The graph of f(x) = 2^x + 1 is shown below. Explain how to find the average rate of change between x = 0 and x = 3.

Answer:

d.) Line AE

Step-by-step explanation:

We have been given a diagram. We are asked to find the intersection of planes ADE and BEA.

Upon looking at our given diagram, we can see that both planes intersect only at two points that are point A and E respectively.

We can also see that the line AE is a common side of both planes, therefore, line AE is the intersection of planes ADE and BEA.

The equation of the line passing through the point A (2, 0) that is parallel to the line y = 3x - 5 is y = 3x - 6.

To find the equation of a line parallel to the line y = 3x - 5 and passing through point A (2, 0), we can use the fact that parallel lines have the same slope.

The given line has a slope of m = 3. Therefore, any line parallel to it will also have a slope of m = 3.

Now, using the point-slope form of the equation of a line, which is:

[tex]\[ y - y_1 = m(x - x_1) \][/tex]

where m is the slope of the line and [tex](x_1, y_1)[/tex] is a point on the line, we can substitute the values we know:

For point A (2, 0):

[tex]x_1[/tex] = 2

[tex]y_1[/tex] = 0

Slope m = 3

The equation becomes:

y - 0 = 3 (x - 2)

y = 3x - 6

This line has the same slope as the given line, y = 3x - 5, and passes through the point A (2, 0). Therefore, it is parallel to the given line and passes through the given point.

Answer with Step-by-step explanation:

An explicit formula for the sequence

14,5,-4,-13...

given by Imran  is g(n)=14-9(n-1)

and by Aubrey is g(n)=14-9n

We have to determine who is right

g(n)= 14-9n

g(1)=14-9

    = 5

Hence, formula given by Aubrey is wrong

g(n)=14-9(n-1)

g(1)=14-9(0)=14

g(2)=14-9(1)=5

g(3)=14-9(2)= -4

g(4)=14-9(3)= -13

Hence, formula given by Imran is correct

Hence, correct option is:

Just Imran

Answer:

Only Imran

Step-by-step explanation:

The perimeter is equal to 60 feet and has the formula:

Perimeter = 2 l + 2 w

60 = 2 l + 2 w

The area is equal to 200 square feet and has the formula:

Area = l w

200 = l w

Rewriting area in terms of l:

l = 200 / w

Combining this with the perimeter formula:

60 = 2 (200 / w) + 2 w

60 = 400 / w + 2 w

Multiplying all by w:

60 w = 400 + 2 w^2

Dividing by 2 and rearranging:

w^2 – 30 w = - 200

Completing the square:

(w – 15)^2 = - 200 + (-15)^2

(w – 15)^2 = 25

w – 15 = ±5

w = 10, 20

Hence the dimensions of the garden is 10 feet by 20 feet

The width and length of the rectangular garden, given an area of 200 square feet and a total available perimeter of 60 feet, are 10 feet and 20 feet respectively.

To solve this problem, we can use the formula for the area of a rectangle, which is length × width = area, and the perimeter of a rectangle, which is 2(length + width) = perimeter. We know the total perimeter available (which is the ornamental fencing) is 60 feet and the area is 200 square feet.

Let's denote the length of the rectangle as L and the width as W. We can then set up these two equations:

We can simplify the first equation to get L + W = 30 and then isolate either L or W to substitute into the area equation. Let's isolate L to get L = 30 - W.

We then substitute this into the area equation to get: (30 - W)W = 200. Solving this quadratic equation, the possible solutions are W=10 and W=20. However, if W=20, that would leave 0 feet for the length, which is not possible. Therefore, we have W=10 and L=20.

https://brainly.com/question/31677552

#SPJ11

Approximately 84.13% of times are more than 91 seconds, and approximately 0.13% of times are more than 63 seconds.

To find the percentage of times that are more than 91 seconds and more than 63 seconds, we can use the properties of a normal distribution and the standard normal distribution table (also known as the z-table).

Given:

Mean (μ) = 84 seconds

Standard deviation (σ) = 7 seconds

1. Probability of times more than 91 seconds:

First, we need to find the z-score for the value 91 seconds:

[tex]\(z = \frac{X - \mu}{\sigma} = \frac{91 - 84}{7} = \frac{7}{7} = 1\)[/tex]

Now, using the z-table, find the area under the standard normal curve to the right of [tex]\(z = 1\)[/tex]. The z-table provides the percentage of values below a given z-score, so we need to find the complement (1 - percentage) to get the percentage of values above [tex]\(z = 1\).[/tex]

From the z-table, the area to the right of [tex]\(z = 1\)[/tex] is approximately 0.1587.

So, the percentage of times more than 91 seconds is [tex]\(1 - 0.1587 = 0.8413\)[/tex] or 84.13%.

2. Probability of times more than 63 seconds:

Similarly, we need to find the z-score for the value 63 seconds:

[tex]\(z = \frac{X - \mu}{\sigma} = \frac{63 - 84}{7} = \frac{-21}{7} = -3\)[/tex]

Now, using the z-table, find the area under the standard normal curve to the right of [tex]\(z = -3\)[/tex]. Again, we need to find the complement to get the percentage of values above [tex]\(z = -3\).[/tex]

From the z-table, the area to the right of [tex]\(z = -3\)[/tex] is approximately 0.9987.

So, the percentage of times more than 63 seconds is [tex]\(1 - 0.9987 = 0.0013\)[/tex] or 0.13%.

Therefore, approximately 84.13% of times are more than 91 seconds, and approximately 0.13% of times are more than 63 seconds.

To know more about time:

https://brainly.com/question/13932039

#SPJ2

Answer:

3 feet = 36 inches...

THEN

8 x 36 = 288 inches squared!

Step-by-step explanation:

hope this helped

Answer:c

Step-by-step explanation:

The answer is the square root of terms separated by addition and subtraction cannot be calculated individually.

To find expression cannot be rewritten as during the next step and explain.

Algebraic expressions are combinations of variables , numbers, and at least one arithmetic operation.

The statement that best explains why the expression cannot be rewritten as during the next step is that the square root of terms separated by addition and subtraction cannot be calculated individually.

So, the square root of terms separated by addition and subtraction cannot be calculated individually.

Learn more about expression here:

https://brainly.com/question/6684029

#SPJ5

Answer:

He had a total of $43 at the beginning of the day

Step-by-step explanation:

Step 1

Express the amount of money Darryl had in the beginning as follows;

A=E+R

where;

A=initial amount he had at the beginning

E=total expenditure

R=total remainder after spending

In our case;

A=unknown

E=Amount spent on book+amount spent on compact disc+amount spent on magazine

E=(16+20+2)=$38

R=$5

Step 2

Substitute the values in the expression and solve for A;

A=(38+5)=43

He had a total of $43 at the beginning of the day

see the attached figure to better understand the problem

Let

x------> the length side of a rectangle

y-------> the width side of a rectangle

we know that

the perimeter of a rectangle is equal to the formula

[tex]P=2x+2y[/tex]  

in this problem

[tex]AB=DC=x[/tex]

[tex]AD=BC=y[/tex]

Step 1

Find the distance AB

[tex]A(-6,4)\\B(2,8)[/tex]

we know that

the distance's formula between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2} +(x2-x1)^{2}}[/tex]

substitute the values

[tex]d=\sqrt{(8-4)^{2} +(2+6)^{2}}[/tex]

[tex]d=\sqrt{(4)^{2} +(8)^{2}}[/tex]

[tex]dAB=\sqrt{80}\ units[/tex]

Step 2

Find the distance BC

tex]B(2,8)\\C(4,4)[/tex]

we know that

the distance's formula between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2} +(x2-x1)^{2}}[/tex]

substitute the values

[tex]d=\sqrt{(4-8)^{2} +(4-2)^{2}}[/tex]

[tex]d=\sqrt{(-4)^{2} +(2)^{2}}[/tex]

[tex]dBC=\sqrt{20}\ units[/tex]

Step 3

Find the perimeter

we know that

the perimeter of a rectangle is equal to the formula

[tex]P=2x+2y[/tex]

[tex]P=2AB+2BC[/tex]

we have

[tex]dAB=\sqrt{80}\ units=8.9\ units[/tex]

[tex]dBC=\sqrt{20}\ units=4.5\ units[/tex]

substitute the values of the distance in the formula

[tex]P=2*8.9+2*4.5=26.8\ units[/tex]

therefore

the answer is

The perimeter of the rectangle is equal to [tex]26.8\ units[/tex]

Answer:

[tex]y\leq-3x+5[/tex]

Step-by-step explanation:

we know that

The solution of the inequality is the shaded area below the solid line (the gray area)

The slope of the solid line is negative

The y-intercept of the solid line is positive

The equation of the solid line is equal to [tex]y=-3x+5[/tex]

therefore

the equation of the inequality is equal to

[tex]y\leq-3x+5[/tex]

Answer: 16

Step-by-step explanation:

The number of outcomes exist , when a coin is flipped (tails , head) = 2

The number of possible outcomes , when 'n' number of coins are flipped :_

[tex]2^n[/tex]

For n= 4, the number of possible outcomes , when four coins are flipped :_

[tex]2^4=2\times2\times2\times2=16[/tex]

Hence, the possible outcomes exist when four fair coins are flipped = 16

Answer:

true

Step-by-step explanation:

Answer:

the other person is correct

Step-by-step explanation:

Final answer:

Based on the ratio of 1:4 for black socks to white socks, and knowing there are 8 black socks, we calculate the number of white socks to be 32.

Explanation:

The question asks us to find the number of white socks when given the ratio of black socks to white socks in a drawer and the number of black socks. The ratio is 1:4, which implies for every black sock, there are 4 white socks. Since there are 8 black socks, to find the number of white socks, we multiply the number of black socks by the ratio of white socks to black socks, which would be 8 * 4 = 32. Therefore, there are 32 white socks in the drawer.

Answer:

[tex]x=\frac{-1+-i\sqrt{15}}{4}[/tex]

Step-by-step explanation:

[tex]2x^2+x+2=0[/tex]

Apply quadratic formula to solve for x

[tex]x=\frac{-b+-\sqrt{b^2-4ac}}{2a}[/tex]

a=2, b= 1, c=2

Plug in the value in the quadratic formula

[tex]x=\frac{-1+-\sqrt{1^2-4(2)(2)}}{2(2)}[/tex]

[tex]x=\frac{-1+-\sqrt{-15}}{4}[/tex]

Square root of -1 is 'i'

[tex]x=\frac{-1+-i\sqrt{15}}{4}[/tex]

The solution of the given quadratic equation is,

x = [-1±i√15]/4

Hence option 3rd is correct.

The given quadratic equation is,

2x²+x+2=0

Here we can see that it is of the form of ax² + bx + c = 0.

Since we know that
The quadrature formula for ax² + bx + c = 0 is

⇒ x = [-b±√(b²- 4ac)]/2a

Here we have,

a = 2

b = 1

c = 2

Put these value in quadrature formula we get,

⇒ x = [-1±√(1²- 4x2x1)]/2x2

      = [-1±√(1- 16)]/4

      = [-1±√(-15)]/4

Since we know that, i = √-1

Therefore,

⇒ x = [-1±i√15]/4

To learn more about quadratic equation visit:

https://brainly.com/question/30098550

#SPJ6