please help!
A shipping container will be used to transport several 40-kilogram crates across the country by rail. The greatest weight that can be loaded into the container is 24500 kilograms. Other shipments weighing 13100 kilograms have already been loaded into the container. Write and solve an inequality which can be used to determine xx, the number of 40-kilogram crates that can be loaded into the shipping container.

Answer:

At least 8 rows

Step-by-step explanation:

45 divided by 9 is 5. That is 5 rows

9x3= 27 and there are 23 adults. So that is 3 rows

5+3=8

8 rows in total.

The total number of cartons needed more to pack small 15 cartons than 35 large cartons is108 cartons.

Division is defined as one of the four basic operations of arithmetic in mathematics.

The parameters for this question are:

Total number of cartons =2835

Number of small cartons needed = 15 cartons

Number of large cartons needed = 35 cartons

To package the orange juice in large cartons we need [tex]\frac{2835}{35} =81 cartons[/tex]

Also, to package 15 small cartons we need [tex]\frac{2835}{15} =189 cartons[/tex]

Number of more small cartons than large cartons is

Small cartons -large cartons

=189-81=108 more cartons.

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The inverse function of the function f(x) = 2x - 4 will be x/2 +2.

What is inverse function?

A function that returns the initial value for which a function has produced output is called an inverse function. If f(x) is a function that produces the value y, then f-1(y), which is the inverse function of y, will produce the value x. Inverse and reciprocal functions should not be confused. The output's original value is returned by the function's inverse, which is represented by the symbol f-1 (x). While the reciprocal of a function is represented by 1/f(x) or f(x)-1

Those that do are referred to as invertible. For a function f: X Y to have an inverse, it must possess the characteristic that there is exactly one x in X such that f(x) = y for every y in Y. This characteristic guarantees the existence of a function g: Y X that has the required connection to f.

f(x) = 2x - 4

y = 2x - 4

So x = y +4 /2

x = y/2 +2

Now to get the inverse of the function  put the x value in y

So [tex]f^{-1}[/tex](x) = x/2 +2

Hence, inverse function will be x/2 +2.

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Answer:

No.

Step-by-step explanation:

Because the equation has an exponent, it is quadratic, and not linear.

Answer:1

Step-by-step explanation:

Answer:

  (a)  A = W(140 -W)

  (b)  W = 70

  (c)  4900 square yards

Step-by-step explanation:

You want an expression for the rectangular area that can be enclosed by 280 yards of fence, if that area has width W. Further, you want the value of W that maximizes the area, and the size of that maximum area.

The perimeter of the rectangle with length L and width W is ...

  P = 2(L +W)

Then the length can be found from the width as ...

  L = P/2 -W

For P=280, this is ...

  L = 140 -W

The area is the product of length and width:

  A = LW

  A = (140 -W)(W)

The area expression describes a downward-opening parabola with zeros at W=0 and W=140. The vertex (maximum) of the parabola is on the line of symmetry, halfway between these zeros. The value of W there is ...

  W = (0 +140)/2 = 70

The area is largest for W = 70.

For that value of W, the area is ...

  A = (140 -70)(70) = 70² = 4900 . . . . . square yards

__

Additional comment

The generic solution to the area problem when fence is on all sides is that the shape is a square.

If the cost of fence is different for the different sides, the total cost in the east-west direction is equal to the total cost in the north-south direction when cost is minimized.

Answer:

expanded: 7+0.08

standard: 7.08

Step-by-step explanation:

The hundredths place is the second digit after the decimal, so 8 hundredths is 0.08.

Answer:

A trapezoid is isosceles if and only if its diagonals are congruent. So if we can prove that the bases are parallel and the diagonals are congruent, then we know the quadrilateral is an isosceles trapezoid, as Cool Math accurately states.

Step-by-step explanation:

Answer:

4 [tex]\frac{1}{8}[/tex]

Step-by-step explanation:

Answer: y=x−2 y = x − 2

Step-by-step explanation:

Using trigonometric ratio the distance to the control tower is 750.7ft

In trigonometry, there are six trigonometric ratios, namely, sine, cosine, tangent, secant, cosecant, and cotangent. These ratios are written as sin, cos, tan, sec, cosec(or csc), and cot in short.

The values of these trigonometric ratios can be calculated using the measure of an acute angle, θ in the right-angled triangle given below. This implies that the value of the ratio of any two sides of the triangle here depends on angle C.

Using trigonometric ratio, the distance is

tan θ = opposite / adjacent

tan 47 = x / 700

x = 700 tan 47

x = 750.7 ft

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Applying the definition of an Isosceles triangle, given that isosceles triangle TIC has a vertex angle I of 90 degrees, the measure of angle T is 45 degrees.

In geometry, an isosceles triangle is a triangle that has at least two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case. Examples of isosceles triangles include the isosceles right triangle, the golden triangle, and the faces of bipyramids and certain Catalan solids.

The two equal sides are called the legs and the third side is called the base of the triangle. The other dimensions of the triangle, such as its height, area, and perimeter, can be calculated by simple formulas from the lengths of the legs and base. Every isosceles triangle has an axis of symmetry along the perpendicular bisector of its base. The two angles opposite the legs are equal and are always acute, so the classification of the triangle as acute, right, or obtuse depends only on the angle between its two legs.

An Isosceles triangle has a vertex angle and two equal base angles.

Given that triangle TIC is an isosceles triangle:

angle I is the vertex angle = 90 degrees

angle T is a base angle

angle C is also a base angle

Thus:

angle C and angle T are congruent or equal to each other.

Therefore,

    Angle T = (180 - 90)/2

⇒ Angle T = 90/2

⇒ Angle T = 45 degrees.

applying the definition of an isosceles triangle, given that isosceles triangle TIC has a vertex angle I of 90 degrees, the measure of angle T is 45 degrees.

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The sphere's radius is 5, and its center is at (0, 3, -4).

A sphere is a geometrical object that resembles a two-dimensional circle in three dimensions.

In three-dimensional space, a sphere is a collection of points that are all located at the same distance from a single point.

The radius of the sphere is denoted by the letter r, and the given point is its center.

List a few typical sphere examples from everyday life.

In everyday objects, sphere shapes can be found in the form of marbles, balls, oranges, yarn, and bubbles.

So, the center and radius of the sphere will be:

We have the sphere's equation, which is given by and has a radius of r.

(x - h)² + (y - k)² + (z - l)² = r² ...(1)

We must convert the following equation in order to determine the center and radius of the provided sphere.

x² + y² + z² - 6y + 8z = 0

By combining the x, y, and z terms and filling in the square, we obtain

x² + (y² - 6y + 9) +(z² + 8z + 16) = 9 + 16

(x - 0)² + (y - 3)² + (z + 4)² = 52

So, the sphere's center is at (0, 3, -4) and its radius is 5.

Therefore, the sphere's radius is 5, and its center is at (0, 3, -4).

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Complete question:

Find the center and radius of the sphere x2 + y2 + z2 - 6y + 8z = 0.

The number of nickels and the number of dimes that Joseph has are 12 and 5 respectively.

An equation of degree one is known as a linear equation.

A linear equation of two variables can be represented by ax + by = c.

Let the no. of nickels be N and no. of dimes be D.

∴ N + D = 17...(i) and 0.05N + 0.1D = 1.45...(ii)

Multiplying (ii) by 100 we get 5N + 10D = 145...(iii)

Now multiply (i) by 5 we get 5N + 5D = 85...(iv)

Now subtracting (iv) from (iii) we get,

5D = 60.

D = 12 hence N = 5.

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The equation that models the function is P(t) = 20400(1,09)⁺ and the fox population in 2008 is 40648

From the question, we have the following parameters that can be used in our computation:

Initial population of fox = 20400

Rate of growth = 9 percent per year

These parameters can be presented as

Initial population of fox, a = 20400

Rate of growth, r = 9%

An exponential function is represented as

P(t) = a(1 + r)⁺

So, we have:

P(t) = 20400(1 + 9%)⁺

Evaluate

P(t) = 20400(1,09)⁺

Recall that

t = 0 in 2000

So, the value of t in 2008 is

t = 2008 - 2000

t = 8

Substitute t = 8 in P(t) = 20400(1,09)⁺

So, we have

P(8) = 20400(1.09)⁸

Evaluate

P(8) = 40648

So, the population is 40648

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Answer:

The height of the 4th bounce would be 4.7458321; rounded would be 4.8.

Step-by-step explanation:

We can figure this question out by first converting the 83% into a decimal, by bringing back 2 decimal places:

0.83.

And then setting up this equation:

0.83 x 10 = 8.3

Now, this is for 1 bounce. We have to do this 4 more times:

0.83 x 8.3 = 6.889

3rd time:

0.83 x 6.889 = 5.71787

4th time:

0.83 x 5.71787 = 4.7458321.

Now, we can round this answer to:

4.8

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Answer:

160 minutes can be spent on long distance calls each month.

Step-by-step explanation:

first we know that there is standard charge of $17 for basic service, $0.05 cost per minute with a budget of $25.

let's write that into an equation to solve for (a) which will be number of minutes.

17 + a(0.05) = 25

solving:

17 + a(0.05) = 25

carry across the 17 whilst changing the sign, or some people is also thought to minus on both sides to get rid of a certain variable.

a(0.05) = 25 - 17

a(0.05) = 8

carry across the multiplication of 0.05 which will then turn into division, or divide by 0.05 on both sides to remove it.

[tex]a = \frac{8}{0.05} [/tex]

a = 160

therefore 160 minutes can be spent on long distance calls each month.

You can redefine your answer more simply to hours by dividing by 60, which gives 2 hours and 40 minutes

If triangle has 2 congruent sides and 2 congruent angles ,such a triangle is known as Isosceles triangle.

What is congruent triangle?

Congruence of triangles: 2 triangles square {measure} aforesaid to be congruent if all 3 corresponding sides square measure equal and every one the 3 corresponding angles square measure equal in measure. These triangles may be slides, rotated, flipped and turned to be looked identical. If repositioned, they coincide with one another. The image of congruity is’ ≅’.

Main Body:

A triangle with two congruent sides and congruent base angles is termed as an isosceles triangle.

If two sides of a triangle are congruent, then by isosceles triangle property, the angles opposite to these sides are congruent.

That is, base angles of the triangle are congruent.

Then, such a triangle is known as Isosceles triangle.

Therefore, option B is correct.

The actual question with option is in figure.

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Answer: -23

Step-by-step explanation:

[tex]jk^2 -m=(-5)(2^2)-3=-5(4)-3=-20-3=-23[/tex]

The true statements are

The side length of the transparent cube is given as

Length = 10 millimetres

The volume of the cube is calculated as

Volume = Length³

Substitute the known values in the above equation, so, we have the following representation

Volume =10³

Evaluate

Volume = 1000 cubic millimetres

1000 cubic millimetres and 30 cubic millimetres do not have the same value

So, the co-worker is incorrect.

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The various types of inverse function are the inverse of trigonometric functions, rational functions, hyperbolic functions and log functions

If the function is denoted by ‘f’ or ‘F’, then the inverse function is denoted by f⁻¹or F⁻¹.

A function accepts values, performs particular operations on these values and generates an output. The inverse function agrees with the resultant, operates and reaches back to the original function.

The various types of inverse function are:

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The relation:

(9, -1) (4,2) (5,3) (8, -1) (3, 0)

Is a function, because each element of the domain appears only once.

A relation maps elements from a set, called the domain, into elements from another set, called the range.

Such that the element x being mapped into the element y is written as:

(x, y).

A relation is a function only if each element in the domain is mapped into only one element of the range.

Here we have the relation:

{  (9, -1) (4,2) (5,3) (8, -1) (3, 0)}

We can see that no element of the domain appears twice, so yes, this is a function.

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Answer:

add up the exponents of each term and select the highest sum.

The equation that best defines the length of the equal piece is 4x+2¹-12

We should know that an equation is a mathematical model that shows the equality of two sides of an expression

Based on the given condition 12-24=4*x

Applying multiplicative distribution -12=4x

Rearrange the equation 4x=-12

Calculate the product of the quotient x=-3

Now 24feet divided by -3 =-4

Since it deals with length =4

In conclusion the equation that determines the length of each equal piece is  4x+2¹-12

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There are four basic properties of numbers: commutative, associative, distributive, and identity.

1.Commutative Property

a. Addition

. When two numbers are added, the sum is the same regardless of the order in which the numbers are added.

3 + 5 = 8       or       5 + 3 = 8

b. Multiplication. When two numbers are multiplied together, the product is the same regardless of the order in which the numbers are multiplied.

3 x 5 = 15       or       5 x 3 = 15

2.Associative Property

a. Addition. When three or more numbers are added, the sum is the same regardless of the way in which the numbers are grouped.

6 + (4 + 3) = 13   or   (6 + 4) + 3 = 13

b. Multiplication. When three or more numbers are multiplied, the product is the same regardless of the way in which the numbers are grouped.

6 x (4 x 3) = 72   or   (6 x 4) x 3 = 72

3.Distributive Property

The sum of two numbers times a third number is equal to the sum of each addend times the third number.

5 x (7 + 2) = 45   or   5 x 7 + 5 x 2 = 45

4.Identity Property

a. Addition. The sum of any number and zero is that number.

12 + 0 = 12

b. Multiplication, The product of any number and one is that number.

18 x 1 = 18

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1 must be the root of the polynomial [tex]$3 x^2+x-4$[/tex].

We are given that polynomial [tex]$3 x^2+x-4$[/tex] is being divided by factor [tex]$(\mathrm{x}-1)$[/tex]

It is also said that when David perform the mathematical operation it gives remainder 0 .

Remainder 0 represents that divisor [tex]$(\mathrm{x}-1)$[/tex] is a factor polynomial [tex]$3 x^2+x-4$[/tex].

As x-1 is a factor of the given ploynomial, we can get one of the root of by setting it equal to 0 and solve for x.

Therefore,

x-1=0

Adding 1 on both sides, we get

[tex]$$\begin{aligned}& x-1+1=0+1 \\& x=1 .\end{aligned}$$[/tex]

Therefore, 1 must be the root of the polynomial [tex]$3 x^2+x-4$[/tex].

Polynomials are sums of terms of the form k⋅xⁿ, where k is any number and n is a positive integer. For example, 3x+2x-5 is a polynomial. Introduction to polynomials. This video covers common terminology like terms, degree, standard form, monomial, binomial and trinomial.

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Answer:

We can be able to use compatible numbers to estimate the quotient of 925/29 if the whole number that is part of the decimal is less than the divisor, we need to be able to rename the decimal.

Step-by-step explanation:

The area of the larger floor is 64 square units when w = 8 and l = 8. which is the correct answer would be an option (B).

To compare the values, we must first calculate each given situation. The area of any given rectangle is length times width.

If w = 7 and l = 9

A = l × w = 8 × 6 = 48

If w = 8 and l = 8

A = l × w = 8 × 8 = 64

So, the second case would obtain a larger area.

Therefore, the area of the larger floor is 64 square units when w = 8 and l = 8.

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Yes, a cubic graph is an exponential.

What is Cubic Graph?

A cubic graph in the study of graph theory is a graph with all of its vertices having degree three. A cubic graph is a 3-regular graph, to put it another way. Trivalent graphs are another name for cubic graphs. A cubic bipartite graph is known as a bicubic graph.

What is Exponential?

The mathematical expression f(x)=exp or ex denotes the exponential function. Unless otherwise stated, the phrase usually refers to the positive-valued function of a real variable, though it can also be applied to complex numbers or extrapolated to other mathematical objects like matrices or Lie algebras.

Graphs of Exponential Functions if;

When the base is greater than 1, the exponential function has the following characteristics and you can easly understand from this :

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Answer:

change 5 weeks to days(5*7)-35days

then convert the days to seconds

35*86400/10*86400

answer 7/2

Answer:

The integers could be 8 and 4, just checked with a calculator