c=6$

$\displaystyle a+c=3$

And also

$\displaystyle b=2$

Using the above equation and the value of b in the third equation, we have

$\displaystyle \left\{\begin{matrix}a+c=3\\ 4a+c=6\end{matrix}\right.$

Subtracting the first equation from the second

$\displaystyle 3a=3$

$\displaystyle a=1$

And therefore

$\displaystyle c=2$

Now we have all the values, the quadratic function is

$\displaystyle \boxed{f(x)=x^2+2x+2}$

6 0

2 years ago

Answer Key Question 1 (Worth 1 points) (02.02) A store offers a 15% discount on all items in the store during a sale. All store

Sunny_sXe [5.5K]

C=71.91. plug 100 into the equation as x, then solve for C

7 0

2 years ago

Which of the following expressions is equivalent to the expression x - (-3)?

Paraphin [41]

The answer is C hope this helped you

7 0

2 years ago

Read 2 more answers

I play a gambling game in which I will win different amounts of money with different likelihood's. Suppose that I win X dollars

Nataliya [291]

Answer:

$p = 0.05$

Step-by-step explanation:

Given

See attachment for the distribution

Required

Find p

To find p, we make use of:

$\sum P(x) = 1$

So, we have:

$0.50 + 0.25 + 0.13 + 0.07 + p = 1$

$0.95 + p = 1$

Make p the subject

$p = 1 - 0.95$

$p = 0.05$

7 0

3 years ago

And Art teacher has 1 1/2 pounds of red clay and 3/4 pound of yellow clay. the red clay in the yellow clay together. each studen

dalvyx [7]

1 1/2 + 3/4 = 2 1/4

2 1/4 divided by 1/8 = 18

18 students

7 0

2 years ago