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Thepotemich [5.8K]
3 years ago
7

Use the table to describe the locations of the zeros of the quadratic function $f$ .

Mathematics
1 answer:
MissTica3 years ago
3 0

Answer:

The zeros are between -4 and -3, and between 0 and 1

Step-by-step explanation:

Here, we want to location of the zeros

As we can know, at the zeros of a quadratic function, the y value at those point is zero

So whenever we have y value being zero, we have it that the x value at that point is a zero or root of the quadratic function

Now, looking at the table, we can see that between the point x = -4 and -3; y moved from -2 to 2

For this movement to occur, we must have passed through 0 as we have -1 ,0 and 1 between the numbers as -2 and 2

So obviously, the root is between -4 and -3

Secondly as we can see, f(x) moved from 2 to -2

The numbers between here are 1 , 0 and -1

So definitely the root lies between the x values of 0 and 1

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What is a35 for the arithmetic sequence presented in the table below?
Kryger [21]

Answer: choice B) a35 = -118

=====================================================

Explanation:

When n = 5, an = 32 as shown in the first column of the table. This means the fifth term is 32. Plug in those values to get

an = a1+d(n-1)

32 = a1+d(5-1)

32 = a1+4d

Solve for a1 by subtracting 4d from both sides

a1 = 32-4d

We'll plug this in later

Turn to the second column of the table. We have n = 10 and an = 7. Plug those values into the formula

an = a1+d(n-1)

7 = a1 + d(10-1)

7 = a1+9d

Now substitute in the equation in which we solved for a1

7 = a1+9d

7 = 32-4d+9d ... replace a1 with 32-4d

7 = 32+5d

5d = 7-32

5d = -25

d = -25/5

d = -5

This tells us that we subtract 5 from each term to get the next term.

Use this d value to find a1

a1 = 32-4d

a1 = 32-4*(-5)

a1 = 32+20

a1 = 52

The first term is 52

--------------

The nth term formula is therefore

an = 52 + (-5)(n-1)

which simplifies to

an = -5n + 57

To check this result, plug in n = 5 to find that a5 = 32. Similarly, you'll find that a10 = 7 after plugging in n = 10. I'll let you do these checks.

--------------

Replace n with 35 to find the 35th term

an = -5n + 57

a35 = -5(35) + 57

a35 = -175 + 57

a35 = -118

7 0
3 years ago
75% of what number is 42?
Anna35 [415]
75            42
-----         -----
100           x

75 x= 4200
---       ------
75       75

x = 56



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