What is the value of the expression shown below?

he table represents an exponential function. What is the multiplicative rate of change of the function? 0.2 0.25 0.5 0.75

Mila [183]

The Answer is C) 0.5

6 0

3 years ago

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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

3 years ago

Which one has a greater value the square root of 2 or 2.8

tester [92]

square root of 2.8 because its approximate form is 1.6733201 while square root of 2 is 1.4142136

6 0

3 years ago

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What is the area of the shaded segment ?

Zarrin [17]

9514 1404 393

Answer:

5.1 cm²

Step-by-step explanation:

The area of a segment is given by the formula ...

A = 1/2r²(α -sin(α)) . . . . . where α is the central angle in radians

For this segment, its area is ...

A = 1/2(6 cm)²(7π/18 -sin(70°)) ≈ 5.077 cm²

The area of the segment is about 5.1 square centimeters.

_____

The angle is converted to radians by multiplying by π/180°. Then a 70° angle is π(70°/180°) = 7π/18 radians.

7 0

2 years ago

Determine if the lines are parallel, perpendicular, or neither 4x+5y=10 and 5x -4y= 28

Viktor [21]

To do this, we will need to compare the slopes and the y int. So we will put each equation in y = mx + b form, where m will be the slope and b will be the y int..

4x + 5y = 10
5y = -4x + 10
y = -4/5x + 2.....the slope here is -4/5...the y int is 2

5x - 4y = 28
-4y = -5x + 28
y = 5/4x - 7...the slope here is 5/4...and the y int is -7

for the lines to be parallel, they would need the same slope and different y intercepts. So, as u can see, they are not parallel because they do not have the same slope.

for the lines to be perpendicular, the lines would have to have negative reciprocal slopes. They do....u have perpendicular lines. To find the negative reciprocal of a number, u flip the number and change the sign. One line had a slope of -4/5....the negative reciprocal is : flip the number making it -5/4....change the sign, making it 5/4...which is the slope of the other line...so these slopes are negative reciprocals.

so u have perpendicular lines

6 0

2 years ago