A soccer field is 100 yd wide and 130 yd long. find the length of the diagonal of such a field. give an exact answer as a radical expression and an approximation to three decimal places.

Answers

Answer 1

Answer:

10√269 ≈ 164.012 yd

Step-by-step explanation:

You want the length of the diagonal of a 100 yd by 130 yd soccer field.

Pythagorean theorem

The diagonal of the field is the hypotenuse of the right triangle created by that diagonal and the sides of the field. The length of the hypotenuse is given by the Pythagorean theorem.

c² = a² +b²

c² = 100² +130² = 10,000 +16,900 = 26,900

c = √26900 = 10√269 ≈ 164.012

The length of the diagonal is 10√269 ≈ 164.012 yards.

Additional comment

As a practical matter, it would be difficult to measure this distance with an accuracy better than 0.1 yards.

Related Questions

Use the grouping method to factor the polynomial below completely.

x3 – 4x2 + 3x – 12

A. (x2 + 4)(x – 3)
B. (x2 – 4)(x + 3)
C. (x2 – 3)(x + 4)
D. (x2 + 3)(x – 4)

Answers

After factor simplification of the polynomial, The answer is D

The answer is d
Hope that helped!!!!!!

What is the excluded value of the rational expression: x-4/6 divided by x+1/7?
A. -1
B. 4
C. -7
D. None of the above

Answers

For this case we have the following expression:
((x-4) / (6)) / ((x + 1) / (7))
Rewriting we have:
7 (x-4) / 6 (x + 1)
We observe that the expression is not defined for the values where the denominator is equal to zero.
We have then:
x + 1 = 0
x = -1
Answer:
The excluded value of the rational expression is:
A. -1

A function has a constant halving time. What type of function does this represent?

A. Decreasing linear
B. Exponential decay
C. Exponential growth
D. Increasing linear

Answers

The function which has a constant halving time is in the following form

[tex]A(t) = A_{0} ( \frac{1}{2} )^ \frac{t}{h} [/tex]
Where: A₀ is the initial amount
              h is the half life time or the halving time.
              t    is the time
              A(t) the amount that remains at time t

The previous function represents an Exponential decay function.

so, The correct answer is option B. Exponential decay

Answer:

Step-by-step explanation:

through how many radians does the minute hand of a clock turn in three hours?
•3π
•6π
•9π

Answers

9 pi would be the answer

6π
180 degrees is 1π, so therefore it going around 3 full rotations(1080 degrees) it would be 6π

Tom caught 4 fish and his son caught 12 fish.The number of fish that Tom caught was what percent of the total number of fish?

Answers

total number of fish = 12+4= 16
tom % of fish = 4 divided by 16 = 0.25 =25%

Tom caught 25% of the fish.

20 points!
Looking at circle O, ∠BOC is a(n)
Please contact your teacher immediately if you do not see the image.

Question options:

minor angle

central angle

inscribed angle

major angle

Answers

Central angle. It is in the center

Short Answer B
A central angle is one that goes through the center of a circle. It's two ends are the endpoints of the chord BC which you should draw on your sheet.

If you do, we can talk about the other answers.
An inscribed angle is one that has it's vertex on the circumference. <BAC is an example. A is the vertex.

A major angle is the part above BC that goes around the circle such that the angle is larger than 180 degrees. It is described above by BAC going clockwise. It is associated with the arc of a circle.

A minor angle is the angle not included in the major angle. In this case it is the angle formed by sweeping around from B to C underneath the chord BC

Which value of h makes 10/8+h=9/3-2 a true statement?

Answers

h = -0.25 I think don't really know, okay?

I used an app called photomath and got h=-1/4. I attached a screenshot

How would I find the diameter?

Answers

By measuring the width of the circle or sphere radius is half of the diameter

After creating a new email address, Gareth initially receives n emails per year. The number of emails received increases by 7% each year after that. The following expression represents the number of emails received after x years.

x(1 + 0.07)^x

Which of the following best represents the expression?

the product of the number of emails received initially and one plus the factor of increase raised to the number of years that the amount of emails Gareth received has increased

the product of the number of emails received initially and the factor of decrease raised to a period of x years

the product of the number of emails received initially and one plus the factor of decrease raised to the number of years that the amount of emails Gareth received has increased

the product of the number of emails received initially and the factor of increase raised to a period of x years

Answers

The correct answer is Option A.

The formula to find the number of emails x years after making the email account is:

[tex]N(x)= N_{o}(1+0.07)^{x} [/tex]

where, [tex] N_{o} [/tex] is the number of emails in the first year.

So, the number of emails x years after creating the account is the product of [tex] N_{o} [/tex], the number of emails in first year, and (1+0.07)^x, the sum of 1 and rate of increased raised to the number of years.

Hence option A is the correct answer.

Answer:

The correct answer is Option A.

Step-by-step explanation:

cheryl went on a 3-hour train traveled at an average speed of 75 miles per hour.what was the total distance in miles that cheryl traveled?

Answers

75x3=225

Cheryl went a total of 225 miles in 3 hours.

You're going to divide 75/3.to get your answer

What is the surface area of a conical grain storage tank that has a height of 43 meters and a diameter of 14 meters? Round the answer to the nearest square meter.
A. 1,100 square meters
B. 1,112 square meters
C. 2,507 square meters
D. 2,605 square meters

Answers

we know that
[surface area of the cone]=pi*r²+pi*r*l
where
r is the radius
l is the slant height
l²=h²+r²
h=43 m
r=14/2---> 7 m
l²=43²+7²----> l²=1898--------> l=43.57 m
[surface area of the cone]=pi*7²+pi*7*43.57----> 1111.53 m²----> 1112 m²

the answer is the option
B. 1,112 square meters

Julio considers the reduction of the triangle.

What is the correct cross product that he should use to solve for the missing dimension?
(8)(12) = 21x
(8)(21) = 12x
(12)(8) = 12x
(12)(21) = 8x

Answers

For this case we observe that the triangles are similar.
Therefore, we can use the following relationship:
(12) / (21) = (8) / (x)
From here, we can clear to know the value of the incognita x.
Answer:
the correct cross product that should be used to solve for the missing dimension is:
(12) / (21) = (8) / (x)

Answer:

(12)(21) = 8x or d

Step-by-step explanation:

If and represent rational expressions and b0 and y0, what is true of their product? Check all that apply.

Answers

Their product will be rational. Can I see the answer options?

Correct options are Options B, D, E. The product of two rational expressions (a/b) and (x/y) is a rational expression, specifically the ratio of ax and by, or equivalently ax/by. Incorrect options include ay/bx and a/y(x/b).

To determine the product of two rational expressions (a/b) and (x/y), where b ≠ 0 and y ≠ 0, let's explore the given options. Here are the truths about the product:

The product is a rational expression: When you multiply two rational expressions, the result is also a rational expression. This follows from the definition of rational expressions, which are ratios of polynomials.

The product is the ratio of ax and by: Mathematically, multiplying the numerators and denominators of the two rational expressions gives us (ax)/(by).

The product is equivalent to ax/by: This restates the above ratio in a simplified expression form, confirming that the multiplication results in (ax)/(by).

As we can see, the other expressions mentioned (ay/bx, a/y(x/b), a/(y(x/b))) are not correct representations of the product. Correct options are Options B, D, E.

Complete question:

If a/b and x/y represent rational expressions and b0 and y0, what is true of their product? Select three options.

A. The product is equivalent to ay/bx

B. The product is a rational expression.

C. The product is equivalent to a/y(x/b)

D. The product is the ratio of ax and by.

E. The product is equivalent to ax/b(y)

O'Farrell offers 2 different after school clubs. The Ukulele club has 30 students and attendance is increasing by 6 students per month. MESA has 45 students and attendance is increasing by 3 students per month. After how many months will there be the same number of students in each club?

Answers

month 6, work down below

months / students
0 30 45
1 36 48
2 42 51
3 45 54
4 51 57
5 57 60
6 63 63

it is 14 because its 14

What is -2(3x+12y-5-17x-16y+4) simplified?

-40x+8y+2

28x+8y+2

28x+6y+2

-28x-8y+2

Answers

[tex] -2(3x+12y-5-17x-16y+4) [/tex]

Combine like terms:
[tex]=-2(-14x-4y -1)[/tex]

Distribute 02:
[tex]=28x + 8y + 2[/tex]

A simplified expression involves rewriting an expression in a simpler form

The simplified expression is: 28x+8y+2

The expression is given as:

-2(3x+12y-5-17x-16y+4)

Collect like terms

-2(3x-17x+12y-16y-5+4)

Evaluate the like terms

-2(-14x-4y-1)

Open the bracket

28x+8y+2

Hence, the simplified expression is: 28x+8y+2

Answers

For this case we have the following function:
f (x) = x + 4 if -4 <= x <3
f (x) = 2x-1 if 3 <= x <6
We observe that the function is defined from x = -4 (including it) to x = 6 (without including it).
Therefore, the domain of the function is:
[-4, 6]
Answer:
[-4, 6]
option 3

What is the focus of the parabola? [tex]y= \frac{1}{4} x^{2} -x+3[/tex]

Enter your answer in the boxes.

(__ , __)

Answers

we know that
the equation of the parabola is of the form
y=ax²+bx+c
in this problem
y=1/4x²−x+3
where
a=1/4
b=-1
c=3
the coordinates of the focus are
(-b/2a,(1-D)/4a)
where D is the discriminant b²-4ac
D=(-1)²-4*(1/4)*3-----> D=1-3---> D=-2
therefore
x coordinate of the focus
-b/2a----> 1/[2*(-1/4)]----> 2

y coordinate of the focus
(1-D)/4a------> (1+2)/(4/4)---> 3

the coordinates of the focus are (2,3)

Please help me with 8, 9, and 10 thanks! Show work too

RANDOM ANSWERS WILL BE MODERATED!

Answers

In 8, 9, 10, all the triangles are similar, meaning corresponding sides have the same ratio.

8. hypotenuse / (short side) = 25/x = x/9
x² = 25*9 = 5²×3²
x = √(5²×3²) = 5*3 = 15

9. (long side) / (short side) = x/7 = 9/x
x² = 7*9
x = √(9*7) = 3√7

10. (short side) / (long side) = x/48 = 48/64
x = 48²/64 = 36

Help Please
A survey was taken of 36 people to see if they owned a car and/or a truck. The results are shown in the Venn diagram.

Enter your answers in the boxes to complete the two-way table based on the given data.
First picture is how they want you to put the answers in & the second one is the grid with the numbers

Answers

The two way table is attached.

According to the Venn diagram, 4 people own a car and a truck. 15+4=19 people own a car, and 4+9=13 people own a truck. This leaves us 36-(15+4+9)=36-28=8 people that do not own a car or a truck.

We put 8 in the Don't Own a Truck row under the Don't Own a Car column.
We put 4 in the Own a Truck row under the Own a Car column.
We put 19 in the Total row under the Own a Car column.
We put 15 in the Don't Own a Truck row under the Own a Car column.

We put 13 in the Own a Truck row under the Total column.
We put 9 in the Own a Truck row under the Don't Own a Car column.
We put 23 in the Don't Own a Truck row under the Total column.
We put 8 in the Down Own a Truck row under the Don't Own a Car column.

We put 36 in the Total row under the Total column.
We put 17 in the Total row under the Don't Own a Car column.

After a 40% discount an item costs $360. what is the original cost

Answers

Original Price = Final Price / (100 - Discount)

So...

OP = 360 / 100 - 0.40
OP = 360 / 0.60
OP = 600

The original price is $600.

To check, do 600 - (600 * 0.40) in a calculator. You get 600 - 240 = 360, the discounted cost.

Answer:

It is $600

Step-by-step explanation:

hope it helps, murdle

2. How many real number solutions are there to the equation 0 = –3x² + x – 4? (1 point)

Answers

given
[tex] - 3 {x}^{2} + x - 4[/tex]
finding the determinant will tell us how many solutions
the determinant is
[tex] {b}^{2} - 4ac[/tex]
so we have
a=-3
b=1
c=-4

so the determinant is
[tex] {1}^{2} - 4( - 3)( - 4) = 1 - 48 = - 47[/tex]
now we know if d=0 there is 1 real solution if d<0 there are complex solutions and if d>0 there are 2 real solutions.
since d=-47<0 there are no real solutions only complex ones

Final answer:

The equation has no real number solutions.

Explanation:

To find the number of real number solutions to the equation 0 = –3x² + x – 4, we can use the discriminant of the quadratic equation. The discriminant is calculated as b² - 4ac, where a, b, and c are coefficients of the equation in the form ax² + bx + c = 0. If the discriminant is positive, the equation has two distinct real solutions. If the discriminant is zero, the equation has one real solution. And if the discriminant is negative, the equation has no real solutions.

In this case, a = -3, b = 1, and c = -4. Let's calculate the discriminant:

b² - 4ac = (1)² - 4(-3)(-4) = 1 - 48 = -47

Since the discriminant is negative, the equation 0 = –3x² + x – 4 has no real number solutions.

y=-6x^2+100x-180
x=selling price of each soccer ball
y=daily profit from soccer balls

The vertex is located at (8.33, 236.67). What does this point represent in context?

Answers

In the figure we have the graphic of this equation. So, the vertex is the maximum of this function. This point means that the maximum daily profit from soccer balls is:

[tex]y = 236.67[/tex]

And this happens when the selling price of each soccer ball is:

[tex]x = 8.33[/tex]

So if you want to get the best daily profit, this is the price you must sell each soccer ball.

Refer the below solution for better understanding.

Step-by-step explanation:

Given :

[tex]y = -6x^2+100x-180[/tex]

where,

x = selling price of each soccer ball.

y = daily profit from soccer balls.

Solution :

The vertex shows the maximum value of y and x.

y = 236.67 shows the maximum daily profit and this happens when selling price of each soccer ball is x = 8.33.

Refer the below graph for better understanding.

For more information, refer the link given below

https://brainly.com/question/10712002?referrer=searchResults

A quilt is in the shape of a regular pentagon. It is made from 5 pieces of fabric that are congruent triangles. Each triangle has an area of 16 inches.What is the area of the quilt?

Answers

Multiply 16 × 5 because each triangle is 16 inches and you have 5 triangles.

16 × 5 = 80

The area of the quilt is 80 inches².

Final answer:

The area of the quilt, which is a regular pentagon made from five congruent triangles, is 80 square inches, determined by multiplying the area of one triangle (16 inches) by five.

Explanation:

The area of the quilt which is in the shape of a regular pentagon can be determined by calculating the area of the five congruent triangles that make up the pentagon. Since each triangle has an area of 16 inches, we can find the total area by simply multiplying the area of one triangle by the number of triangles.

To calculate the total area of the quilt:

First, determine the area of one triangle, which is given as 16 inches.Next, since there are five congruent triangles in the pentagon, multiply the area of one triangle by 5.The total area of the quilt would be 16 inches (per triangle) × 5 triangles = 80 inches.

Therefore, the total area of the quilt is 80 square inches.

The solution to 15 a2 − 1 = 5 2a − 2 is a = . The extraneous solution is a = .

Answers

For this case the correct expression is:
15 / (a ^ 2 - 1) = 5 / (2a - 2)
Rewriting we have:
3 / (a ^ 2 - 1) = 1/2 (a - 1)
6 / (a ^ 2 - 1) = 1 / (a - 1)
6 (a - 1) = (a ^ 2 - 1)
6 (a - 1) = (a-1) (a + 1)
(a + 1) = 6
a = 6-1
a = 5
Answer:
The solution is:
a = 5

Answer:

5 and 1

1 is extraneous

Step-by-step explanation:

Write the equation of a horizontal line that passes through the point (3, -3).

Answers

check the picture below.

How to calculate 95th percentile from mean and standard deviation of an exponential distribution?

Answers

0down voteaccepted

The qthqth quantile of a random variable XX is the value xx such that

Pr[X≤x]=q.Pr[X≤x]=q.So in your case q=0.25q=0.25, and0.25=Pr[X≤x]=FX(x)=1−e−x/β.0.25=Pr[X≤x]=FX(x)=1−e−x/β.This gives us e−x/4=0.75e−x/4=0.75, orx=−4log0.75≈1.15073.x=−4log⁡0.75≈1.15073.This assumes that the parametrization of the exponential distribution is by scale; i.e., if β=4β=4 this means E[X]=β=4E⁡[X]=β=4, rather than by rate--in which case E[X]=1/β=1/4E⁡[X]=1/β=1/4.

How much does the school have to charge for each candy bar to make a profit of 10 dollars per box?

Answers

the complete question is
A school purchases boxes of candy bars.
• Each box contains 50 candy bars.
• Each box costs $30.
How much does the school have to charge for each candy bar to make a profit of
$10 per box?

step 1
charge for each box $10
so
the new box cost $10+$30=$40

step 2
divide the new box cost to total candy bars
$40/50=$0.80

the answer is
the school have to charge for each candy bar $0.80

A bunch bowl is in the shape of a hemisphere. The top rim has a circumference of 116cm.
A) determine the volume of the punch bowl to the nearest cubic centimeter.
B) If there are 1,000 cubic centimeters in a liter and 3.785 liters in a gallon, determine, to the nearest tenth of a gallon, how much punch can fit in the bowl.

Answers

The hemisphere is half the volume of a sphere. Since we are given the circumference, we can solve for the radius of the sphere. That is
[tex]C=2\pi r[/tex]

[tex]116\:cm=2\pi r[/tex]

[tex]r=\frac{116}{2\pi }=18.462\:cm[/tex]

Part A
We can now compute for the volume of the hemisphere.
[tex]V=\frac{1}{2}\times \frac{4}{3}\pi r^3=\frac{1}{2}\times \frac{4}{3}\pi \left(18.462\right)^3=13179\:cm^3[/tex]

Part B
We just need to convert the volume into its corresponding gallons
[tex]13179\:cm^3\times \frac{1\:Liter}{1000\:cm^3}\times \frac{1\:gallon}{3.785\:Liters}=3.5\:gallons[/tex]

Find the approximate surface-area-to-volume ratio of the Moon. The radius of the Moon is 1,080 miles. A. 0.0009 B. 0.0028 C. 360 D. 3,240

Answers

we know that
surface area of a sphere=4*pi*r²

volume of a sphere=(4/3)*pi*r³

the ratio surface area to volume
=4*pi*r²/[(4/3)*pi*r³]-----> 3/r----> 3/1080-----> 0.0028

the answer is
the option B. 0.0028

9. WILL GIVE BRAINLIEST IF CORRECT

Answers

Answer is: A;
Re-arrange formula to give: sin q = -1/square root of 2
Now, sin (3 pie/4) = sin(135) = -1/square root of 2
Also, sin(5 pie/4) = sin(235) = -sin(45) = -1/square root of 2

rearrange the equation we get;

sinq = -2/2sqrt(2) = -1/sqrt(2)

answer is letter A. 3pi/4 , 5pi/4

Hope this helps your question! Goodluck

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