Graph the image of this figure after a dilation with a scale factor of 1/3 centered at the origin.



Use the polygon tool to graph the dilated figure.

Answer:

y > -1/6 x+1

Step-by-step explanation:

The graph line is dotted.  Dotted lines means greater than or less than.  ( <, >)

Solid lines means less than or equal to     or greater than or equal to   (≤,≥)

Since the graph is shaded above the line, that means y is greater than the line.  If it were shaded below the line,  y would be less than.

y > -1/6 x+1

Mr. Ramirez donates 23 books.

To find the number of books that Mr. Ramirez donates, we first need to calculate the total number of books he receives. Since each set has 16 fiction books and 14 nonfiction books and he receives 4 sets, the total number of books he receives is 4 sets * (16 fiction books + 14 nonfiction books) = 4 * (16 + 14) = 4 * 30 = 120 books.

Since Mr. Ramirez puts 97 books in his library, he donates the remaining books. To find the number of books he donates, we subtract the number of books he keeps from the total number of books he receives: 120 books - 97 books = 23 books.

Therefore, Mr. Ramirez donates 23 books.

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Mr. Ramirez donates 23 books.

To find out how many books Mr. Ramirez donates, we need to first calculate how many books he receives in total.

Each set has 16 fiction books and 14 nonfiction books, so each set contains 16 + 14 = 30 books.

Since Mr. Ramirez receives 4 sets, he receives a total of 4 x 30 = 120 books.

We know that Mr. Ramirez keeps 97 books in his library, so he donates the rest.

To find out how many books he donates, we subtract the number of books kept from the total number of books received:

120 - 97 = 23 books.

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Answer:

x=5.

Step-by-step explanation:

set 7x-4=31 and solve.

Answer:

B)

X=5

Step-by-step explanation:

7x-4=31

+4 on both sides

7x=35

divide by 7 on both sides

x= 5

Answer:

Step-by-step explanation:

Alright, lets get started.

The original photo size is 4 inches wide and 6 inches tall.

So, the ratio of width and height will be = [tex]\frac{4}{6}=\frac{2}{3}[/tex]

The new enlarged photo will be of the same ratio means 2:3

The width of enlarged photo is given as 12 inches.

Suppose new height of enlarged photo is H, so

[tex]\frac{12}{H}=\frac{2}{3}[/tex]

Cross multiplying

[tex]2H=36[/tex]

Dividing 2 in both sides

[tex]H=18[/tex] inches

So the height of new enlagred photo will be 18 inches.  :   Answer

Hope it will help :)

Answer:

The original price was $26.40

Step-by-step explanation:

Set up the equation(s) for this situation. The total price was for six shovels, three of which were discounted by 33.3% from the initially marked-down price X:

$102 = 3 * (X-$6) + 3 * ((X-$6) * (2/3))

102 = 3X - 18 + 3 * (2/3) * X - 3 * (2/3) * 6

102 = 5X - 30

X = $26.40

Answer:

The correct option is C.

Step-by-step explanation:

Let triangle ABC and XYZ are similar.

If two triangles are similar, then ratio of their corresponding sides are same.

Since ABC and XYZ are similar, therefore sides AB, BC and AC are corresponding to the sides XY, YZ and XZ respectively.

[tex]\frac{AB}{XY}=\frac{BC}{YZ}=\frac{AC}{XZ}[/tex]

From the above equation we can conclude that

[tex]\frac{BC}{YZ}\neq \frac{AC}{YX}[/tex]

[tex]\frac{BC}{YZ}\neq \frac{BA}{XZ}[/tex]

[tex]\frac{AC}{XZ}\neq \frac{BA}{XZ}[/tex]

Therefore option A,B and D are incorrect.

Answer:  BC/YZ = AC/XZ

Step-by-step explanation:

Remember the end letters need to be the same. So if you look at your choices this is the only one that is in order   BC  AC

                                                                         YZ   XZ

took the test

Answer:

she give each kid about 6

Step-by-step explanation:

26/.25=104

104/16= 6.5

Answer:

Third option

Step-by-step explanation:

You are correct, right angle forms a 90°

Hope that helps

Answer:

The third option.

Step-by-step explanation:

The first option is acute becuase the angle is less that 90 degrees.

The second options is obtuse because it is more than 90 degrees.

The third option is a right angles becuase it makes an 90 degree angle.

The fourth option is also obtuse because it is more than 90 degrees.

Answer:

the ratio of the area is 3:5

Step-by-step explanation:

Find a common factor of 6 and 10 and then divide it, the common factor is 2

6 divided by 2 is 3

10 divided by 2 is 5

so your ratio area is 3:5

Hope this helps :)

The expression that represents the total paid by the company is 295 + 15d.

A straight line on the coordinate plane is represented by a linear function.

A linear function always has the same and constant slope.

In another word, a linear function is a function that varies linearly with respect to the changing variable.

As per the given,

The fee for a food booth is $200 plus $5 per day.

Total cost for d days will be = 200 + 5d

The fee for a game booth is $95 plus $10 per day.

Total cost for d days will be = 95 + 10d

Total cost for d days = (200 + 5d) + (95 + 10d)

⇒ 200 + 95 + 5d + 10d

⇒ 295 + 15d

Hence "The expression that represents the total paid by the company is 295 + 15d".

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Step-by-step explanation:

We have been given the linear regression equation for a data set is y=-2.8x+70.8 where y is the temperature in degrees Fahrenheit and x is the number of hours since 8 am.

We can see that our given line is in slope-intercept form: [tex]y=mx+b[/tex], where, m = Slope of line and b = y-intercept.  

Upon comparing our given equation with slope intercept form we can see that the slope of the equation (m) is -2.8. The slope represents that temperature is dropping at a rate of 2.8 Fahrenheit per hour after 8 am.

Answer:At a company fish fry, 1/2 in attendance are employees.

Employees’ spouses are 1/3 of the attendance. What is

the percentage of the people in attendance who are not

employees or employee's spouses?

One half of X are employees.

One third of X are employee's spouses.

Step-by-step explanation:1/2 + 1/3 = 3/6 + 2/6 = 5/6

Then we subtract that fraction from one whole, or 1,

to see what fraction is left.  That is, we say

1 minus 5/6

which is

1 - 5/6

Now write 1 as 6/6

6/6 - 5/6

We get 1/6

So 1/6 is left.  Now we need to make that into

a percent by multiplying it by 100 and tacking on a "%"

1/6 × 100

1/6 × 100/1

100/6

50/3

16 2/3 %

So 16 2/3 % of the people in

attendance are neither employees

nor employee's spouses.

Now let's check:

1/2 are employees.  That's 50%

1/3 are wmployee's spouses. That's 33 1/3%

15 2/3 % are neither employees nor employee's spouses.

Add them up

50     %

33 1/3 %

16 2/3 %

--------

99 3/3 %

And 99 3/3% = 100%

16.67% of the people in attendance are neither employees nor their spouses.

To calculate the percentage of people who are neither employees nor their spouses, we need to consider the total attendance as 100%. Since half of the attendance, i.e., 50%, are employees and one third, i.e., about 33.33%, are spouses, we add these figures to find the combined percentage of employees and spouses. We then subtract this combined percentage from 100% to find the percentage of people who are neither.

Combined percentage of employees and spouses: 50% (employees) + 33.33% (spouses) = 83.33%

Now, to find the percentage who are neither employees nor spouses, we subtract the combined percentage from 100%:

Percentage of neither: 100% - 83.33% = 16.67%

Therefore, 16.67% of the people in attendance are neither employees nor their spouses.

Answer:

the third table listed here

Step-by-step explanation:

A "proportional" relationship has the same y/x ratio for all values of x and y.

... first table: all entries but one have y/x = 1/3. The 3rd entry has y/x = 0.4—not the same.

... second table: 6/4 ≠ 8/6

... third table: all entries reduce to y/x = 15

... fourth table: 3/2 ≠ 4/3

Answer:

option D

Step-by-step explanation:

First term is -2

common ratio = -5/2

To get second term we multiply first term -2  by common ratio -5/2

[tex]-2 * \frac{-5}{2} =\frac{10}{2} = 5[/tex]

To get third term we multiply second term 5  by common ratio -5/2

[tex]5 * \frac{-5}{2} =\frac{-25}{2}[/tex]

To get fourth term we multiply third term -25/2  by common ratio -5/2

[tex]\frac{-25}{2}*\frac{-5}{2} =\frac{125}{4}[/tex]

Option D is correct

The first five terms of the geometric sequence with a first term of -2 and a common ratio of -5/2 are -2, 5, -12.5, 31.25, and -78.125.

To find the terms of a geometric sequence, we start with the first term and multiply each subsequent term by the common ratio. In this case, the first term, a1, is -2 and the common ratio, r, is -5/2.

The first term (a1) is -2

The second term (a2) is -2*(-5/2) = 5

The third term (a3) is 5*(-5/2) = -12.5

The fourth term (a4) is -12.5*(-5/2) = 31.25

The fifth term (a5) is 31.25*(-5/2) = -78.125

Therefore, the first five terms of the sequence are -2, 5, -12.5, 31.25, and -78.125.

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Answer:

2/15

Step-by-step explanation:

How many marbles are in the bag

4blue + 3 green + 7 red + 1 yellow = 15 marbles

On the 1st draw:

 red/total  = 7/15

Since we keep the marble, there are only 14 marbles left

4blue + 3 green + 6 red + 1 yellow = 14

On the 2nd draw:

blue/total  = 4/14  = 2/7

To find the probability of the two draws, we multiply them together

1st draw * 2nd draw

7/15 * 2/7 = 2/15

Look at the picture.

[tex\alpha+\beta=180^o[/tex] - supplementary angles

Therefore we hve the equation:

[tex](14x-6)+(15+5x)=180\\\\(14x+5x)+(-6+15)=180\\\\19x+9=180\qquad\text{subtract 9 from both sides}\\\\19x=171\qquad\text{divide both sides by 19}\\\\\boxed{x=9}[/tex]

Answer: x = 3

Those angle markings tell us that all three angles are the same measure (60 degrees). So this is an equilateral triangle with each side congruent to each other.

Pick 2 sides, equate the expressions, solve for x. I'm going to pick AB and AC to work with

AB = AC

6x - 3 = 3x+6

6x-3x = 6+3

3x = 9

x = 3

----------

This works with any pair of sides, such as AC and BC

AC = BC

3x+6 = 5x

6 = 5x-3x

6 = 2x

2x = 6

x = 3

----------

and let's do the last one to be complete (it's optional)

AB = BC

6x-3 = 5x

6x-5x = 3

x = 3

Either way, we get the same result each time.

Answer:

Add [tex]-x^2+2xy[/tex]

Step-by-step explanation:

The polynomial [tex]x^2+y^2-2xy+1[/tex] can be added to eliminate the x terms by adding the additive inverse. We add [tex]-x^2+2xy[/tex] which has the inverse sign value of the polynomial terms.

[tex](x^2+y^2-2xy+1)+(-x^2+2xy)[/tex]

[tex]x^2-x^2+y^2-2xy+2xy+1[/tex]

When we simplify, this leaves [tex]y^2+1[/tex] without an x term.

Answer:

-x^2+2xy

Step-by-step explanation:

x^2 + y^2 -2xy + 1 +something  = y^2 +1

This will get rid of the x and x^2 terms

Subtract y^2 from each  side

x^2 + y^2 -y^2 -2xy + 1 +something  = y^2-y^2 +1

x^2 -2xy+1 +something  = 1

Subtract 1 from each side

x^2 -2xy+1 -1+something  = 1-1

x^2 -2xy+something  = 0

Subtract x^2 from each side

x^2 -x^2 -2xy+something  = 0-x^2

-2xy+something  = -x^2

Add 2xy to each side

2xy -2xy+something  = -x^2+2xy

something = -x^2+2xy

We need to add  -x^2+2xy

Remember a binomial is 2 terms

[tex]\dfrac{4x^2-x}{16x^2-1}=\dfrac{x(4x-1)}{(4x)^2-1^2}\\\\\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=\dfrac{x(4x-1)}{(4x-1)(4x+1)}=\dfrac{x}{4x+1}\\\\Answer:\ \boxed{\dfrac{4x^2-x}{16x^2-1}=\dfrac{x}{4x+1}}[/tex]

By simplifying  (4x ² - x ) / (16 x² -1) we get :

= x / 4x + 1 .

The basic rules and steps for simplifying any algebraic expression are as follows:

Given equation, (4x ² - x ) / (16 x² -1)

Factorize 4x² - x ,

= x ( 4x - 1) / 16x² - 1

factorize 16x² -1,

= x (4x - 1) / (4x + 1 ) (4x - 1 )

By cancelling common factor 4x - 1,

= x / 4x + 1

Simplifying (4x ² - x ) / (16 x² -1)  =  x / 4x + 1 .

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The equation tells you that Henry swims 1.6·1 = 1.6 laps when x = 1 minute.

The table tells you Larry swims 4.5 laps in 2.5 minutes. Dividing these numbers by 2.5 tells you Larry swims 4.5/2.5 = 1.8 laps in 2.5/2.5 = 1 minute.

Henry's rate is 1.6 laps per minute; Larry's rate is 1.8 laps per minute.

___

1.8 is larger than 1.6, so Larry swims faster than Henry. That is, Larry swims farther in the same amount of time, or takes less time to swim the same distance.

E = 360/n

is the formula to use when computing the exterior angle E for any regular polygon with n sides. For an octagon, we have 8 sides meaning n = 8 leads to

E = 360/n = 360/8 = 45

The exterior angle of a regular octagon is 45 degrees

Repeat for n = 6 (hexagon) to get E = 360/n = 360/6 = 60. A regular hexagon has exterior angles of 60 degrees each.

We see that the regular octagon's exterior angles (45) are smaller than the regular hexagon's exterior angles (60)

-------------------------------------------

Answer: less than (choice B)

Final answer:

The measure of each exterior angle of a regular octagon is less than the measure of each exterior angle of a regular hexagon since the sum of the exterior angles is always 360 degrees and there are more sides on an octagon to divide this sum. The correct option is: B- Less than

Explanation:

To determine whether the measure of each exterior angle of a regular octagon is greater than, less than, or equal to the measure of each exterior angle of a regular hexagon, we must first understand how to calculate the measure of an exterior angle in a regular polygon. The sum of the exterior angles of any polygon is always 360 degrees, regardless of the number of sides. Therefore, to find the measure of a single exterior angle, you would divide 360 degrees by the number of sides the polygon has.

For a regular hexagon, which has six sides, the exterior angle is calculated as 360 ÷ 6, which equals 60 degrees. For a regular octagon, which has eight sides, the exterior angle is calculated as 360 ÷ 8, which equals 45 degrees.

Comparing the two measurements, we can clearly see that the measure of each exterior angle of a regular octagon is less than the measure of each exterior angle of a regular hexagon.

Answer: 5 hours

Step-by-step explanation:

$35 per hour is the rate

$25 is the flat fee

$200 is the maximum you can spend

⇒ 35x + 25 ≤ 200

            -25     -25

    35x          ≤ 175

  ÷35              ÷35

         x         ≤   5

Answer:

212 teachers are needed for an enrollment of 2,650 students.

Step-by-step explanation:

This is a kind of question that can be solved using proportions.

Proportions are used when we are asked about finding one unknown value, knowing the value of others that keep a ratio among all of them, including the unknown value.

In this case, we know that a school board estimated that 4 teachers are needed for every 50 students:

[tex]\\ \frac{4_{teachers} }{50_{students}}=ratio[/tex]  

If we divide 4 teachers by 50 students, we obtained a ratio, or a constant relationship that remains between teachers and students, that is, how many teachers are needed for the number of students, or more generally "how many times the first number contains the second" [Wikipedia, 2019].

We can also notice that more students require more teachers (which is a relation of direct proportionality), that is, if we require more students, more teachers are also required in the same ratio or constant already mentioned.

Then, we can make a proportion among these values because they keep the same ratio of teachers to students (but can also be students to teachers).

So, we can pose the following question:

If four (4) teachers are needed for every 50 students, how many teachers are needed to attend 2,650 students? Then,

[tex]\\ \frac{4_{teachers}}{50_{students}} = \frac{X_{teachers}}{2650_{students}} [/tex] = the same ratio or constant.

To know the amount of teachers needed for 2,650 students:

[tex]\\ X_{teachers} = \frac{2650_{students} * 4_{teachers} }{50_{students}}[/tex].

or,

[tex]\\ X_{teachers} = \frac{2650 * 4_{teachers} }{50}[/tex].

[tex]\\ X_{teachers} = 212_{teachers}[/tex].

So, for an enrollment of 2,650 students there should be 212 teachers, according to the ratio (teachers/students) previously determined by the school board.

Answer: b) 625 - 25 |x - 1990| = 550

Step-by-step explanation:

According to the question,

The annual profit of a company was determined by subtracting from $625,000 the product of $25,000 and the number of years either before or after 1990.

That is, On  x year the total profit is,

P(x) =  625,000 - 25,000 |x - 1990|

But again according to the question,

On x years the profit is $ 550,000

Thus, 625,000 - 25,000 |x - 1990| = 550,000

⇒ 625 - 25 |x - 1990| = 550 ( by dividing both sides by 1000)

Therefore, Option b) is correct.

The correct equation for determining the year when the profit was $550,000 is 625 - 25 | x - 1990 | = 550, where x represents the year, option B.

The annual profit of the company can be determined by the equation that subtracts the product of a certain amount ($25,000) and the number of years before or after 1990 from $625,000. If we are given that the profit was $550,000 in year x, we need to find the value of x that satisfies this condition. We will represent the difference in years as the absolute difference from 1990, which accounts for years before and after 1990 equally.

The correct equation based on this would be the one that represents the profit ($550,000) after subtracting the product of $25,000 and the absolute difference in years from $625,000. Thus, the correct equation should subtract from $625,000 (not add to it), and it should involve the absolute value of x - 1990 to denote the number of years before or after 1990.

The equation that fits these criteria is:

625 - 25 | x - 1990 | = 550

Here, when we solve for x, we're trying to find the year in which the profit was $550,000. Therefore, option (b) is the correct choice.

Answer:

22.5

Step-by-step explanation:

If you expand the series, you can see the first few terms of the series:

We can see the series is 0, 0.5, 1, 1.5, ....

This is an arithmetic series with common difference (the difference in 2 terms) 0.5 and first term 0.

We know formula for sum of arithmetic series:

[tex]s_{n}=\frac{n}{2}(2a+(n-1)d)[/tex]

Where,

Substituting these into the formula, we get the 10th partial sum to be:

[tex]s_{10}=\frac{10}{2}(2(0)+(10-1)(0.5))\\s_{10}=5(0+(9)(0.5))\\s_{10}=5(0+4.5)\\s_{10}=5(4.5)\\s_{10}=22.5[/tex]

So the sum of the first 10 terms is 22.5. Third answer choice is right.

Answer is 22.5  so c :)

Answer:

Please, see the attached files.

Step-by-step explanation:

Please, see the attached files.

Thanks.