What is the product of 3 2/3 + 14 2/5?

In geometry, reflections and glide reflections are transformations that result in a preimage and an image with opposite orientations. This happens because a reflection flips an object over a line, creating a mirror image with reverse orientation. A glide reflection combines a translation and a reflection, also leading to opposite orientation.

In mathematics, particularly in geometry, when we talk about a preimage and an image, we refer to the original shape and the shape after transformation respectively. The transformation that results in a preimage and image with opposite orientations is reflections and glide reflections. A reflection is a transformation that flips a figure over a line, thus turning it into its mirror image. This reverses the orientation of the figure. A glide reflection involves a translation (or glide) followed by a reflection. Again, the result will have an orientation opposite to the original (or preimage).

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Answer:

Total rent costing for traveling for 4 days, 389 miles is $447.31

Step-by-step explanation:

Given : a car rental costs $35 per day plus $0.79 per mile.

We have to find the total rent costing for traveling for 4 days, 389 miles.

Since, Cost of car rent per day is $35

Thus, Cost of car rent for 4 days is $ 35 × 4 = $140

Also, Cost of car rent per miles is $0.79

Thus, Cost of car rent for  389 miles is $ 0.79 × 389 = $307.31

Thus, total car rental cost = Cost of car rent for 4 days + Cost of car rent for  389 miles.

Total car rental cost = $140 +  $307.31

Total car rental cost = $447.31

Thus, total rent costing for traveling for 4 days, 389 miles is $447.31

The business will pay $506.99 on the loan in the sixth month, after making monthly payments of 12% of the remaining balance on an $8000 loan.

To determine how much the business will pay in the sixth month on a loan where they pay off 12% of the remaining balance each month, we need to use a decay formula. This is a type of exponential decay since the amount owed is decreasing by a fixed percentage each month. The formula to find the remaining balance after each payment is:

Balance after n payments = Initial amount * (1 - rate)^n

Starting with an initial loan amount of $8000 and a monthly payment rate of 12% (or 0.12 in decimal form), we calculate the remaining balance each month until the sixth month:

Now we can find out how much will be paid in the sixth month by calculating 12% of the balance at the end of the fifth month:

Sixth month payment = 12% of 4224.96
Sixth month payment = 0.12 * 4224.96
Sixth month payment = $506.99
The business will pay $506.99 in the sixth month.

The component form of a vector represents it as the sum of its scalar components along the coordinate axes. It is used to describe a vector's individual directional effects in a Cartesian coordinate system, often denoted by Axi + Ayj for 2D vectors, and an additional Azk for 3D vectors.

The component form of a vector refers to its representation as the sum of its separate parts along the coordinate axes. In a two-dimensional system, a vector can be broken down into the x and y components. Each component is essentially the projection of the vector along one of the coordinate axes. For example, in a rectangular (Cartesian) coordinate system, a two-dimensional vector A with an initial point and a terminal point can be represented by the difference in the x-coordinates (horizontal component) and the difference in the y-coordinates (vertical component).

The formula to represent a two-dimensional vector in component form is A = Axi + Ayj, where Ax and Ay are the scalar components of the vector along the x-axis and y-axis, respectively, and i and j are the unit vectors in the direction of the x-axis and y-axis. In three-dimensional space, an additional z-component is included, resulting in the component form A = Axi + Ayj + Azk, with k being the unit vector along the z-axis.

Answer:

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Step-by-step explanation:

Answer:

Option A is correct

x= -2 is an approximate solution of [tex]2x^2-2 = -0.5x+4[/tex]

Step-by-step explanation:

As per the statement:

Fran graphs the equations

[tex]y=2x^2-2[/tex] and

[tex]y = -0.5x + 4[/tex]

Equate these two equations:

[tex]2x^2-2 = -0.5x+4[/tex]

You can see the graph for these equations as shown.

Since, the line and the parabola intersects at x = -2 and x = 1.5.

From the given options:

x = -2 is the solution for these equations.

Therefore, the value is an approximate solution of [tex]2x^2-2 = -0.5x+4[/tex] is, x = -2

Answer:  B. A parallelogram with a pair of congruent consecutive sides and diagonals that are congruent.

Step-by-step explanation:

We know that a parallelogram is a quadrilateral having congruent opposite  sides and its diagonals bisect each other.

A square is a kind of parallelogram having all its consecutive sides equal and both diagonals congruent to each other.

Its all 4 angles are right angle.

let's check all the statements :

A. A parallelogram with a pair of congruent consecutive sides and diagonals that bisect each other.

→It can be rhombus ∵ it also has same characteristics.

B. A parallelogram with a pair of congruent consecutive sides and diagonals that are congruent.

→ It only occurs in square.

C. A parallelogram with a right angle and diagonals that are congruent .

→ it can be a rectangle ∵ it has all its angles right angle and diagonals are congruent.

D. A parallelogram with diagonals that bisect each other.

→ It is the basic property of parallelogram , it can describe a rhombus or rectangle both.

The statement that must be true is (b) A parallelogram with a pair of congruent consecutive sides and diagonals that are congruent.

A parallelogram has parallel and congruent opposite sides

However, the following must be true about parallelograms that can be regarded as squares:

Hence, the true statement is (b)

Read more about parallelograms at:

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