the square has a radius of 3 square root 2 what is the apothem?

Answers

Answer 1

Final answer:

The apothem of the square is equal to half the length of a side of the square, which can be calculated by doubling the radius. In this case, the apothem is 3√2.

Explanation:

The apothem of a square is a line segment drawn from the center of the square to any side of the square, perpendicular to that side. The apothem is equal to half the length of a side of the square.

Given that the square has a radius of 3√2, we can determine the length of a side of the square by doubling the radius. So, the length of a side is 2 * 3√2 = 6√2.

Therefore, the apothem of the square is half the length of a side, which is (6√2)/2 = 3√2.

Related Questions

Please check my work!

Answers

That is correct! The graph shows that the students their are 40 students that have both a part-time job and a cell phone. B) Is correct.

If a line contains the point (0, -1) and has a slope of 2, then which of the following points also lies on the line?

A. (2, 1)
B. (1, 1)
C. (0, 1)

Answers

The answer is B because y=2x-1

Answer:

The point that lie on the line is:

B. (1,1)

Step-by-step explanation:

We are given that a line passes through the point (0,-1) and has a slope of 2.

We know that the equation of a line passing through (a,b) and having slope m is given by:

[tex]y-b=m(x-a)[/tex]

Here we have: (a,b)=(0,-1) and m=2

This means that the equation of line is:

[tex]y-(-1)=2(x-0)\\\\y+1=2x\\\\y=2x-1[/tex]

Now we will check which option is true.

(2,1)

when x=2

we have:

[tex]y=2\times 2-1\\\\\\y=4-1\\\\\\y=3\neq 1[/tex]

Hence, option: A is incorrect.

(1,1)

when x=1

we have:

[tex]y=2\times 1-1\\\\\\y=2-1\\\\\\y=1[/tex]

Hence, option: B is correct.

(0,1)

when x=0

we have:

[tex]y=2\times 0-1\\\\\\y=0-1\\\\\\y=-1\neq 1[/tex]

Hence, option: C is incorrect.

Find the probability of a couple having a baby girlgirl when their fourthfourth child is born, given that the first threethree children were all girlsall girls. assume boys and girls are equally likely. is the result the same as the probability of getting all girlsall girls among fourfour children?

Answers

Every single time a person has a baby, it has a 50% chance of being a boy or a girl. Having 3 girls previously will not change anything. These events are independent. So the probability of having a baby girl given that the first 3 were girls is 50% or 1/2 or 0.5.

However, prior to having any kids, the probability of having all girls among 4 children is : 1.2 * 1/2 * 1/2 * 1/2 = 1/16...so the result are different.

If F(theta)=tan theta=3, find F(theta+pi)

Answers

Given:
f(θ) = tan(θ) = 3

Note that
[tex]tan(x+y) = \frac{tanx + tany}{1-tanx \, tany} [/tex]

Note that tan(π) = 0.
Therefore
f(θ + π) = tan(θ+π)
= (tanθ + tan π)/(1 -tanθ tan π)
= 3/1 = 3

Answer: 3

As given
[tex]f(\theta) = tan( \theta) = 3[/tex]

So [tex]f(\theta + \pi) = tan (\theta + \pi)[/tex]

And we know [tex]tan(\theta + \pi) = -tan(\theta)[/tex] because it is in second quadrant and tan is negative in second quadrant.

So [tex]f(\theta + \pi) = -tan(\theta) = -3[/tex]

So answer is -3.

P(A)=25,P(B|A)=920,P(A∩B)=?

Answers

Final answer:

We use the product rule in probability to find P(A∩B) = P(B|A) * P(A). Substituting given values, P(A∩B) = (9/20) * 25, which equals 11.25.

Explanation:

The subject area of this question is probability, a topic within mathematics. Here, we are asked to find the intersection of Events A and B given the probabilities of A and the conditional probability of B given A. The rule of product in probability states that P(A∩B) = P(B|A) * P(A).

Let's calculate: P(B|A) is given as 9/20 while P(A) is 25. Thus,

P(A∩B) = P(B|A) * P(A) = (9/20) * 25 = 11.25

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A computer simulation tossed a 10-faced die 5 times. How many possible outcomes exist? 9,765,625 100,000 252 100

Answers

10 * 10 * 10 * 10 * 10 = 100,000

Answer:

Possible outcomes in tossing a 10-faced die 5 times is:

100,000

Step-by-step explanation:

A computer simulation tossed a 10-faced die 5 times.

Number of outcomes in each throw=10

Number of outcomes in 2 throws

=Number of outcomes in first throw×number of outcomes in second throw

=10×10

= 100

Hence, Number of outcomes in 5 throws

=10×10×10×10×10

=100,000

Possible outcomes in tossing a 10-faced die 5 times is:

100,000

F a company provides 1 1/4 vacation days to its employees every month, how many vacation days does an employee get every year?

Answers

1 1/4 per month

12 months per year

1 1/4 * 12 =

5/4 * 12/1 = 60/4 = 15

they get 15 days per year

10 POINTS!!! TO ANSWER CORRECTLY AND BRAINLIEST!!!!

Convert these unlike fractions to equivalent like fractions and add them. You must use the LCD to get the answer correct. If possible, reduce the final sum.

Answers

1/5 = 3/15
2/3 = 10/15
3/15 + 10/15 = 13/15

The LCD is 15, so multiply the numerator and denominator of 1/5 by 3, this leaves us with 3/15. Now, multiply the numerator and denominator of 2/3 by 5,
this leaves us with 10/15. Now, if we add 3/15 and 10/15, we get 13/15. This cannot be simplified because 13 is a prime number, thus it is only divisible by itself and 1.

what is the least common multiple of X and Y? X=2*2*2*2 Y=2*2*2*3

Answers

[tex]\text{lcm}(x,y)=2^4\cdot3=48[/tex]

The least common multiple is the product of the highest occurring primes of the numbers prime factorizations, in this case:

2*2*2*2*3=48

Solve the equation by completing the square. Round to the nearest hundredth if necessary. x^2-3x-3=0

Answers

x^2 - 3x = 3
(x - 1.5)^2 - 2.25 = 3
(x - 1.5) = +/- sqrt 5.25

x = 1.5 +/- sqrt5.25

x = -0.79, 3.79 to nearest hundredth

This is the answer I wrote it all out

The population of a species of rabbit triples every year. This can be modeled by f(x) = 4(3)x and f(5) = 972. What does the 4 represent? (1 point) The starting population of the rabbits The population of the rabbits after five years The rate the population increases The number of years that have passed

Answers

Exponential functions are of the form:

y=ab^x, y=final amount, a=initial amount, b=rate, t=time

So the value a, 4 in this case, is the starting population of the rabbits.

Answer: The starting population of the rabbits

Step-by-step explanation:

Given: The population of a species of rabbit triples every year. This can be modeled by f(x) = 4(3)x and f(5) = 972.

We know that the exponential growth function is given by :-

[tex]f(x)=Ab^x[/tex], where A is the initial amount and b is the multiplicative rate of change in time x.

As compared to the given exponential function, we have

A=4

Therefore, 4 represents the starting population of the rabbits

decimal fundamentals
add 729.3 + 3.4006

Answers

732.7006 is the answer to this question

Two cars leave the same location at the same time but one car is heading north and the other is heading south. After 3 hours, the cars are 360 miles apart. If the car heading north is traveling 10 miles per hour slower than the car heading south, what are the two speeds of the cars?

SHOW THE EQUATION

Answers

3x +3(x-10) = 360

3x +3x-30 =360

6x-30 =360

6x=390

X = 390/6 = 65

65-10 =55

One car was driving 65 mph

The other was 55 mph

[tex]d=vt[/tex]
[tex]360=(v_{s})(3)+(v_{n})(3)[/tex]
[tex]360=(v_{s})(3)+((v_{s}-10)(3)[/tex]
[tex]360=3v_{s}+3v_{s}-30[/tex]
[tex]390=6v_{s}[/tex]
[tex]v_{s}=\frac{390}{6}=65[/tex]
[tex]v_{n}=v_{s}-10=65-10=55[/tex]

The south car is traveling at 65mph. The north car is traveling at 55mph.

The graph shows f(x) = 1/2 and its translation, g(x).

Which describes the translation of f(x) to g(x)?

Answers

As you can see, each point on f(x) is moved up 4 units to get to g(x), so the function is g(x) = f(x) + 4. The f(x) function cannot possibly be f(x)=1/2, though, because that would be a horizontal line through y = 1/2 and that function is clearly not a horizontal line. So whatever f(x) is REALLY, add 4 to the tail end of it to show its translation.

Answer:

The translation function g(x) is given as:

[tex]g(x)=\dfrac{1}{2^x}+4[/tex]

step-by-step explanation:

The parent function is f(x) and its representation is given as:

[tex]f(x)=\dfrac{1}{2^x}[/tex]

Now the graph g*x) is obtained by translation of the graph f(x) by some units.

Now as the graph of g(x) is a shift of the graph f(x) or the graph g(x) is translated by 4 units upwards.

hence the function g(x) is represented by:

g(x)=f(x)+4.

Hence the translation function g(x) is given as:

[tex]g(x)=\dfrac{1}{2^x}+4[/tex]

Prove that if m, d, and k are integers and d > 0, then (m + dk) mod d = m mod
d.

Answers

from the rules of modular arithmetic, (A+B)mod C= (A)modC +(B)modC

So, (m + dk) mod d = (m) mod d+ (dk) mod d

clearly (dk) mod d = 0, as one of the things (dk) mod d represents, is the remainder of dk, when divided by d, which is clearly 0.

Thus

(m + dk) mod d = (m) mod d+ (dk) mod d= (m) mod d+ 0=(m) mod d

(m + dk) mod d =(m) mod d

Final answer:

To prove that (m + dk) mod d = m mod d, we can use the definition of the modulo operation and properties of integers.

Explanation:

To prove that (m + dk) mod d = m mod d, we can use the definition of the modulo operation and properties of integers. Let's assume that m and d are integers, d > 0, and k is an integer.

Start with the left-hand side: (m + dk) mod d.Using the distributive property, we can rewrite (m + dk) as m mod d + (dk mod d).Since any number mod d is less than d, (dk mod d) is equivalent to 0.Therefore, (m + dk) mod d simplifies to m mod d + 0, which is equal to m mod d.Since the left-hand side is equal to the right-hand side, we have proved that (m + dk) mod d = m mod d.

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Help please..........,.,,,

Answers

A, the cost of 6 show tickets is $30, the blue dot is where 30 and 6 intersect. Hope this helps.

A is your answer its 30 dollars for 6 tickets

Find the missing factor n(n-3)+2(n-3)=() (n-3)

Answers

Greetings!

Solve for the missing factor: [tex](x)[/tex]
[tex]n(n-3)+2(n-3)=x(n-3)[/tex]

Divide both sides by [tex](n-3)[/tex]:
[tex] \frac{n(n-3)}{(n-3)} + \frac{2(n-3)}{(n-3)}= \frac{x(n-3)}{(n-3)} [/tex]

Cancel Common Factors:
[tex]n+2=x[/tex]

The Missing Factor is:
[tex]\boxed{n+2}[/tex]

I hope this helped!
-Benjamin

Convert 48°36'12" to the nearest thousandth of a degree

Answers

48 degrees remains

divide minutes by 60

36/60 = 0.6

then divide seconds by 3600

12/3600=0.003 ( to nearest thousandth)

now add them all up

48 +0.6 + 0.003 = 48.603 degrees

PLEASE HELP ME!!!!

Part A: Amir rented a scooter at $43 for 3 hours. If he rents the same scooter for 8 hours, he has to pay a total rent of $113.

Write an equation in the standard form to represent the total rent (y) that Amir has to pay for renting the scooter for x hours.

Part B: Write the equation obtained in Part A using function notation.

Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals.

Answers

Part A:

The equation in standard form is given Ax+By+C = 0
where x is the gradient of a straight line (or the rate of change)

The rate of change = (113-43) / (8-3) = 70/5 = 14
This value means there's an increase of $14 for every hour rented.

We also need to work out the value of C, which is the fixed value (happen at x=0)

We know that Amir paid $43 for 3 hours.
Amir would have paid $29 for 2 hours
Amir would have paid $15 for 1 hour
Since the hourly rate is $14, the fixed fee is 15 - 14 = $1

The equation that represents the total cost of renting a scooter is

y = 14x + 1

Rearranging this equation to get the standard form
14x - y + 1 = 0

Part B:

Writing the equation as function ⇒ f(x) = 14x + 1

Part C:

To graph the equation, we can start by choosing the x-intervals, say we have the value of x between 0 and 10

x 0 1 2 3 4 5 6 7 8 9 10
y 1 15 29 43 57 71 85 99 113 127 141

Each pair of x-value and y-value is then plotted on a graph then each plot is joined to draw a straight line.

Answer:

Step-by-step explanation:

Part A: The two points that represent this situation are (3,43) and (8,113). To put this in standard form, I will first find the slope-intercept form. I did this in the image below.

Now, to find the standard form I will rearrange, 14x -y +1 = 0.

Part B: To put this in function notation I simply take my slope-intercept equation of y=14x+1, and replace y with f(x) so, f(x)=14x+1

Part C: To graph this, put the y, intercept at 1, and give the line a slope of 14/1. Label the x-axis with hours, from 0 - 8, and the y-axis with dollars, from 0-150.

Find the value of the variable and DF if D is between C and F if CD 4y -9, DF 2y-7, and CF 14.

Answers

CF = CD + DF (since D is simply a point on the line, and C to that point added onto F to that point is CF), so 4y-9+2y-7=14. Adding it up, we get 6y-16=14 and adding by 16 we get 30=6y. Dividing both sides by 6, we get y=5. Plugging that into DF, we get 10-7=DF=3

Derive the equation of the parabola with a focus at (−5, 5) and a directrix of y = −1.

Answers

check the picture below.

so, the left-part of the picture is the focus point and the directrix... .so.. notice, the focus is above the directrix, meaning is a vertical parabola and is opening upwards.

now, looking at the right-part of the picture, bear in mind that, the vertex is "p" units away from the directrix and the focus, so, the vertex is half-way between those fellows, notice in the picture what "p" is, keep in mind that, because the parabola is opening upwards, "p" is a positive unit, thus is 3.

[tex]\bf \textit{parabola vertex form with focus point distance}\\\\ \begin{array}{llll} (y-{{ k}})^2=4{{ p}}(x-{{ h}}) \\\\ \boxed{(x-{{ h}})^2=4{{ p}}(y-{{ k}}) }\\ \end{array} \qquad \begin{array}{llll} vertex\ ({{ h}},{{ k}})\\\\ {{ p}}=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array}\\\\ -------------------------------\\\\[/tex]

[tex]\bf \begin{cases} h=-5\\ k=2\\ p=3 \end{cases}\implies [x-(-5)]^2=4(3)(y-2) \\\\\\ (x+5)^2=12(y-2)\implies \cfrac{(x+5)^2}{12}=y-2\implies \cfrac{(x+5)^2}{12}+2=y \\\\\\ \cfrac{1}{12}(x+5)^2+2=y[/tex]

Answer: D

Step-by-step explanation: took the test

for which of the following numbers does 5 appear in the tens place ?
*check all that applies*
a. 125.634
b. 56.89
c. 1250
d. 3.5
e. 92.57

Answers

5 appear in the tens place

answer:
b. 56.89
c. 1250

The answers are b and c. It's talking about the "tens" place, not the "tenths" place, so neither d or e are correct.

From a deck of 52 cards, one card is drawn at random. Match the following subsets with their correct probabilities.
1. P(face card)
2. P(seven of hearts)
3. P(no black)
4. P(king)
5. P(diamond)

Answers

1.3/13(if you mean jacks queens and kings)
2.1/52
3.1/2
4.1/13
5.1/4

Answer:

P(face card)=3/13 P(seven of hearts)=1/52P(no black)=1/2P(king)=1/13P(diamond)=1/4

Step-by-step explanation:

We know that there are a total 52 cards out of which:

There are 12 face cards ( 4 kings,4 queen and 4 jack)

There are 4 pack:

13- spades 13- club 13-heart 13-diamond.

Out of which there are 26 black cards( 13 spade and 13 club)

There are 26 red cards( 13 heart and 13 diamond)

Now , we are asked to find the probability of each of the following,

P(face card)

Since there are total 12 face cards out of 52 playing cards.

Hence,

P(face card)=12/52=3/13

P( seven of hearts)

As there is just 1 seven of heart out pf 52 cards.

Hence, P(seven of hearts)=1/52

P(no black)

This means we are asked to find the probability of red card.

As there are 26 red card.

Hence P(no black)=26/52=1/2

P(king)

As there are 4 kings out of 52 cards.

Hence, P(king)=4/52=1/13

P(diamond)

As there are total 13 cards of diamond.

Hence,

P(diamond)=13/52=1/4

D: y> -1/3 x+1 helpppp

Answers

The answer is A. It is less than or equal to because the line is solid instead of dashed. It is less than because the shaded portion is below the line.

A ball is thrown from an initial height of 1 meter with an initial upward velocity of 13 m/s. The ball's height h (in meters) after t seconds is given by the following.

h=1+13t-5t^2

Find all values of t for which the ball's height is 8 meters.

Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)

Answers

Here the answer is: 0.76 and 1.84

I hope I don't have to explain it again.

For t=1.84 and t=0.76 the ball's height is 8 meters in equation h=1+13t-[tex]5t^{2}[/tex].

What is equation?

An equation is a relationship between two or more variables expressed in equal to form. Equation of two variables look like ax+ by=c. It is solved in order to find the values of variables.

How to solve equation?

We have been given an equation h=1+13t-[tex]5t^{2}[/tex] and we have to find the values of t for which h=8.

So,

1+13t-[tex]5t^{2}[/tex]=8

[tex]-5t^{2}[/tex]+13t+1-8=0

[tex]-5t^{2}[/tex]+13t-7=0

Removing negative signs.

[tex]5t^{2}[/tex]-13t+7=0

We cannot solve through factorization so e use the following formula:

x=-b+-[tex]\sqrt{b^{2} -4ac}/2a[/tex]

t=(13+-[tex]\sqrt{-13^{2} -4*5*7}[/tex])/2*5

t=(13+-[tex]\sqrt{169-140}[/tex])/10

t=(13+5.38)/10, (13-5.38)/10

t=1.838, 0.762

By rounding off to nearest hundred t=1.84, 0.76.

Hence value of t for which h=8 meters are 1.84 and 0.76.

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Aiko stands 5 m from a tree. At that distance, the angle of elevation from the ground to the top of the tree is 80°. Approximately how tall is the tree?

Answers

This is the concept of trigonometry, the height of the tree will be given by:
tan theta=[opposite]/[adjacent]
theta=80
height=h
adjacent=5 m
hence;
tan80=h/5
hence;
h=5tan80
h=28.36 m

Determine whether the sequence converges or diverges. If it converges, give the limit.

11, 44, 176, 704, ...

Answers

The term to term rule is multiplying by 4 and if we continue doing this, we will move towards very large positive numbers.

This sequence, therefore, diverges to infinity

Rewrite the rational exponent as a radical.

5 to the 3 over 4 power, to the 2 over 3 power

A.the cube root of 5 squared
B. the twelfth root of 5
C. the square root of 5
D.the cube root of 5 the fourth power

Answers

[tex]\left( 5^{ \frac{3}{4} } \right)^{ \frac{2}{3} }=5^{ \frac{3}{4} *\frac{2}{3} }=5^{ \frac{1}{2} }= \sqrt{5} [/tex]

C. the square root of 5

What is the length of the hypotenuse of the triangle?

Answers

15^2 + 8^2 = 225 + 64 = 289

square root 289 = 17

answer

length of the hypotenuse of the triangle = 17 cm (3rd choice)

Answer:

length of the hypotenuse = 17 cm

Step-by-step explanation:

To find the length of the hypotenuse of any triangle we use pythagorean theorem

[tex]c^2 = a^2 + b^2[/tex]

Where c is the hypotenuse

a and b are the legs of the triangle

Given : a= 8 cm, and b= 15 cm

We find hypotenuse C

[tex]c^2 = 15^2 + 8^2[/tex]

[tex]c^2 = 225 + 64[/tex]

[tex]c^2 = 289[/tex]

Take square root on both sides

c= 17

So length of the hypotenuse = 17 cm

need help solving for the midpoint between point a and point b

Answers

A is located at (-3,-5) B is located at (1,-9)

-3 + 1 = -2/2 =-1

-5 + -9 = -14/2 = -7

midpoint is (-1,-7)

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