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3 years ago

The graph below plots a function f(x):

1 answer:

4 0

By definition we have that the average rate of change of the function is given by:
$AVR = \frac{f(x2) - f(x1)}{x2 - x1}
$
Substituting values we have:
$AVR = \frac{100 - 50}{2 - 0}$
Rewriting we have:
$AVR = \frac{50}{2}$
$AVR = 25$
Answer:
If x represents time, the average rate of change of the function f(x) in the first two seconds is 25.

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Solve the given linear Diophantine equation. Show all necessary work. A) 4x + 5y=17 B)6x+9y=12 C) 4x+10y=9

aliina [53]

Answer:

A) (-17+5k,17-4k)

B) (-4+3k,4-2k)

C) No integer pairs.

Step-by-step explanation:

To do this, I'm going to use Euclidean's Algorithm.

4x+5y=17

5=4(1)+1

4=1(4)

So going backwards through those equations:

5-4(1)=1

-4(1)+5(1)=1

Multiply both sides by 17:

4(-17)+5(17)=17

So one integer pair satisfying 4x+5y=17 is (-17,17).

What is the slope for this equation?

Let's put it in slope-intercept form:

4x+5y=17

Subtract 4x on both sides:

5y=-4x+17

Divide both sides by 5:

y=(-4/5)x+(17/5)

The slope is down 4 and right 5.

So let's show more solutions other than (-17,17) by using the slope.

All integer pairs satisfying this equation is (-17+5k,17-4k).

Let's check:

4(-17+5k)+5(17-4k)

-68+20k+85-20k

-68+85

That was exactly what we wanted since we were looking for integer pairs that satisfy 4x+5y=17.

Onward to the next problem.

6x+9y=12

9=6(1)+3

6=3(2)

Now backwards through the equations:

9-6(1)=3

9(1)-6(1)=3

Multiply both sides by 4:

9(4)-6(4)=12

-6(4)+9(4)=12

6(-4)+9(4)=12

So one integer pair satisfying 6x+9y=12 is (-4,4).

Let's find the slope of 6x+9y=12.

6x+9y=12

Subtract 6x on both sides:

9y=-6x+12

Divide both sides by 9:

y=(-6/9)x+(12/9)

Reduce:

y=(-2/3)x+(4/3)

The slope is down 2 right 3.

So all the integer pairs are (-4+3k,4-2k).

Let's check:

6(-4+3k)+9(4-2k)

-24+18k+36-18k

-24+36

That checks out since we wanted integer pairs that made 6x+9y=12.

Onward to the last problem.

4x+10y=9

10=4(2)+2

4=2(2)

So the gcd(4,10)=2 which means this one doesn't have any solutions because there is no integer k such that 2k=9.

6 0

2 years ago

Help ASAP I need the answer now please.

DiKsa [7]

Answer:

B. 94

Step-by-step explanation:

Angle B = 180 - 143 = 37°.

Angle B + Angle C + Angle D = 180°

37° + 49° + Angle D = 180°

Angle D = 180° - 86° = 94°

5 0

3 years ago

Help me plz with this question!

sashaice [31]

I hope this help in some sort of way you can message me if you need more help

5 0

2 years ago

This is for today help pls!!!

ryzh [129]

Answer:

Perimeter=25 units

Area= 43 units^2

Step-by-step explanation:

one side = 5 units so perimeter is 5x5=25

split into 5 equal triangles

base =5, height =3.44, formula for area=(base)(height)(0.5)

area of each triangle =(5)(3.44)(0.5)=8.6

entire area=5(8.6)=43

6 0

3 years ago

Write a function to represent each problem situation Carmen deposits $1000into simple interest account.The rate for the account

kolezko [41]

The function the represent the balance in the account as a function of time t is p(t) = 1000 + 40t

<h3><u>Solution:</u></h3>

Given that,

Carmen deposits $1000 into simple interest account

The rate for the account is 4%

To find: function the represent the balance in the account as a function of time t

Given is simple interest account

The formula for simple interest is given as:

$S.I = \frac{ prt}{100}$

Where, "p" is the principal and "r" is the rate of interest and "t" is the number of years

In simple interest,

total amount after "t" years = principal + simple interest

Here in this question, Carmen deposits $1000

$p_0 = 1000$

$r = 4 \% = \frac{4}{100} = 0.04$

Thus we can frame a function as:

total amount after "t" years = principal + simple interest

$p(t) = p_0 + (p_0 \times r \times t )$

$p(t) = 1000 + (1000 \times 0.04)t\\\\p(t) = 1000 + 40t$

Where, p(t) is the amount after "t" years and $p_0$ is the principal sum

Thus the function is obtained

7 0

3 years ago