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3 years ago

Use synthetic division to divide (x3 + x2 – 40x – 4) ÷ (x – 6).

Mathematics

1 answer:

eduard3 years ago

8 0

Answer:

A. x^2 + 7x + 2 R 8

Step-by-step explanation:

(x^3 + x^2 – 40x – 4) ÷ (x – 6).

6 | +1 1 - 40 -4

| 6 42 12

------|----------------------------------------------------

| 1 7 2 | 8

x^2 + 7x + 2 + [8/(x - 6)]

Answer:

A. x^2 + 7x + 2 R 8

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a game is played with a circular spinner that contains 7 different colors. the design of the spinner is the order in which the c

dmitriy555 [2]

Answer:

This spinner can be designed in 5040 ways.

Step-by-step explanation:

Number of possible arrangements:

The number of possible arrangements of n elements is given by:

$A_{n} = n!$

In this question:

7 colors, so:

$A_{7} = 7! = 5040$

This spinner can be designed in 5040 ways.

8 0

3 years ago

Find the area of the shaded portion in each of the following

MrRa [10]

Answer:

30.5 cm^2

Step-by-step explanation:

<h3><u>General outline</u></h3>

Find the area of the full circle
Find the area of the rectangle
Find the difference (full circle area - rectangle area)

<h3><u>Step 1. Find the area of the full circle</u></h3>

Recall the formula for the area of a circle: $A_{circle}=\pi r^2$ where $\pi \approx 3.14$ , and "r" is the radius of the circle (distance from center to any point on the edge).

From the diagram, the radius is 5cm.

$A_{circle}=\pi r^2$

$A_{circle}=(3.14)(5[cm])^2$

$A_{circle}=78.5[cm^2]$

<h3><u>Step 2. Find the area of the rectangle</u></h3>

Recall the formula for the area of a rectangle: $A_{rectangle}=bh$ where "b" is the base of the rectangle (length of bottom or length of top), "h" is the height of the rectangle (distance from bottom to top).

From the diagram, the base is 8cm, and the height is 6cm.

$A_{rectangle}=bh$

$A_{rectangle}=(8[cm])(6[cm])$

$A_{rectangle}=48[cm^2]$

<u />

<h3><u>Step 3. Find the difference (full circle area - rectangle area)</u></h3>

Having found the areas for each of the first parts, we can find the difference to find the shaded area:

$A_{shaded}=A_{circle}-A_{rectangle}$

$A_{shaded}=(78.5[cm^2])-(48[cm^2])$

$A_{shaded}=30.5[cm^2]$ <u />

6 0

2 years ago

All of the members of our spray-painting team paint at the same speed. If 20 team members can paint a 4800 square foot wall in 3

KATRIN_1 [288]

Answer:

It takes 70 minutes for 9 team members (painting 60 sq ft per minute) to paint a 4200 sq ft wall.

Step-by-step explanation:

4800 ÷ 20 = 240 sq ft per team member in 36 minutes

240 ÷ 36 = 6.67 sq ft per team member in 1 minute

6.67 × 9 = 60 sq ft per 9 team members in 1 minute

4200 ÷ 60 = 70 minutes (or 1 hour and 10 minutes)

3 0

3 years ago

What is the percent of change if 30 is decreased to 25?

Luden [163]

Answer:

16.67%

Step-by-step explanation:

initial rate=30

final rate =25

decreased rate = 30 - 25= 5

Now,

Decreased % = (5 / 30) * 100%

= 16.67%

3 0

3 years ago

Read 2 more answers

Determine whether the graph represents a function . If it does represent a function , give its domain and range.

laiz [17]

Answer:

A function is a relationship that maps elements from a set (the domain) into elements from another set (the range)

Such that each element in the domain can be mapped into only one element from the range.

Let's see graphs 18, 20,24 and 30.

Remember that the axis that represents the domain is the horizontal one (usually represented with x), and the vertical axis represents the range (usually represented with y)

18) Here we can see that the point x = 1 his mapped into two different values of y.

we have the pair (1, 2) and the pair (1, -3)

And something similar happens for x = 2.

Then we can conclude that this is not a function.

20) Here we have a linear relationship.

Linear relationships are almost always functions, the only case when these are not functions is when the linear equation is something like x = a.

Linear equations can be written as:

y = a*x + b

So x can be any value, and thus y also can be any value.

Then the domain is the set of all real numbers, and the range is the set of all real numbers.

24) Here we have a quadratic function whose arms go down.

This is a function, now let's see the domain and range.

Quadratic functions are written as:

y = a*x^2 + b*x + c

There is no value of x can cause some problem in this equation, then this function works for all values of x, then the domain is the set of all real numbers.

Now, let's look at the graph.

We can see that the function goes up, reaches a maximum, and then goes down again.

Then the range will be the set of all the values smaller than the maximum we can see in the graph, this is:

y ∈ (-∞, 15]

or simply:

y ≤ 15.

30) Here again, we can see that for x = 0 there are two different values of y.

the same happens for x = -1, x = -2, and a lot of other values.

Then this is not a function, because it is mapping values of the domain into different values of the range.

3 0

3 years ago