Explain how to use 2s facts to find 4 x 9

It will take [tex]4\frac{2}{7}\ hours[/tex] to cover same distance.

Step-by-step explanation:

Given,

Time period = 5 hours

Speed = 60 km/h

Distance = Speed * Time

Distance = 60*5 = 300 km

Now,

Distance = 300km

Speed = 70 km/h

Distance = Speed * Time

Time = [tex]\frac{Distance}{Speed}[/tex]

[tex]Time=\frac{300}{70}\\\\Time=\frac{30}{7}\\\\Time= 4\frac{2}{7}\ hours[/tex]

It will take [tex]4\frac{2}{7}\ hours[/tex] to cover same distance.

Keywords: speed, distance

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A descending sort would list the data from tallest to shortest in the height field of a database about trees.

The kind of sort that would list the data from tallest to shortest in the height field of a database about trees is a descending sort. This sort arranges the data in reverse order, with the tallest tree at the top and the shortest tree at the bottom. To perform a descending sort in a database, you can use the ORDER BY clause with the DESC keyword in the SQL query.

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A table is given containing the values of x and y.

The equation of the line is modeled by the values in the table.

As we can see in the table, we get to know that;

The y value is increased by 5 whereas the value of x is increased by 2.

So, we will put the numbers over each other for slope.

Therefore, slope=5/2

Now, we will put the slope value in the model equation;

y=mx+b

y=5/2x+b

Now, in the place of y and x we will be putting (2,1) in their place;

1=5/2(2)+b

b=1-5=-4

So, the final equation we get as;

y=5/2x-4

Hence, the equation of the line that is modeled by the values in the table shown is y=5/2x-4.

equation, statement of equality between two expressions consisting of variables and/or numbers. In essence, equations are questions, and the development of mathematics has been driven by attempts to find answers to those questions in a systematic way.

A mathematical equation which represents the relationship of two expressions on either side of the sign. It mostly has one variable and equal to symbol. Example: 2x – 4 = 2.

An equation is a statement that says that the value of two mathematical expressions is equal. In simple words, an equation says that two things are equal. It is denoted by the equal to sign '='. Example of an Equation: 8+2= 12-2. The above equation says that the left side of the equation is equal to the right side.

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Answer:

x intercepts at (-3,0), and (1,0)

there is a minimum at (-1,-4)

Step-by-step explanation:

Please see attached image for the requested graph of the function [tex]f(x) = x^2+2x-3[/tex], and observe that the crossings of the x-axis are at the points (-3,0), and (1,0) , marked in red in the image.

We can also see that there is no maximum, but a minimum value, and located at the point (-1,-4) [marked in green in the image]

Answer:

4x

Step-by-step explanation:

The calculated cost of spraying the rectangular field is $846

Calculating the cost of spraying the rectangular field

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

Dimension = 720 m by 500 m

Unit cost = $23.50 per hectare

The area of the field is calculated as

Area = 720 m * 500 m

So, we have

Area = 360000 square meters

Converted to hectares, we have

Area = 36 hectares

So, we have

Cost = $23.50 per hectare * 36 hectares

Evaluate

Cost = $846

Hence, the cost of spraying the rectangular field is $846

Answer:

The x-intercept is the ordered pair (9,0)

Step-by-step explanation:

we know that

The x-intercept is the value of x when the value of y is equal to zero

so

The x-intercept is a ordered pair with a y-coordinate equal to zero

therefore

In this problem

The x-intercept is the ordered pair (9,0)

The x-intercept from the list of ordered pairs (8,10), (3,-4), (0,8), (4,-3), (9,0) is 9, as it is the x-value of the pair where the y-coordinate is zero.

To find the x-intercept from a list of ordered pairs, you need to look for the pair where the y-coordinate is zero. The x-intercept is the x-value in this pair.

From the list of ordered pairs given in the question, which are (8,10), (3,-4), (0,8), (4,-3), (9,0), we identify that the x-intercept is in the pair where y is equal to 0.

Thus, the x-intercept from the list is 9, as it appears in the ordered pair (9,0).

Answer:

25% or 1/4. I don't know how to type Vietnamese.

Answer:

Step-by-step explanation:

when x=35

y=-35+175=140

Answer:

in polynomial form

Step-by-step explanation:

if you have any question then reply me

The area of the rectangle can be found by multiplying its width by its height, which is a polynomial expression in this case.

To find the area of a rectangle, we multiply its width by its height. In this case, the width of the rectangle is y3+6y and the height is 2y3+5. So, the area of the rectangle is:

A = width × height

A = (y3+6y) × (2y3+5)

A = 2y^6 + 5y^3 + 12y^4 + 30y

This is the area of the entire rectangle, expressed as a polynomial in standard form.

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The width (W) of the prism is 16 cm.

The length (L) of the prism is 16 cm.

The height (H) of the prism is 10 cm.

The formula for the surface area of any right prism with width W, length L, and height H is the following:

A = 2 (WL + LH + WH)

Substituting using our given values changes the equation to:

A = 2 (16*16 + 16*10 + 16*10)

= 2 (256 + 160 + 160) = 2 (576)

= 1152

Thus, the surface area is 1152 cm².

Let me know if you need any clarifications, thanks!

Answer:

1152

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

That seems like it would be the correct equation.

Answer:

a

Step-by-step explanation:

it is the tell how many days

Final answer:

In geometry, corresponding sides are sides that have the same relative position in two similar figures. To identify the corresponding sides in the given question, we need to find the sides with the same position in the figures RGK and MQB. The corresponding sides of RGK and MQB are RG = MQ, RK = MB, and GK = QB.

Explanation:

In geometry, corresponding sides are sides that have the same relative position in two similar figures. To identify the corresponding sides in the given question, we need to find the sides with the same position in the figures RGK and MQB.

In this case, RGK and MQB are both triangles, so we need to compare their corresponding sides. The corresponding sides of a triangle are the sides that are in the same position (opposite vertices) in the two triangles.

Therefore, the corresponding sides of RGK and MQB are:

RG = MQ

RK = MB

GK = QB

Note: As you missed to identify what we have to find in this question. But, after a little research, I am able to find that we had to find the Mode for the data given in your question. So, I am assuming we have to calculate the the Mode. Hopefully, it would clear your concept regarding this topic.

Answer:

The mode of the data = 75

Step-by-step explanation:

Lets visualize the given data in a table to show the frequency distribution:

Daily expenditure on milk (in Rs)           Number of households

                 0-30                                                           5

                30-60                                                          6        

                60-90                                                          9

                90-120                                                         6

                120-150                                                        4

Here the maximum frequency is 9.

So, modal class is 60-90.

As the formula to calculate the mode:

[tex]Mode = l_{1} + h (\frac{f_{1}-f_{0}}{2f_{1}-f_{0}-f_{2}} )[/tex]

Here, the maximum

[tex]l_{1} =60, f_{1} =9, f_{0}=6, f_{0}=6, h=30[/tex]

[tex]l=[/tex] is the lower limit of the class

[tex]f_{1} =[/tex] is the frequency of the modal class

[tex]f_{0} =[/tex] is the frequency of the previous modal class

[tex]f_{2} =[/tex] is the frequency of the next previous modal class

[tex]l=[/tex] is the class size

So,

[tex]Mode = l_{1} + h (\frac{f_{1}-f_{0}}{2f_{1}-f_{0}-f_{2}} )[/tex]

[tex]Mode = 60 + 30 (\frac{9-6}{2(9)-6-6} )[/tex]

[tex]Mode = 60 + \frac{(30)(3)}{6}[/tex]

[tex]Mode = 60 + 15=75[/tex]

∴ The mode of the data = 75

Keywords: mode, frequency distribution

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ans is 9/4 .................

Answer:225.28

Step-by-step explanation: 98 become 100 and 22528 stays the same.

Answer:

See the explanation.

Step-by-step explanation:

Given function [tex]f(x)=x^3-x^2-6x+2[/tex]

And the interval [tex][0,3][/tex]

According to Rolle's Theorem

Let [tex]f(x)[/tex] be differentiable on the open interval [tex](a,b)[/tex] and continuous on the closed interval [tex][a,b][/tex]. Then if [tex]f(a)=f(b)[/tex], then there is at least one point [tex]x\ in\ (a,b)[/tex] where [tex]f'(x)=0[/tex].

So,

[tex]f(0)=0^3-0^2-6\times0+2\\\\f(0)=2\\\\Similarly\\\\f(3)=3^3-3^2-6\times3+2\\\\f(3)=27-9-18+2\\\\f(3)=2\\\\We\ can\ see\ f(0)=f(3)\\\\Now,\\\\f'(x)=\frac{d}{dx}(x^3-x^2-6x+2)\\\\f'(x)=3x^2-2x-6\\\\put\ f'(x)=0\\\\3x^2-2x-6=0\\[/tex]

We will find the value of [tex]x[/tex] for which [tex]f'(x)[/tex] became zero.

[tex]If\ ax^2+bx+c=0\\\\Then,\ x_{1}=\frac{-b+\sqrt{b^2-4ac}}{2a}\\ \\And\ x_{2}=\frac{-b-\sqrt{b^2-4ac}}{2a}\\\\f'(x)=3x^2-2x+6=0\\a=3,\ b=-2,\ c=6\\\\\ x_{1}=\frac{-(-2)+\sqrt{(-2)^2-4\times3\times(-6)}}{2\times3}\\\\x_{1}=\frac{2+\sqrt{76}}{6}=\frac{2+2\sqrt{19}}{6}\\\\x_{1}=\frac{1+\sqrt{19}}{3}\\\\x_{2}=\frac{-(-2)-\sqrt{(-2)^2-4\times3\times(-6)}}{2\times3}\\\\x_{1}=\frac{2-\sqrt{76}}{6}=\frac{2-2\sqrt{19}}{6}\\\\x_{2}=\frac{1-\sqrt{19}}{3}[/tex]

We can see

[tex]x_{1}=\frac{1+\sqrt{19}}{3}=1.786\\\\and\ 1.786\ is\ in\ [0,3][/tex]

There is at least one point [tex]1.786\ in\ (0,3)[/tex] where [tex]f'(x)=0[/tex].

Rolle's theorem requires a function to be continuous on [a, b], differentiable on (a, b), and have f(a) = f(b). After verifying these conditions are met for f(x) = x^3 - x^2 - 6x + 2, we look for a point in (0, 3) where f'(x) = 0. We cannot find such a point in the interval, suggesting an error in the application of the theorem.

To verify Rolle's theorem for the function f(x) = x^3 - x^2 - 6x + 2 in the interval [0,3], we need to ensure that the function meets the criteria stated by the theorem:

The function f must be continuous on the closed interval [a, b].

The function f must be differentiable on the open interval (a, b).

The function f must satisfy f(a) = f(b).

f(x) = x^3 - x^2 - 6x + 2 is a polynomial, which is continuous and differentiable everywhere. Therefore, it satisfies the first two conditions of Rolle's theorem on any interval, including [0,3].

Now we need to check the third condition:

f(0) = (0)^3 - (0)^2 - 6(0) + 2 = 2
f(3) = (3)^3 - (3)^2 - 6(3) + 2 = 2

Since f(0) = f(3), the third condition is also met. Hence, Rolle's theorem applies, and there must be at least one c in (0, 3) such that f'(c) = 0.

To find c, we take the derivative of f(x):

f'(x) = 3x^2 - 2x - 6

Set f'(x) equal to zero and solve for x:

3x^2 - 2x - 6 = 0
Factors into (3x + 2)(x - 3) = 0
So x can be either x = -2/3 or x = 3. Since -2/3 is not in our interval, the only possibility in the interval (0, 3) is at x = 3. However, in this case, the point x = 3 is an endpoint, hence it's not within the open interval (0, 3).

Thus, we need to conclude that there has been a mistake, as x = 3 does not satisfy the condition for Rolle's theorem within the open interval (0, 3).

Answer:

1) [tex]x=\dfrac{5}{2}[/tex]

2)  [tex]t_1=-1[/tex] and [tex]t_2=6[/tex]

3) (0,12)

4) [tex]\left(\dfrac{5}{2},\dfrac{49}{2}\right)[/tex]

Step-by-step explanation:

The function [tex]h(t) =-2t^2 + 10t + 12[/tex] represents the height (h) of the ball after t seconds.

Find the vertex of the parabola:

[tex]t_v=-\dfrac{b}{2a}=-\dfrac{10}{2\cdot (-2)}=\dfrac{5}{2}\\ \\h_v=h\left(\dfrac{5}{2}\right)=-2\cdot\left(\dfrac{5}{2}\right)^2+10\cdot \dfrac{5}{2}+12=-2\cdot \dfrac{25}{4}+25+12=-\dfrac{25}{2}+37=\dfrac{49}{2}[/tex]

Hence, the vertex of the function is at point [tex]\left(\dfrac{5}{2},\dfrac{49}{2}\right).[/tex]

The axis of symmetry of the function is vertical line which passes through the vertex, so its equation is

[tex]x=\dfrac{5}{2}[/tex]

To find y-intercept, equat t to 0 and find h:

[tex]h=-2\cdot 0^2+10\cdot 0+12=12[/tex]

Hence, y-intercept is at point (0,12)

To find the roots of the quadratic finction, equate h to 0 and solve the equation for t:

[tex]h=0\Rightarrow -2t^2+10t+12=0\\ \\t^2-5t-6=0\ [\text{Divided by -2}]\\ \\D=(-5)^2-4\cdot 1\cdot (-6)=25+24=49\\ \\t_{1,2}=\dfrac{-(-5)\pm \sqrt{49}}{2\cdot 1}=\dfrac{5\pm 7}{2}=6,\ -1[/tex]

Therefore, two roots are [tex]t_1=-1[/tex] and [tex]t_2=6[/tex]

The correct answer is:

The light bulb consumes 1056 watt-hours per day, calculated by dividing the total watt-hours by the total number of days.

To find out how many watt-hours the light bulb consumes per day, we need to divide the total watt-hours consumed by the total number of days.

Given:

- Total watt-hours consumed = 5280 watt-hours

- Total time = 5 days and 12 hours

First, let's convert the total time to hours:

[tex]\[ \text{Total time} = 5 \times 24 \text{ hours} + 12 \text{ hours} = 120 + 12 = 132 \text{ hours} \][/tex]

Now, we can calculate the watt-hours consumed per day:

[tex]\[ \text{Watt-hours per day} = \frac{\text{Total watt-hours}}{\text{Total number of days}} \]\[ \text{Watt-hours per day} = \frac{5280 \text{ watt-hours}}{5 \text{ days}} \]\[ \text{Watt-hours per day} = \frac{5280}{5} \text{ watt-hours} \]\[ \text{Watt-hours per day} = 1056 \text{ watt-hours} \][/tex]

So, the light bulb consumes 1056 watt-hours per day.

Answer:

Angle bisector

Step-by-step explanation:

Find the measure of the angle COA. By angle addition postulate,

[tex]m\angle COX=m\angle AOX+m\angle COA[/tex]

From the diagram,

[tex]m\angle COX=80^{\circ}\\ \\m\angle AOX=40^{\circ},[/tex]

then

[tex]80^{\circ}=m\angle COA+40^{\circ}\\ \\m\angle COA=80^{\circ}-40^{\circ}=40^{\circ}[/tex]

Find the measure of the angle BOA. By angle addition postulate,

[tex]m\angle BOX=m\angle AOX+m\angle BOA[/tex]

From the diagram,

[tex]m\angle BOX=60^{\circ}\\ \\m\angle AOX=40^{\circ},[/tex]

then

[tex]60^{\circ}=m\angle BOA+40^{\circ}\\ \\m\angle BOA=60^{\circ}-40^{\circ}=20^{\circ}[/tex]

Find the measure of the angle COB. By angle addition postulate,

[tex]m\angle COX=m\angle BOX+m\angle COB[/tex]

From the diagram,

[tex]m\angle BOX=60^{\circ}\\ \\m\angle COX=80^{\circ},[/tex]

then

[tex]80^{\circ}=m\angle COB+60^{\circ}\\ \\m\angle COB=80^{\circ}-60^{\circ}=20^{\circ}[/tex]

This means, the measures of angles COB and BOA are the same and are equal half the measure of angle COA, so angles COB and BOA are congruent. This means, the ray OB is the angle bisector of angle COA

Answer:

$2.49 per visit

Step-by-step explanation:

Mean or Average Value

It's referred to as the center of a numerical data set. In some circumstances, a list of values needs to be expressed as a single number who best represents them.

The registration fee of the health club is $49. It also charges a $17.50 monthly fee. In one year, the total cost will be $49 + 12*$17.50 = $259. If Ed Parker visits the club 2 times a week for a year, it will make an approximate of 2*52=104 visits a year. The mean cost by visit will be:

$259/104= $2.49 per visit

Answer:

3.55

Step-by-step explanation:

Answer:

Option B is correct.

[tex]x=-8[/tex]

Step-by-step explanation:

Given:

The given equation is.

[tex]7x=-56[/tex]

Solve above equation for value of x.

[tex]7x=-56[/tex]

[tex]x=-\frac{56}{7}[/tex]

[tex]x=-8[/tex]

Therefore. the value of [tex]x=-8[/tex]

Answer:

a) If both gyms sold 80 total memberships, Gym A sold 12 more gold membership.

Step-by-step explanation:

Here is the complete question: 40% of the memberships sold by Gym A were gold memberships. 25% of the memberships sold by Gym B were gold memberships.  

Which statement must be true?

a) If both gyms sold 80 total memberships, Gym A sold 12 more gold membership.

b) If both gyms sold the same number of memberships, Gym A sold 15 more gold membership.

c) Gym A sold more gold membership than Gym A did.

d) If Gym B sold 50 membership, 25 would be gold memberships.

Given: Gym A have sold 40% gold membership of total membership.

Gym B have sold 25% gold membership of total membership.

Lets take option A first to find if it is true statement.

As per option A, There are total number of membership is 80.

∵ Gym A has sold 40% gold membership.

∴ Gym A gold membership= [tex]40\% \times 80[/tex]

⇒ Gym A gold membership= [tex]\frac{40}{100} \times 80= 32 member.[/tex]

∴ Gym A gold membership= 32.

Now, Gym B

∵ Gym B has sold 25% gold membership.

∴ Gym B gold membership= [tex]25\% \times 80[/tex]

⇒ Gym B gold membership= [tex]\frac{25}{100} \times 80=20 member.[/tex]

∴ Gym B gold membership= 20.

Next finding difference gold membership for Gym A and Gym B

[tex]32-20= 12 \ membership[/tex]

Hence, we can say option A is correct as Gym A have sold 12 more gold membership, if total number of membership sold by both Gym is 80.

Answer:maybve

Step-by-step explanation:

no

Answer:

B. When its angles are right angles.

Step-by-step explanation:

A rhombus is a quadrilateral with all 4 sides congruent. The sides can be slanted, which would keep it from being a square. If you make all the sides of a rhombus straight vertically and horizontally so you have 4 right angles, you have a square. A square is a quadrilateral with all 4 sides AND all 4 angles congruent.

Answer:

[tex]y = - \sqrt{x - 5} + 3[/tex]

Step-by-step explanation:

The function [tex]y = - \sqrt{x - 5} + 3[/tex] has a domain x ≥ 5.

This is because the function remains real for (x - 5) ≥ 0 as negative within the square root is imaginary.

Hence, (x - 5) ≥ 0

⇒ x ≥ 5

Now, for all x values that are greater than equal to 5 the value of [tex]- \sqrt{x - 5}[/tex] will be negative.

So, [tex]- \sqrt{x - 5} \leq  0[/tex]

⇒ [tex]- \sqrt{x - 5} + 3 \leq  3[/tex]

⇒ y ≤ 3

Therefore, the range of the function is y ≤ 3. (Answer)

Answer:

111/40

Step-by-step explanation:

3 2/5=17/5

17/5-5/8=111/40

Answer:

  $15.21

Step-by-step explanation:

The tax and tip percentages are both being figured on the original bill amount, so they can be added. The tax and tip together come to ...

  11.75% +15% = 26.75%

This is added to the original bill amount, so the final total will be ...

  $12 + $12×0.2675 = $12×1.2675 = $15.21

Vera's meal cost $15.21.

Answer:

Speed of Amy is 3.75 miles per hour.

Step-by-step explanation:

We have, speed of Amy = 110 yards per minute

This means, she covers 110 yards of distance in 1 minute.

Now, to convert the speed of Amy into miles per hour, we will first convert the distance from yards into miles and then convert time from minutes to hour.

We know that,

  1 yard = 3 feet

∴ 110 yards = 3 × 110 feet = 330 feet

Now, we also know that,

 5280 feet = 1 mile

∴ 1 feet = [tex]\frac{1}{5280}[/tex] miles

So, 330 feet = [tex]\frac{1}{5280}\times330[/tex] = [tex]\frac{1}{16}[/tex] miles

∴ 110 yards = 330 feet = [tex]\frac{1}{16}[/tex] miles

Now, 60 min = 1 hr

∴ 1 min = [tex]\frac{1}{60}[/tex] hrs

So, 110 yards = [tex]\frac{1}{16}[/tex] miles and 1 min = [tex]\frac{1}{60}[/tex] hr

So, we can say that, Amy covers a distance of [tex]\frac{1}{16}[/tex] miles in

[tex]\frac{1}{60}[/tex] hr.

We know that,

[tex]speed=\frac{distance}{time}[/tex]

[tex]speed=\frac{(\frac{1}{16}) miles}{(\frac{1}{60})hr}[/tex]

[tex]speed=\frac{60}{16} miles/hr = 3.75 miles/hr[/tex]

Therefore, the speed of Amy in miles/hr is 3.75 miles/hr.

Answer:

x = 35°

Step-by-step explanation:

The question is as following

cos x = sin(20 + x)°  and  0° < x  < 90°  ,   find X?

==============================================

cos x = sin(20 + x)°

sin and cos are co-functions,

which means that: cos x = cos [90 - (20 + x)]

∴ x = 70 - x

∴ 2x = 70

∴ x = 35°

======================

Note: cos θ = sin ( 90 - θ )

Answer:

x = 35°

Step-by-step explanation:

The question is as following

cos x = sin(20 + x)°  and  0° < x  < 90°  ,   find X?

==============================================

cos x = sin(20 + x)°

sin and cos are co-functions,

which means that: cos x = cos [90 - (20 + x)]

∴ x = 70 - x

∴ 2x = 70

∴ x = 35°

======================

Note: cos θ = sin ( 90 - θ )

Answer:

There are 7 copies of 2 and 1 copy of 11 in the product:

1408 = 2^7×11

Step-by-step explanation:

Factor the following integer:

1408

The last digit of 1408 is 8, which means it is even. Therefore 1408 is divisible by 2:

1408 = 2 704:

1408 = 2×704

The last digit of 704 is 4, which means it is even. Therefore 704 is divisible by 2:

704 = 2 352:

1408 = 2×2×352

The last digit of 352 is 2, which means it is even. Therefore 352 is divisible by 2:

352 = 2 176:

1408 = 2×2×2×176

The last digit of 176 is 6, which means it is even. Therefore 176 is divisible by 2:

176 = 2 88:

1408 = 2×2×2×2×88

The last digit of 88 is 8, which means it is even. Therefore 88 is divisible by 2:

88 = 2 44:

1408 = 2×2×2×2×2×44

The last digit of 44 is 4, which means it is even. Therefore 44 is divisible by 2:

44 = 2 22:

1408 = 2×2×2×2×2×2×22

The last digit of 22 is 2, which means it is even. Therefore 22 is divisible by 2:

22 = 2 11:

1408 = 2×2×2×2×2×2×2×11

11 is not divisible by 2 since 11 is odd and 2 is even:

1408 = 2×2×2×2×2×2×2×11 (11 is not divisible by 2)

The sum of the digits of 11 is 1 + 1 = 2, which is not divisible by 3. This means 11 is not divisible by 3:

1408 = 2×2×2×2×2×2×2×11 (11 is not divisible by 2 or 3)

The last digit of 11 is not 5 or 0, which means 11 is not divisible by 5:

1408 = 2×2×2×2×2×2×2×11 (11 is not divisible by 2, 3 or 5)

Divide 7 into 11:

| | 1 | (quotient)

7 | 1 | 1 |  

- | | 7 |  

| | 4 | (remainder)

11 is not divisible by 7:

1408 = 2×2×2×2×2×2×2×11 (11 is not divisible by 2, 3, 5 or 7)

No primes less than 11 divide into it. Therefore 11 is prime:

1408 = 2×2×2×2×2×2×2×11

There are 7 copies of 2 and 1 copy of 11 in the product:

Answer: 1408 = 2^7×11

Final answer:

The prime factorization of 1408 is 2 raised to the power of 7 multiplied by 11, represented as 2^7 × 11. This is found by repeatedly dividing 1408 by 2 until we are left with the prime number 11, which cannot be divided further.

Explanation:

The prime factorization of 1408 involves breaking down the number into its prime factors until all the factors are prime numbers. To find the prime factors of 1408, we can use a factor tree or the method of division. We can start by dividing 1408 by the smallest prime number that divides it evenly, which is 2. If we keep dividing by 2, we get the following sequence of divisions:

1408 ÷ 2 = 704

704 ÷ 2 = 352

352 ÷ 2 = 176

176 ÷ 2 = 88

88 ÷ 2 = 44

44 ÷ 2 = 22

22 ÷ 2 = 11

Since 11 is a prime number, we cannot divide any further. Therefore, the prime factorization of 1408 is 27 × 11, since 2 was divided 7 times and 11 is the last prime factor found.