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insens350 [35]
2 years ago
8

(1,3),(2,6),(3,9),(4,12) is the relation a function

Mathematics
1 answer:
stealth61 [152]2 years ago
7 0
Yes. It passes the vertical line test, and each input has only one output.
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A football team took possession of the ball on the 50 yard line. They lost 5 yards on the first down, and lost another 6 yards o
trapecia [35]

Answer: The answer should be 39 yard line

Step-by-step explanation: If you start at the 50 and remove 11 yards you will have 39 yards left

5 0
3 years ago
Consider the function f(x) defined by the finite set f(x)={(−2,5),(0,4),(1,−3)}. Graph the function f(x) and the transformation
Lelu [443]

let's calculate it step by step.

I'll assume that the function we look for is quadratic, because we only got 3 points

I plotted the 3 points for checking the equation later, and some intuited insight. see screenshot 1

let's write the general form of quadratic equations:

f(x) = a*x² + b*x + c

our goal is to correctly determine a, b and c

since we know from the 2nd point that

f(0) = a*0² + b*0 + c = 4

we can say

<em><u>c = 4</u></em>

this one comes almost for free

now to the next point, the 3rd one

f(1) = a*1² + b*1 + 4 = -3

we can write it as

a + b + 4 = -3

we can rearrange that to

<em><u>a = -b -7</u></em>

lastly, to the first point

f(-2) = a*(-2)² + b*(-2) + 4 = 5

simplified to

4a -2b + 4 = 5

since sort of defined a, let's plug it into our newest equation

4*(-b-7) -2b +4 = 5

we just swapped a for what its equal to.

now we just got numbers and b's

simplify it to

-4b -28 -2b +4 = 5

-6b -24 = 5

-6b = 29

<em><u>b = -29/6</u></em>

now we use the exact value of b to plug it into the rather simple equation from earlier. into this one

a = -b -7

a = -(-29/6) -7

a = 29/6 -42/6

<em><u>a= -13/6</u></em>

now that we got a, b and c we can write the whole equation

<em><u>f(x) = -13/6*x² -29/6*x +4</u></em>

see the graphic check in screenshot 2

second part of the problem:

if we want to move the whole graph 4 units down, we effectivly just cancel the +4 part

g(x) = f(x) -4 = f(x) = -13/6*x² -29/6*x +4 -4

<em><u>g(x) = -13/6*x² -29/6*x</u></em>

see screenshot 3 for the graph

5 0
2 years ago
The sum of two consecutive integers is at most 3. what is the greatest possible value for the greater integer?
Rudik [331]
2 consecutive integers...x and x + 1

x + x + 1 < = 3
2x + 1 < = 3
2x < = 3 - 1
2x < = 2
x < = 1

x + 1 = 1 + 1 = 2.......the greatest possible value for the greatest integer is 2
8 0
2 years ago
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
Which number line represents the solution set for the inequality 3(8-4x) &lt; 6(x - 5)?
STatiana [176]

Answer:

x>3

Step-by-step explanation:

We are given with the inequation 3(8-4x) < 6(x - 5)

Dividing both sides in the above in equation by 3 we get

(8-4x)<2(x-5)

Distributing 2 over (x-5)

(8-4x)<2x-10

8-4x<2x-10

adding 10 and 4x on both hand sides we get

8+10<2x+4x

18<6x

Dividing both sides by 6 we get

3<x

Hence the solution to the given in equation is x>3

7 0
3 years ago
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