On the following checking account record, enter the figures and add or subtract them to keep the running total correct.
Balance Forward
Check
No.
Date
3427 2/14
3428 2/15
2/17
3429 2/22
3430 2/22
Checks Issued To
or Description of Deposit
Alfred's Market
Sunnyside Cafe
Deposit (paycheck)
City Water and Power
Amount of Check Amount of Deposit
$90.48
$65.00
$54.47
$375.99
$381.33
$299.88
Check
or Dep.
Balance $
Check
or Dep.
Balance $
Check
or Dep.
Balance $
Check
or Dep.
Balance
Check
or Dep.

The value of the equation that defines the function is f(x) = 3(5/3)ˣ

From the question, we have the following parameters that can be used in our computation:

(0, 3) and (1, 5)

An exponential function is represented s

y = abˣ

Where,

a = y when x = 0

So, we have

y = 3bˣ

Using the other point, we have

3b = 5

This gives

b = 5/3

So, we have

f(x) = 3(5/3)ˣ

Hence, the equation defining f is f(x) = 3(5/3)ˣ

Read more about exponential function at

brainly.com/question/2456547

#SPJ1

Answer:

d

Step-by-step explanation:

Answer:

Step-by-step explanation:

When x = 0

      y = 3x -1

         = 3*0 - 1 = 0 - 1

      y = -1

(0 , -1)

When x = 1,

y = 3*1 - 1 = 3 - 1

y = 2

(1 , 2)

Plot these points (0,-1) and (1, 2) in the graph and join them

Answer:

140 units3

Step-by-step explanation:

The  volume of the prism below is 420 cubic units.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

The prism is a three-dimensional shape that has base area, and height. The volume of a prism is equal to the product of base area and height of a prism.

The volume of the prism= B×H

Where, B is base area of prism, and H is height of prism.

Given that,

Length of  prism (L) = 12 centimeters

Width of prism(W) = 14 centimeters

B=1/2×12×5

=30

Now volume of prism = 30×14

=420 cubic units

Hence, the  volume of the prism below is 420 cubic units.

To learn more on Three dimensional figure click:

https://brainly.com/question/2400003

#SPJ7

10 is because the coefficient means which ever number has a variable

Hope this helps! :D and may i have brainliest?

The probability that a randomly selected point within the circle would fall in the red- shaded area is 45. 833 %

The arc that is covered by the red - shaded area in the circle has a degree measure of 165 degrees. This is out of the total circle angle measure of 360 degrees.

This therefore means that the probability that a randomly selected point within the circle would fall in the red- shaded area can be found to be :

= Angle measure of red - shaped area / Total area x  100 %

= 165 / 360 x 100 %

=0. 45833 x 100 %

= 45. 833 %

Find out more on probability at https://brainly.com/question/22690728

#SPJ1

Answer:

True

Step-by-step explanation:

3 X 1 = 3

4 X 1 = 4

3 + 4 = 7

Hope this helps!

Answer:

(3, 1) is a solution

Step-by-step explanation:

If the coordinates are solutions of the equation, you should be able to solve the equation to get the y-value when you input the x-value;

So in the case of (3, 1), input x = 3 and solve for y:
(3) + 4y = 7

4y = 4

y = 1

Solving the equation gives y = 1, which is the same as the given coordinates, hence it is a solution or,  in other words, this point falls on the line graphed by the equation

Answer:

daymn

it's gonna be okay

Answer:r=2 cos^4(theta)

Step-by-step explanation:To find the values of theta where the maximum r-values occur on the graph of the polar equation r = 2 cos^4(theta), we need to find where the derivative of r with respect to theta is equal to zero, since the maximum r-values occur at these points.

First, we can simplify the equation by using the identity cos(2theta) = 2cos^2(theta) - 1 and substituting cos^2(theta) = (1 + cos(2theta))/2. This gives:

r = 2 cos^4(theta) = 2(1/2 + 1/2 cos(2theta))^2 = 1 + cos(2theta) + cos^2(2theta)/2.

Next, we can take the derivative of r with respect to theta, using the chain rule:

dr/dtheta = -sin(2theta) - 2cos(2theta)sin(2theta).

Setting this equal to zero and factoring out sin(2theta), we get:

sin(2theta)(-1 - 2cos(2theta)) = 0.

This equation is satisfied when sin(2theta) = 0 or cos(2theta) = -1/2.

When sin(2theta) = 0, we have 2theta = k*pi for some integer k. Therefore, theta = k*pi/2.

When cos(2theta) = -1/2, we have 2theta = 2*pi/3 + 2*k*pi or 2theta = 4*pi/3 + 2*k*pi for some integer k. Therefore, theta = pi/3 + k*pi or theta = 2*pi/3 + k*pi.

These are the values of theta where the maximum r-values occur on the graph of the polar equation r = 2 cos^4(theta).

We will find the probability of getting each color of marble, and we will see that getting red and blue is equally likely, while getting green is less likely.

If we draw a marble at random from the box, all of them will have the same probability of being drawn.

Then the probability of getting a given color is given by the quotient between the number of marbles of that color and the total number of marbles.

Probability of getting red:

P = 11/25 =  0.44  This is really close to 50%, so this is equally likely.

Probability of getting blue:

P = 11/25 =  0.44  This is really close to 50%, so this is equally likely.

Probability of getting green:

P = 3/25 = 0.12 This is really close to 0%, so this is less likely.

If you want to learn more about probability, you can read:

https://brainly.com/question/251701

Answer:

(2) Real and equal (i.e., repeated roots), if D = 0.

Step-by-step explanation:

.In a quadratic equation ax2 + bx + c = 0, if discriminant is D= b2 - 4ac, then roots of the quadratic equation are

Real and equal (i.e., repeated roots), if D = 0.

If the D > b² - 4ac then it's real and distinct.

Answer:

Domain: x \(\geq\) -5

Range: y \(\geq\) -3

Step-by-step explanation:

The domain is all the possible inputs or x value.  x will be greater than -5.

The range is all of the possible outputs or y value.   y will be greater than -3

Answer:

Domain:  [-5, ∞)

Range:  [-3, ∞)

Step-by-step explanation:

The given graph shows a continuous curve with a closed circle at the left endpoint (-5, -3) and an arrow at the right endpoint.

A closed circle indicates the value is included in the interval.

An arrow shows that the function continues indefinitely in that direction.

The domain of a function is the set of all possible input values (x-values).

As the leftmost x-value of the curve is x = -5, and it continues indefinitely in the positive direction, the domain of the  graphed function is:

The range of a function is the set of all possible output values (y-values).

From observation, it appears that the minimum y-value of the curve is y = -3. The curve continues indefinitely in the positive direction in quadrant I. Therefore, the range of the graphed function is:

Answer:

(10,-3)

Step-by-step explanation:

The function has a vertical asymptote at x = -6 and a hole at x = -5.

To find the points of discontinuity, we need to look for values of x that make the denominator of the fraction equal to zero. We can factor the denominator of the rational function as follows:

x² + 11x + 30 = (x + 6)(x + 5)

So the function is undefined for x = -6 and x = -5, since these values make the denominator equal to zero.

These are the points of discontinuity for the rational function.

At x = -6, the function has a vertical asymptote. To see this, we can examine the behavior of the function as x approaches -6 from the left and right:

As x approaches -6 from the left (i.e., x < -6), the denominator becomes a large negative number, while the numerator is a small negative number. So the fraction becomes a large negative number. As x approaches -6 from the right (i.e., x > -6), the denominator becomes a large positive number, while the numerator is a small positive number. So the fraction becomes a large positive number. Therefore, the function has a vertical asymptote at x = -6.

At x = -5, the function has a hole.

To see this, we can factor out the common factor (x + 6) from the numerator and denominator of the fraction:

y = (x + 6)/(x + 6)(x + 5) = 1/(x + 5)

So the function is undefined at x = -5, but we can see that the numerator and denominator have a common factor of (x + 5), which cancels out. Therefore, the function has a hole at x = -5, and can be defined at this point by the limit as x approaches -5:

lim (x -> -5) y = lim (x -> -5) 1/(x + 5) = -∞

To learn more about the function;

brainly.com/question/28303908

#SPJ1

The response is B) 5√6 in accordance with the provided assertion.

The hypotenuse of a right triangle is its longest side; its "opposite" side is the side that confronts the angle in issue; and its "adjacent" half is the side that faces it.

In a 45°-45°-90° triangle, the two legs are congruent, and the hypotenuse is equal to the leg multiplied by √2.

In this case, the leg length is given as 5√3.

Thus, the hypotenuse will have the following length:

hypotenuse = leg x √2 = 5√3 x √2 = 5√(3 x 2) = 5√6

Therefore, the answer is B) 5√6.

To know more about Hypotenuse visit:

https://brainly.com/question/29407794

#SPJ1

Answer:

x - 4 yards.

Step-by-step explanation:

Given:

Area of rectangle = 3x^2 - 12x square yards

Width = 3x yards

To find:

Length of rectangle

Solution:

The area of a rectangle is equal to the product of its length and width.

Area of rectangle = Length * Width

Substituting the given values, we get:

3x^2 - 12x = Length * 3x

Length =( 3x^2 - 12x )3x

Length = x-4

Therefore, the length of the rectangle is x - 4 yards.

Answer: The length of the rectangle is x - 4 yards.

Step-by-step explanation:

We can create an equation to solve this word problem, where the variable L = length.

3x  ×  L  = \(3x^2 - 12x\)

We need to solve for the variable L, to find the length of the rectangle.

First lets factor the right side of the equation to make it easier to divide with.

3x  ×  L  = \(3x^2 - 12x\)

We can factor out 3x from the right side of the equation.

3x  ×  L  = 3x(x - 4)

Now we need to get the variable L by itself (isolating the variable). In order to do that, we can divide both sides by 3x.

3x ×  L  = 3x(x - 4)

/3x           /3x

L = x - 4

The length of the rectangle is x - 4 yards.

Answer:

There are six blue bows and ten silver bows. = 6:10

There are four red bows out of ten bows. = 4:10

There are three black bows out of a bag of ten bows. = 3:10

There are three silver bows for every four red bows in a bag. 3:4

Weare asked to write a proof of the Exterior angle Theorem that states that the sum of exterior angles in any polygon adds to 360 degrees.

Consider first the theorem that states that the sum of the interior angles of a polygon of "n" sides is given by:

180 * (n-2)

We also know that since the exterior angles of the polygon are all "supplementary" angles to the interior angles, then the addition of ALL interior angles PLUS the addition of ALL exterior angles of a polygon of "n" sides must give:

Sum ALL interior Angles + Sum ALL exterior Angles = n * 180

We can now use the theorem mentioned above about the sum of the interior angles of a polygon of "n" sides as: 180 * (n - 2)

Then we can find the Sum of ALL experior angles by subtracting the formula as shown:

Sum ALL interior Angles + Sum ALL exterior Angles = n * 180

180 * (n - 2) + Sum ALL exterior Angles = n * 180

using distributive property

180 n - 360 + Sum ALL exterior Angles = n * 180

subtract 180 n from both sides

- 360 + Sum ALL exterior Angles = n * 180 - 180 n

- 360 + Sum ALL exterior Angles = 0

add 360 to both sides

Sum ALL exterior Angles = 0 + 360

Sum ALL exterior Angles = 360

which is what we wanted to prove.

Answer: Felix spent 5 hours doing chores and 3 hours doing homework

Step-by-step explanation:

It says that x represent chores, y represents homework

Answer:

(5, 3)

Step-by-step explanation:

x represents hours of chores y represents hours of homework

Answer:

Please remember

n

√

x

is written as

x

1

n

in exponential form

Hence

3

√

x

2

y

can written as

(

x

2

y

)

1

3

As

(

x

a

)

b

is nothing but

x

a

⋅

b

3

√

x

2

y

=

(

x

2

y

)

1

3

=

x

2

⋅

(

1

3

)

*

y

1

3

=

x

2

3

*

y

1

3

Step-by-step explanation:

Answer:

-189

Step-by-step explanation:

\(\int^9_0 \ |6x-6| \ dx\)

⇒ 6x - 6 = 0

6x = 6

x = 1

\(\int^9_0 \ (6x- 6 ) \ dx = \int^9_0 \ -(6x - 6) \ dx\)

\(= - \Big[ \dfrac{6x^2}{2}- 6x \Big]^9_0\)

\(= - \Big[ \dfrac{6(9)^2}{2}- 6(9) - 0 \Big]\)

\(= -(243 - 54 - 0 )\)

= -189

Answer: x<4

Step-by-step explanation:

If we break this down as

-2+4x<14 and we add 2 to both sides

4x+<16 and divide by 4

and you get x<4

Answer:

B -5/6

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

y = -1 + 2/3 x

3 = -1 + 2/3 × 6

3 = -1 + 12/3

3 = -1 + 4

3 = 3   Yes, checks out

9514 1404 393

Answer:

  182 seconds, or 3 minutes 2 seconds

Step-by-step explanation:

The second lap takes ...

  (50 s)(1 +20%) = (50 s)(1.2) = 60 s

The third lap takes ...

  (60 s)(1.2) = 72 s

The three laps take 50 +60 +72 = 182 seconds, or 3 minutes 2 seconds.

Answer:189.75

Step-by-step explanation: 220 * 0.15 = 33

220 + 33 = 253

253 * 0.25 = 63.25

253 - 63.25 = 189.75