lesson 6.1
Graph the image of the figure using the transformation given.
options are out of the last 3 images

The given expression (7 x 10³)(5.4 x 10⁴)/ 9 x 10² as a number in scientific notation is 4.2 × 10^5.

According to the question.

We have an expression (7 x 10³)(5.4 x 10⁴)/ 9 x 10².

Since, we have to write the above expression as a number in scientific notation.

As we know that, scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.

Thererefore, the expression (7 x 10³)(5.4 x 10⁴)/ 9 x 10² as a number in scientific notation

(7 x 10³)(5.4 x 10⁴)/ 9 x 10²

= (7 × (10^7) × 54)/ 9 × (10^2) × 10

= 7 × 6 × 10^(7 - 3)

= 42 × 10^4

= 4.2 × 10^5

Hence, the given expression (7 x 10³)(5.4 x 10⁴)/ 9 x 10² as a number in scientific notation is 4.2 × 10^5.

Find out more information baout scientific notation here:

https://brainly.com/question/18073768

#SPJ1

Shown in pic

Source: Trust me

Answer:

365 x 4 = 1460

Step-by-step explanation:

The area model shows that 365 multiplied by 4 is equal to 18.

First, we draw a rectangle to represent the number 365. We divide it into three parts vertically to represent the digits 3, 6, and 5.

  3       6       5

Next, we draw a rectangle to represent the number 4. We position it to the right of the rectangle for 365.

  3       6       5

                  4

To find the area, we calculate the individual areas of each section and then add them up.

The area of the rectangle representing 3 is 3 times the height, which is 1.

 3       6       5

 |         |         |

 |         |         |

 |         |         |

The area of the rectangle representing 3 is 3.

The area of the rectangle representing 6 is 6 times the height, which is 1.

  3       6       5

 | |       |         |

 | |       |         |

 | |       |         |

The area of the rectangle representing 6 is 6.

The area of the rectangle representing 5 is 5 times the height, which is 1.

  3       6       5

 | | |     |         |

 | | |     |         |

 | | |     |         |

The area of the rectangle representing 5 is 5.

The area of the rectangle representing 4 is 4 times the height, which is 1.

  3       6       5

 | | |     | |     |

 | | |     | |     |

 | | |     | |     |

So, the area of the rectangle representing 4 is 4.

Now, the total area, we add up the areas of the individual sections:

= 3 + 6 + 5 + 4

= 18

Therefore, the area model shows that 365 multiplied by 4 is equal to 18.

Learn more about Area model here:

https://brainly.com/question/30664807

#SPJ6

Answer:

x/(1-x)

Step-by-step explanation:

We start by induction. The first 2 terms are x/(1-x^2) and x^2/(1-x^4), respectively. When we add them together using special factorizations, we get: (x^3+x^2+x)/(1-x^4). We quickly realize that the numerator is a geometric series. Applying the following formula, we can simplify our expression to (x^4-x)/(1-x^4)(x-1). Now, we introduce our 3rd term, and add that to our sum. That gets us: (x^7+x^6+...+x)/(1-x^8). This is another Geometric series, and we apply the exact same formula, for this new fraction: (x^8-x)/(1-x^8)(x-1). We realize this is a pattern, and we can utilize this pattern for the sum of the first n terms.
We look at the exponents. For the first 3 terms, the Degree is 8, for the first 2 terms, the Degree is 4. We take note that this looks like x^2^n.

Using that our general formula IS: (attached to this text) (x^2^n-x)/(1-x^2^n)(x-1). Now, when 0<x<1 and n approaches infinity, what do we get?
all terms x^2^n are so small, it's basically redundant, and can be crossed off. This leaves us with -x/(x-1), which can be simplified to x/(1-x).

Answer:

A

Step-by-step explanation:

95 [tex]\leq[/tex] 3.99s + 15.20

-15.20.          -15.20

79.80 [tex]\leq[/tex] 3.99s

    /            /

3.99       3.99

20 [tex]\leq[/tex] s

The ruler postulate is that A. the distance between two points can be determined by the absolute value of the difference of the real number values of the two points.

The set of points on a line can be arranged in such a way that the set of real numbers and the set of points correspond exactly, and the distance between any two points is equal to the absolute value of the difference between the corresponding numbers.

Therefore, the ruler postulate is that the distance between two points can be determined by the absolute value of the difference of the real number values of the two points.

In conclusion, the correct option is A.

Learn more about postulate on:

https://brainly.com/question/25091636

#SPJ1

The required absolute value equation is |x - 87.4| = 1.5

Also,  if the thermometer reads 87.4° F, the least possible temperature is 85.9° F and the greatest possible temperature is 88.9° F

In this question, the thermometer is accurate within 1.5 degrees of the actual temperature in degrees Fahrenheit.

We need to find the least and greatest possible temperature if the thermometer reads 87.4° F

Let x be the temperature in degrees Fahrenheit.

From given information, an absolute value equation would be,

|x - 87.4| = 1.5

We know that, | ±a | = a

x - 87.4 = ±1.5

Case 1: x - 87.4 = 1.5

            x = 1.5 + 87.4

            x = 88.9° F

Case 2: x - 87.4 = -1.5

             x = -1.5 + 87.4

             x = 85.9° F

Therefore, the required absolute value equation is |x - 87.4| = 1.5

Also,  if the thermometer reads 87.4° F, the least possible temperature is 85.9° F and the greatest possible temperature is 88.9° F

Learn more about an absolute value equation  here:

https://brainly.com/question/2166748

#SPJ1

The intersection of M and F is {d}.

The union of M and F is {b, d, e, h, j}

A set is a collection that is used to model a collection of different things. A set can be described as a collection of objects whose elements are fixed and cannot be changed.

To write a set in a roster form, the elements in the set are written in a row within curly brackets - { }. The elements in the set would be separated by commas.

The intersection represents only elements that are common to two or more sets. Th sign used to represent intersection is ∩. The union of sets are all the elements in the set. The sign used to represent union is U.

The intersection of M and F = d.

It is only d that is in both set M and set F.

The union of M and F = {b, d, e, h, j}

Here is the complete question:

The sets M and F are given below.

M= ( b, d, h)

F= (d, e, j)

find the union of M and F. Find the intersection of M and F.

Write your answers using set notation (in roster form).

To learn more about set operations, please check: brainly.com/question/13014058

#SPJ1

Answer: 27

Step-by-step explanation:

3^2 = 3 x 3= 9  

9 x 3 = 27

In linear equation, 95 is Meghan's amount of money is changing .

What in mathematics is a linear equation?

Based on the given conditions, formulate ( 1100  - 720 ) ÷ 4

Calculate the sum or difference = 380/4

Cross out the common factor = 95

Learn more about linear equation

brainly.com/question/11897796

#SPJ1

The range of the function y = x^2 + 4x + 7 is y >= 3

The equation of the function is given as

y = x^2 + 4x + 7

Start by differentiating the above function

So, we have

y' = 2x + 4

Set the above equation to 0

So, we have

2x + 4 = 0

Divide through the equation by  2

So, we have

x + 2 = 0

Evaluate the like terms:

x = -2

Substitute x = -2 in y = x^2 + 4x + 7

y = (-2)^2 + 4(-2) + 7

Evaluate the expression

y = 3

The leading coefficient of the equation y = x^2 + 4x + 7 is positive

This means that the vertex is a minimum

So, the range is

y >= 3

Hence, the range of the function y = x^2 + 4x + 7 is y >= 3

Read more about range at

https://brainly.com/question/2264373

#SPJ1

1. The missing side of triangle is 10 CM

2. The missing side of triangle is 13 mi

3. The missing side of triangle is 3[tex]\sqrt{2}[/tex] mi

4. The missing side of triangle is [tex]\sqrt{219}[/tex] yd

The Pythagoras theorem equation is expressed as, , [tex]c^{2}[/tex]=[tex]a^{2}[/tex]+[tex]b^{2}[/tex], where 'c' = hypotenuse of the right triangle and 'a' and 'b' are the other two legs. Hence, any triangle with one angle equal to 90 degrees produces a Pythagoras triangle and the Pythagoras equation can be applied in the triangle.

We have different right triangles and their measurements.

we have to find the missing side of triangle.

The Pythagoras theorem equation is expressed as, [tex]c^{2}[/tex]=[tex]a^{2}[/tex]+[tex]b^{2}[/tex]

1. For diagram 1,

Let the length c=x,

a=6

b=8

then according to the Pythagoras theorem.

⇒[tex]x^{2}[/tex]=[tex]6^{2}[/tex]+[tex]8^{2}[/tex] ⇒  [tex]x^{2}[/tex]= 36+64=100

⇒x=10

therefore missing side of triangle is 10 CM

2. For diagram 2,

Let the length c=x,

a=5

b=12

then according to the Pythagoras theorem.

⇒[tex]x^{2}[/tex]=[tex]5^{2}[/tex]+[tex]12^{2}[/tex] ⇒  [tex]x^{2}[/tex]= 25+144=169

⇒x=13

therefore missing side of triangle is 13 mi

3. For diagram 3,

Let the length c=x,

a=3

b=3

then according to the Pythagoras theorem.

⇒[tex]x^{2}[/tex]=[tex]3^{2}[/tex]+[tex]3^{2}[/tex] ⇒  [tex]x^{2}[/tex]= 9+9=18

⇒x=3[tex]\sqrt{2}[/tex]

therefore missing side of triangle is 3[tex]\sqrt{2}[/tex] mi

4. For diagram 4,

Let the length a=x,

c=16,

b=[tex]\sqrt{37}[/tex]

then according to the Pythagoras theorem.

⇒[tex]16^{2}[/tex]=[tex]x^{2}[/tex]+[tex](\sqrt{37} )^{2}[/tex] ⇒  [tex]x^{2}[/tex]= 256-37=219

⇒x=[tex]\sqrt{219}[/tex]

therefore missing side of triangle is [tex]\sqrt{219}[/tex] yd

To learn more about Pythagoras theorem here :https://brainly.com/question/21926466

#SPJ1

Answer:

1491.94

Step-by-step explanation:

7.1/100 = x/1605.96

=114.02

1605.96-114.02=1491.94

Answer:

www

Step-by-step explanation:

www

Answer:

(-4;2)

Step-by-step explanation:

The graph show us line on the -4 and 2 and I think the answer us (-4;2)

Answer:

Step-by-step explanation:

x³-6x²+x-5

but it is divided by x+2

x+2=0.

x=-2.

(-2)³-6(-2)²+(-2)-5.

-8-6*4-2-5.

-8-24-7

-15-24

Answer:

C is correct! for the slope, N is represented.

Step-by-step explanation:

The slope of the line that contains the points (1, 9) and (3, 4) is 4−93−1=−52.

slope=y2−y1x2−x1=4−93−1=−52

The negative reciprocal is 25, which is the slope of the perpendicular line.

Answer:

w-q=h

Step-by-step explanation:

4w-q=4h

4w/4-q=4h/4

w-q=h

Answer:

m=√14,−√14

Decimal Form:

m=3.74165738, -3.74165738

Step-by-step explanation:

Applying the same-side-interior angles theorem, the values are:

x = 95°

z = 35

An examples of angles that are referred to as same-side-interior angles are x° and 85°.

According to the same-side-interior angles theorem, the sum of x and 85 will give 180 degrees if lines h and o are parallel to each other.

Since h║o, therefore:

x + 85 = 180

x + 85 - 85 = 180 - 85

x = 95°

(6z - 115)° and x° are vertical angles, therefore:

6z - 115 = x

Plug in the value of x

6z - 115 = 95

6z - 115 + 115 = 95 + 115

6z = 210

6z/6 = 210/6

z = 35

Thus, applying the same-side-interior angles theorem, the values are:

x = 95°

z = 35

Learn more about the same-side-interior angles theorem on:

https://brainly.com/question/16976757

#SPJ1

Answer:

x = √(5) - 8

x = -√(5) - 8

Step-by-step explanation:

Let's solve the problem,

→ (x+8)² - 43 = -38

→ x² + 64 - 43 = -38

→ x² + 21 = -38

→ x² = -38 - 21

→ x = √(-59)

→ [ x = √(5) - 8 ]

(or) [ x = -√(5) - 8 ]

Hence, it is the value of x.

The probability of randomly sampling 25 workers from the general population and their mean productivity being 28.2 or higher is 0.0192.

It should be noted that from the information, after the special training was complete the 25 workers produced 28.2 units every hour with stand deviation of 2.9.

Therefore, the probability of randomly sampling 25 workers from the general population and their mean productivity being 28.2 or higher will be:

= 1 - P[(Z (28.2 - 27)/29/✓25)]

= 1 - P(Z < 2.07)

It should be noted that this will be looked on the distribution table.

= 1 - 0.9808

= 0.0192

Therefore, the probability of randomly sampling 25 workers from the general population and their mean productivity being 28.2 or higher is 0.0192.

Learn more about probability on

brainly.com/question/24756209

#SPJ1

Step-by-step explanation:

by bringing all terms to the same fractions (with the same denominator).

so, we have

7

5/7

that means we want to bring both numbers to .../7 form.

7 means 7 whole units.

1 whole unit has now many parts ?

if we aim for 2 parts, that makes 1 whole unit 2/2.

if we aim for 3 parts, 1 whole unit is 3/3.

...

you see, 3/3 = 1/1 = 1.

that is the whole trick.

so, we are looking for 7 parts, and 1 whole unit is 7/7.

now we have 7 whole units.

how many parts are those ?

well, 7 × 7/7 = 49/7

there we go.

we have

7 - 5/7 = 49/7 - 5/7 = 44/7 = 42/7 + 2/7 = 6 2/7

The best prediction of the population in the year 2013 is 3541 based on the fact that the population decreases by 1.4% every year

What is the number of years between 2008 and 2013?

The number of years between 2008 when the population figure was at 3,800 and 2013 is 5 years, hence when determining the population for the year 2013 we need to bear in mind that the population has decreased by 1.4% over a period of 5 years

FV=PV*(1-r)^N

FV= best prediction of the population in the year 2013

PV=population in 2008=3800

r=decreasing rate of the population=1.4%

N=number of years that have passed between 2008 and 2013

FV=3800*(1-1.4%)^5

FV=3541

Find out more about decreasing rate on:brainly.com/question/8042072

#SPJ1

Answer:4/3

Step-by-step explanation:from point (0,-1) to (4,4)

From first point on the y it goes up 5and 4 to the right

Or you can use formula m= y2-y1 / x2-x1

(X1,y1) (x2,y2).                  m= 4- -1/4-0 m= 5/4

(0,-1).   (4,4)

Answer:270 calories in 3 servings; 450 calories in

5 servings.

270 ÷3   90     450 ÷ 5     90

 3    ÷3    1        5    ÷ 5        1

The unit rates are the

same so they are equal.

hope it helps! :)

Answer: {y,x} = {-9,-2}

Step-by-step explanation:

The amount of external financing Tobin Supplies Company have to seek assume there is no increase in liabilities other than that which will occur with the external financing is $58,250

What is the appropriate formula for external financing?

The formula that models the amount of external financing Tobin supplies company requires is a function of its increase in assets minus the retained earnings which would be used to part-fund the increase in assets

external funds needed=increase in assets-retained earnings

increase in assets=$105,000

retained earnings=net income-dividends

net income=sales*profit margin

net income=$550,000*10%

net income=$55,000

dividend payout ratio=15%

dividends=$55,000*15%

dividends=$8250

retained earnings=$55,000-$8250

retained earnings=$46,750

external funds needed=$105,000-$46,750

external funds needed=$58,250

Find out more about external funds needed on:https://brainly.com/question/14998305

#SPJ1

The time taken to exhaust the money will be 33 days.

Total amount = 100

Let the number of days be represented by x.

Therefore, the appropriate expression will be:

(3 × x) = 100

3x = 100

Divide

x = 100/3

x = 33.33

Therefore the time taken will be 33 days.

Learn more about expressions on:

brainly.com/question/22048677

#SPJ1