Points that are on the same line are collinear. Use the definition of slope to determine whether the given points are collinear.Prove that the quadrilateral with vertices (2,5),(4,8),(7,6) , and (5,3) is a rectangle.

Answer:

Step-by-step explanation:

Tessellation in trapezoid is possible only if it is rotated

see the fig, attached.

But tessellation in parallelogram is possible both rotated and non rotated

see the fig, attached.

A tessellation or tiling is the seamless application of one or more geometric shapes, known as tiles, to a surface, frequently a plane. Tessellation in mathematics can be expanded to include other geometries and higher dimensions.

A tiling constructed of materials like cemented ceramic hexagons or squares is referred to as a real-world tessellation. Such tilings may be ornamental designs or serve practical purposes such providing long-lasting and water-resistant pavement, floor, or wall coverings.

Tessellations were historically employed in Islamic art, such as the Moroccan architecture and the ornamental geometric tiling of the Alhambra palace. They were also used in Ancient Rome.

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The evaluation of each expression is 3/2 , 1/2.

What is logarithms:

Logarithms are the other way of writing the exponents. A logarithm of a number with a base is equal to another number. A logarithm is just the opposite function of exponentiation. For example, if 102 = 100 then log10 100 = 2.

Hence, we can conclude that,

Log b x = n  or   bn = x

Where b is the base of the logarithmic function.

This can be read as “Logarithm of x to the base b is equal to n”.

In this article, we are going to learn the definition of logarithms, two types of logarithms such as common logarithm and natural logarithm, and different properties of logarithms with many solved examples.

What is properties of logarithms:

Properties of logarithms functions are used to solve logarithm problems. We have learned many properties in basic math's such as commutative, associative and distributive, which are applicable for algebra. In the case of logarithmic functions, there are basically five properties.

This are as follows:

The product property

The quotient property

Power rule

Change of base rule

Reciprocal rule

Now,

3log₉ 3 = [(9)^x]^3 = 3

[(3^2)^x]^3 = 3

x = 3/2

Second part,

1/4 log₉ 81

= 1/2

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The equation in slope-intercept form is x – 5y = -12

Given,

y = -5x – 8

This is in slope-intercept form, y = mx + b

Where, m is slope and b is y-intercept.

Here, m = -5

Perpendicular lines have slopes that are negative reciprocals, [tex]m_{p}[/tex] = -1/m

Here we need equation of line through (-2, 2) with slope -1/-5 = 1/5

y = (1/5)x + b

where (-2, 2) is on the line.

2 = 1/5(-2) + b

2 = -2/5 + b

b = 2 + 2/5 = 12/5

therefore, equation we need is:

y = 1/5x + 12/5

that is,

1/5x – y = -12/5

Multiplying 5 in both sides, we get

5(1/5x) – 5y = (-12/5)5

That is, the equation we need is:

x – 5y = 12

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Step-by-step explanation:

the area of a rectangle is

length × width.

so, in our case

30 × 6 = 180 cm²

be careful to use the right unit for the result. an area is measured in square units based on the units of the given lengths. hence cm² as the given lengths are in cm.

Answer:

-3.4

Step-by-step explanation:

"| |" are absolute value which means |-4| is actually 4. However, if there is a  negative outside of the lines, than the answer is negative.

Experiment: Rolling three dice simultaneously

No of possible outcomes: 6*6*6 = 216

The Sample space is shown below:

(1,1,1) (1,1,2) (1,1,3) (1,1,4) (1,1,5) (1,1,6)

(1,2,1) (1,2,2) (1,2,3) (1,2,4) (1,2,5) (1,2,6)

(1,3,1) (1,3,2) (1,3,3) (1,3,4) (1,3,5) (1,3,6)

(1,4,1) (1,4,2) (1,4,3) (1,4,4) (1,4,5) (1,4,6)

(1,5,1) (1,5,2) (1,5,3) (1,5,4) (1,5,5) (1,5,6)

(1,6,1) (1,6,2) (1,6,3) (1,6,4) (1,6,5) (1,6,6)

(2,1,1) (2,1,2) (2,1,3) (2,1,4) (2,1,5) (2,1,6)

(2,2,1) (2,2,2) (2,2,3) (2,2,4) (2,2,5) (2,2,6)

(2,3,1) (2,3,2) (2,3,3) (2,3,4) (2,3,5) (2,3,6)

(2,4,1) (2,4,2) (2,4,3) (2,4,4) (2,4,5) (2,4,6)

(2,5,1) (2,5,2) (2,5,3) (2,5,4) (2,5,5) (2,5,6)

(2,6,1) (2,6,2) (2,6,3) (2,6,4) (2,6,5) (2,6,6)

(3,1,1) (3,1,2) (3,1,3) (3,1,4) (3,1,5) (3,1,6)

(3,2,1) (3,2,2) (3,2,3) (3,2,4) (3,2,5) (3,2,6)

(3,3,1) (3,3,2) (3,3,3) (3,3,4) (3,3,5) (3,3,6)

(3,4,1) (3,4,2) (3,4,3) (3,4,4) (3,4,5) (3,4,6)

(3,5,1) (3,5,2) (3,5,3) (3,5,4) (3,5,5) (3,5,6)

(3,6,1) (3,6,2) (3,6,3) (3,6,4) (3,6,5) (3,6,6)

(4,1,1) (4,1,2) (4,1,3) (4,1,4) (4,1,5) (4,1,6)

(4,2,1) (4,2,2) (4,2,3) (4,2,4) (4,2,5) (4,2,6)

(4,3,1) (4,3,2) (4,3,3) (4,3,4) (4,3,5) (4,3,6)

(4,4,1) (4,4,2) (4,4,3) (4,4,4) (4,4,5) (4,4,6)

(4,5,1) (4,5,2) (4,5,3) (4,5,4) (4,5,5) (4,5,6)

(4,6,1) (4,6,2) (4,6,3) (4,6,4) (4,6,5) (4,6,6)

(5,1,1) (5,1,2) (5,1,3) (5,1,4) (5,1,5) (5,1,6)

(5,2,1) (5,2,2) (5,2,3) (5,2,4) (5,2,5) (5,2,6)

(5,3,1) (5,3,2) (5,3,3) (5,3,4) (5,3,5) (5,3,6)

(5,4,1) (5,4,2) (5,4,3) (5,4,4) (5,4,5) (5,4,6)

(5,5,1) (5,5,2) (5,5,3) (5,5,4) (5,5,5) (5,5,6)

(5,6,1) (5,6,2) (5,6,3) (5,6,4) (5,6,5) (5,6,6)

(6,1,1) (6,1,2) (6,1,3) (6,1,4) (6,1,5) (6,1,6)

(6,2,1) (6,2,2) (6,2,3) (6,2,4) (6,2,5) (6,2,6)

(6,3,1) (6,3,2) (6,3,3) (6,3,4) (6,3,5) (6,3,6)

(6,4,1) (6,4,2) (6,4,3) (6,4,4) (6,4,5) (6,4,6)

(6,5,1) (6,5,2) (6,5,3) (6,5,4) (6,5,5) (6,5,6)

(6,6,1) (6,6,2) (6,6,3) (6,6,4) (6,6,5) (6,6,6)

Favorable outcome (three similar numbers, i.e. getting an identical number in all the three dice) : 6

Probability = No of favorable outcomes/Total no of outcomes = 6/216 = 0.0278

The quotient in this Carl multiplies the both value instead of dividing so that is the mistake that made by Carl.

The quotient of 4 divided by 2 1/3 and also explain the mistake that done by Carl

The value of 4  1/3 is 14/3

And the value of 2  1/3 is 7/3

So then we divide 4 2/3 by 2 1/3 is,

[tex]\frac{14 / 3}{7 / 3}=\frac{14}{3} \frac{3}{7}[/tex]

      =2

Carl's mistake is thinking that his quotient (2) is equal to the value of the terms involved in it. In fact, 2 is just a multiplier for 7/3 and doesn't have any specific value associated with it.

Hence, this is the quotient in this Carl multiplies the both value instead of dividing so that is the mistake that made by Carl.

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The probability that the event that the second part is defective will be 0.0564.

From the information, the bin of 50 manufactured parts contains 3 defective parts and 47 nondefective

Therefore, the probability of having a defective and non defective parts will be:

= 47/50 × 3/50

= 0.94 × 0.06

= 0.0564

Therefore, the probability that the event that the second part is defective will be 0.0564.

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The total salary for the month will be $4535

From the information, Alex earns a weekly base salary of $650 as a car salesman. He also earns a 9% commission on his monthly sales after the first $10,000.

If he sold 7 cars whose average price was $4,500 each. The total amount will be:

= $4500 × 7.

= $31500

The commission will be

= 9% × ($31500 × $10000)

= 9% × $21500

= $1935

The total salary for the month will be:

= ($650 × 4) + $1935

= $4535

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Answer:

4 × 3

Step-by-step explanation:

4 is being added 3 times.

Dan is left with £66 after the total spending.

An expense is the amount of operations incurred by a business in order to generate revenue.

As for the given question;

The total earning per week is £495.

Spending on rent is 1/5.

1/5 of  £495 = 495/5 = 99

Spending on rent is  £99.

Now, spending on food is 2/3 of  £495.

Food spending = (2/3)×495 = £330

Let the money left is 'x'.

Total expenses = Total income

food cost + rent cost + saving = 495

99 + 330 + x = 495

x = 495 - 429

x = 66

Thus, the savings by the Dan is  £66.

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The temperature will be represented by the negative number -21.7 degrees.

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

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that the quantity is a positive or negative number the record low temperature for a date is 21.7 degrees below zero.

T = 0 - 21.7

T = -21.7 degrees

Therefore, the temperature will be represented by the negative number -21.7 degrees.

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Answer: 23 + 2c

Step-by-step explanation:

     To write an expression, we will look at the wording of the phrase given;

The sum of ➜ addition

twice Chau's height ➜ 2c

The sum of 23 and twice Chau's height.

23 + 2c

The given sequence is geometric, with common ratio = 0.1.

A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.

Given: 7, 0.7, 0.07, 0.007,...

Here, 0.7/7 = 0.07/0.7 = 0.007/0.07 = 0.1

That is, the given sequence follows the only necessary condition required for a sequence to be geometric.

Hence, The given sequence is geometric, with common ratio = 0.1.

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The width of the lake on the scale drawing is 30 cm.

Based on the given conditions, formulate 1500*2/100

Cross out the common factor: 15*2 = 30

Get the result as 30 cm

An object is enlarged in a scale drawing. An expansion increases or decreases the size of an object by multiplying each of its lengths by a scale factor. Typically, a ratio is used to describe the scale of a drawing. a representation of a real thing with correct sizes that have been scaled back or blown up slightly (called the scale). The scale is represented by the length in the drawing, a colon (":"), and then the actual length that corresponds to it.

Hence, the width of the lake on the scale drawing is 30 cm.

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The solution of the given rational equation [tex]\frac{x}{x+1}+\frac{3}{x+4}=\frac{x+3}{x+4}[/tex] is x = 0

In this question, we have been given a rational equation.

[tex]\frac{x}{x+1}+\frac{3}{x+4}=\frac{x+3}{x+4}[/tex]

We need to find the solution of the above rational equation.

[tex]\frac{x}{x+1}+\frac{3}{x+4}\\\\=\frac{x(x+4)+3(x+1)}{(x+1)(x+4)}\\\\ =\frac{x^{2}+4x+3x+3 }{(x+1)(x+4)} \\\\=\frac{x^{2} +7x+3}{(x+1)(x+4)}[/tex]

So given equation would be,

[tex]\frac{x^{2} +7x+3}{(x+1)(x+4)}=\frac{x+3}{x+4}\\\\x^{2} +7x+3=(x+1)(x+3)\\\\x^{2} +7x+3=x^{2} +x+3x+3\\\\x^{2} +7x+3=x^{2} +4x+3\\\\7x-4x=3-3\\\\3x=0\\\\x=0[/tex]

Therefore, the solution of the given rational equation [tex]\frac{x}{x+1}+\frac{3}{x+4}=\frac{x+3}{x+4}[/tex] is  x = 0

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The required number of combinations is 24.

Given that,
To make an outcome tree to show all possible combinations. you have three pairs of shorts four shirts, flip-flops, and sneakers.

In arithmetic, combination and permutation are two different ways of grouping elements of a set into subsets. In a combination, the components of the subset can be recorded in any order. In a permutation, the components of the subset are listed in a distinctive order.

Here,

                                       flip flops                  
         short 1                    short 2                    short 3
Shirt 1                shirt 2                      shirts 3                  shirts 4
Number of combinations = 12
                                         
                                       sneakers
         short 1                    short 2                    short 3
Shirt 1                shirt 2                      shirts 3                  shirts 4
Number of combinations = 12

Total number of combination = 12 + 12 = 24

Thus, the required number of combinations is 24.

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The volume of the solid generated by revolving the region bounded by the given curve and lines about the x-axis is V = 8π/3

The volume of a solid, given by the function f(x), over an interval between a and b, is given by:

[tex]V = \pi \int\limits^a_b {f(x)^2} \, dx[/tex]

To find the area, integrate around that area. We're revolving around the x-axis so the area will be a circle;

V = ∫A(x)dx =  ∫(πr²)dr

Then we subtract them from each others.

∫(πr₂² - πr₁²)dr

Now substitute the value and integrate;

∫(π(2)² - π(2x)²)dr

∫(4π - 4πx²)dr

4π∫(1 - x²)dr

Now integrate from 0 to 1 since that's where our boundary is.

V = 4π∫(1 - x²)dr = 8π/3

Therefore, The volume of the solid generated by revolving the region bounded by the given curve and lines about the x-axis is V = 8π/3

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The force on one of the ends due to hydrostatic pressure is 332.8lb.

How is a hydrostatic pressure produced?

The force on one of the ends due to hydrostatic pressure is 332.8lb

Data;

Density = 62.4 lb/ft^3

length = 4ft

radius = 2ft

Force Due to Pressure

The force due to hydrostatic pressure can be calculated as

From the attached diagram

F = Pressure * area

density = 62.4 lb/ft³

depth of water = 2- y

pressure  = ( 2- y ) ( 62.4)

                = 124.8 - 62.4

We can proceed as

x² + ( y - 2)² = 2²

x² = 4 - ( y - 2)²

x = ± √4y - y²

this implies that

2x = 2 √4y - y²

The area is given as

δA = ( 2x) * δy

δA = 2√4y - y² δy

The force would be given by

δF = ( 2- y ) ( 62.4) (2 √ 4y - y²)δy

The total force is given by

F = [tex]\int\limits^2_0 {( 2 - y)} \, (62.4) ( 2\sqrt{4y - y^{2} } dy[/tex]

F = 124.8 [tex]\int\limits^2_0 {( 2-y)} \,( \sqrt{4y - y^{2} } dy[/tex]

F = 124.8 [tex][ -\frac{1}{3} y( y- 4 ) ( \sqrt{4y - y^{2} }[/tex]

F = 124.8 [tex][ -\frac{1}{3} (2) ( 2-4) \sqrt{4(2) - 2^{2} }[/tex]

F = 332.8lb

The force on one of the ends due to hydrostatic pressure is 332.8lb

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The simplification of the given each sum or difference of the expression [tex]\frac{5x}{x^{2} -x-6} + \frac{4}{x^{2} +4x+4}[/tex] is equal to [tex]\frac{5x^{2} +14x-12}{(x-3)(x+2)^{2}}[/tex] , restriction on the variables is given by x ≠ 3 , x≠ -2.

As given in the question,

Given expression : [tex]\frac{5x}{x^{2} -x-6} + \frac{4}{x^{2} +4x+4}[/tex]

Simplify the given expression by taking least common multiple,

[tex]\frac{5x}{x^{2} -x-6} + \frac{4}{x^{2} +4x+4}\\\\\\= \frac{5x}{x^{2} -3x+2x-6} + \frac{4}{(x+2)^{2}} \\\\\\= \frac{5x(x+2)+4(x-3)}{(x-3)(x+2)^{2}}\\ \\=\frac{5x^{2} + 14x-12}{(x-3))x+2)^{2}}[/tex]

Restriction on the variables is given by x ≠ 3 , x≠ -2.

Therefore, simplification of the given each sum or difference of the expression [tex]\frac{5x}{x^{2} -x-6} + \frac{4}{x^{2} +4x+4}[/tex] is equal to [tex]\frac{5x^{2} +14x-12}{(x-3)(x+2)^{2}}[/tex] , restriction on the variables is given by x ≠ 3 , x≠ -2.

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A scale drawing of a school bus has a scale of ; inch to 6 feet. If the length of the school bus is 4, inches on the scale drawing, what'is the actual length of the bus?

Answer:

a=−2 and b=−2

Step-by-step explanation:

Let's solve your system by substitution.

7a−12b=10;−2a−4b=12

Step: Solve7a−12b=10for a:

7a−12b=10

7a−12b+12b=10+12b(Add 12b to both sides)

7a=12b+10

7a/7=12b+10/7

(Divide both sides by 7)

[tex] \sf \: a = \frac{12}{7} b + \frac{10}{7} [/tex]

Step: Substitute: 12/7b+10/7 for a in−2a−4b=12:

−2a−4b=12

−2(12/7b+10/7)−4b=12

−52/7b + −20/7=12(Simplify both sides of the equation)

−52/7b+−20/7+20/7=12+20/7

(Add 20/7 to both sides)

−52/7b=104/7

[tex] \sf \: \frac{ \frac{ - 52}{7}b }{ \frac{ - 52}{7} } = \frac{ \frac{104}{7} }{ \frac{ - 52}{7} } [/tex]

(Divide both sides by (-52)/7)

b=−2

Step: Substitute −2 for b in a =12/7b+10/7:

a=/12/7b+10/7

a=12/7(−2)+10/7

a=−2(Simplify both sides of the equation)

we  know she poured already 2 qts of a 62% sugar solution, hmmm how much will that be in quarts?  well, just (62/100) * 2 = 1.24 quarts.

we also know she wants to mixed say "x" quarts of a 38% sugar solution, how many quarts will that be?  well, (38/100) * x = 0.38x.

let's make a quick table from that as well as including the desired mixture.

[tex]\begin{array}{lcccl} &\stackrel{solution}{quarts}&\stackrel{\textit{\% of }}{amount}&\stackrel{\textit{qts of }}{amount}\\ \cline{2-4}&\\ \textit{62\% solution}&2&0.62&1.24\\ \textit{38\% solution}&x&0.38&0.38x\\ \cline{2-4}&\\ desired~mixture&y&0.54&0.54y \end{array}\qquad \begin{cases} ~\hfill 2+x&=y\\\\ 1.24 + 0.38x &= 0.54y \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{substituting on the 2nd equation}}{1.24 + 0.38x ~~ = ~~ 0.54(\underset{y}{2 + x})}\implies 1.24+0.38x=1.08+0.54x \\\\\\ 0.16+0.38x=0.54x\implies 0.16=0.16x\implies \cfrac{0.16}{0.16}=x\implies \stackrel{qts}{1}=x[/tex]

Using the given information, the equation of the circle with radius 2 and center at (-1 , -5) is (x + 1)^2 + (y + 5)^2 = 4.

The general form of the equation of  circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.

Given the radius and center of the circle, substitute these values to the general form of the equation of the circle.

(x - h)^2 + (y - k)^2 = r^2

where (h , k) = (-1 , -5)

r = 2

(x - -1)^2 + (y - -5)^2 = 2^2

(x + 1)^2 + (y + 5)^2 = 4

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Answer:

5 points

Step-by-step explanation:

because yes

Answer:

I think its 3 20.

Step-by-step explanation:

The formula a=m-a represents the actual cost, a, of an item with original price loss m after a coupon for in dollars off is applied.

n = m - a

In light of this:

The formula a = m - n's expression

where;

a = the item's real cost

m = initial cost

n = the monetary value of the coupon

The goal is to figure out how much the coupon is worth.

To calculate the quantity of the coupon, we must subtract n from the above statement, where n is the number of coupons in dollars.

As a result, if a = m - n

a + n Equals m

n = m - a

Profit and loss are expressions used to determine whether or not a sale is economic. we use these expressions frequently. However, the difference between the two is appertained to as profit, If the selling price is advanced than the cost price. However, the difference is appertained to as the loss, If the selling price is lower than the cost price. The cost price of a product is the price at which it's bought.

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