3.2.3. In the table below, the written explanation of the steps have been provided, show the
mathematical steps for the explanations given.
WH
Factorize x²+x-12
Mathematical steps.
x² + 4x -3x - 12
(x+4)(x-3)
Explanation
Rewrite the middle term of the trinomial
using the values from the chart above.
Group pairs of terms.
Factor out the HCF of the first group.
Factor out the HCF of the second group.
Factor out HCF of the two terms
The final factorized answer
SURINATE

ANSWER

The solutions are 0.4 and 2

EXPLANATION

STEP 1: add 1 to both sides of the equation:

STEP 2: take square root on both sides of the equation. Remember that the square root has two results - one positive and one negative:

STEP 3: add 6 on both sides of the equation:

Here we have to start separating the results, one with +4 and the other with -4:

STEP 4: divide both sides by 5:

The solutions are x = 0.4 and x = 2

Answer:

Ok to find square root you need to find something times itself to get that number and since that is a negative it is a negative number x itself ONCE

I tried my best so put -150 in a calculator divide it by 2 and you shall get the square root of -150

Step-by-step explanation:

It would take approximately 12.18 milliseconds to access Block (2, 20, 0) on the disk, assuming that the read/write head is initially positioned on Block (0,0,0).

First, the seek time component of the access time refers to the time it takes for the read/write head to move to the correct track on the disk. In this case, the read/write head must move from track 0 to track 20, which means a seek operation is required.

For simplicity, let's assume that the rotational speed of the disk is 7200 RPM (revolutions per minute) and that there are 8 sectors per track. This means that each sector is separated by an angular distance of 45 degrees (360 degrees / 8). To reach the 2nd sector on track 20, the head must wait for the disk to rotate by (2-1) sectors * 45 degrees/sector = 45 degrees.

The time it takes for the disk to rotate by 45 degrees can be calculated as (45 / 360) * (1 / (7200 / 60)) = 7.14 milliseconds.

This component depends on the size of the block and the transfer rate of the disk. Let's assume that the block size is 4 KB and that the transfer rate is 100 MB/s. The transfer time can be calculated as (4 KB / 100 MB/s) = 0.04 milliseconds.

Adding up the three components, we get the total access time as follows:

Total access time = seek time + rotational latency + transfer time

Total access time = 5 ms + 7.14 ms + 0.04 ms

Total access time = 12.18 ms

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Complete Question:

Assuming that the R/W head is initially on the first block (0,0,0) of the disk, compute the access time of each of the following blocks:

Block (2, 20, 0):

In order to solve the equation, we should do:

Then, in the step to isolate the variable term (4x), we should add 3 to both sides of the equality (see step 2).

Answer: C: 3.

Answer:

Step-by-step explanation:

Point A = (5, 6)  is reflected across the x axis which is y =0.

When the point is reflected across the x axis, the x coordinate

remains positive, but the y coordinate becomes negative.

The 6 becomes negative (-6).

So the coordinates of A' are (5, -6) which is the first answer.

Answer:

17/30

Step-by-step explanation:

Number of students = 30

Number of girls and A students = 13+4 = 17

Probability of a student being chosen at random being either a girl or an A student = Total Number of girls and A students/Total No of students = 17/30

Probably of a student chosen at random being either a girl or an A student would be 17/30

The probability of choosing a girl or an A student is 17/30 or 0.567.

There are a couple of ways to approach this problem, but one common method is to use the formula:

                  P(girl or A) = P(girl) + P(A) - P(girl and A)

where P(girl) is the probability of choosing a girl, P(A) is the probability of choosing an A student, and P(girl and A) is the probability of choosing a student who is both a girl and an A student.

To calculate each of these probabilities, we first need to find the total number of girls and A students in the class:

                 Total number of girls: 13

                 Total number of A students: 4 boys + 5 girls = 9

Now we can calculate each probability:

                  P(girl) = number of girls / total number of students = 13 / 30

                  P(A) = number of A students / total number of students = 9 / 30

                  P(girl and A) = number of girls who made an A / total number of students = 5 / 30

Plugging in the values, we get:

                  P(girl or A) = P(girl) + P(A) - P(girl and A)

                  = 13/30 + 9/30 - 5/30

                  = 17/30

Therefore, the probability of choosing a girl or an A student at random from the class is 17/30, or about 0.567.

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Step-by-step explanation:

\(Area = \: \frac{bh}{2} \\ : b = 16.9 \: h = 10.4 \\ \)

\(Area = \frac{16.9 \times 10.4}{2} = \frac{175.76}{2} = 87.88 {ft}^{2} \)

Base = 16.9

height = 10.4

Area = ½b×h

A = ½(16.9×10.4)

A = ½(175.76)

Area = 175.76/2

A = 87.88ft²

Answer:

\(\Large \boxed{\mathrm{87.88 \ ft^2 }}\)

Step-by-step explanation:

\(\displaystyle area \ of \ triangle \ = \ \frac{base \times height }{2}\)

\(\displaystyle area \ of \ triangle \ = \ \frac{16.9 \times 10.4 }{2}\)

\(\displaystyle area \ of \ triangle \ = \ \frac{175.76}{2}\)

\(\displaystyle area \ of \ triangle \ = \ 87.88\)

The manager can find the volume of the container using the formula lwh. The employee correctly determines that the container can be filled with 3 layers of 21. He can find the volume of the container by multiplying the number of bento boxes that fill the container by the volume of one bento box. The volume found by using the formula is equal to the volume of the total number​of bento boxes in the container.

In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:

Volume of a rectangular prism = LWH

Where:

Part a.

Therefore, the manager can use the following formula;

Volume of container = LWH

Volume of container = 7/2 × 3/2 × 3/2

Volume of container = 63/8 cm³.

Part b.

For the number of bento boxes that can fill the container, we have:

Number of bento boxes = Volume of container/Volume of bento boxes

Number of bento boxes = 63/8/(1/2)³

Number of bento boxes = 63/8/1/8

Number of bento boxes = 63/8 × 8

Number of bento boxes = 63 bento boxes = 3 layers × 21.

Part d.

Volume of container = Volume of bento boxes

63/8 cm³ = 63 × 1/8 cm³

63/8 cm³ = 63/8 cm³ (equal).

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The equation formed after the transformations is given as follows:

\(g(x) = \frac{1}{6}\sqrt{x + 3}\)

The parent function in this problem is defined as follows:

\(f(x) = \sqrt{x}\)

For the vertical shrink by a factor of 1/6, the function is multiplied by 1/6, hence it is given as follows:

\(g(x) = \frac{1}{6}\sqrt{x}\)

For the translation left 3 units, we have that x -> x + 3, hence:

\(g(x) = \frac{1}{6}\sqrt{x + 3}\)

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A) The domain is x ≥ 0

Then the range is y ≥ 205

B) The point (300, 505) means that after the initial amount of $205, the amount deposited in dollars is $300 while the total amount of savings is now $505.

The domain of a function is defined as all the possible input values that make the function possible.

The range of a function is defined as all the possible output values for which the function holds.

A) We are given the function that represents the amount of money in a savings account that started with $205 after a deposit of x dollars as;

f(x) = 205 + x

Since x represents the amount deposited, then we can say that the values will be greater than or equal to zero. Thus;

The domain is x greater than or equal to zero.

Then the range will be greater than or equal to zero.

B) At (300, 505), it means that after the initial amount of $205, the amount deposited in dollars is $300 while the total amount of savings is now $505.

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The line of best fit for the set of data in this problem is given as follows:

y = 0.613x + 4.142.

To find the regression equation, which is also called called line of best fit or least squares regression equation, we need to insert the points (x,y) of the data-set in the calculator.

The points for this problem are given as follows:

(-2, 2.9), (-3.5, 2), (1.4, 4.8), (-4.2, 1.5), (0,4), (2.8, 6), (-1.5, 3.5).

Inserting these points into a calculator, the line of best fit is given as follows:

y = 0.613x + 4.142.

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Answer:

69.23%

Step-by-step explanation:

Given:

Maria's Diner offers its clients a choice of regular and diet soda.

Last night, the diner served 65 sodas in all, 45 of which were regular.

To Find:

What percentage of the sodas were regular?

Solve:

Base on the given, All we have to do is

45/65 = 0.6923076923 Which rounds to 69.23%

We did that because

The total = 65 sodas in all

Regular = 45 sodas

Thus

45 out of 65 are regular

which means divide

45/65.

Hence, 60.23% of the sodas were regular.

Kavinsky

The intermediate step in completing the square is\($x^2 + 2ax + (a^2) = b - a^2 + (a^2)$\)

To complete the square for the equation \($(x+a)^2=b$\), we can follow these steps:

1. Expand the left side of the equation: \($(x+a)^2 = (x+a)(x+a) = x^2 + 2ax + a^2$\).

2. Rewrite the equation by isolating the squared term and the linear term: \($x^2 + 2ax = b - a^2$\).

3. To complete the square, take half of the coefficient of the linear term, square it, and add it to both sides of the equation:

\($x^2 + 2ax + (a^2) = b - a^2 + (a^2)$\).

4. Simplify the right side of the equation: \($x^2 + 2ax + (a^2) = b$\).

This step can be represented as: \(\[x^2 + 2ax + (a^2) = b - a^2 + (a^2)\]\)

This intermediate step helps us rewrite the equation in a form that allows us to factor it into a perfect square.

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Answer:

The equation of this line is y = -4.

Answer:

y=-4

Step-by-step explanation:

zero slope m=0

y-y1=m(x-x1)

y-(-4)=0(x-(-9))

y+4=0

y=-4

The linear equation we need to solve is:

$27.50*w = $309.99 - $144.99

And the solution is w = 6.

How to write and solve the equation?

We know that the cost of the gaming chair is $309.99.

To buy this, you already have saved $144.99, and save another $27.50 per week, then the amount you have after w weeks is:

f(w) = $144.99 + $27.50*w

So the linear equation we need to solve is:

$144.99 + $27.50*w = $309.99

To solve this we need to isolate w.

$144.99 + $27.50*w = $309.99

$27.50*w = $309.99 - $144.99

w = ($309.99 - $144.99)/$27.50 = 6

So they can buy the chair after 6 weeks.

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Given the expression

We are asked if the above is an example of a complex fraction.

A complex fraction can be defined as a fraction in which the denominator and numerator or both contain fractions.

A complex fraction containing a variable is known as a complex rational expression. For example,

1) 3/(1/2) is a complex fraction whereby, 3 is the numerator and 1/2 is the denominator.

2) (3/7)/9 is also a complex fraction with 3/7 and 9 as the numerator and denominator respectively.

3) (3/4)/(9/10) is another complex fraction with 3/4 as the numerator and 9/10 as the denominator.

Answer: Yes, 3/(1/8 ) is a complex fraction

D

Step-by-step explanation:

The points dx are at -1, 1, 2 and 3 so it must be D

Answer:

To find the range,

first see the value of each points -

first = (3,5)

second = (2,0)

third = ( 1,3)

fourth, ( -1, 2)

let's take X Axix to find the range

so the range is ( -1, 1 , 2 ,3)

Option D is correct

Answer:

8 lessons

Step-by-step explanation:

x45 + 100 ≤ 500

x45 ≤ 500 - 100

x45 ≤ 400

x ≤ 8

8 * 45 + 100 ≤ 500

360 + 100 ≤ 500

460 ≤ 500

Answer:

Plug g(x) into all the x values in your f(x) and the answer is 3 because it makes the denominator 1-1 which makes it 0 and is thus discontinuous

Step-by-step explanation:

#The x side is same with 80° so

11x + 3 = 80°

11x = 80 - 3

11x = 77

x = 7

The percentage of NFL players retire at a younger age is A ) 0.62 % and the age is C ) 34.8 years .

Given :

The retirement age for NFL players follows a normal distribution with a mean of 33 years and a standard deviation of 2 years. A player gets injured and decided to retire at 28 years old.

percentage of NFL players retire at a younger age is :

P ( X < 28 ) = P ( x - μ / σ < 28 - 33 / 2 )

= P ( z < -5 / 2 )

= P ( z < -2.5 )

we know that at z score using calculator we can know the probability :

= 0.0062

= 0.0062 * 100%

= 0.62%

The age would he be if he played longer than 90% of all players is B ) 34.8 years old .

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Answer: Area = 56.52 units

Step-by-step explanation:

Pi = 3.14

Area of triangle formula is base x height divided by 2.

6 (3.14) = 18.84

18.84 x 3 = 56.52 units

Siama and Wills used different methods to find the differences between (5x + 6x) and (2x - 1) but they both arrived at the same answer.

I prefer Wills method because it is easier and less complicated.

Wills method:

(5x + 6x) - (2x - 1)

Subtract both 2x and -1

5x + 6x - 2x - - 1

5x + 4x + 1

In conclusion, Wills method is preferred when both methods are compared.

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Answer:

16

Step-by-step explanation:

1. Use acronym PEMDAS (parentheses, exponents, multiplication/division, addition/subtraction) to determine the order of operations.

2. Since there are no parentheses or exponents, multiply first:

4*5=20

3. Now, the expression reads 20+-4.  Adding a negative is the same as subtracting that value.

20-4=16

Hope this helps!!

Answer:

=197060718

Step-by-step explanation:

51661−61661+(611)(5561)(58)

=−10000+(611)(5561)(58)

=−10000+(3397771)(58)

=−10000+197070718

=197060718

Answer:

C) 260 square inches.

Step-by-step explanation:

To find the surface area of a pyramid, we can use the formula.

Surface Area = (1/2) x Perimeter of Base x Slant Height + Base Area

where l is the length of one side of the square base, s is the slant height, and Base Area is the area of the square base.

In this case, the base of the pyramid is a square with side length l = 10 inches, so its area is

Base Area = l^2 = 10^2 = 100 square inches

To find the perimeter of the base, we can simply multiply the length of one side by 4

Perimeter of Base = 4l = 4 x 10 = 40 inches

We are also given that the slant height of the pyramid is s = 8 inches.

Now we can substitute the values into the formula.

Surface Area = (1/2) x Perimeter of Base x Slant Height + Base Area

Surface Area = (1/2) x 40 x 8 + 100

Surface Area = 160 + 100

Surface Area = 260 square inches

Therefore, the surface area of the pyramid is 260 square inches.

Answer:360 in

Step-by-step explanation:

The distance between Basti and Cian is approximately 138.2 ft. Option D

To find the distance between Basti and Cian, we can use the Law of Sines, which relates the lengths of sides to the sines of their opposite angles in a triangle.

Let's label the points: A, B, and C. Ali is at point A, Basti is at point B, and Cian is at point C.

Given:

Angle ABC = 50 degrees (angle opposite side AC)

Angle BAC = 60 degrees (angle opposite side BC)

Ali is 150 ft away from Basti (side AB)

We want to find the distance between Basti and Cian, which is side BC.

Using the Law of Sines, we have:

BC/sin(50) = AB/sin(60)

Substituting the known values:

BC/sin(50) = 150/sin(60)

To find BC, we can rearrange the equation:

BC = (150/sin(60)) * sin(50)

Using a calculator to evaluate the expression:

BC ≈ 138.2 ft

Option D is correct.

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Answer:

Smallest element in the set of range is -3

Step-by-step explanation:

From the given set of ordered pairs,

x-value of each pair represents the Domain of the relation.

y-value of the pair represents the Range of the relation.

Set of domain:

{0, 1, 2, 3, 4, 5, 6}

Set of Range:

{1, 3, 2, 5, 2, -3, 2}

Smallest number in the set of range = -3.

Therefore, smallest element in the set of range is -3.