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Answers

Answer 1

Answer:

1)

Given the triangle RST with Coordinates  R(2,1), S(2, -2) and T(-1 , -2).

A dilation is a transformation which produces an image that is the same shape as original one, but is different size.  

Since, the scale factor [tex]\frac{5}{3}[/tex] is greater than 1, the image is enlargement or a stretch.  

Now, draw the dilation image of the triangle RST with center (2,-2) and scale factor [tex]\frac{5}{3}[/tex]

Since, the center of dilation at S(2,-2) is not at the origin, so the point S and its image [tex]S{}'[/tex] are same.

Now, the distances from the center of the dilation at point S to the other points R and T.  

The dilation image will be[tex]\frac{5}{3}[/tex] of each of these distances,

[tex]SR=3[/tex], so [tex]S{}'R{}'[/tex]=5 ;


[tex]ST=3[/tex], so [tex]S{}'T{}'=5[/tex]  

Now, draw the image of RST i.e R'S'T'

Since, [tex]RT=3\sqrt{2}[/tex] [By using hypotenuse of right angle triangle] and [tex]R{}'T{}'=5\sqrt{2}[/tex].


2)

(a)

Disagree with the given statement.

Side Angle Side postulate (SAS) states that:

If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle then these two triangles are congruent.

Given: B is the midpoint of [tex]\overline{AC}[/tex] i.e [tex]\overline{AB}\cong \overline{BC}[/tex]

In the triangle ABD and triangle CBD, we have

[tex]\overline{AB}\cong \overline{BC}[/tex]   (SIDE)            [Given]

[tex]\overline{BD}\cong \overline{BD}[/tex]   (SIDE)            [Reflexive post]

Since, there is no included angle in these triangles.

∴ [tex]\Delta ABD[/tex] is not congruent to [tex]\Delta CBD[/tex] .

Therefore, these triangles does not follow the SAS congruence postulates.

(b)

SSS(SIDE-SIDE-SIDE) states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

Since it is also given that  [tex]\overline{AD}\cong \overline{CD}[/tex].

therefore, in the triangle ABD and triangle CBD, we have

[tex]\overline{AB}\cong \overline{BC}[/tex]   (SIDE)            [Given]

[tex]\overline{AD}\cong \overline{CD}[/tex]   (SIDE)           [Given]

[tex]\overline{BD}\cong \overline{BD}[/tex]   (SIDE)            [Reflexive post]

therefore by, SSS postulates [tex]\Delta ABD\cong \Delta CBD[/tex].

3)

Given that:  [tex]\angle1=\angle 3[/tex] are vertical angles, as they are formed by intersecting lines.

Therefore

, by the definition of linear pairs

[tex]\angle 1[/tex] and [tex]\angle 2[/tex] and [tex]\angle 3[/tex]  and [tex]\angle 2[/tex] are linear pair.

By linear pair theorem, [tex]\angle 1[/tex] and [tex]\angle 2[/tex]   are supplementary, [tex]\angle 2[/tex] and [tex]\angle 3[/tex]  are supplementary.

[tex]m\angle1+m\angle 2=180^{\circ}[/tex]

[tex]m\angle2+m\angle 3=180^{\circ}[/tex]

Equate the above expressions:

[tex]m\angle 1+m\angle 2=m\angle 2+m\angle 3[/tex]

Subtract the angle 2 from both sides in the above expressions

∴[tex]m\angle 1=m\angle 3[/tex]

By Congruent Supplement theorem: If two angles are supplements of the same angle, then the two angles are congruent.


therefore, [tex]\angle 1\cong \angle 3[/tex].















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Related Questions

A store sells 18 costumes per day in the 5 days before Halloween. How many costumes do they sell in this time period?

Answers

They sell 18 costumes per day, times 5 days.


So,

18 costumes per day * 5 days

18*5 =90

Final answer:

To find the total number of costumes sold, multiply the daily sales of 18 costumes by the 5 days before Halloween, which equals 90 costumes.

Explanation:

If a store sells 18 costumes per day during the 5 days before Halloween, we can calculate the total number of costumes sold by multiplying the daily sales by the number of days.

Here is the calculation:

Determine the number of costumes sold per day: 18 costumes.Multiply this number by the number of days: 18 costumes/day × 5 days = 90 costumes.

Therefore, the store sells a total of 90 costumes in the 5 days before Halloween.

This calculation method provides a straightforward way to determine the overall sales volume for the specified period, making it accessible for analysis and planning. The systematic breakdown into steps, including the identification of daily sales and multiplication by the number of days, enhances transparency in understanding the final result. Such clear and concise procedures contribute to effective business forecasting and logistical decision-making during peak periods like Halloween.

Can someone help me do this?

Answers

A. -13ab

B. 5a^2b

C. 3

Is a reference angle always in the first quadrant or can it be in other quadrants? HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP

Answers

The reference angle is defined as the smallest angle that theta could make between the terminal arm and the x axis.

That definition limits the answer to your question as yes, it is in the first quadrant.

q + 12 - 2 (q-22)>0



step by step please hurry ); <3

Answers

see the attached photo, with sign changed correctly

q + 12 - 2(q - 22) > 0     |use distributive property

q + 12 +(-2)(q) + (-2)(-22) > 0

q + 12 - 2q + 44 > 0      |combine like terms

(q - 2q) + (12 + 44) > 0

-q + 56 > 0       |subtract 56 from both sdies

-q > -56      |change the signs

q < 56

Lenny has $74. He spent $24 on video games, and $21 at the grocery store. How much does lenny have left? $

Answers

If you spend money, you have less money than before. Subtraction is the operation that describes this "taking quantities away".

So, you start with 74$. You spend 24$, so we have to subtract 24:

[tex] 74-24 = 50 [/tex]

Then, you spend 21$. So, we have to subtract again:

[tex] 50-21 = 29 [/tex]

So, you're left with 29$ after you buy the video game and the groceries.

The cheerleaders are practicing a dance routine in which all 36 of them need to be in a triangular formation. there will be two more cheerleaders in each row than the previous row. how many rows will be in the formation

Answers

If you start with 1 cheerleader in row A, then you'll have 3 cheerleaders in row B (add on 2), and then 5 cheerleaders for row C (add on another 2), etc etc.

Note how: 1+3+5 = 4+5 = 9 which is a perfect square. Also note that 36 is a perfect square.

Rule: The sum of the first positive n odd numbers is going to be equal to n^2. In the example of adding the first three odd numbers (1,3,5), we have n^2 = 3^2 = 9 as the sum

So as you can see, we'll have n = 6 rows because n^2 = 6^2 = 36 and

1+3+5+7+9+11 = 36

which is the sum of the first six positive odd numbers. So we'll have 1 cheerleader in row A, 3 in row B, 5 in row C, 7 in row D, 9 in row E, 11 in row F to have 6 rows total.

Final answer:

To determine the number of rows in the triangular formation, set up an equation and solve for x. The number of rows is 6.

Explanation:

To determine the number of rows in the triangular formation, we can set up a series of equations.

Let x be the number of rows.

The first row will have 1 cheerleader, the second row will have 3 cheerleaders, the third row will have 5 cheerleaders, and so on.

We can set up the equation: 1 + 3 + 5 + ... + (2x-1) = 36.

This is the sum of an arithmetic sequence with a common difference of 2. Solving for x, we get x = 6.

Therefore, there will be 6 rows in the formation.

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can you please help me with these two questions?

Answers

For this question you are required to determine what is called a slope and y-intercept. To thoroughly explain, a slope is a constant factor while a y intercept is simply a number on the y-axis, for instance (0,1)

In order to determine slope, you would take two ordered pairs  and use the following y2 - y1 divided by x2 - x1 to determine slope.

On the first attachment, take two ordered pairs.

-1 - (-3) divided by 1-0

2/1 = 2

m = 2

On the second attachment, use a principle called rise over run to determine the slope.

Using the method above, we “rise” two boxes and “run” one box, therefore the slope for the second attachment would be 2 and if we go down 2 we determine that the y-intercept is 0

Applying the explanation, we determine for the first attachment that the most sufficient answer is y = 2x - 3

The answer for the second attachment is y = 2x

A basketball player won 80% of the games he pichted.If he picthed 35 ballgames how many games did he win

Answers

28 games won

we require to calculate 80% of 35

80% = [tex]\frac{80}{100}[/tex] = 0.8

games won = 0.8 × 35 = 28


Can someone please help me im struggling with this problem :(

Answers

It is given that ABCD is a parallelogram, so AB || DC by the definition of parallelogram. So, ∠1 ≅ ∠2 by the alternate interior angles theorem. It is also given that DC bisects ∠BDE, so ∠2 ≅ ∠3 by the definition of angle bisector. Therefore, ∠1 ≅ ∠3 by the transitive property of congruence (in which ∠1 ≅ ∠2, ∠2 ≅ ∠3, ∴ ∠1 ≅ ∠3 by transitive property of congruence)

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~Rise Above the Ordinary, Senpai

Nick invests $3,500 in an account earning 11% interest compounded annually. Krista invests $4,000 in an account earning 4% interest compounded annually. Who will have more money in their account after 2 years? How much more?

Answers

Krista will have more money in 2 years time than Nick and she will get $14.05 more than Nick. Hope this helps.

Answer:

Krista's have more amount by $14.05

Step-by-step explanation:

Nick's Case

Principal = $3500

Rate of interest = 11% = 0.11

Time = 2 years

Formula : [tex]A=P(1+R)^t[/tex]

[tex]A=3500(1+0.11)^2[/tex]

[tex]A=4312.35[/tex]

Krista's case

Principal = $4000

Rate of interest = 4% = 0.04

Time = 2 years

Formula : [tex]A=P(1+R)^t[/tex]

[tex]A=4000(1+0.04)^2[/tex]

[tex]A=4326.4[/tex]

Nick's amount = $4312.35

Krista's amount = $4326.4

So, Krista's have more amount

Difference =  $4326.4-$4312.35=$14.05

Hence Krista's have more amount by $14.05

Tamara is going to the laundromat. She needs 6 quarters for each of the 4 machines that she is using. How many dollar bills must she insert into the change machine to have enough quarters to do her laundry?
A) 3
B) 4
C) 5
D) 6
E) 7

Answers

6 x 4 = 24

24 / 4 (#ofquartersinadollar) = 6
It’s option D.

Your Answer is D.


Simple addition of the value of Quarters can get us the correct answer.

It would take $1.50 to run one machine, and $1.50 x 4 = 6

What are the like terms of 10a+4b+3a-15b

Answers

10a + 3a are like terms because of the a. This equals to 10a

4b-15b are like terms because of the b and this equals to -11b

Expression: 10a-11b

The like terms in the expression are 10a and 3a, as well as 4b and -15b.

We have,

The like terms of the expression 10a + 4b + 3a - 15b are the terms that have the same variable(s) raised to the same power(s).

In this case, the like terms are:

10a and 3a (both have the variable 'a')

4b and -15b (both have the variable 'b')

Thus,

The like terms in the expression are 10a and 3a, as well as 4b and -15b.

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Which of the following is equal to the expression below?

[tex](160*243)^{\frac{1}{5} }[/tex]

A. 80

B. 96

C. [tex]5\sqrt[5]{5}[/tex]

D. [tex]6\sqrt[5]{5}[/tex]

Answers

160 = 2 x 2 x 2 x 2 x 2 x 5 = 2^5 x 5

243 = 3 x 3 x 3 x 3 x 3 = 3^5

So

(160 * 243)^1/5

= 5th root of (160 * 243)

= 5th root of (2^5 * 5 * 3^5)

= 2 * 3 * (5th root of 5)

= 6 * (5th root of  5)

Answer is D. 6 * (5th root of  5)

The resultant expression, equivalent to [tex](160*243)^{1/5}[/tex] is Option (D) [tex]6\sqrt[5]{5}[/tex]

Exponents and its properties -

An exponent refers to the number of times a number is multiplied by itself. It is represented as a number or letter written above and to the right of a mathematical expression called the base. It indicates that the base is to be raised to a certain power. x is the base and n is the exponent or power.

Represented as [tex]x^{n}[/tex]

What are some of the properties of exponents ?[tex]x*x*x[/tex] ........ upto n times = [tex]x^{n}[/tex][tex](x^{n})^{1/n} = x[/tex][tex](x^{n}*y^{n} )^{1/n} = xy[/tex]How to solve the given exponent problem to get the equivalent expression ?

Given expression is [tex](160*243)^{1/5}[/tex].

Now we are separating the expression,

160 = 2*2*2*2*2*5 = [tex]2^{5}*5[/tex]

243 = 3*3*3*3*3 = [tex]3^{5}[/tex]

∴ [tex](160*243)^{1/5}[/tex] =  [tex](2^{5}*5*3^{5})^{1/5}[/tex] = [tex]2*3*5^{1/5}[/tex] = [tex]6\sqrt[5]{5}[/tex]

Thus the equivalent expression is Option (C) [tex]6\sqrt[5]{5}[/tex]

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Convert the following measures of capacity.
a. 35 cubic meters to liters
b. 450 cubic centimeters to milliliters
c. 19.74 cubic meters to cubic decimeters
d. 926 cubic centimeters to cubic decimeters

Answers

Answer:

a)35 cubic meters=35000 liters.

b)450 cubic centimeters= 450 milliliters.

c)19.74 cubic meters=19740 cubic decimeters.

d)926 cubic centimeters=0.926 cubic decimeters.

Step-by-step explanation:

a) since one cubic meter = 1000 liters,

              35 cubic meters=35 X 1000=35000 liters

b) Since one cubic centimeters=1 milliliter,

               450 cubic centimeters=450 milliliters.

c)Since one meter = 10 decimeters, one cubic meter=10³ decimeters.

Hence 19.74 cubic meters= [tex]19.74X10^{3} =19740[/tex] cubic decimeters.

d) Since once centimeter=0.1 decimeter, 1 cubic centimeter=0.1³ decimeters.

Hence 926 cubic centimeters=[tex]926X0.1^{3}=0.926[/tex] cubic decimeters.

a. 35 cubic meters to liters:

1 cubic meter = 1000 liters

so 35 cubic meters = 35 x 1000 = 35,000 liters

b. 450 cubic centimeters to milliliters:

1 cubic centimeter = 1 milliliter

Therefore 450 cubic centimeters = 450 milliliters

c. 19.74 cubic meters to cubic decimeters:

1 cubic meter = 1000 cubic decimeters

so 19.74 cubic meter = 19.74 x 1000 = 19740 cubic decimeters

d. 926 cubic centimeters to cubic decimeters:

1 cubic centimeters = 0.001 cubic decimeters

so 926 cubic centimeters = 926 x 0.001 = 0.926

Andre earns $165 for each digital projector that she sells if she works five days a week for 11 hours each day and sales 12 digital projectors a week on average what is her average hourly wage

Answers

(165*12)/5*11 = AHW (average hourly wage)

1980/55 = AHW

36 = AHW

$36 is her average hourly wage.

Answer: Hi!

Andre earns $165 for each digital projector that she sells.

We know that she works 11 hours per day, 5 days per week and that she sells 12 digital projectors a week. We want to know the average hourly wage.

First, we need to know how much she wins in the week. This is the number of digital projectors sold multiplied by the profit for each one:

12*$165 = $1980

And now we need to see how the amount of hours that she works each week, this is 11 hours per day and 5 days per week, then she works 11*5 = 55 hours per week.

Now we can divide the earns per week by the number of hours that she works each week, and obtain the average hourly wage:

$1980/55 = $36

So Andre wins an average of $36 per hour.

In Exercises 29–34, graph the function and identify intervals on which
the function is increasing, decreasing, or constant.

30. ƒ1x2 = 0 x + 1 0 + 0 x - 1 0 - 3

32. h1x2 = 0.51x + 222 - 1

34. ƒ1x2 = x3 - x2 - 2x


In Exercises 41– 46, use a grapher to find all local maxima and minima
and the values of x where they occur. Give values rounded to two decimal
places.


42. g1x2 = x3 - 4x + 1

44. ƒ1x2 = 1x + 321x - 122


In Exercises 47–54, state whether the function is odd, even, or neither.

48. g1x2 = x3

50. g1x2 = 3/
1 + x2

52. ƒ1x2 = x3 + 0.04x^2 + 3

Answers

im confused what is the wuestion i will aanswer still in the comments

Yolanda used a reconciliation worksheet provided by her bank. Line 5 should equal line 6 at the end of the reconciliation, but it does not. Mega Bank Reconciliation Worksheet Amount 1. Enter the statement closing balance. $ 345 89 2. Enter the sum of any outstanding deposits or credits. $ 0 00 3. Add lines 1 and 2. $ 345 89 4. Enter the sum of any outstanding checks or debits. $ 37 51 5. Subtract line 4 from line 3. $ 308 38 6. Enter your checkbook balance. $ 328 37 Note: Lines 5 and 6 should be equal at the end of the reconciliation. Yolanda wants to first look for a single transaction that could have caused this problem with reconciliation. What is the amount of the transaction that Yolanda should look for in order to find a solution to the problem? A. $17.52 b. $19.99 c. $20.01 d. $37.51

Answers

The best answer for the question is B. $19.99


Answer is 19.99 dollars

Explanation:

Let us draw the reconciliatin done by Yolanda linewise

Banking reconciliation Worksheet Amount of Mega

1) Closing balance                                                       $ 345 89

2) the sum of any outstanding deposits or credits.         0.00

3)   Sum of 1 and 2                                                          345.89

4. sum of any outstanding checks or debits.                $ 37 51 5.

5) (3)-(4)                                                                           $ 308 38

6) checkbook balance.                                                   $ 328 37  

7) Difference (6)-(5)                                                         $   19.99


SInce difference is exactly 19.99 dollars Yolanda should look for the amount 19.99 dollars to find a solution to the problem i.e. to see the reason for the difference between lines 5 and 6                

Which is the simplified form of p to the power 0

Answers

NAMASTE :)

HERE IS YOUR ANSWER:

[tex] {p}^{0} = 1[/tex]


Any variable or constant having power zero is equal to one... :)

Answer:

the correct option is D : 1

Step-by-step explanation:



The coordinates of the vertices of △PQR are P(1, 4) , Q(2, 2) , and R(−2, 1) . The coordinates of the vertices of △P′Q′R′ are P′(−1, 4) , Q′(−2, 2) , and R′(2, 1) .



Which statement correctly describes the relationship between △PQR and △P′Q′R′ ?

△PQR is congruent to △P′Q′R′ because you can map △PQR to △P′Q′R′ using a translation 2 units to the left, which is a rigid motion.
△PQR is congruent to △P′Q′R′ because you can map △PQR to △P′Q′R′ using a reflection across the y-axis, which is a rigid motion.
△PQR is not congruent to △P′Q′R′ because there is no sequence of rigid motions that maps △PQR to △P′Q′R′ .
△PQR is congruent to △P′Q′R′ because you can map △PQR to △P′Q′R′ using a reflection across the x-axis, which is a rigid motion.

Answers

ANSWER


The correct  answer is B


EXPLANATION

If we analyse the coordinates carefully, you realize there is a mapping of

[tex](x,y)\rightarrow(-x,y)[/tex]

This is a reflection in the y-axis.


Since the transformation is a reflection, the shape is preserved. Therefore, the image triangle P'Q'R' of triangle

PQR are congruent.



Answer:

B

Step-by-step explanation:

It costs $100 to be a member of a music club. A member of the club pays $20 per music lesson. A nonmember pay $30 per music lesson. How many music lessons must a member and a nonmember take so the cost for each is the same?

Answers

Let x be amount of music lessons
Member = 100 + 20x
Non member = 30x
Must be same, so 100 + 20x = 30x
Solve for x:
Group like terms.
100 = 30x - 20x
100 = 10x
100/10 = x
x=10
10 music lessons for member and non member to have same costs of $300.
Im not very good at maths. But this seems easy :D. I'm still a beginner, but please give me points.

Final answer:

A member and a nonmember must each take 10 music lessons in order for the cost to be the same for both.

Explanation:

To find the number of music lessons that must be taken by a member and a nonmember so that the cost for each is the same, we can set up an equation. Let x represent the number of music lessons. For a member, the cost is $100 + $20x, and for a nonmember, the cost is $30x. We can set up the equation:

100 + 20x = 30x

To solve for x, we can subtract 20x from both sides:

100 = 10x

Then, we can divide both sides by 10:

x = 10

Therefore, a member and a nonmember must each take 10 music lessons in order for the cost to be the same for both.

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In 8 minutes,josh was able to type 496 words.What's his typing speed in words per minute

Answers

62 words per minute. You would divide 8 from 496 since you need to find out how many words he can type in a minute. Your answer is 62 words per minute.

Hope this helped! :)

Select the correct answer from each drop-down menu.
Use the given expression to complete the statements.

Answers

5 is a coefficient.  A coefficient is a number multiplied by a variable.


(2y+13) is a factor.  It can be multiplied by 8 to get an extended answer.


-1 is a constant.  A constant is a number that does not change.


Hope this helps!

Answer:

coefficient, factor and constant

Step-by-step explanation:

The given expression is:

[tex]5x-8(3y+13)-1[/tex]

From the given expression , we get

In the first term, [tex]5[/tex] is a coefficient of x (A coefficient is a number multiplied by a variable.).

In the second term, [tex]3y+13[/tex] is the factor (It can be multiplied by 8 to get an extended answer)

In the third term, [tex-1[/tex] is a constant (A constant is a number that does not change)

Vito owned 120 shares of a stock before tha corporation instituted a 5 for 3 split. Before the split, the stock was selling at 16 a share. Vito now has 200 shares of te stick that is worth about $26.67 each

Answers

Vito owned 120 shares of a stock before that corporation instituted a 5 for 3 split. Before the split, the stock was selling at 16 a share. Vito now has 200 shares of the stock that is worth about $26.67 each



Answer   =======>    False    

Post-split number of shares:    5/3   *    120      =    200

post-split price:        3/5   *   16      =     $9.60




Hope that helps!!!                    : )

The given condition is 'False'.

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

Vito owned 120 shares of a stock before the corporation instituted a 5 for 3 split.

And, Before the split, the stock was selling at 16 a share.

Here,

Vito now has 200 shares of the stock that is worth about $26.67 each

Since, Vito owned 120 shares of a stock before the corporation instituted a 5 for 3 split.

Hence, Post split number of shares = 5/3 × 120

                                                       = 200

So, Post split price = 3/5 × 16 = $9.60

Thus, The given condition is false.

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Joyce makes bracelets that she sells for $1.25 each. If she sells 40 of her bracelets, how much money will she make

Answers

1.25x40=50

joyce should make $50

A café sold 1,400 beverages in one month. If 60% of those beverages were coffee, how many coffees did the café sell in the month

Answers

the proprtion of coffees sold is 0.6 times to total sales so 1400×0.6 is the amount of coffes sold which equals 840

Number of beverages sold by cafe= 1,400

Number of beverages which were coffee= 60 % of number of beverages sold.

So, number of coffees that the café sell in the month= 60 % of 1400

    [tex]=\frac{60}{100}\times 1,400\\\\= 60 \times 14\\\\=840[/tex]

Keep in mind, x % of y is , [tex]\frac{x y}{100}[/tex]

Number of Coffees that cafe sell in month= 840

A cafeteria uses 556 kg of rice each week. The rice comes in bags that hold 13 kg each.


How many bags of rice does the cafeteria use each week?
A. 42
B.42 1/3
C.42 10/13
or
D.43 1/3

Answers

42 bags of rice is what the cafeteria use each week.

If you offered an item of $17.85 if the seller states he normally sells the same item of $19.95 what percentage discount is he offering you

Answers

I'm pretty sure it's a 9.5% discount

If a student drinks 64 ounces of coffee each day, how many gallons do they drink per year? Round to the nearest tenth. Please help fast!!

Answers

Final answer:

A student who drinks 64 ounces of coffee each day consumes 182.5 gallons per year, after converting ounces to gallons (64 ounces/day × 365 days/year, then divided by 128 ounces/gallon).

Explanation:

To calculate the amount of coffee a student drinks per year in gallons, we first need to understand the relationship between ounces and gallons. We know that 1 gallon is equivalent to 128 fluid ounces. So, to find out how many gallons 64 ounces represent, we divide 64 by 128.

64 ounces per day × 365 days per year = 23,360 ounces per year.

Next, divide the total annual ounces by the number of ounces in a gallon:

23,360 ounces per year ÷ 128 ounces per gallon = 182.5 gallons per year.

Therefore, rounded to the nearest tenth, a student drinks 182.5 gallons of coffee each year.

Need help asap please! A toy company has determined that the revenue generated by a particular toy is modeled by the following equation: 13x - 0.025x² The variable x is measured in thousands of toys produced, and r(x) is measured in thousands of dollars. What is the maximum revenue the company can earn with this toy?

Answers

The equation is r(x) = 10x - 0.025x² where x is measured in thousands of toys produced, and r(x) is measured in thousands of dollars.

For maximum r, r'(x) = 0

It becomes: r'(x) = [tex]10-0.025\times2x=0[/tex]

= [tex]10-0.5x=0[/tex]

[tex]x=\frac{10}{0.05}[/tex]

x= 200

Hence, r(200) = [tex]10\times200-0.025\times200^{2}[/tex]

Solving it we get,

r(200) = 1000

Hence, maximum revenue the company can earn with this toy is $1000.

What is [tex]15^{2}[/tex]

Answers

Amayo943,

Remember that with exponents you have to multiply the number of exponets by the same number it's in for example: [tex]1^2 = 1 \times 1[/tex] In this case you need to know that:

[tex]15^2 = 15 \times 15[/tex][tex]15 \times 15 = 225[/tex][tex]=225[/tex]

Therefore your answer is "225."

Hope this helps!

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