You want to construct a patio of 80 square feet with a length of 10 feet. What is the width of the patio?​

Answer:

Hey!

Your answer is 14m (2sf)

Step-by-step explanation:

WE HAVE TO USE PYTHAGORAS! ⇒ a²+b²=c² THEN √c = (unknown side)

Here: 12² + 8²= 208

Now SQUARE-ROOT 208! ⇒ √208

ANSWER: 14.42220510185596

The answers there are rounded up so we round this number to get 14m!

B IS YOUR OPTION!

The equation of the line y = (5/3)x + (10/3) represents the line passing through the point (3, 5) that cuts off the smallest area from the first quadrant.

To find the equation of the line that passes through the point (3, 5) and cuts off the least area from the first quadrant, we need to consider the slope of the line.

Any line passing through the point (3, 5) can be written in a point-slope form as:

y - 5 = m(x - 3)

where m is the slope of the line. We want to find the slope that minimizes the area cut off by the line.

Consider a line passing through the origin with slope m. The area cut off by this line in the first quadrant is given by:

A(m) = (1/2)(3)(m*3) = (9/2)m

Note- that the area cut off by the line passing through (3, 5) with slope m is equal to the area cut off by the line passing through the origin with slope m plus the area of the triangle formed by the point (3, 5), the origin, and the point where the line intersects the y-axis. The y-intercept of the line passing through (3, 5) with slope m is given by:

y - 5 = m(x - 3)

y = mx - 3m + 5

Setting x = 0, we get:

y = -3m + 5

The coordinates of the point where the line intersects the y-axis are (0, -3m + 5), and the area of the triangle is:

(1/2)(3)(|-3m + 5 - 0|) ⇒ (3/2)|-3m + 5|

Therefore, the total area cut off by the line passing through (3, 5) with slope m is:

A(m) = (9/2)m + (3/2)|-3m + 5|

To find the slope that minimizes this expression, we need to consider two cases:

Case 1: -3m + 5 ≥ 0, i.e., m ≤ 5/3

In this case, the expression simplifies to:

A(m) = (9/2)m + (9/2)m - (3/2)(5)

= (9m - (15/2)

This expression is minimized when m = 5/3, which is within the range of possible slopes.

Case 2: -3m + 5 < 0, i.e., m > 5/3

In this case, the expression simplifies to:

A(m) = (9/2)m - (9/2)m + (3/2)(5)

= (15/2)

This expression is minimized when m = 5/3, which is again within the range of possible slopes.

Therefore, the line passing through (3, 5) with slope m = 5/3 cuts off the least area from the first quadrant. The equation of the line is:

y - 5 = (5/3)(x - 3)

Simplifying, we get:

y = (5/3)x + (10/3)

To know more about the "equation of the line":https://brainly.com/question/13763238

#SPJ11

The volume of the octahedron is 4000 cubic centimeters.

To find the volume of the octahedron, we'll first find the volume of one pyramid and then multiply it by 2 since the octahedron is made up of two pyramids.

Step 1: Find the height of one pyramid.
Since the overall height of the octahedron is 30 cm and it's made up of two pyramids of equal height, the height of one pyramid is 30 cm / 2 = 15 cm.

Step 2: Calculate the volume of one pyramid.
The formula for the volume of a pyramid is (1/3) * base_area * height.
In this case, the base is a square with sides measuring 20 cm, so the base area is 20 cm * 20 cm = 400 cm².

Step 3: Apply the formula.
Volume of one pyramid = (1/3) * 400 cm² * 15 cm = 2000 cm³.

Step 4: Find the volume of the octahedron.
Since the octahedron consists of two identical pyramids, we'll multiply the volume of one pyramid by 2.
Volume of octahedron = 2 * 2000 cm³ = 4000 cm³.

To learn more about octahedron : brainly.com/question/18369918

#SPJ11

The expression 2 sin(4x) cos(9x) can be written as the difference of two functions using trigonometric identity as: sin(13x) - sin(5x).

To write the expression 2 sin(4x) cos(9x) as the sum or difference of two functions, we can use the trigonometric identity:

sin(A) cos(B) = (1/2)[sin(A + B) + sin(A - B)]

Applying this identity to the given expression:

2 sin(4x) cos(9x) = 2 * (1/2)[sin(4x + 9x) + sin(4x - 9x)]

Simplifying:

= sin(13x) + sin(-5x)

Note that sin(-θ) = -sin(θ), so we can rewrite sin(-5x) as -sin(5x):

= sin(13x) - sin(5x)

Therefore, the expression 2 sin(4x) cos(9x) can be written as the difference of two functions: sin(13x) - sin(5x).

To know more about trigonometric identity, click here: brainly.com/question/12537661

#SPJ11

The area of a rectangle with a width of 8.6 cm and a height of 4.7 is 40.42 \(cm^{2}\). The total area of 40.42 \(cm^{2}\) has 4 significant figures.

By knowing the width and height of a rectangle we will be able to determine the area of the shape by multiplying them. Or the area of a rectangle can be found by multiplying the two sides.

Given,

Then the area of the rectangle:

Area = Width x height

Area = 8.6 cm x 4.7 cm

Area = 40.42 \(cm^{2}\)

So, the area of the rectangle above is 40.42 \(cm^{2}\) and it has 4 significant figures provided that zeros located between non-zero numbers are significant figures.

Learn more about Area here: https://brainly.com/question/25292087

#SPJ4

We know that the highest common factor (HCF) of N and 500 is 2^2 x 5^2. So we can write:

N = (2^2 x 5^2) x m (where m is a product of any remaining prime factors in N)

500 = (2^2 x 5^2) x n (where n is a product of any remaining prime factors in 500)

We can simplify these expressions by dividing both sides by 2^2 x 5^2:

N/(2^2 x 5^2) = m

500/(2^2 x 5^2) = n

So, we have:

N/(2^2 x 5^2) = 2^p x 5^q x 7^r/(2^2 x 5^2) = m

500/(2^2 x 5^2) = 2^2 x 5^3/(2^2 x 5^2) = n

Simplifying further:

N/(2^2 x 5^2) = 2^(p-2) x 5^(q-2) x 7^r = m

500/(2^2 x 5^2) = 5 x n

Now, we can compare the prime factors on both sides to find the values of p, q, and r.

Comparing the powers of 2:

For N: p - 2 = 2

=> p = 4

Comparing the powers of 5:

For N: q - 2 = 3

=> q = 5

Comparing the powers of 7:

For N: r = 0 (since there is no 7 in 500)

So we have:

N = 2^4 x 5^5

To find r, we can use the fact that the lowest common multiple (LCM) of N and 500 is 2^3 x 5^3 x 7. Since the LCM is the smallest number that is a multiple of both N and 500, it must contain all the prime factors of N and 500, raised to their highest powers:

LCM = 2^4 x 5^3 x 7^1

Comparing the powers of 7:

For N: r = 1

So we have:

N = 2^4 x 5^5 x 7^0 = 5000

Therefore, p = 4, q = 5, and r = 0, and the prime factorization of N is 2^4 x 5^5 x 7^0 = 5000.

Answer:

$1.88

Step-by-step explanation:

$15.04/8 pounds = $1.88

Answer:

$1.88 per Lb

Step-by-step explanation:

15.04 / 8 = 1.88

Answer:

A - Z = X

A - Z + Z = X + Z

A = X + Z

The exact value of sin (A-B) in simplest form for positive acute angle A and B is found to be 221/1445.

We can use the trigonometric identity sin(A - B) = sinAcosB - cosAsinB to find the exact value of sin(A - B) for positive acute angles.

From the given information, we know that cosA = 4/5 and sinB = 8/17. Using identities, sin²A + cos²A = 1 and sin²B + cos²B = 1:

sinA = √(1 - cos²A)

= √(1 - (4/5)²)

= 3/5

cosB = √(1 - sin²B)

= √(1 - (8/17)²)

= 15/17

Now, we can substitute these values into the identity:

sin(A - B) = sinAcosB - cosAsinB

sin(A - B) = (3/5)(15/17) - (4/5)(8/17)

sin(A - B) = 9/17 - 32/85

sin(A - B) = (765 - 544)/1445

sin(A - B) = 221/1445

Therefore, the exact value of sin(A - B) in simplest form is 221/1445.

To know more about trigonometric identities, visit,

https://brainly.com/question/24496175

#SPJ4

Answer: 126

Step-by-step explanation:

First we know that 5 hours = 90$, so we divide 90 and 5 which equals 18.
Then we do 18 x 7= 126.

Answer: 126

Answer:

35 yards

Step-by-step explanation:

19+16= 35

Hope this helps! :)

Answer:

35 yards

Step-by-step explanation:

Hope this helps! (:

The map that sends a subgroup of the Galois group G to a subfield of E containing Q is known as the Galois correspondence. It establishes a one-to-one correspondence between the subgroups of G and the subfields of E containing Q.

Given a subgroup H of G, the corresponding subfield of E is the fixed field of H, denoted as E^H. It is defined as the set of all elements in E that are fixed under every automorphism in H. In other words, E^H = {α ∈ E : σ(α) = α for all σ ∈ H}.

Conversely, given a subfield F of E containing Q, the corresponding subgroup of G is the Galois group of the extension E/F, denoted as Gal(E/F). It is the set of all automorphisms in G that fix every element in F. In other words, Gal(E/F) = {σ ∈ G : σ(α) = α for all α ∈ F}.

The Galois correspondence establishes the following properties:

1. If H is a subgroup of G, then E^H is a subfield of E containing Q.

2. If F is a subfield of E containing Q, then Gal(E/F) is a subgroup of G.

3. The map is inclusion-reversing, meaning that if H₁ and H₂ are subgroups of G with H₁ ⊆ H₂, then E^H₂ ⊆ E^H₁. Similarly, if F₁ and F₂ are subfields of E containing Q with F₁ ⊆ F₂, then Gal(E/F₂) ⊆ Gal(E/F₁).

4. The map is order-preserving, meaning that if H₁ and H₂ are subgroups of G, then H₁ ⊆ H₂ if and only if E^H₂ ⊆ E^H₁. Similarly, if F₁ and F₂ are subfields of E containing Q, then F₁ ⊆ F₂ if and only if Gal(E/F₂) ⊆ Gal(E/F₁).

These properties establish the 1-1 correspondence between subgroups of G and subfields of E containing Q, which is a fundamental result in Galois theory.

To learn more about polynomial: https://brainly.com/question/1496352

#SPJ11

The value of cos I as a fraction in simplest terms is 4/5.

This is a problem based on trigonometry. Trigonometry is a field of mathematics that explores the connections between triangle side lengths and angles. The length of the hypotenuse is 25. The length of the perpendicular is 15. The length of the base is unknown. We know that the angle ∠IJK = 90°.

We need to find the value of Cos(I). But we don't know the value of the length of the base of the triangle. So, we will first find Sin(I).

Sin(I) = 15/25

Sin(I) = 3/5

We know the trigonometric identity that Sin²θ + Cos²θ = 1.

Sin²I + Cos²I = 1

Cos²I = 1 - Sin²I

Cos²I = 1 - (3/5)²

Cos²I = 1 - (9/25)

Cos²I = (25 - 9)/25

Cos²I = 16/25

Cos(I) = √(16/25)

Cos(I) = 4/5

To learn more about angles, visit :

brainly.com/question/28451077

#SPJ1

Answer:

the answer is 41

Step-by-step explanation:

C. 41

Step-by-step explanation:

Answer:

The diameter of a circle passes through the center of the circle and has its endpoints on the circle itself. The diameter of any circle is two times the length of that circle's radius.

Step-by-step explanation:

To find the diameter of a circle, you need to know the radius of the circle, double it to get the diameter. The radius is the distance from the center of the circle to its edge. If the radius of the circle is 4 cm, then the diameter of the circle is 4 cm x 2, or 8 cm. If you know the circumference of the circle, divide it by π to get the diameter.

Answer:

9x=2

Step-by-step explanation:

4 - 6(3 - 2x) = 3(x -4)

4 - 18 + 12x = 3x - 12

12x - 14 = 3x - 12

12x - 3x = 14 - 12

9x = 2

hope you are happy with the answer ;)

There are total 35 students in the class.

Given that,

Vikas ranks 9th in the class,

Assume that there are 'n' number of students in the class  

Therefore,

There are 8 students who have scored better than him.

So, The total number of students with a rank better or equal to Vikas,

= 8 + 1 (Vikas himself)

= 9.

Now, his friend got the 35th rank which is the last rank

This means that there are a total of 35 students in the class.

Also, also given that,

Vikas's rank from the last is 27th,

This means that there are 26 students who have scored lower than Vikas.

So, the total number of students with a rank worse or equal to Vikas,

= 26 + 1 (Vikas himself)

 = 27.

Therefore, The total number of students in the class = 35.

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ12

Store #1 has the better price amount , as the price per dozen eggs is $1.44, whereas Store #2 is $1.29 per dozen eggs.

Store #1 has the better price, as the price per dozen eggs is $1.44, whereas Store #2 is $1.29 per dozen eggs. To compare the prices, we need to calculate the cost per dozen eggs for each store. To do this, we divide the cost by the number of eggs. For Store #1, the cost per dozen eggs is $1.44 divided by 12, which is $0.12. For Store #2, the cost per dozen eggs is $4.68 divided by 36, which is $0.13. Therefore, Store #1 has the better price, as it is cheaper than Store #2. By comparing prices, we can find the best deal for our money. It is important to compare prices to get the best value for our money, as it can help us save money in the long run. Additionally, by comparing prices, we can make sure we are getting the highest quality product at the best price.

Learn more about amount here

https://brainly.com/question/28970975

#SPJ4

Answer:

a=7

Step-by-step explanation:

7+3=10

If the current dispatch rate is one bus every 1 minute and the average traveling time is currently 5 minutes, dispatching buses every 0.5 minute will actually increase the average traveling time to 10 minutes, not reduce it to 4.5 minutes as suggested by the branch manager.

Assuming that the current dispatch rate is one bus every 1 minute, and the average traveling time (a round trip) is currently 5 minutes, we can use the following formula to estimate the average traveling time with the proposed dispatch rate:

new average traveling time = current average traveling time / (new dispatch rate / current dispatch rate)

Plugging in the values, we get:

new average traveling time = 5 / (0.5 / 1) = 10 minutes

To know more about Branch manager:

https://brainly.com/question/14894196

#SPJ4

The statement that proves that angle XWY is equal to angle ZYW is

A. If two parallels are cut by a transverse, then alternate interior angles are congruent

Alternate interior angles are a pair of angles that are formed on opposite sides of a transversal line when two parallel lines are intersected by the transversal.

When a transversal intersects two parallel lines, it creates eight angles. Among these angles, the alternate interior angles are located on the inside of the parallel lines and on opposite sides of the transversal.

In a parallelogram, the two opposite sides are parallel to each other hence the line crossing them will lead to formation of alternate interior angles

Learn more about alternate interior angles at

https://brainly.com/question/20344743

#SPJ1

The prefix "kilo-" in the metric system means one thousand. Therefore, one kilometer equals 1000 meters.

The metric system is a decimal-based system that uses prefixes to denote multiples and submultiples of units. In this system, the prefix "kilo-" represents a factor of one thousand, which is equivalent to 10^3. For instance, one kilogram is equal to one thousand grams, and one kilometer is equal to one thousand meters. Similarly, other prefixes like "centi-" (one hundredth), "milli-" (one thousandth), and "mega-" (one million) are used in the metric system to denote different multiples and submultiples of units.

In conclusion, the prefix "kilo-" in the metric system represents a factor of one thousand. Therefore, when we use this prefix with the unit of length "meter," we get "kilometer," which is equal to 1000 meters.

Learn more about decimal here: https://brainly.com/question/30958821

#SPJ11

A "required parameter" requires an assigned value for the argument used to call the method, while "optional parameters" do not need to be included in the method call and have a default value assigned to them.

The type of parameter that requires that the argument used to call the method must have an assigned value is a "required parameter".

Required parameters are parameters that must be included in the method call, and the argument passed for the required parameter must have a value assigned to it. If a required parameter is not included in the method call, or if the argument passed for the required parameter does not have a value assigned to it, an error will be thrown.

In contrast, there are also optional parameters, which are parameters that do not need to be included in the method call. If an optional parameter is not included in the method call, the method will use a default value assigned to the parameter.

In many programming languages, the syntax for specifying required and optional parameters in a method or function call is specified using different symbols, such as parentheses or square brackets.

Learn more about programming languages here:

https://brainly.com/question/22695184

#SPJ4

Answer:

f(x) = -1/x^2 + 4e^x + 5x + 1 + 1/x - 4e^(-1)

Step-by-step explanation:

We can find the function f(x) by integrating f'(x) with respect to x:

â«f'(x) dx = â«(2/(x^3) + 4e^x + 5) dx

f(x) = -1/x^2 + 4e^x + 5x + C

To find the constant C, we can use the given initial conditions:

f(-1) = 1 = -1/(-1)^2 + 4e^(-1) - 5 + C

C = 1 + 1/1 - 4e^(-1)

f(x) = -1/x^2 + 4e^x + 5x + 1 + 1/x - 4e^(-1)

Therefore, the function f(x) is:

f(x) = -1/x^2 + 4e^x + 5x + 1 + 1/x - 4e^(-1)

The amount of Gallons of gas that Dan's tank can hold is; 18 Gallons

Let the total capacity of Dan's tank be x.

Thus, since it is 1/3 full, then we can say that the capacity is now; x/3

Now, we are told that he buys 9 gallons of gas and this makes it 5/6 full. Thus, the equation to represent all these is;

(x/3) + 9 = 5x/6

Multiply through by 6 to get;

2x + 54 = 5x

5x - 2x = 54

3x = 54

x = 54/3

x = 18 gallons

Read more about Fraction Word Problems at; https://brainly.com/question/24132459

#SPJ1

Answer:

C)

Step-by-step explanation:

Answer:

okay then

Step-by-step explanation:

Answer: gtyrehretr

Step-by-step explanation: