Hamburgers are sold in packages of 20, while buns are sold in packages of 12. What are the least numbers of packages you should buy in
order to have the same number of hamburgers and buns?

As angles opposite congruent sides in a triangle are congruent, and also since the interior angles of a triangle add to 180 degrees, if we let angle EFG have a measure of x, then angle GEF also measures x, and thus:

82+x+x=180

2x=98

x=49

Thus, angle EFG is 49 degrees.

So, by the exterior angle theorem, angle DEG measures 82+49=131 degrees

The distance between the 1st and the 3rd poles is 140 meters.

What is the arithmetic operation?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.

ESB poles are placed along a road 70 meters apart.

So the distance between two poles is 70 meters.

So the distance between 1 and 3rd will be = 2*70 =140metets

Hence, the distance between the 1st and the 3rd poles is 140 meters.

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Complete Question:
Esb poles are placed along a road 70 metres apart. What is the distance between the 1st and the 3rd poles?

answer:

Answer is c this was difficult

Answer:

14 feet

Step-by-step explanation:

s2 = 196

The projection matrices and as we have verified that \(P = A(A^TA)^{-1}A^T.\)

Let's start by defining the matrices we will use for this problem. The matrix A is given by A = [1 1 0 1 0 0], which means that A is a 3x6 matrix with three rows and six columns. The vector b is given by b = [2 3 4], which is a 3x1 matrix with three rows and one column.

To project b onto the column space of A, we need to find a vector p that is in the column space of A and is as close as possible to b. We can do this by solving the equation \(A^T Ax = A^T b\), where \(A^T\) is the transpose of matrix A. This equation is known as the normal equation of the least-squares problem, and it gives us the vector p that is the projection of b onto the column space of A.

We can also find the error vector e = b - p, which is the difference between b and its projection onto the column space of A. This error vector is perpendicular to the column space of A, which means that it lies in the null space. To verify this, we can take the dot product of e with each column of A, which should be zero for each column.

To compute the projection matrix P, we can use the formula

\(P = A(A^TA)^{-1}A^T.\)

This matrix projects any vector onto the column space of A.

We can also verify that P² = P and P = \(P^T\), which means that P is an idempotent matrix and a symmetric matrix.

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Answer:

The answer is 9y + 18

Step-by-step explanation:

Multiply using the distributive property.

Hoped this helped!

The formula for the area of ​​a triangle is (1/4)√(105a?)

By applying the triangle inequality theorem, we can verify that the given formula represents the length of the sides of a triangle. This theorem states that the sum of his two sides of a triangle must be greater than his third side.

Given the expressions 2a?, 6a + 5, and 10a?, applicable

2a? + 6a + 5 > 10a? (sum of first two pages greater than third)

2a?+10a?> 6a+5 (1st and his 3rd sides sum greater than 2nd)

6a + 5 + 10a? >2a? (sum of last 2 pages greater than first page)

Therefore, the given formula can express the length of the sides of a triangle.

According to Heron's formula, the area of ​​a triangle with side lengths a, b, and c is

Area = √(s(s-a)(s-b)(s-c))

where s is the semicircle of the triangle and is defined as

s = (a + b + c) / 2

Replacing the given formula with a, b, c, we get:

s = (2a? + 6a + 5 + 10a?) / 2

= 6a? + 3a + 5/2

Find the value of s to calculate the area of ​​the triangle.

Area = √((6a? + 3a + 5/2)((6a? + 3a + 5/2)-(2a? + 6a + 5))((6a? + 3a + 5/2)-(10a?)))

= √((6a? + 3a + 5/2)(2a? - 3a + 5/2)(-4a? + 3a + 5/2))

= √((15/4)(a?)(-5/4)(-a?)(-7/4)(a?))

= √(105a?/16)

= (1/4)√(105a?)

So the formula for the area of ​​a triangle is (1/4)√(105a?). 

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If an equation isn't in the y is mx + b form, we can still find the intercepts by substituting 0 where necessary and solving for the remaining variable.

When y = 0, we solve the equation for x to determine the x-intercept. The line crosses the x-axis at y=0, explaining this. If an equation isn't in the y = mx + b form, we can still find the intercepts by substituting 0 where necessary and solving for the remaining variable.

With x = 0, solve for y to determine the y-intercept.

Utilizing the given points, determine the slope.

In the expression for the line, y = mx + c, include the slope's value.

Now solve the equation y = mx + c to determine the value of c using the values of any of the supplied locations.

Place y = 0 in y = mx + c to determine the x-intercept.

Place x = 0 in y = mx + c to determine the y-intercept.

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Answer:

a. 0.8 = 0.5 + 0.3

b. 30.9 = 2.7 + 28.2

c. 15.4 = 3.1 + 2.4 + 9.9

d. 17.4 = 15.2 + 1.4 + 0.8

e. 42.5 = 39.2 + 2.5 + 0.8

f. 8 = 4 + 4

g. 35 = 23 + 8 + 4

h. 84 = 53 + 3 + 28

i. 121 = 11 + 17 + 93

j. 35 = 24 + 8 + 3

The antiderivative of 7ex is 7ex, and the antiderivative of 6 sec2(x) is 6 tan(x). Thus, the most general antiderivative is F(x) = 7ex + 6 tan(x) + C, where C represents the constant of integration.

To find the antiderivative of the given function f(x) = 7ex 6 sec2(x), we integrate each term separately. The antiderivative of 7ex is simply 7ex, as the exponential function ex is its own antiderivative.

Next, we consider the antiderivative of 6 sec2(x). The derivative of the tangent function tan(x) is sec2(x), so the antiderivative of sec2(x) is tan(x). However, there is a coefficient of 6 in front of sec2(x), so the antiderivative becomes 6 tan(x).

Combining these results, we have F(x) = 7ex + 6 tan(x) as the antiderivative of the original function f(x) = 7ex 6 sec2(x). The "+ C" at the end represents the constant of integration, as any constant added to the antiderivative remains undetermined. Therefore, the most general antiderivative of f(x) is F(x) = 7ex + 6 tan(x) + C, where C is a constant.

To verify this result, we can differentiate F(x) and confirm that it indeed yields the original function f(x). Taking the derivative of F(x) with respect to x will give us back 7ex 6 sec2(x), thus confirming the correctness of the antiderivative.

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Answer:

Total Area = 1200 in^2

Step-by-step explanation:

There is a triangle and a rectangle.

Arca Triangle: Area = 1/2 * Base* Height

Area = 1/2 * 40 in * 30 in = 600 in^2

Area Rectangle: Area = Length* Width

Area = 30 in * 20 in = 600 in^2

Total Area = Area Rect + Area Tri

Total Area = 600 in^2 + 600 in^2 = 1200 in^2

Therefore, a factor of the given expression 27x³ - 22x² - 250x + 2574 is 9x - 14 or 3x + 13.

In mathematics, an expression is a combination of numbers, variables, and operators (such as +, -, ×, ÷, etc.) that represents a value or a quantity. Expressions can be simple or complex, and they can involve arithmetic operations, functions, and algebraic operations. Expressions can be evaluated, simplified, or manipulated using mathematical rules and techniques. They are used in many areas of mathematics, including algebra, calculus, and geometry, as well as in other fields such as physics, engineering, and economics.

Here,

One possible way to find a factor of 27x³- 22x² - 250x + 2574 is to use synthetic division with a possible root of the polynomial. We can try x = 2, since it is a common factor of the constant terms 22 and 2574. Using synthetic division with x = 2, we get:

2  |  27  -22  -250  2574

  |     54    64  -372

  |------------------

     27   32  -186  2202

The remainder is 2202, which means that x - 2 is not a factor of 27x³ - 22x² - 250x + 2574. However, the quotient is 27x² + 32x - 186, which we can factor further using the quadratic formula or factoring by grouping:

27x² + 32x - 186 = (9x - 14)(3x + 13)

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In doing a quantity takeoff for 100 square feet of single wythe concrete masonry wall, with a thickness of 8", we would need  14.06 8x8x16 block and 10.14 cubic feet mortar.

Number of blocks:

Since each block is 8x8x16 inches, the volume of one block is:

Volume of one block = Length x Width x Height

                                   = 8 inches x 8 inches x 16 inches

                                   = 1024 cubic inches

To calculate the number of blocks needed, we divide the wall area by the area of one block:

Number of blocks = Wall area in square inches / Area of one block

                              = 14,400 square inches / 1024 cubic inches

                              ≈ 14.06

Rounding to the nearest whole number, the correct answer is 14 blocks.

Amount of mortar:

To determine the amount of mortar needed, we multiply the wall area by the joint thickness:

Volume of mortar = Wall area x Joint thickness

                              = 100 square feet x 1 square foot/144 square inches x 8 inches x 3/8 inches

                              ≈ 10.14 cubic feet

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Answer:

y = x + 7

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 1, thus

y = x + c ← is the partial equation

To find c substitute (- 3, 4) into the partial equation

4 = - 3 + c ⇒ c = 4 + 3 = 7

y = x + 7 ← equation of line

Hope this helps.

Step-by-step explanation:

4y = - 4x +20 (2x) + 4y = 12

4y = -4x + 40x + 4y = 12

36x = 4y - 4y _12

36 x = 12

÷12

36x ÷ 12 = 12 ÷ 12

3x = 1

÷3

3x ÷ 3 =1

x = 1 over 3

The amount of the 11% note is $110 and the amount of the 9% note is $90.

Code snippet

Note Type | Principal | Interest | Interest Rate

------- | -------- | -------- | --------

11% | $100 | $11 | 11%

9% | $100 | $9 | 9%

Use code with caution. Learn more

The interest for the 11% note is calculated as $100 * 0.11 = $11. The interest for the 9% note is calculated as $100 * 0.09 = $9.

Therefore, the total interest for the two notes is $11 + $9 = $20. The principal for the two notes is $100 + $100 = $200.

So the answer is $110 and $90

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Answer:

3x^4 -2x^3 -2x^2 +4x -10

Step-by-step explanation:

Add them term by term

Two congruent right triangles are formed by the tangents and the line connecting P to the circle's centre. They are congruent because one of the pairs of matching sides in each of those two triangles is represented by the tangent segments from P to the sites of tangency with the circle.

The kite-shaped quadrilateral that is created by the two radii and the two tangents has two pairs of adjacent sides.

The radii, the tangents, and the line from P to the centre of the circle combine to form two congruent right triangles. The tangent segments from P to the sites of tangency with the circle are congruent because they represent one of the pairs of corresponding sides in each of those two triangles.The two radii and the two tangents combine to form a quadrilateral with two pairs of adjacent sides, which is why it is a kite.

Lines that cross a circle at a single point are known as tangents.  Where the tangent crosses the radius of the circle, it is perpendicular to the tangent. Any curved shape can take into account tangent. Since the tangent is a straight line, its equation will take the form y = m x+ c .

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The Area of Trapezium is 50, 267 mm².

We have,

base 1 = 224 mm

base 2 = 77 mm

Height = 334 mm

Now, Area of Trapezium

= 1/2 (Sum of parallel side) x height

= 1/2 (224 + 77) x 334

= 1/2 x 301 x 334

= 50, 267 mm²

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SOLUTION

Given the question in the question tab, the following are the solution steps to get the rental cost for each movie and each video game.

Step 1: Write the representation for the two rentals

Let m represents movies

Let v represent video games

Step 2: Write the statements in form of a mathematical equation

Step 3: Solve the equations above simultaneously using elimination method to get the values of m and v

Rental cost for each movies is $3.25

Rental cost for each video games $5.50

High clouds are those that form at altitudes of at least 20,000 ft (6000 m).

At high altitudes, ice crystals form due to which cloud formation occurs.   Cirrus, cirrostratus, and cirrocumulus clouds are a few types of clouds. Cirrostratus clouds frequently form a thin, white layer that resembles a veil and covers the entire sky. Small, spherical, white clouds called cirrocumulus develop in long rows. Because they can provide information about changes in atmospheric pressure, temperature, and moisture levels in the upper atmosphere, these high clouds are crucial for meteorologists to investigate.

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Answer:

1 orange per half a minute (30 seconds)

Answer:

Yes, they are both equal.

Step-by-step explanation:

This is because in both cases, you are subtracting, -7 + -2 = -9. -7 - 2 = -9.

The volume of salt water in million cubic kilometers would be: 1330.56 million cubic meters.

From the figures given, we are first told that the total volume of water on earth is 1386 million cubic kilometers. 96% of this figure is salt water. So, to know the exact amount this constitutes from the orginal figure, we will do 96% of 1386 million cubic meters.

The result is 1330.56 million cubic meters. So, the total volume of salt water in million cubic meters is 1330.56.

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Answer:

√194 or 13.9

Step-by-step explanation:

√(x2 - x1)² + (y2 - y1)²

√[-2 - (-7)² + [4 - (-9)]

√(5)² + (13)²

√25 + 169

√194

= 13.9