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3 years ago

8

The diagonal of a TV is 28 inches long. Assuming that this diagonal forms a pair of 30-60-90 right triangles, what are the exact

length and width of the TV?

1 answer:

larisa [96]3 years ago

4 0

24 inches by 14 inches.

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Whole numbers, repeating decimals, and decimals that never end

Step-by-step explanation:

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What Is 4/14 in simplest form?

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3 years ago

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

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

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3 years ago

How to solve the mindbender

Salsk061 [2.6K]

Answer:

Step-by-step explanation:

To get from the top square to the bottom square, multiply by - 3 So the middle position of the bottom square is - 30. If you solve all of the top square, you can get the bottom square easily enough.

The diagonal of the top square adds to 13 + 10 + 7 = 30

The top line of the top square must add to 30 as well 13 + 11 + 6. Put 6 in the middle position.

The right hand vertical line must add to 30. 11 + 7 + 12 = 30

The middle row must add to 30. 10 + 12 + 8. 8 goes in the left position of the middle row.

Let's summarize what we have so far.

13 6 11

8 10 12

7

We can fill in the last two spaces by adding to 30

13 6 11

8 10 12

9 14 7

That completes the top magic square.

To get the bottom magic square, multiply by -3

- 39 - 18 -33

-24 -30 -36

-27 -42 -21

5 0

2 years ago