Suppose that the functions and g are defined for all real numbers x as follows. f(x) = x + 3; g(x) = 2x - 2 Write the expressions for (fg)(x) and (f - g)(x) and evaluate (f + g)(3)

Answer:

\sqrt[29]

Explanation:

Given the coordinate (5,10) and (10, 12). The formula for calculating the distance between two points is expressed as;

Given that;

x1 = 5

y1 = 10

x2 = 10

y2 = 12

Substitute:

Hence the distance between the points is \sqrt[29]

Step 1

Given;

Putting these values in, we have;

Therefore,

Answer;

The common difference between each term is -3.

19 - 22 = -3

16 - 19 = -3

13 - 16 = -3

The recursive formula of an arithmetic sequence follows the pattern below:

where d = common difference and number of terms "n" must be more than or equal to two.

To be able to get the recursive formula, we will plug in the common difference assuming that first term a₁ = 22. Therefore, the recursive formula is:

Jane, Chau, and Deshaun have $22, $16 and $44 respectively in their wallets.

let x represent represent the amount of Jane.

let Y represent represent the amount of chau.

let z represent represent the amount of Deshaun.

Jane, Chau, and Deshaun have a total of $82"  can be represented as

x + y + z = $82 .......(1)

Deshaun has 4 times what Jane has. It  can be represented mathematically as

y = 2x     .......(2)

Chau has $6 less than Jane. It can be represented mathematically as

z= x- 6   .......(3)

we can now solve the equations using the substitution method

substitute equation (2)  and (3)  into equation (1)

x + y + z = $82

x + 2x + x-6 = $82

4x -6 = $82

4x - 6  = $82

4x = $82 + 6

4x = 88

x = $22

from equation 2

y = 2x

y = 2 x 22 = $44

z = x- 6

z = 22 - 6

z=$16

Jane, Chau, and Deshaun have $22, $16 and $44 respectively in their wallets.

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Given

Dimensions of deck = 24 by 24

dimensions of ply wood = 4 by 8

Find

Number of sheets of ply wood needed to cover the deck

Explanation

number of sheets = area of deck divided by area of 1 ply wood

so ,

area of deck =

and

area of ply wood =

so ,

number of sheets needed =

Final Answer

Hence , the required number of sheets of ply wood is 18

In order to find the vertex of this quadratic equation, first let's find the coefficients a, b and c from the standard form of the quadratic equation:

Comparing with the given equation, we have a = -5, b = -270 and c = -520.

Now, let's calculate the x-coordinate of the vertex using the formula below:

Using this value of x in the equation, we can find the y-coordinate of the vertex:

Therefore the vertex is located at (-27, 3125).

The sample methodology whose accuracy is better than another is the one with more approximation, this comes from the number of repetitions.

Therefore, option A is the one with more approximation, which mean the least error margin.

To answer this question, we need to solve the equation for y in the third case:

We can see from this case that for every value of x, there must be a value in y, and this is the main condition for a relationship to be a function. Then, y is a function of x.

In the fourth case, we have a similar case, for every possible value of x, there must be a value for y. Then, y is a function of x.

As we can see, the red graph is for the linear equation and the black one is for the one with the radical ( y = -sqrt(x+1)).

If we pass a vertical line to either function (alone), we will have only a point that passes through this vertical line, and with this graphical information, we can also say that both are functions of y (for each case).

Answer:

12/6 or 1/2

Step-by-step explanation:

you just plug the coordinates into demos calculator and then look at rise over run.

The range of the data is the difference between the maximum data value and the minimum.

In a box plot, the maximum and the minimum are indicated by the dots at the end of the horizontal line.

Here,

Maximum = 10

Minimum = 4.5

Thus, the range of the data is:

If she decides to plant a 2-foot wide rectangular flower garden along one side of the pool and patio but outside the fence. She measures the length of the fence to be 44 feet long. The area of the flower garden is 88 square feet.

Using this formula to determine the area of the flower garden

Area = Width × Length

Where:

Width = 2 feet

Length = 44 feet

Let plug in the formula

Area = 2 × 44

Area = 88 square feet

Therefore the area is 88 square feet.

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1) Let's make a sketch to better understand this:

Suppose Shaq was on 40 feet after the snack he slipped 20 feet and then 6 feet.

After the snack, He traveled 20 +4 = 24 feet

From the initial point, He went 24 feet down.

Explanation

Question 57

To find the extreme values

So, we will have the steps below

Step 1:

Step2:

Step 3:

Step 4:

Thus, we will have

Hence, our answer is

Answer

Part A: 100 square units

Part B: 39 square units

Part C: 48 square units

Explanation

Part A

Scale: 1cm represent 2 units on x-axis and 1cm represents 5 units on y-axis.

Firstly, we convert the figure into two composite plane shapes, that is, a rectangle and a triangle.

Area of composite shapes = area of rectangle + area of triangle

= Length x Width + 1/2(base x height)

= 10 x 8 + 1/2(10 x 4)

= 80 + 20

= 100 square units

Part B

Scale: 1cm represent 3 units on x-axis and 1cm represents 1 unit on y-axis.

Convert the figure into two composite plane shapes, that is, a rectangle and a trapezium.

Area of composite shapes = area of rectangle + area of trapezium

= Length x Width + 1/2(sum of parallel sides)(perpendicular height)

= 3 x 9 + 1/2(3 + 9)(2)

= 27 + 1/2(24)

= 27 + 12

= 39 square units

Part C

Scale: 1cm represent 2 units on x-axis and 1cm represents 2 units on y-axis.

Convert the figure into two composite plane shapes, that is, a trapezium and a triangle.

Area of composite shapes = area of trapezium + area of triangle

= 1/2(sum of parallel sides)(perpendicular height) + 1/2(base x height)

= 1/2(4 + 8)(6) + 1/2(4 x 6)

=1/2(12 x 6) + 1/2(24)

= 36 + 12

= 48 square units

The given triangle is:

From the properties of triangle,

The sum of all angle in a triangle is equal to 180 degree

In triangle ABC,

Angle A + Angle B + Angle C = 180

70 + 50 + x = 180

120 +x = 180

x = 180 -120

x = 60

The missing angle is 60 degree

Answer: B. 3/5

This question can be solved by using trigonometric identities.

The lines AD and BC cross at a point where we have two pairs of vertically opposite angles.

The angles labelled (2x +50) and 100 are vertically opposite angles.

Vertically opposite angles are equal. Therefore;

ANSWER:

The value of x is 25. The correct answer is option A

The angles sum up to give 180°

Only one of the angles can be an obtuse angle, we can;t have two bothuse angle in a triangle. BUT we can have two acute angles and one obtuse angle in a triangle.

We can also have a 90 degree and 2 acute angle in a triangle.

Examples

The angles sum up to give 180°

Only one of the angles can be an obtuse angle, we can;t have two bothuse angle in a triangle. BUT we can have two acute angles and one obtuse angle in a triangle.

We can also have a 90 degree and 2 acute angle in a triangle.

Examples

Let's begin by identifying key information given to us:

Number of seats = 20

Number of reservation = 23

14 regular customers show up. So, we have:

The number of seats left is:

Overbooking means that more than 6 remaining customers show up (that could mean 7 or 8 or 9 of the remaining customers show up)

The probability of more than 6 customers arriving is given by:

EXPLANATION

Given the function f(x) = (x-6)^2 + 1

Expanding (x-6)^2 + 1 by applying the Perfect Square Formula:

Simplify:

Expanding (x-6)^2 + 1 by applying the Perfect Square Formula:

Axis of simmetry : x=6

The quadratic function has the same shape than the parent function y=x^2 because there is NOT a coefficient within x.

we have that

The incenter is the center of the triangle's incircle, the largest circle that will fit

AR=AT=AS -----> radius of the inscribed circle in the triangle

therefore

AT=3 units

ANSWER:

a)

b)

EXPLANATION:

Given:

a) When x = -4, let's go ahead and solve for y;

When x = 0, let's go ahead and solve for y;

When x = 4, let's go ahead and solve for y;

b) Using the above values, we can go ahead and the equation as seen below;

To find the equation in the form

the slope is defined by:

To find b you can replace any of the points on the equation an clear for b

(x,y)=(4,3)

to check if the answer is correct replace 2 as x in the equation.

since the answer was 0 and point was 2,0 the equation is correct.

Given the expression:

You can simplify it as follows:

1. Distribute the positive sign. Since the sign between the parentheses is positive, it does not change the signs of the second parentheses:

2. Add the like terms.

By definition, like terms have the same variables with the same exponent.

In this case, you need to add the terms with exponent 3 and add the terms with exponent 2. Notice that:

Then, you get:

Hence, the answer is:

From the question, we're told that Hector earns $210.00 for working 2hours every week. Let's go ahead and determine

Given:

OP = 20 in

QP = 26 in

Since R is the midpoint of OP, then, OR = RP

Thus

To find the length of QR, use pythagoras theorem below:

Input values into the formula:

Subtract 10² from both sides:

Take the square root of both sides:

Therefore, the length of QR is 24 in

Simplify the inequality.

So answer is x<-7.

Part A

The sun can produce 3.9 * 10^33 ergs of radiant energy per second