1) Multiply. Write your answer in scientific notation.
60. (5 x 102)

A brief definition of a triangle according to Euclidean geometry is shown below:

Closed figure consisting in three non-colinear, all of them coplanar, points named vertices and three line segments associated to each pair of points named sides.

To understand what a triangle is, we need to understand some basic concepts of the Euclidean geometry. There are three undefined terms, that is, fundamental elements that cannot be defined but are described in terms of its attributes. Those terms are point, line and plane. The atributes of each element are described below:

A line can be formed by knowing the location of two distinct points on a plane. Lines can be continuous lines (endless), line segments (lines with finite length) or semirrays (lines with only one endpoint).

Let suppose that we have three points not collinear to each other, then we construct line segments for each pair of collinear points. Then, we create a triangle, whose brief definition is shown below:

Closed figure consisting in three non-colinear, all of them coplanar, points named vertices and three line segments associated to each pair of points named sides.

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Let us prepare an inequality statement to answer the question.

There is a one-time fee of $85 and a fee of $23 per guest. If x represents the number of guests, the amount spent will be:

If the amount spent cannot exceed $1750, we have the inequality statement to be:

We can solve as follows:

Since we cannot have a fraction of a person, the answer will be 72.

her maximum number of guests is 72.

The equation D show the multiplication property of inequality if n+4 =11

What is inequality ?

inequality, When two numbers or algebraic expressions are stated to be greater than, greater than or equal to, less than, or less than or equal to each other in order. Inequalities can be stated as either statements of fact in the form of theorems, which are solved using methods similar to those used to solve equations, or as questions. For instance, the triangle inequality states that the length of the remaining side is greater than or equal to the sum of the lengths of any two sides of a triangle. Many of these inequalities, including the Cauchy-Schwarz inequality, are used in the proofs of many of mathematical analysis' most significant theorems.

Sol-

If n+4 =11

Then by applying the product rule -

(n+4)×2 =11×2

So the correct option is D.

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New coordinate are P(0,0) ,Q(-4,2) ,R(6,6)

A coordinate plane is a two-dimensional surface made up of two number lines. It is produced when a horizontal line crosses the origin, which is the location where the X- and Y-axes meet. The numbers on a coordinate grid are used to find points. Using a coordinate plane, you may graph points, lines, and many other things. It functions as a map and gives precise driving instructions between two locations. The definition of a coordinate plane is as follows: A coordinate plane, also known as a rectangular coordinate plane grid, is made when the X-axis and Y-axis, two horizontal lines, cross.

Given that :P(0,0) , Q(-2,1) , R(3,3)

(x,y)→(2x,2y)

P(0,0)

Q(-4,2)

R(6,6)

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Answer:

35.224137931

Step-by-step explanation:

2010: 1266.66

1970: 35.96

1266.66/35.96=35.224137931

Without the actual data for the average prices of gold in 2010 and 1970, I cannot provide the exact quotient. However, if we assume that we have the data, we can calculate the quotient by dividing the average price of gold in 2010 by the average price of gold in 1970. The resulting quotient would indicate how many times more expensive gold was in 2010 compared to 1970.

For example, if the average price of gold in 2010 was $1,500 per ounce and the average price in 1970 was $35 per ounce, then the quotient would be:

$1,500 / $35 = 42.86

This means that the average price of gold in 2010 was 42.86 times more expensive than the average price in 1970.

It is important to note that the actual quotient will depend on the actual data for the average prices of gold in 2010 and 1970.

The conversion of dry measurements are:

a. 352 quarts

b. 48 pints

c. 3.03 bushels

d. 140 pecks

a. 11 bushels to quarts

32 quarts make up one bushel, which is a unit of dry volume.

1 bushel = 32 quarts

11 bushels = (32 × 11) quarts = 352 quarts

b. 3 pecks to pints

A peck, which equals 16 dry pints in imperial and American usage, is a unit of dry volume.

1 peck = 16 pints

3 pecks = 3 × 16 = 48 pints

c. 97 quarts to bushels

As we know, 1 bushel = 32 quarts

1 quart = 1/32 bushel

97 quarts = 97/32 ≅ 3.03 bushels

d. 1,120 quarts to pecks

A peck is an imperial and American customary dry volume measurement unit that is equal to 8 dry quarts.

1 peck = 8 quarts

So, 1 quart = 1/8 peck

1120 quarts = 1120/8 pecks = 140 pecks

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Given : Regular price of MP3 player was $200. It was marked down by $60.

Required: Percent discount

Explanation:

Marked Price = $200

Discount given = $60

So, percent discount =

Final answer : Percentage discount is 30%

A number is stated mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. The fraction of the counters that Lesley gets is 5/9.

A number is stated mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

A fraction exists a quantity that exists not a whole number. In Math's, a fraction usually contains a numerator and a denominator.

The fraction of the counters that Lesley gets

= number of counters she gets / total number of counters

= 10/18 = 5/9

Therefore, the fraction of the counters that Lesley gets 5/9.

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a) A vertical analysis of the income statement for AT&T is as follows:

                                                      AT&T        Percent

Revenue                                     $132,447        100%

Cost of Services (Expenses)         60,611        45.8%

Selling & Marketing Expense      39,697       30.0%  

Depreciation & other expenses 20,393        15.4%

Operating Income                       $11,746         8.9%

b) A vertical analysis of the income statement for Verizon is as follows:

                                                    Verizon      Percent

Revenue                                     $127,079       100%

Cost of Services (Expenses)         49,931        39.3%

Selling & Marketing Expense        41,016       32.3%

Depreciation & other expenses   16,533       13.0%

Operating Income                      $19,599       15.4%

A financial statement vertical analysis is a comparison of each line item on the financial statement as a percentage of the base figure.

For the income statement, the base figure is the revenue, which is set to 100%.  For the balance sheet, the base figure is the total assets or total liabilities and equity, which are set to 100%.

The vertical analysis uses the following formula = Financial statement line item divided by the total base figure X 100.

                                                      AT&T     Percent

Revenue                                     $132,447  100% ($132,447/$132,447 x 100)

Cost of Services (Expenses)         60,611  45.8% ($60,611/$132,447 x 100)

Selling & Marketing Expense      39,697  30.0% ($39,697/$132,447 x 100)

Depreciation & other expenses 20,393   15.4% ($20,393/$132,447 x 100)

Operating Income                       $11,746    8.9% ($11,746/$132,447 x 100)

                                                    Verizon    Percent

Revenue                                     $127,079  100% ($127,079/$127,079 x 100)

Cost of Services (Expenses)         49,931   39.3% ($49,931/$127,079 x 100)

Selling & Marketing Expense        41,016  32.3% ($41,016/$127,079 x 100)

Depreciation & other expenses   16,533  13.0% ($16,533/$127,079 x 100)

Operating Income                      $19,599  15.4% ($19,599/$127,079 x 100)

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We get 1.37 when we evaluate log 23.6

Given,

log 23.6

We have to evaluate this using a calculator or desmos.

Desmos:

Desmos is a free math teaching and graphing application that is accessible on the web, iOS, and Android. There are classroom activities available to assist students in learning about a number of arithmetic concepts in addition to graphing equations.

Evaluation of logarithms:

You can use a calculator to assess logarithms by utilising the change of base formula, M = log a, M log a, and selecting either the common log or the natural log.

Lets evaluate log 23.6

log 23.6 = 1.372912003

Lets round to 2 decimal places:

log 23.6 = 1.37

That is,

We get 1.37 when we evaluate log 23.6

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Answer:

The answer would be £36

Step-by-step explanation:

12+12+12=36

The expression is equivalent to the 360[tex]k^2[/tex] - 48k

Given the Expression :
8k5∙9k−2(6k2)2

It means

(8k × 5) × 9k - 2(6k × 2) × 2

Now, Multiply the monomials

360[tex]k^2[/tex] - 2(6k × 2) × 2

Again, Multiply the monomials,

= 360[tex]k^2[/tex] - 48k

Hence, The expression is equivalent to the 360[tex]k^2[/tex] - 48k

What is Monomial ?

A monomial is a polynomial, which has only one term. A monomial is an algebraic expression with an single term but can have multiple variable and a higher degree too.

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When we reflect a point along the x-axis, the x coordinate stays the same BUT the y coordinate is negated.

A point (x,y) becomes (x, -y)

et us apply this rule to the points J, A, and R. SThis is shown below:

The graph of the triangle will look like >>>

The quotient of 550six and 50six​ is obtained by the calculation to be   11 six

We know that the result that we obtain after we have carried out a division operation is called a quotient. In this case, we have been required to carry out the operation of division in base six.

We could start by converting the both values to base 10 as follows;

(5 * 6^2) + (5 * 6^1) + (0 * 6^0) = 180 + 30 + 0 = 210 ten

(5 * 6^1) + (0 * 6^0) = 30 + 0 = 30 ten

Then we carry out the division in base ten; 210 ten/30 ten = 7 ten

We convert back to base six to obtain 11 six

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The answer is

(a) the fixed cost when zero items are produced is $500 .

(b) cost for making 25 items is $750  .

(c) the domain and range of cost function is [0,100] and [500,1500] respectively  .

It the question ,

it is given that

the cost function is C(x)=10x+500  

Part(a)

to determine the fixed cost when 0 items are produced

Since 0 items are produced , we substitute the value x=0 in the cost function , we get

C(0)=10(0)+500

= 500

the fixed cost is $500.

Part(b)

to find the cost of making 25 items , we substitute x=25

On substituting the x=25 , we get

C(25)=10(25)+500

= 250+500

=750

the cost for 25 items is $750.

Part(c)

to find the domain of the cost function C(x)

Given that the maximum cost allowed is 1500

So, 1500=10x+500

10x=1500-500

10x=1000

x=100

So minimum 0 items and maximum 100 items can be produced ,

hence the Domain is [0,100]

to find the range

substituting x=0, the cost = $500

on substituting x=100 , the cost = $1500

the Range is [500,1500]

Therefore , (a) the fixed cost when zero items are produced is $500 .

(b) cost for making 25 items is $750  .

(c) the domain and range of cost function is [0,100] and [500,1500] respectively  .

The given question is incomplete , the complete question is

The cost in dollars of making x items is given by C(x)=10x+500. The fixed cost is determined when zero items are produced.

(a) Find the fixed cost for this item.

(b) What is the cost of making 25 items?

(c) Suppose the maximum cost allowed is $1500. What are the domain and range of the cost function, C(x) ?

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The value of x based on the given expression - 2/5x + 3 = 2/3x + 1/3 is 2 1/2

- 2/5x + 3 = 2/3x + 1/3

- 2/5x - 2/3x = 1/3 - 3

(-6 - 10)x / 15 = (1-9) / 3

-16/15x = -8/3

x = - 8/3 ÷ -16 / 15

x = - 8/3 × -15/16

= (-8 × -15) / (3 × 16)

= 120 / 48

= 2 1/2

In conclusion, the solution to the expression - 2/5x + 3 = 2/3x + 1/3 is 2 1/2

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The degree of our simplified answer is =  4

what is polynomials ?

Polynomials are sums of the terms of form k· x^ n, where k is any number  and n is positive integers. polynomials are algebraic expression that consist of variable and coefficient. variables are also sometimes called Indeterminates

an example of polynomial with one variable is x^2+x-12.

so,

after expanding the identity (4t^2-5u)^2, it becomes:

 16t^4+25u^2-40ut^2

as we know in case of polynomial highest degree from the polynomial is consider as the degree of that polynomial.

hence,

           The degree of this equation is 4.

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The common difference of each given sequence is:

a. -3

b. 3

c. -4

d. 5

An arithmetic sequence or progression is defined as a series of numbers whereby each term of the sequence is determined by adding a constant (known as the common difference) to the previous term to get the next term in the sequence.

The common difference is the number that is added to each term of an arithmetic sequence to get the next term of the sequence.

The common difference, d = difference between two consecutive terms in the sequence.

Subtract the first term from the second term or the second term from the third term to get the common difference of the sequence.

a. Common difference = 7 - 11 = 4 - 7 = 1 - 4 = -3.

b. 23 - 20 = 26 - 23 = 29 - 26 = 3.

c. 12 - 16 = 8 - 12 = 4 - 8 = -4.

d. 3 - (-2) = 8 - 3 = 13 - 8 = 5

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Answer:

a. -3

b. 3

c. -4

d. 5

Step-by-step explanation:

Have a good day!

The interest that will be earned when the city is issuing bonds to raise money for a building project is $670.

It should be noted that the formula for the calculation is the interest is given as:

Interest = Principal × Rate × Time / 100

where P = $6700

R = 2%

Time = 5 years

Interest = Principal × Rate × Time / 100

Interest = (6700 × 2 × 5) / 100

= 670

The interest is $670.

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The equivalent expression of 2⁻³ / 2⁻⁵ will be 2².

Option A is true.

What is a mathematical expression?

Expression in math is defined as the collection of the numbers, variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The mathematical expression is,

⇒ 2⁻³ / 2⁻⁵

Now, The rule of exponent is;

[tex]\frac{a^{x} }{a^{y} } \\a^{x} * a^{-y} \\a^{x+ (-y)} \\a^{x-y}[/tex]

Hence, Solve the expression by rule of exponent as;

The mathematical expression is,

⇒ 2⁻³ / 2⁻⁵

⇒ 2⁻³ / 2⁻⁵

⇒ 2⁻³ × 2⁵

⇒ 2⁻³⁺⁵

⇒ 2²

So, 2⁻³ / 2⁻⁵ = 2²

Thus, The equivalent mathematical expression of 2⁻³ / 2⁻⁵ will be 2².

Option A is true.

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According to the graph we have:

1. If the lines A and B cut by the secant D are parallel, then the collateral angles are supplementary, i.e. add up to 180°. In this case:

2. Solve for x:

Answer: x = 24

3. Angle 6 corresponds to angle 3x + 7 so they are equal. So:

Where: x = 24

Substitute the value:

Answer: <6 = 79°

Linear Decay  is the equation .

What is Linear Decay?

Is linear decay exponential?

Scientists are studying the growth of a particular virus in a large community.

The case count, C, in the community after d days can be modeled with the equation: C = 181(1.07)d

This equation is showing Linear Decay .

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Consider the first equation,

This equation passes through (0,-2) and (2,1).

second

This equation passes through (0,2) and (4,0).

Now we can plot the points and join them to get the corresponding lines on the graph as,

It is observed that the two lines intersect at point (2,1).

So the solution to the given equations must be x=2 and y=1.

The correct approaches that can be used to solve the increase in area are

The area of the circle has an estimated increment of 527.52 square mm

The area of a shape is the amount of space on the shape

For all regular quadrilaterals, you multiply the side lengths to determine the area

From the question, the given parameters are:

Previous radius = 42

New radius = 44

Calculate the change in the radius

dr = New radius - Previous radius

Substitute the known values in the above equation

So, we have

dr = 44 - 42

Evaluate

dr = 2

The above method leads to a differentiation problem where dr = 2

So, the correct approaches to the problem include

The area of a circle is

A = πr²

Differentiate

d(A) = 2πr * dr

Where

r = 42

dr = 2

So, we have

d(A) = 2 * 3.14 * 42 * 2

Evaluate

d(A) = 527.52

Hence, the estimated increase in the area is 527.52 square mm

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From the given equation :

This can be written in the slope-intercept form :

where m is the slope

and b is the y-intercept

Rewriting the equation :

The equation will be y = 1/2 x + 4

the slope is m = 1/2

nd the y-intercept is b = 4

Note that parallel lines have the same slope.

So the slope of parallel line is m = 1/2

Perpendicular lines have a slope of negative reciprocal with each other.

So the slope of perpendicular line to this line is m = -2

Equation of parallel line :

we have :

Let's say the line passes at the origin (0, 0)

If a line passes thru the origin, the y-intercept is always b = 0

Therefore, the equation of parallel line is y = 1/2 x

quation of perpendicular line :

we have :

Let's also say that the line passes at the origin (0, 0)

and the y-intercept is also b = 0

he equation of the perpendicular line is yy = -2x

raphing these equations will be :

Original line (Blue)

Parallel line (Orange)

Perpendicular line (Pink)

y-intercepts :

(0, 0) and (0, 4)

[tex] = - 6x - 8x - 5 + 8 \\ = - 14x + 3[/tex]

The third option is the answer!!!

The number of ways that the line up can be possible when eleven bands have volunteered to perform but there is only enough time for five of the bands to play is 462 ways.

Eleven bands have volunteered to participate in the charity concert, but there is only enough time for five of them to do so. This involves combinations and permutations, it should be highlighted.

Therefore, the number of ways that the line up can be possible will be:

n! / (n − r)!

where n is the number of things to choose from and we choose r of them

= 11! / (11 - 5)!5!

= 11! / 6!5!

= 462

There are 462 ways.

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Answer:(5,4) , (4,-2) , (-1,0) , (-2,-4)

Step-by-step explanation: Each input can only have one output

The equation of line is given by y-12=4(x-5).

What is equation of line with slope intercept form?

The equation of a line in point-slope form can be written as

y-y_1=m(x-x_1) where (x_1,y_1) is the points line passes through.

(y-12)=4(x-5)

Where m=4 and x_1=5,y_1=12

Hence, the equation of line is

y=4x-5+12

y=4x+7

The equation of line with the form of slope intercept form is y-12=4(x-5).

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The thing that has occurred if an increase in temperature accompanies a reaction is A. Energy was released.

There are many other types of reactions in chemistry, but the exothermic reaction and the endothermic reaction are the two most common forms.

Respiratory reaction is an example of an exothermic reaction, which is one in which energy is released in the form of heat. Exothermic reactions transfer energy from the system to the environment, raising the ambient temperature.

An endothermic reaction is one in which energy is removed from the system during the process. An example of an endothermic reaction is photosynthesis, in which plants use solar energy to produce food.

Therefore, a chemical reaction is said to be exothermic when it releases energy and causes a change in the environment's temperature.

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