Why 55 gallon drum size?

Answer:

v=9+√481 20,  9−√481 20

Step-by-step explanation:

The slope of a line that is parallel to the line containing the points (3, 4) and (2, 6) is -2.

To find the slope of a line that is parallel to the line containing the points (3, 4) and (2, 6), we first need to find the slope of the line containing these points. We can use the slope formula:

m = (y2 - y1) / (x2 - x1)

Where:

m = slope

(x1, y1) = coordinates of the first point (3, 4)

(x2, y2) = coordinates of the second point (2, 6)

Substituting the given values, we get:

m = (6 - 4) / (2 - 3)

m = -2

The slope of the line containing the points (3, 4) and (2, 6) is -2.

Since we are looking for a line that is parallel to this line, the slope of the parallel line will also be -2.

Therefore, the slope of the parallel line is -2.

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Answer:

The equation 4x - 3y > 12 can be graphed by finding two points that satisfy the inequality. For example, you could use the points (0, 4) and (3, 0). Then, you can plot the points on a graph and draw the line that passes through them. This line is the graph of the inequality. You can also put the equation into slope-intercept form by rearranging the equation to y = (4/3)x - (4/3). The graph of y = (4/3)x - (4/3) is the same as the graph of the original inequality.

Using the laws of exponents, we can rewrite the expression as:

b^4 * b^(-1/4) = b^(4 - 1/4) Simplifying the exponent, we get:

b^(15/4). Therefore, the expression in the form bn is b^(15/4).

To rewrite the expression b^4 * b^(-1/4) in the form bn, we need to apply the laws of exponents. The law of exponents states that when multiplying two powers with the same base, we can add the exponents. In this case, we have b^4 multiplied by b^(-1/4), which means that we have the same base b. Using the law of exponents, we add the exponents 4 and -1/4 to get 4 - 1/4 = 15/4. Thus, we have simplified the expression b^4 * b^(-1/4) to b^(15/4). This is in the form of bn, where b is the base and n is the exponent. Therefore, the expression b^4 * b^(-1/4) is equivalent to b^(15/4).

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43% of the total trip had they travelled when Tallulah fell asleep

percentage, a relative value indicating hundredth parts of any quantity.

Given that Tallulah's family took a road trip to the Grand Canyon.

Tallulah slept for the last 129 miles of the trip.

the total length of the trip was 300 miles

We have to find the percentage of the total trip had they travelled when Tallulah fell asleep

x/100×300=129

3x=129

Divide both sides by 3

x=43%

Hence, 43% of the total trip had they travelled when Tallulah fell asleep

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The solution to the system of equations is x = 5 and y = -2, or (5,-2) in coordinate form.

An equation is a mathematical statement that shows that two expressions are equal. It is usually written as an expression on the left-hand side (LHS) and an expression on the right-hand side (RHS) separated by an equal sign (=).

The expressions on both sides of the equation can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The variables in an equation represent unknown values that can vary, while the constants are fixed values that do not change.

Equations are used to represent mathematical relationships or describe real-world situations. They can be used to solve problems, make predictions, and test hypotheses.

To solve an equation, one must find the value of the variable that makes the LHS equal to the RHS. This is done by performing mathematical operations on both sides of the equation to isolate the variable. The goal is to get the variable by itself on one side of the equation, with a specific value on the other side.

Equations can be simple or complex, linear or nonlinear, and can involve one or more variables. Examples of equations include:

2x + 5 = 13

y = 3x^2 - 2x + 7

4a + 2b - 3c = 10

Equations are used in many areas of mathematics and science, including physics, chemistry, and engineering, among others.

Substitute the value of y in the second equation with the expression for y from the first equation:

2x + 3(4x-22) = 4

Simplify and solve for x:

2x + 12x - 66 = 4

14x = 70

x = 5

Substitute the value of x in the first equation to solve for y:

y = 4(5) - 22

y = -2

Therefore, the solution to the system of equations is x = 5 and y = -2, or (5,-2) in coordinate form.

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The correct option is (d) if A is divided by 2, B is divided by approximately 1.414.

Proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.

Here,
If A varies inversely as the square of B, it means that A is equal to some constant k divided by the square of B:

A = k/B²

To find the effect on B when A is multiplied by 4, we can use the inverse variation formula and substitute 4A for A,

4A = k/B^2

Simplifying this expression, we get:

B² = k/(4A)

To find the effect on B when A is multiplied by a certain factor, we can use this formula and substitute the new value of A,

a) If A is multiplied by 1.5:

1.5A = k/B²

B² = k/(1.5A)

The effect on B depends on the value of k and the original value of B, which are not given. So we cannot determine the effect on B with the information given.

b) If A is multiplied by 4:

4A = k/B²

B² = k/(4A)

Since 4A is four times the original value of A, B^2 will be divided by 4, so B will be multiplied by √4, which is 2. Therefore, when A is multiplied by 4, B is multiplied by 2.

c) If A is multiplied by 2:

2A = k/B²

B^2 = k/(2A)

Since 2A is half the original value of A, B^2 will be multiplied by 2, so B will be divided by √2, which is approximately 1.414. Therefore, when A is multiplied by 2, B is divided by approximately 1.414.

d) If A is divided by 2:

A/2 = k/B²

B² = k/(A/2)

Since A/2 is half the original value of A, B² will be multiplied by 2, so B will be divided by √2, which is approximately 1.414. Therefore, when A is divided by 2, B is divided by approximately 1.414.

Therefore, the correct option is (d) if A is divided by 2, B is divided by approximately 1.414.

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The area of a rhombus with an angle measuring 30 degrees and sides measuring 9 inches, the answer will be 40.5 inches.

By using trigonometry,

Here, it is given that:

Side which is 's' is equal to 9 inches

Angle which is denoted as 'A' is equal to 30 degrees

Square of side s is equal to 9 × 9 = 81 inches

Area of rhombus, A = s² × sin (30°)

A = 81 × 1/2

A = 40.5 inches

A rhombus is a particular kind of parallelogram in geometry where two pairs of opposite sides are congruent. Accordingly, a rhombus has equal length on each side. Square and rhombus are frequently confused in students. The main distinction between a square and a rhombus is that a square has all internal angles that are right angles, whereas a rhombus does not.

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Answer:

  λ = 3

Step-by-step explanation:

You want the value of λ that places point C = λ(i -3j) on the line between A(-5i -11j) and B(23i -4j).

The parameterized line between A and B is ...

  P = A +t(B -A)

where P is a point on AB. We can set P = C to find the value of t that identifies the point on AB. Comparing that to C, we can determine the value of λ.

  λ(i -3j) = -5i -11j +t(23i -4j -(-5i -11j)) = (-5+28t)i +(-11 +7t)j

Equating components gives two equations in the unknowns λ and t:

Multiplying the second equation by -4 and adding the first gives ...

  -4(-3λ) +λ = -4(-11 +7t) +(-5 +28t)

  13λ = 39 . . . . . . . simplify

  λ = 3 . . . . . . . . . divide by 13

The percent that accurately reflects the white section in the circle is 38%. So, the correct option is A).

To find the percentage of the circle that is white, we need to divide the area of the white region by the area of the entire circle and multiply by 100.

Looking at the diagram, we can see that the white region takes up about 3/8 of the circle, or 37.5% (since 3/8 is equal to 0.375 or 37.5%). This is closest to answer choice A, which is 38%.

Therefore, the percent that accurately reflects the white section in the circle is 38%.

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Answer:

f(n)= f( n-1 ) + 6

Answer:

The transformation of stretching the function vertically by a factor of 4 means that every y-value of f(x) is multiplied by 4, so the new function is:g(x) = 4sin(x)The transformation of shifting the function downward by 3 units means that the entire graph is shifted downward by 3 units, so we subtract 3 from the y-value of g(x), giving:g(x) = 4sin(x) - 3Therefore, the equation of the new function g(x) is g(x) = 4sin(x) - 3

Step-by-step explanation: hope this helps0^0

Answer:

a, d=90 degre

and b, b=90degree

Answer:

h = 9.9

b = 4.6

Step-by-step explanation:

The first triangle is an isosceles right triangle
The base leg = vertical leg = 7

diagonal = 7√2 = 9.9  (rounded to nearest tenth)

h = 9.9

For the 30-60-90 triangle
if the vertical leg is x, the base leg = vertical leg / √3 = 8/√3 = 4.6

b = 4.6

The volume of Miriam’s popcorn container is 71.875 inches³.

Volume is defined as the set of three dimensional coordinates enclosed by a two - dimensional surface. We can write the volume as -

V = ∫∫∫f(x, y, z) dxdydz

Given is that Miriam’s popcorn container is 11.5 inches high but with a base whose side length is 2.25 inches.

We can write the volume of Miriam’s popcorn container as -

V = Area of base x height

V = (2.25 x 2.25) x (11.5)

V = 71.875 inches³

Therefore, the volume of Miriam’s popcorn container is 71.875 inches³.

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The speed of the bullet is 1000 m/s when A 10 kg gun recoils with a speed of 0.1 m/s after it fires a 0.001 kg bullet.

As we know that here gun + bullet system is isolated from all other external force systems

so here the momentum of the system is always conserved

so we will say

m₁v₁i + m₂v₂i = m₁v₁f + m₂v₂f

here we know that

v₁i = v₂i = 0

m₁ = 10kg

m₂ = 0.001kg

v₁f = 0.1m/s

now we will have

0+0  = 10(0.1) + 0.001v₂f

by solving the above equation we will have

v₂f = 1000m/s.

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The correct question is:

A 10 kg gun recoils with a speed of 0.1 m/s after it fires a 0.001 kg bullet. What is the speed of the bullet?

Answer:

a=3

Step-by-step explanation:

the sum of anterior angle of a triangle is =180

57+81+14a=180

138+14a=180

42=14a

42/14=14a/14

3=a

therefore a=3.

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The magnitude and direction of the vector is 7.3 units and 15.9° north of east respectively.

option B.

To find the magnitude and direction of MN, we can use the distance formula and trigonometry.

The distance formula is:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Using the coordinates of M(-3,-2) and N(4,0), we get:

d = √((4 - (-3))² + (0 - (-2))²)

d = √(49 + 4)

d = √(53)

d ≈ 7.3 units

To find the direction, we can use trigonometry. We can first find the angle between the line and the positive x-axis using:

tan θ = (y₂ - y₁)/(x₂ - x₁)

tan θ = (0 - (-2))/(4 - (-3))

tan θ = 2/7

θ = arc tan (2/7) =  15.9°

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Answer:

15 = 9 + j

Step-by-step explanation:

"15 is 9 more than j"

"15 is"  may be written as "15 ="

"9 more than j" may be written as "9+j"

Put these two expression together:

15 = 9 + j

The mathematical phrase "e to the ipi" is composed of the imaginary unit i (the square root of -1 raised to the power of pi), which is symbolized by "pi," and the mathematical constant "e" (Euler's number).

The expression "e to the ipi" may be expressed as follows:

[tex]e^{(i*pi)}[/tex]

The following formula is known as Euler's formula:

[tex]e^{(ipi)}[/tex] = cos(pi) + isin(pi)

where "cos" and "sin" are the sine and cosine functions, respectively.

We may reduce this formula to using the cosine and sine trigonometric identities.

[tex]e^{(i*pi)}[/tex] = -1

"e to the ipi" hence equals a negative one. This startling and outstanding finding ties together various crucial mathematical ideas, including calculus, complex numbers, and trigonometry.

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The area of the shaded sector is given as follows:

24π cm².

The length of the arc is given as follows:

2π.

The area of a circle of radius r is given by π multiplied by the radius squared, as follows:

A = πr²

The radius is the distance of the center of the circle to a point on the circumference of the circle, hence:

r = 12.

The entire area has an angle measure of 360º, hence the area of the sector with a central angle of 60º is given as follows:

A = 60/360 x π x 12²

A = 24π cm².

The circumference of a circle is given as follows:

C = 2πr.

Hence the length of the arc is given as follows:

C = 2 x 60/360 x π x 6

C = 2π.

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A null space calculator finds the null space of a matrix used in linear algebra.

An invalid space mini-computer is a web-based instrument used to track down the invalid space, otherwise called the portion, of a framework. The invalid space of a framework is the arrangement of all vectors that fulfill the condition Ax= 0, where An is the lattice and x is the vector of questions. The invalid space can be utilized to decide if an arrangement of straight conditions is steady or not, and to find the reason for the arrangement space. An internet based invalid space number cruncher permits clients to enter a network and get the invalid space, as well as different properties like the position, determinant, and eigenvalues of the framework. This can be helpful for understudies and experts in fields like science, physical science, and designing who need to address frameworks of straight conditions and dissect the properties of networks.

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In metric system length measured by using kilometres, milimter and miles etc. Thus, the conversion of 2.25 inches to mili meters is equals to the 57.15 mm.

Inches (also called in. ) is a unit of measurement used in US customer measurement systems. It is also part of the imperial measurement system. A millimeter (abbreviation mm) is a unit of measurement in the metric system. Like the inch, it is used to measure the length of an object, especially small ones. "Millimetre" is the US spelling, while in the UK it is spelled "millimetre". To convert from one measurement unit to another, multiply by the conversion factor. Formula to convert inches to millimeters, [X] mm = 25.4 × [Y] in ---(1)

We need to convert 2.25 inches to millimeters. So using the formula, millimeter = 25.4 × 2.25 inches

= 57.15

Hence, required value is 57.15 mm.

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The wax cost to cover the floor is $1,569.75.

The correct option is B.

The area is the amount of area occupied by an object's flat (2-D) surface or shape.

Given:

A maintenance worker needs to wax a restaurant floor shaped like the image shown.

A six-sided figure.

There is a horizontal base of 35 feet then another horizontal base below it of 20 feet.

The longest side is to the right and is 40 feet.

The top is 30 feet.

There is a perpendicular from the vertex of the top to the first base of 35 that is labeled 15 feet.

The total area of the composite figure is,

= (15 x10) + (20 x 40) + (1/2 x 25 x 15)

= 1137.5 square feet.

If the wax cost $1.38 a square foot,

the cost is,
= 1137.5 x 1.38

= $1569.75

Therefore, the total cost is $1569.75.

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The total marginal cost of using 8 bottles is $8.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Marginal utility of 1 bottle of Gatorade costs =  1$

Now,

The total marginal cost of using 8 bottles.

= 8 x $1

= $8

Thus,

The total marginal cost of using 8 bottles is $8.

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The complete question:

Marginal utility of 1 bottle of Gatorade that costs 1$.

Find the total marginal cost for using 8 bottles of Gatorade.

From the decimal theory 10 has no decimal places, as it is a whole number.

As per the data given in the above question are as bellow,

The provided details are as bellow,

We have given the number as 10.

we have to find the decimal in the given number.

Thus we have to know about decimal value.

The tenths place is represented by the first digit following the decimal. The hundredths place is represented by the digit that follows the decimal. Up until there are no more digits, the remaining ones keep the place values filled in.

Here don't have any decimal value in the given number 10.

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The length of the addition to the room will be 8 feet.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.

Given that Teri has a living room that is 9 feet wide and has an area of 108 square feet. She is adding to the room. The remodelled living room will have a total area of 180 square feet.

The added length will be calculated as:-

TA = A₁ + A₂

180 = 108 + 9x

72 = 9x

x = 72 / 9

x = 8 feet

Therefore, the length of the room addition will be 8 feet.

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Answer:

Hi! In order to determine how much money Aiden will have in his account after 8 months, let's figure out how much he deposits each month.

He started with $250. After one month, he had $586; after two months, he had $922; after three months, he had $1,258. Each month, there is a gain of $336.

Therefore, after four months, Aiden will have $1,594. After five months, he will have $1,930. After six months, he will have $2,266. After seven months, he will have $2,602. Finally, after eight months, he will have $2,938.

Hope this helps!