Translate the graph according to the rule (x, y) → (x + 2, y).

The first graph goes with the question.

Carl's horse traveled approximately 31.4 feet further than Allison's horse in one complete turn of the carousel. The distances were calculated using the circumference formula for each horse based on their distance from the centre of the carousel.

The question involves comparing the distances traveled by horses on a carousel based on their distance from the center of the ride. To find out how much further Carl's horse traveled compared to Allison's, we need to calculate the circumference of the circular paths each horse took during one complete turn of the carousel and then find the difference between these two distances.

To calculate the circumference (C) of a circle, we use the formula C = 2πr, where π (pi) is approximately 3.14159 and r is the radius of the circle, in this case, the distance from the center of the carousel to the horse.

For Carl's horse:
CCarl = 2π(15 feet) ≈ 2π×15 ≈ 94.2 feet

For Allison's horse:
CAllison = 2π(10 feet) ≈ 2π×10 ≈ 62.8 feet

The difference in the distances traveled by the horses in one complete turn is CCarl - CAllison, which is approximately 94.2 feet - 62.8 feet = 31.4 feet. Therefore, Carl's horse travelled about 31.4 feet further than Allison's horse in one complete turn.

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:

Step-by-step explanation:

Shelly's first race time is 43.13 seconds.

Shelly's second race times is 43.1 seconds.

Basically, she improved 0.03 seconds, because 43.13 - 43.1 = 0.03.

If she keeps this patterns that means she will improve 0.03 each race.

So, the third race times is 43.1 - 0.03 = 43.07 seconds.

The fourth race time is 43.07 - 0.03 = 43.04 seconds.

Therefore, the time in the fourth race is 43.04 seconds, because she's improving at a constant rate of 0.03 seconds per race.

Answer:

9/16

Step-by-step explanation:

(2+1/4)/4=(8/4+1/4)/4=(9/4)(1/4)=9/16

Answer: Choice C)

y = (x-2)(x-2)

note: This is the same as y = (x-2)^2

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

The x intercept or root is x = 2, so x-2 is a factor. There is only one root visible, but this is a parabola, so it's technically a double root (it repeats itself). That is why (x-2) shows up twice giving (x-2)(x-2)

If the equation was simply y = x-2, then it would be a linear equation instead of a curved parabola.

Note how plugging in x = 2 leads to the following y value

y = (x-2)(x-2)

y = (2-2)*(2-2)

y = 0*0

y = 0

So (2,0) is the only x intercept.

Answer:

(-∞,7) U (7,∞)

Step-by-step explanation:

f(x)= x+2

g(x) = x-7

[tex]\frac{f(x)}{g(x)} =\frac{x+2}{x-7}[/tex]

Here we have x-7 in the denominator

To find domain we set the denominator =0  and solve for x

x-7=0

Add 7 on both sides

x=7

x=7 makes the denominator 0 that is undefined

So we ignore 7 for x

Hence domain is

(-∞,7) U (7,∞)

Answer:

The correct answer i believe is A.

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:

(C) 17.15

Step-by-step explanation:

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.

The answer is 26.46. I got it correct on my GoFormative.

The price of shoe store merchandise after markup price will be equal to 26.46.

The Latin phrase "per centum," which means "by the hundred," is where the English word "percentage" comes from. Percentage segments are those with a numerator of 100. In other words, it is a connection where the whole is always deemed to be valued 100.

As per the given data given in the question,

The wholesale price of merchandise = 24.50

Markup percentage on merchandise = 8%

Then, the amount of increment in the price will be,

(24.50 × 8)/100

= 196/100

=1.96

Then, the price of merchandise after markup will be,

= 24.50 + 1.96

= 26.46

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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: 4.01% interest rate

This value is approximate. It is rounded to the nearest hundredth of a percent.

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

Work Shown:

A = P*e^(r*t)

1833 = 1500*e^(r*5)

1833/1500 = e^(5r)

1.222 = e^(5r)

e^(5r) = 1.222

5r = Ln(1.222)

5r = 0.2004888607494

r = 0.2004888607494/5

r = 0.04009777214989

r = 0.0401

r = 4.01%

Answer:

By the looks of it i would assume 3 grams of protein and 12 calories burned but i am not sure either i am stuck on the same question

Step-by-step explanation:

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

Answer:

Total pay = 400+ 1650* 5/100= 482,5 $

Step-by-step explanation:

[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ H(\stackrel{x_1}{9}~,~\stackrel{y_1}{4})\qquad K(\stackrel{x_2}{7}~,~\stackrel{y_2}{2}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{7+9}{2}~~,~~\cfrac{2+4}{2} \right)\implies (8,3)[/tex]

Answer:

she give each kid about 6

Step-by-step explanation:

26/.25=104

104/16= 6.5

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:

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:

Saul is incorrect. The proper answer should be 6x^3

Step-by-step explanation:

Think of "x^3" as "x". So we have 2x+4x = 6x. Similarly, 2x^3+4x^3 = 6x^3. The exponents of the like terms do not change.

As a more real world example, let's say that we replace "x^3" with "dogs". Saying "2x^3" could mean "2 dogs". Same goes for "4x^3" meaning "4 dogs". So "2x^3+4x^3" turns into "2 dogs + 4 dogs", and you can see that leading to 6 dogs total. The last step is to replace "dogs" with "x^3" to end up with 6x^3. The x^3 stays the same the whole time in much the same way that "dogs" do not change either.

Answer:

saul is incorrect

2x3 + 4x3 is the same as (2 . x^3) + (4 . x^3)

6x6  is the same as 6x . x. x. x. x. x

2x3 + 4x3 simplifies to 6x^3

Step-by-step explanation:

Answer:

P(A or B) = 2/3                      

Step-by-step explanation:

Blue Garments = 1 blue shirt, 1 blue hat, 1 blue pair of pants

Total blue garments = 3

Green garments= 1 green shirt, 1 green hat, 1 green pair of pants

Total green garments = 3

Total no. of garments = blue garments +green garments = 6

A = event that Ivan selects a green garment

P(A) = Favourable outcomes/Total no. of outcomes

P(A)    = 3/6

B = event that Ivan chooses a pair of pants

P(B) = 2/6

We need to find P(A or B) = P(A∪B)

By formula, P(A∪B) = P(A)+P(B)-P(A∩B)

P(A∩B) = Probability that a green pair of pant is chosen = 1/6

P(A∪B) = 3/6+2/6-1/6

           = 4/6

           =2/3

Answer:

1/2

Step-by-step explanation:

Answer: B

Step-by-step explanation:

  x³ - 3x²  + 16x - 48 = 0

→ x²(x - 3)   + 16(x - 3) = 0

→ (x² + 16) (x - 3) = 0

→ (x² - (-16)) (x - 3) = 0

→ (x - 4i)(x + 4i)(x - 3) = 0

→ x - 4i = 0    x + 4i = 0   x - 3 = 0

→  x = 4i          x = -4i        x = 3

2 imaginary roots         and 1 real root

ANSWER:

For the first picture, it is the first answer. This is because of the Exterior Angle Theorem.

For the second picture, use the Exterior Angle Theorem again, but this time, solve for x.

[tex]132 = x + (3x-24)\\132 = 4x - 24\\156=4x\\x=39[/tex]

The m∡B = 39°

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:

X=3

Step-by-step explanation:

We have two linear functions which intersect at a point. Linear functions are lines which are made of points that satisfy the function or relationship.  This means at the intersection, this point (3,-1), both functions have values. An input of x=3 produces y=-1 in both functions.

Answer:

The correct option is 4.

Step-by-step explanation:

If the graph of a function represent in coordinate plane, then x-axis represents the domain of the function and y-axis represents the range of the function.

We have to find the input value that produces the same output value for the two functions on the graph.

From the given graph it is clear that the intersection point of both functions is at (3,-1).

At x=3 the output value of f(x) is -1.

At x=3 the output value of g(x) is -1.

It means both functions have same output -1 at x=3.

Therefore the correct option is 4.

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.

[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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