When adding two numbers, such as 123 and 423, care is taken to first line them up and then add like digits. How does expanding this expression to [(1 × 102) + (2 × 101) + (3 × 100)] + [(4 × 102) + (2 × 101) + (3 × 100)] make the operation more like a polynomial addition problem?

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)

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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 no. of people own computer in 2015 are 92.0953 million.

The interest charged on a loan or deposit is known as compound interest. In our day-to-day lives, it is the concept we use the most. The amount's compound interest is based on both the principal and the interest earned over time. This is the primary distinction between simple and compound interest.

Given annually increase rate of computers = R =  23.2%

people own computer in 1990 = 1/2 million = 0.5 million

let no. of people own computer in 2015 be x

compound interest for annually increase in rate is p[tex](1 + R/100)^{t}[/tex]

where t = time and R = rate

Time = 2015 - 1990 = 25 years

x = 0.5(1 + 23.2/100)²⁵

x = 0.5(1.232)²⁵

x = 0.5 × 184.1906

x = 92.0953 million

Hence 92.0953 million people own computer in 2015.

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from the problem m = 1/2

point slope =

y -2 = 1/2(x+8)

First statement is true.

One fourth of the values are less than or equal to 2.5, and three fourths of the values are above 2.5.

Therefore, The first quartile of a data set is 2.5. this statement represent that One fourth of the values are less than or equal to 2.5, and three fourths of the values are above 2.5.

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Answer:

The center of given circle is X.

Step-by-step explanation:

Given : Circle .

To find: Which point is the center of the circle?

Solution : The diameter of a circle subtends a right angle to any point on the circle is called center of circle .

Therefore, The center of given circle is X.

Answer:

Hence, point X is the center of the circle.

Step-by-step explanation:

We are given a circle.

We have to find the center of a circle.

Circle: It is the set of points in a plane which are equidistant from a particular point called the center of the circle.

As we can see all the points of a circle are equidistant from point X

Hence, point X is the center of the circle.

Hence, correct option is:

B. point X

He needs to sell $400,000 worth of goods.

Base salary = $30000

Percent Commission = 5%

Let the amount of goods that need to be sold be represented by x

Therefore, the equation will be:

30000 + (5% × x) = 50000

30000 + (0.05 × x) = 50000

30000 + 0.05x = 50000

Collect like terms

0.05x = 50000 - 30000

0.05x = 20000

x = 20000/0.05

x = 400000

Therefore, he needs to sell $400,000 worth of goods.

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Answer:

Lexi will use [tex]\frac{5}{6}[/tex] pounds of seeds.

Step-by-step explanation:

Lexi has planted seeds in [tex]\frac{3}{5}[/tex] of the garden. We know that to plant that part she used [tex]\frac{1}{2}[/tex] pound of seeds.

The entire garden is [tex]\frac{5}{5}=1[/tex].

Then if you multiply [tex]\frac{1}{2}[/tex] in [tex]\frac{5}{5}=1[/tex] and then divide the result in [tex]\frac{3}{5}[/tex] you will obtain how many pounds will she use for the entire garden. (It's a rule of three)

[tex](1).\frac{1}{2} :\frac{3}{5}=\frac{1}{2} :\frac{3}{5}=\frac{5}{2.3}=\frac{5}{6}[/tex]

Lexi will use [tex]\frac{5}{6}[/tex] pounds of seeds.

Answer: [tex]-2\dfrac{1}{10}[/tex]

Step-by-step explanation:

The given expression to simplify : [tex]5\dfrac{1}{4}\div-2\dfrac{1}{2}[/tex]   (i)

First we convert mixed fraction into improper fraction as :

[tex]5\dfrac{1}{4}=\dfrac{5\times4+1}{4}=\dfrac{20+1}{4}=\dfrac{21}{4}[/tex]

[tex]-2\dfrac{1}{2}=-\dfrac{2\times2+1}{2}=-\dfrac{4+1}{2}=\dfrac{-5}{2}[/tex]

Now , put them in (i) , we get

[tex]\dfrac{21}{4}\div\dfrac{-5}{2}[/tex]

[tex]=\dfrac{21}{4}\times\dfrac{-2}{5}=\dfrac{-21}{10}=-\dfrac{20+1}{10}=-2\dfrac{1}{10}[/tex]

Hence, the required answer is [tex]-2\dfrac{1}{10}[/tex].

Answer:true

Step-by-step explanation:

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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area is 8*10 = 80 ( Area of square formed by dotted line)

 1/2 *4 * 10 = 20 (Area of small triangle formed by dotted line)

20 +80 = 100 square inches

We are given a parent function f(x) as:

       [tex]f(x)=\dfrac{1}{x}[/tex]

and the transformed function g(x) is given by:

       [tex]g(x)=\dfrac{1}{x+4}-6[/tex]

We know that the transformation of the type:

     f(x) → f(x+a)

is either a shift a units to the left or to the right depending whether a is positive or negative respectively.

Also, the transformation of the type:

   f(x) → f(x)+a

is the shift of the function f(x) either upward or downward depending on whether x is positive or negative respectively.

Here the function g(x) is:

     [tex]g(x)=f(x+4)-6[/tex]

This means that the function g(x) is a shift of the function f(x) 4 units to the left and then it is translated 6 units downward.

Also we may see by the graph.

Answer:

441 cm

Step-by-step explanation: