Simplify |x+3| , if x>5

The result of the synthetic division is the final row. In this case, the result is -3, 5, -15, 18.

A polynomial is an expression consisting of variable and coefficient and are used to model real world situation it is an equation of degree greater than one where the exponents of the variables can be any non-negative integer for example the polynomial equation x 2 + 3x + 2 represent a parable of windcraft polynomial are used in name variety of field such as mathematics and physics.

The process of synthetic division is used to divide polynomials of the form ax^n + bx^n-1 + ... + c, where a is the coefficient of the highest power of the variable x.

To divide -3 into the polynomial 1 8 9 -18 0, the following steps should be taken:

Step 1: Line up the divisor, -3, to the left of the polynomial, as shown below:

-3 | 1 8 9 -18 0

Step 2: Bring down the first coefficient in the polynomial, which is 1, and place it directly below the -3.

-3 | 1 8 9 -18 0
  -3

Step 3: Multiply the -3 by the first coefficient and place the result in the next row, directly below the 8.

-3 | 1 8 9 -18 0
  -3
 -3

Step 4: Add the result to the 8, and place the new result in the next row.

-3 | 1 8 9 -18 0
  -3
 -3
  5

Step 5: Repeat steps 3 and 4 for each coefficient in the polynomial.

-3 | 1 8 9 -18 0
  -3
 -3
  5
 -15
-15
 18

Step 6: The result of the synthetic division is the final row. In this case, the result is -3, 5, -15, 18.
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Complete questions as follows-
Divide Using Synthetic Division
-3|1 8 9 -18 0

Answer:

678

Step-by-step explanation:

it is the 123 formation

The volume of the given triangular prism is 384 cm³.

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

Here, the area of the base is

Area of a rectangle = 1/2 ×Base×Height

= 1/2 ×12×4

= 24 cm²

Now the volume is 24×16

= 384 cm³

Therefore, the volume of the given triangular prism is 384 cm³.

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Answer:

x= 8

90+40=130

180-130=50

50-2=48

48/6=8

Answer: I think it’s cm = b, I think your image is very hard to see

Step-by-step explanation:

The given quadrilateral is a parallelogram.

A parallelogram is a special type of quadrilateral that has both pairs of opposite sides parallel and equal.

The proof is as follows;

          STATEMENTS                                       REASONS

1)  AM = CM and BM = DM                                    Given

2) m ∠ AMB = m ∠ DMC and

m ∠ AMD = m ∠ BMC                          Definition of Vertical angles

3) Δ AMB ≅ Δ DMC and

Δ AMD ≅ Δ BMC                                 By SAS congruency criterion

4) AB = CD and

BC = AD                                                BY CPCTC

5) ABCD is a parallelogram                If both pairs of opposite sides of a                                      

                                                           quadrilateral are congruent then it is    

                                                                           a parallelogram.

Hence, proved, ABCD is a parallelogram.

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An image of triangle NOG after a rotation 90° clockwise about the origin is shown below.

In Mathematics and Geometry, a rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

Next, we would apply a rotation of 90° clockwise about the origin to the coordinate of this triangle NOG in order to determine the coordinate of its image;

(x, y)                →            (y, -x)

Point N = (-4, -1)          →     Point N' (-1, 4)

Point O = (-4, -3)          →     Point O' (-3, 4)

Point G = (0, -1)          →     Point G' (-1, 0)

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the left side of this equation equal the right side through the process of completing the square that establishes the equality between the left side and the right side of the Gaussian integral equation.

using  completing the square method:

Starting with the left side of the equation:

∫\(e^(^-^x^2)\) dx

\(e^(^-^x^2) = (e^(^-x^2/2))^2\)

∫\((e^(^-^x^2/2))^2 dx\)

let  u = √(x²/2) =  x = √(2u²).

dx = √2u du.

∫ \((e^(^x^2/2))^2 dx\)

= ∫ \((e^(^-2u^2)\)) (√2u du)

The integral of \(e^(-2u^2)\)= √(π/2).

∫ \((e^(-x^2/2))^2\) dx

= ∫  (√2u du) \((e^(-2u^2))\\\)

= √(π/2) ∫ (√2u du)

We substitute back  u = √(x²/2), we obtain:

∫ \((e^(-x^2/2))^2\)dx

= √(π/2) (√(x²/2))²

= √(π/2) (x²/2)

= (√π/2) x²

A comparison  with the right side of the equation  shows that they are are equal.

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Answer:

A and B

A is 4/10 which is equivalent to 40/100 (40% in fraction form)

and B is 40/100

(the shortcut is to count the blocks going across and then going down and multiply in this case it gives you 100 for the whole square and 40 shaded)

C is 2/10 or 20%

The number of points to be removed from the graph is 2

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

The graph

From the graph, we can see that

2 points have the same y coordinates

Another 2 points have the same y coordinates

For it to be a function, one of the 2 points must be removed each

So, we have the number of points to be removed from the graph is 2

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Answer:

yeah that makes sense to me

According to the provided statement, the battery is at 75% after 1.25 hours and at 40% after 3 hours.

Percentages are just fractions with a denominator of 100.We place the percentage symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

A. How long does it take for the battery to reach 75% capacity?

To determine x, we must change y to equal 0.75 (75%) in the equation (number of hours)

y= -0.2x+1

0.75= -0.2x+1

0.75+0.2x=1

0.2x=1-0.75

x= 0.25/0.2

x=1.25

B. What is the percentage of battery power remaining at 3 hours?​

To determine y, we must change x = 3 hours in the equation (remaining battery power)

y= -0.2x+1

y= -0.2(3) +1

y= -0.6+1

y= 0.4

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Answer: The explicit formula for the following sequence is:

According to the pattern in the sequence, the explicit formula is as follows:

Therefore the answer is Option(2).

Answer:

a triangle that may not have the same dimensions as the bases

Step-by-step explanation:

The cross section of the figure that is perpendicular to the triangular bases and passes through a vertex of the triangular bases would be a triangle that may not have the same dimensions as the bases.

Answer:

less!

Step-by-step explanation:

billy = 15, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20 = 295

maria = 10, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25 = 360

soooooo that in mind! maria earned more than billy!

The ratio of boys to girls was 10.

Boys:Girls = 10:1

If there were 30 boys then let x be the number of girls.

Let us solve for x.

So, there were 3 girls.

Answer:

hmmm................chupapu

Answer:

6 days

Step-by-step explanation:

This question becomes much easier when written out per day (shown below). The question tells us that she is reducing her run by half every day, so all we need to is divide the previous day by 2 to get the current day. She starts out with 26 miles so this is our day 1 value.

Day 1 = 26 miles

Day 2 = 13 miles (26÷2=13)

Day 3 = 6.5 miles (13÷2=6.5)

Day 4 = 3.25 miles (6.5÷2=3.25)

Day 5 = 1.625 miles (3.25÷2=1.625)

Day 6 = 0.8125 miles (1.625÷2=0.8125)

We can see that by day 6, her total running amount is less that 1 mile, so the final answer is 6 days.

The transformation of f(x) to g(x) is :

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

The functions f(x) and g(x)

Where, we have

f(x) = x

g(x) = 1/9x - 2

The graph of the functions f(x) and g(x) are added as an attachment

And we have the transformations to be:

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Answer:

\(\frac{27}{35} \)

Step-by-step explanation:

\(\frac{6}{5} - \frac{3}{7} \)

\(= \frac{42}{35} - \frac{15}{35} \)

\(= \frac{27}{35} \)

a) A function that gives the area of the playground (in square meters) in terms of x is A(x) = 60x - x².

b) The side length that gives the maximum area that the playground can have is x = 30 m.

c) The maximum area that the playground can have is 900 m².

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths, we have:

120 = 2(x + W)

60 = x + W

W = 60 - x

Therefore, the area of the rectangular playground (in terms of x) is given by this function;

A = LW

A(x) = x(60 - x)

A(x) = 60x - x²

Part b.

For the side length, we would take the first derivative of the area:

A(x) = 60x - x²

A'(x) = dA/dx

A'(x) = 60 - 2x

60 - 2x = 0

x = 60/2

x = 30 m

Part c.

W = 60 - x

W = 60 - 30

W = 30 m.

Therefore, the maximum area is given by;

A = 30 × 30

A = 900 m².

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The figure of the exercise is a Trapezoid, this is characterized by not having any axis of symmetry. The interior angles, as in any quadrilateral, add up to 360º

The value of the underlined digit in the number 27,416,385.( 4 is the underlined number.) is the hundred thousandths place.

The symbols, from 0 to 9 can be described as a digit. For instance, the numbers 2 and 3 are used to represent the number 23.  however amount is represented by a number.

It should be noted that It may be expressed using one, two, three, or even more digits however only single symbol used to represent a number is a digit in the case above we can see that 4 is the hundred thousandths place.

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Answer: If Pedro starts reading at page 20 and reads at an average rate of 25 pages per hour, and Bella starts reading at the same time but starts at page 60 and reads at an average rate of 18 pages per hour,

We can use the formula: distance = rate x time

To find out when they will meet we need to find out when they are on the same page.

let's say t be the time in hours, Pedro will be reading t25 pages, and Bella will be reading t18 pages.

So we can write the equation: 20+t25 = 60+t18

Solving this equation we get t = 2

So, they will meet after 2 hours.

Pedro will be on page 20+225 = 70, and Bella will be on page 60+218 = 96

So they will meet at page 70 when Pedro reaches that page after 2 hours of reading, which means Bella will have read 26 pages more than Pedro on that point.

Step-by-step explanation:

Answer:

its y=x+7

Step-by-step explanation:

y=2/3x-4 is the equation of the line where 2/3 is the slope.

We have to find the equation of line which is passing through points (0, -4) and (3, -2).

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁.

Slope = -2+4/3-0

=2/3

Now let us find the y intercept.

-4=2/3(0)+b

b=-4

The equation of line is y=2/3x-4.

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The possible lengths for the third side 8² + 11² < x²,  8² + 11² = x²

and 8² + 11² ≥ x².

If a² + b² < c² then it is an acute angle triangle.

If a² + b² = c² then it is a right-angle triangle.

If a² + b² ≥ c² then it is an obtuse angle triangle.

Given, Two sides of a triangle have lengths 8 and 11.

Let, The third side be 'x'.

Therefore, The possible lengths for the third side are,

8² + 11² < x²...(i)

8² + 11² = x²...(ii)

8² + 11² ≥ x²...(iii)

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