A vessel sails 32 miles S 45 E. How far south has it sailed?

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.

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

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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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

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

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! :)

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.

The x-intercept is 4

The y-intercept is 3

The slope is -3/4

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:

Answer:boi

Step-by-step explanation:

this is an equation in one variable and has only one solution

14x + 2 = 12x ( subtract 12x from both sides )

2x + 2 = 0 ( subtract 2 from both sides )

2x = - 2 ( divide both sides by 2 )

x = [tex]\frac{-2}{2}[/tex] = - 1 ← one solution

The equation 14x + 2 = 12x has only one solution.

14x + 2 = 12x

subtract 12x from both sides

14x - 12x + 2 = 12x - 12x

2x + 2 = 0

subtract 2 from both sides

2x + 2 - 2 = 0 - 2

2x = - 2

divide both sides by 2

2x / 2 = -2 / 2

x = -1

Therefore, the equation have only one solution.

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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'.

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.

Learn more about the multiplication visit:

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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)

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

If I understand your question correctly, you want to know how many pounds of vegetables the zoo feeds the animals a month if its a 30 day month?

In that case it would be 23 pounds times 30 days which is 690 pounds of vegetables. SO the zoo feeds the animals 690 pounds of vegetables to the animals each month.

Is that what your asking for?

To calculate the total monthly vegetable supply for the zoo animals, you multiply the daily feed amount by the average number of days in a month (23 pounds/day * 30 days/month = 690 pounds/month).

The student's question involves calculating the total amount of vegetables fed to the animals at the zoo over a month. To find this, we can set up a simple multiplication equation, where we multiply the daily food requirement by the number of days in a month. According to the question, the zoo feeds the tortoise, rhinoceros, and zebra a total of 23 pounds of vegetables a day. We are given that an average month is considered to have 30 days. So, the equation to find the total monthly vegetable supply for the animals would be:

23 pounds/day × 30 days/month = Total pounds/month

By multiplying these two numbers together, we get:

23 pounds/day × 30 days/month = 690 pounds/month

So, the zoo feeds the animals a total of 690 pounds of vegetables in an average 30 day month. If we want to express how the supply changes each month, we can write the equation as S = 23 × D, where S represents the total monthly supply and D represents the number of days in the month.

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200 is the volume of the cereal box

The solution is  

[tex]x\le 3 \:or \:x>18[/tex]

[tex]<b><u>EXPLANATION</u></b>[/tex]

[tex]6x-10\le 8\: or \frac{1}{3}x+6>12[/tex]

We group like terms, to obtain;

[tex]6x\le 8+10\: or \frac{1}{3}x>12-6[/tex]

Simplify to get,

[tex]6x\le 18\: or \frac{1}{3}x>6[/tex]

We further simplify to get;

[tex]x\le 3\: or x>18[/tex]

This can also be rewritten as;

[tex]x\le 3, x>18[/tex]

Or

[tex](-\infty 3] \cup (18,+ \infty)[/tex]

This can be represented on the number line as shown in the diagram.

Answer: (-∞,3)∪(18,∞)

Step-by-step explanation:

To solve this problem you must apply the proccedure shown below:

1. You must solve for x, as following:

[tex]6x-10\leq8\\6x\leq18\\x\leq3[/tex]

[tex]\frac{1}{3}x+6>12\\x>3(6)\\x>18[/tex]

2. Therefore, you have that the result is:

(-∞,3]∪(18,∞)

28 games won

we require to calculate 80% of 35

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

games won = 0.8 × 35 = 28

Answer:

the correct option is D : 1

Step-by-step explanation:

A. -13ab

B. 5a^2b

C. 3

Remark

This is much the same as the last inequality that you posted. When it tells you that you have 1 condition that is more than and one condition that is less than, then you need a compound statement. One of A and B is correct. C or D never will be.

At Least 4

This is the more than condition. You need 4 or more pennies to add to the collection. The rule is the same. The pointy end always points towards the smallest amount

4 ≤ x

No more than 2

That means that you can have 2 or under. The pointy end points to the x

2 ≥ x The biggest number (open end of the arrow) points at the 2.

Answer

2 ≥ x or  4 ≤  x That means the answer is A

Answer:

1 and 4 are correct. 2 and 3 are not.

Step-by-step explanation:

1.

When x = 0 where does the horse start?

y = 1.5*sin(0 + 0.5)*2*pi + 1.5

y = 1.5*sin(0.5*2pi) + 1.5

y = 1.5*sin(pi) + 1.5 But sin pi = 0

y = 0 + 1.5 So the horse is starting at the midpoint of it's travel.

2.

This one is a trick question. You can reason it without exact answers. At some point the sin(x + 0.5)*2pi will equal 1. When it does 1.5 * 1 + 1.5 = 3.0 At some other point sin(x + 0.5)*2pi = -1. When that happens the whole thing goes to 0. So the total of the distance traveled is 6 not three.

3.

You can figure this one out by letting x = 0.01 When it does then the value of the function is

y = 1.5*sin [(0.01 + 0.5)*2pi] + 1.5

y = 1.5*sin(0.51*2*pi) + 1.5

y = 1.5*sin(3.204424) + 1.5

y = 1.5*(- .0623) + 1.5

y = -0.9418 + 1.5

y = 1.4058 so it is going downward The value is getting smaller.

4.

The horse starts out in the middle of the pole. What  does x need to equal so that x + 0.5 = 1 ? And why 1. The answer to why 1 is that then the sine function will equal sin(2*pi)

That happens when x = 0.5 which is 1/2 a minute. If it takes 1/2 a minute to execute 1 complete cycle, then in 5 minutes the cycle will be executed 10 times. This one is correct.

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.

Substitution.

Elimination.

Using a Combination of methods.

Using absolute value

I hope this helps!

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

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

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.