Work out the area of the lawn.

ΔAED is the equilateral triangle. Therefore AH is a height of this triangle.

The formula of a height of an equilateral triangle:

[tex]h=\dfrac{a\sqrt3}{2}[/tex]

We have a = 5. Substitute:

[tex]\boxed{AH=\dfrac{5\sqrt3}{2}}[/tex]

You can use the Pythagorean theorem.

[tex]EH^2+AH^2=AE^2\\\\\left(\dfrac{5}{2}\right)^2+AH^2=5^2\\\\\dfrac{25}{4}+AH^2=25\\\\AH^2=25-\dfrac{25}{4}\\\\AH^2=\dfrac{100}{4}-\dfrac{25}{4}\\\\AH^2=\dfrac{75}{4}\to AH=\sqrt{\dfrac{75}{4}}\\\\AH=\dfrac{\sqrt{75}}{\sqrt4}\\\\AH=\dfrac{\sqrt{25\cdot3}}{2}\\\\\boxed{AH=\dfrac{5\sqrt3}{2}}[/tex]

If Circle A has a radius with the length of 5 units then the  exact length of the apothem is 5√3/2

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Circle A has a radius with the length of 5 units.

We have to find the length of apothem

The formula of a height of an equilateral triangle

h=a√3/2

We have a = 5. Substitute:

h=5√3/2

Apply Pythagorean theorem.

(5/2)²+AH²=5²

25/4+AH²=25

AH²=25-25/4

AH²=75/4

Take square root on both sides

AH=5√3/2

Hence, if Circle A has a radius with the length of 5 units then the  exact length of the apothem is 5√3/2

To learn more on Circles click:

https://brainly.com/question/11833983

#SPJ2

Answer:

The answer is C.

Step-by-step explanation:

A. name of ray

B. name of line

C. name of line segment

D. length of segment

Answer:

B is the answer

Step-by-step explanation:

First thing to do is solve the given equation for v

-11v-7 = 4

-11v = 4+7

-11v = 11

v = 11/(-11)

v = -1

Once we know this, we can use it to compute the following

7v-10 = 7*(-1) - 10 = -7 - 10 = -17

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

Answer: -17

Answer:

Correct choice is 4.

Step-by-step explanation:

Tyrone determines it takes him 58.2 minutes to travel 30 miles to work, then he travels with speed

[tex]\dfrac{30}{58.2}=\dfrac{300}{582}=\dfrac{50}{97}\ \text{miles per minute}.[/tex]

If 1 mile = 5,280 feet, then his speed is

[tex]\dfrac{50}{97}\cdot 5280=\dfrac{264000}{97}\ \text{feet per minute}.[/tex]

Since 1 minute = 60 seconds, then his speed is

[tex]\dfrac{264000}{97\cdot 60}=\dfrac{4400}{97}\approx 45.36\ \text{feet per second}.[/tex]

Answer:

45.36 feet ps IS THE ANSWER AND NOW GO AND SOLVE IT

Answer:

16

Step-by-step explanation:

the 9 parts of the ratio is equivalent to 72 books

divide number of books by 9 to find one part of the ratio

[tex]\frac{72}{9}[/tex] = 8 ← 1 part of the ratio

2 parts = 2 × 8 = 16 ← number of bookmarks sold

The problem can be solved using the power of a point theorem. First, let BD = x and EC = x + 12. Construct an equation: 8x = 6(x+12). Solving for x gives BD = 9 and EC = 21. The length of AC is then 35.

This problem can be solved using the concept of power of a point theorem in circle geometry. The power of a point theorem states that for any point outside a circle, the product of the lengths of the two line segments obtained by drawing secants from that point to the circle are always equal.

To apply this theorem to this problem, we'll first denote BD as x. Because the problem states that EC is 12 more than BD, we can denote EC as x + 12.

Now, using the power of a point theorem, we can write the equation (AD)*(DB) = (AE)*(EC). Substituting in the given values and the values we denoted for DB and EC, we get (8)*(x) = (6)*(x+12).

Solving this equation gives x = 9. Therefore, the length of BD is 9, and the length of EC is 21. To find the length of AC, we add the lengths AE, EC, and AD, which gives us AC = 6 + 21 + 8 = 35.

https://brainly.com/question/32546586

#SPJ3

Answer:

Step-by-step explanation:

all you have to is 8x12 multiplied by 2 since there is 2 rooms which is 192

The limit of any constant function is the value of the constant, so the limit is just 5.

For this case we have that by definition:

The limit of a constant function of the form [tex]y = f (x)[/tex], where [tex]f (x) = c[/tex], is the same constant, whatever the value to which the limit tends.

Thus, the limit of "5" when x tends to "2", results in "5".

Answer:

5

Option A

Answer:

23 packages

Step-by-step explanation:

We are told that the school cafeteria needs to buy 200 new forks. Each package contains 9 forks.

To find the number of packages that school cafeteria should buy we will divide total number of needed forks by number of forks in each pack.

[tex]\text{The number of fork packages}=\frac{200}{9}[/tex]

[tex]\text{The number of fork packages}=22.22222[/tex]

Since forks come in package of 9, so cafeteria have to buy whole number packages.

Let us round up our answer to the whole number.

[tex]\text{The number of fork packages}=22.22222\approx 23[/tex]

Therefore, school cafeteria should buy 23 packages of forks.

Answer:

23 packages should the cafeteria buy.

Step-by-step explanation:

Proportion states that the two ratios or fractions are equal.

As per the statement: The school cafeteria needs to buy 200 new forks. If each package contains 9 forks.

then by definition of Proportion;

[tex]\frac{1}{9} = \frac{x}{200}[/tex]   , where x represents the package

By cross multiply;

200 = 9x

Divide both sides by 9 we get;

[tex]\frac{200}{9} =\frac{9x}{9}[/tex]

Simplify:

[tex]x = \frac{200}{9} =22.222[/tex]

Therefore, 23 package should the cafeteria buy.

It is 2.5 not what the other dude said it was

Answer:

The correct answer is Option 4, the fourth graph

Step-by-step explanation:

We will go through why the other graphs are not the correct answer and then explain why the fourth is indeed the correct answer.

Option 1 is wrong because it has the general shape of the graph of an even valued function. These functions are either concave up or concave down.

Option 2 is wrong because it has the general shape of the cubic function. These functions are defined for both negative and positive values of x.

Option 3 is wrong because it is not defined for negative values of x. It has the general shape of the square root function.

Option 4 is correct because it has the general shape of the function [tex]f(x)=\sqrt[3]{x}[/tex]. Functions of this kind are defined for both negative and positive values of x.

Answer: the fourth Graph

Step-by-step explanation:

Answer:

Hello from MrBillDoesMath!

Answer:

p = 12

Discussion:

Assume we have a right trainload (looks like it but no angle indication given).  By the Pythagorean Theorem

p^2 + 5^2 = (p+1) ^ 2          =>

p^2 + 25 = p^2 + 2p + 1     =>

25 = 2p + 1                          =>         (subtract p^2 from both sides)

25 -1 = 2p                            =>         (subtract 1 from both sides)

24 = 2p =>

p = 24/2 = 12                       =>         (divide both sides by 2)

Regards,  

MrB

P.S.  I'll be on vacation from Friday, Dec 22 to Jan 2, 2019. Have a Great New Year!

Answer:

for imagine math it is the top left corner choice that says 1 with two lines coming from it and then a 2 and 3 from each line and so on until 6

Step-by-step explanation:

On Imagine math, It is the very first choice, with the 1 at the top and then the 2 and the 3, then the 4 and 5 and 6. Hope this helped!

Step-by-step explanation:

Answer:

The distance to the earth's horizon from point P is 216.2198187 mi, appriximately 216.22 mi

Step-by-step explanation:

This is a right triangle:

Hypotenuse: c=3959 mi + 5.9 mi → c=3964.9 mi

Leg 1: a=x=?

Leg 2: b=3959 mi

Using the Pytagorean theorem:

a^2+b^2=c^2

Replacing the known values:

(x)^2+(3959 mi)^2=(3964.9 mi)^2

Solving for x: Squaring:

x^2+15,673,681 mi^2=15,720,432.01 mi^2

Subtracting 15,673,681 mi^2 both sides of the equation:

x^2+15,673,681 mi^2-15,673,681 mi^2=15,720,432.01 mi^2-15,673,681 mi^2

x^2=46,751.01 mi^2

Square root both sides of the equation:

sqrt(x^2)=sqrt(46,751.01 mi^2)

x=216.2198187 mi

x=216.22 mi

The distance from the point P to the Earth’s horizon distance is approximately 216.22 mi.

To find the distance from the point P to the earth's horizon, we can use the concept of the earth's curvature.

The distance from the center of the earth to point P is the radius of the earth plus the distance from the center to the surface, which is 3959 + 3964.9 = 7923.9 miles.

The distance to the horizon can be found using the formula for the horizon distance, which is approximately equal to the square root of two times the product of the earth's radius and the total distance from P to the surface of the earth.

So, x = sqrt(2 * 3959 * 7923.9) = 216.22 mi.

Learn more about Earth’s horizon distance here:

https://brainly.com/question/12366928

#SPJ3

The probable question may be:

In the Earth center the radius of the earth is 3959 mi

P is a point outside the circle

the distance from center of the earth surface to point P is 3964.9 mi  and the distance to the earth’s horizon from point P is x ?

Find x

To prove that m

To prove that m<QPS = m<TPV, we need to use the given information and apply the congruent triangles theorem. Let's assume that <QPS = <TPV. From the given information, we can determine that <QPS = I and <TPV = V. Since the angles are congruent and the corresponding sides are proportional, we can conclude that m<QPS = m<TPV.

https://brainly.com/question/22062407

#SPJ2

0.80 per ounce

1.25 ounces

Answer:

2/3 < 4/5

Step-by-step explanation:

because:

2/3 = 0.666

4/5 = 0.8

Answer: at this amount, there are 57.5 calories per ounce

therefore, there are 355 calories in 6 ounces of this ice cream

(since 57.5×6=355.0)

Answer:

345 calories

Step-by-step explanation:

Total Calories = 230 calories

Total amount = 4 ounces

TO find how many calories in 6 ounces of the ice cream

For this question we have to find out the number of calories in one ounce of an ice cream firs

as it is given to us that 230 calories in 4 ounces

so no of calories in one ounce = total calories / no of ounces

                                                   =230 / 4

                                                   =57.5 calories / ounce

Now we know that their are 57.5 calories in one ounce of the ice cream

We have to find no of calories in 6 ounces of ice cream

No of calories = 6 * 57.5

                       =345 calories

so amount of calories in 6 ounces are 345 calories

Answer: (a) 5

Step-by-step explanation:

[tex]\lim_{x \to 2} 5[/tex] means what is the y-value when x = 2 .

The given equation is: y = 5 so the y-value is 5 for all values of x

Answer: (c) 13

Step-by-step explanation:

f(x) = x² + 5x

f'(x) = 2x + 5

f'(4) = 2(4) + 5

      = 8 + 5

      = 13

Answer: (c) 2

Step-by-step explanation:

The question is asking what the y-value is when x = -2.  The graph shows that the coordinate (-2, 2) is on the curve. So, when x = -2, y = 2.

Answer:

lim x→2   5     =5

The slope is 13

lim x→-2   x^2 -2  =2

Step-by-step explanation:

lim x→2   5     =5

The limit of a constant is the constant

f(x) = x^2 +5x

We need to take the derivative

f'(x) = 2x+5

Then evaluate the derivative at x=4  (4,36)

f'(4) = 2*4 +5

     = 8+5

    = 13

The slope is 13

lim x→-2   x^2 -2  =2

Looking at the graph, the value of the function at -2  is about 2

We can also calculate it   (-2)^2 -2 =  4-2 = 2

Answer:

k=3

Step-by-step explanation:

Given equation is

[tex]x^2+y^2 -6y-12=0[/tex]

First we move -12 to the other side by adding 12 on both sides

[tex]x^2+y^2 -6y =12[/tex]

We apply completing the square method to get square form (y-k)^2

Lets take coefficient of y and then divide it by 2

-6 divide by 2  is -3

Then we square it (-3)^2 = 9

We add 9 on both sides

[tex]x^2+y^2 -6y + 9=12+9[/tex]

[tex]x^2+(y^2 -6y + 9)=21[/tex]

Now we factor,  y^2 - 6y +9 is (y-3)(y-3)= (y-3)^2

[tex]x^2+(y-3)^3=21[/tex]

Now we compare with x^2 + (y-k)^2 = 21 and find the value of k

The value of k = 3

Answer:

This system will have a. exactly one solution.

Step-by-step explanation:

When two lines have different slopes it means that they intersect exactly one time.

If they have the same slope, we need to look at the intercept to see if there is none or infinitely many solutions.

However, these have different slopes and therefore have just 1 solution.

The given set of equations has exactly one solution as y = -1 and x = 2.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

To put it another way, the equation needs to be subject to some restrictions.

A linear equation could contain more than one variable. If a variable's maximum power constantly equals one, an equation is considered to be linear.

Given a set of equations,

y = -3x + 5 and y = 3x - 7

By equate,

-3x + 5 = 3x - 7

6x = 12

x = 2 and y = -1

Hence "The given set of equations has exactly one solution as y = -1 and x = 2".

For more about the equation,

brainly.com/question/10413253

#SPJ2

Given is :

The annual income of Richard = $34200

Hence, his monthly income becomes = [tex]\frac{34200}{12}[/tex] = $2850

So, the maximum amount that he can spend per month paying off credit cards and loans and not be in danger of credit overload can be a maximum of 20% of this income.

So, 20% of 2850 is = $570

Hence, approximately $570 can be spent a month.

As, the question has no options to choose from, but the question is complete in itself, so this is the best possible answer.

Answer: $570

Step-by-step explanation:

Answer:

The value for the expression [tex](A+B)^{2}[/tex] is the largest

Step-by-step explanation:

Since both A and B must be greater than 0 and A>B then we can assume the least possible values for B=1 and A=2.

So,

i) 2(A+B) = 2(2+1) = 2*3 = 6

ii) [tex](A+B)^{2}[/tex] = (A+B)*(A+B) = (2+1)*(2+1) = 3*3 = 9

iii) [tex]A^{2} + B^{2}[/tex]  = [tex]2^{2} +1^{2}[/tex] = 4+1 = 5

iv) [tex]A^{2} - B^{2} = 2^{2} - 1^{2}[/tex] = 4-1 =3

Inspecting the answers of the above four expressions, we see that the value for the expression [tex](A+B)^{2}[/tex] is the largest.

Answer: (A+B)^2 is the largest because it equals 9 when A=2 and B=1 are plugged in and the rest are less than 9

Answer:

$307.5

Step-by-step explanation:

We have been given that Elena's aunt bought her a $150 savings bond when she was born. When Elena is 20 years old the bond will have earned 105% interest.

The bond's value after 20 years will be 150 plus 105% of 150.

[tex]\text{Bond's value when Elena will be 20 years old}=150+(\frac{105}{100}*150)[/tex]

[tex]\text{Bond's value when Elena will be 20 years old}=150+(1.05*150)[/tex]

[tex]\text{Bond's value when Elena will be 20 years old}=150+157.5[/tex]

[tex]\text{Bond's value when Elena will be 20 years old}=307.5[/tex]

Therefore, bond will be worth $307.5 when Elena will be 20 years old.

Answer:

Water = 1/5 of the volume of the syrup

Step-by-.step explanation:

Suppose we had  1000 cm^3 of syrup  and the new volume after adding water is x cm^3.  Now the amount of sugar stays the same so we have the equation 35 * 1000 =  25 * x

x = (30 * 1000) / 25 =  30,000 / 25

= 1200 cm^3

So we need to add 200 cm^2 of water .

In general terms,  we need to add water which equals 1/5 of the volume of the syrup,

2x/3=8

2x=24

x=12

It takes Molly 12 minues to run one mile.