Carmen participated in a read-a-thon. Mr.Cole pledged $4.00 per book and gave Carmen $44.How many books did Carmen read?

The area of a square is given by the expression square inches. Find an expression that represents the length of one side of the

Verizon [17]

Answer:

A. x-6

Step-by-step explanation:

The area of a square is given by the expression $x^2-12x+36$ square inches. Now we need to find an expression that represents the length of one side of the square, in inches. To do that we need to factor $x^2-12x+36$ .

$x^2-12x+36$

$=x^2-6x-6x+36$

$=x(x-6)-6(x-6)$

$=(x-6)(x-6)$

$=(x-6)^2$

Since area of square is given by (side)^2

Hence one side of square is (x-6).

So choice A. x-6 is correct.

3 0

3 years ago

Work out the equation of the line which passes through the point (-1, 2)

Brums [2.3K]

Answer:

y = x +3

Step-by-step explanation:

The equation of a parallel line can use the same x- and y-coefficients as the given equation. Only the constant needs to be found to make the line go through the given point.

__

<h3>form of the solution</h3>

The equation of the given line is ...

y = x +4

So, the equation of a parallel line will be ...

y = x +b . . . . . for some y-intercept b

__

<h3>solution</h3>

Using the given point (x, y) = (-1, 2), we can fill in the values and solve for b.

2 = -1 +b

3 = b . . . . . . add 1 to both sides

The desired equation is ...

y = x +3

6 0

2 years ago

Find f. (Use C for the constant of the first antiderivative and D for the constant of the second antiderivative.)

sashaice [31]

Answer:

$f(x) = x^3 -sinx +Cx+D$

Step-by-step explanation:

Given that:

$f ''(x)= 6x +sinx$

We are given the 2nd derivative of a function f(x) and we need to find f(x) from that.

We will have to integrate it twice to find the value of f(x).

Let us have a look at the basic formula of integration that we will use in the solution:

$1.\ \int {(a\pm b)} \, dx =\int {a} \, dx + \int {b} \, dx \\2.\ \int {x^n} \, dx = \dfrac{x^{n+1}}{n+1}+C\\3.\ \int {sinx} \, dx = -cosx+C\\4.\ \int {cosx} \, dx = sinx+C$

$\int\ {f''(x)} \, dx =\int\ {(6x +sinx)} \, dx \\\Rightarrow \int\ {6x} \, dx + \int\ {sinx} \, dx \\\\\Rightarrow 6\dfrac{x^2}{2} -cosx +C\\\Rightarrow 3{x^2} -cosx +C\\\Rightarrow f'(x)=3{x^2} -cosx +C\\$

Now, integrating it again to find f(x):

$f(x) =\int {f'(x)} \, dx =\int{(3{x^2} -cosx +C)} \, dx \\\Rightarrow \int{3{x^2}} \, dx -\int{cosx} \, dx +\int{C} \, dx\\\Rightarrow 3\times \dfrac{x^3}{3} -sinx +Cx+D\\\Rightarrow x^3 -sinx +Cx+D\\\\\therefore f(x) = x^3 -sinx +Cx+D$

5 0

4 years ago

Determine which function(s) are exponential. Select all that apply.

Travka [436]

Answer:

option B and option C represent an exponential function.

Step-by-step explanation:

We know that following are some of the properties of different functions.

Linear Function:

The constant change in x and y

Quadratic Function:

The constant change in x

The constant 2nd differences in y

Exponential Function:

The constant change in x

The constant ratio in y

Determining the nature of the exponential function

Option A)

x 0 1 2 3 4

y 0 1 4 9 16

Here:

There is a constant change in x:

1 - 0 = 1; 2 - 1 = 1; 3 - 2 = 1; 4 - 3 = 1

BUT, there is NO CONSTANT ratio, as

1/0 = ∞, 4/1 = 4, 9/4 ; 16/9

Thus,

Table A DOES NOT represents an exponential function.

Option B)

x 0 1 2 3 4

y 1/3 1 3 9 27

Here:

There is a constant change in x:

1 - 0 = 1; 2 - 1 = 1; 3 - 2 = 1; 4 - 3 = 1

There is also a constant ratio, as

1/[1/3] = 3, 3/1 = 3, 9/3 = 3; 27/9 = 3

As there is constant change in x as well a constant ratio.

Thus,

Table B REPRESENTS an exponential function.

Option C)

x 0 1 2 3 4

y 5 5/2 5/4 5/8 5/16

Here:

There is a constant change in x:

1 - 0 = 1; 2 - 1 = 1; 3 - 2 = 1; 4 - 3 = 1

There is also a constant ratio, as

[5/2]/5= 1/2,

[5/4]/[5/2] = 1/2

[5/8]/[5/4] = 1/2

[5/16]/[5/8] = 1/2

As there is constant change in x as well a constant ratio.

Thus,

Table C REPRESENTS an exponential function.

Option D)

x 0 1 2 3 4

y 4.5 4 3.5 3 2.5

Here:

There is a constant change in x:

1 - 0 = 1; 2 - 1 = 1; 3 - 2 = 1; 4 - 3 = 1

BUT, there is NO CONSTANT ratio, as

4/4.5 = 4/[45/10] = 40/45 = 8/9

3.5/4 = [35/10]/4 = 35/40 = 7/8

3/3.5 = 3/[35/10] = 30/35 = 6/7

2.5/3 = [25/10]/3 = 25/30 = 5/6

Table D DOES NOT represent an exponential function.

Conclusion:

Therefore, option B and option C represent an exponential function.

3 0

3 years ago

Every attendant at a town's Chili Cook-off received a raffle ticket. There were 7 raffle prizes, including 5 that were food item

rjkz [21]

Answer:

0.2143

Step-by-step explanation:

4 0

4 years ago