Complete the following indirect proof (proof by contradiction).
Given: Adjacent angles LA and ZB, formed by the intersection of two lines
Prove: At least one of the angles LA and B has measure 90° or greater

Step-by-step explanation:

please refer to the 3 pages of sketch for details

Sales Tax = $3.00

The total amount paid by the group was $48.15

The amount of the sales tax can be calculated by multiplying the pre-tax bill of $37.50 by the sales tax rate of 8%:

Sales tax = $37.50 * 8% = $3.00

The total amount paid including tax and tip can be calculated by adding the amount of the sales tax to the pre-tax bill and then calculating the tip on the new total:

Total = $37.50 + $3.00 + ($37.50 + $3.00) * 18% = $37.50 + $3.00 + $7.65 = $48.15

So the total amount paid by the group was $48.15.

So the expanded form of the odometer reading 35,467.219 is:

5 x 1000 + 3 x 100 + 4 x 10 + 6 x 1 + 7 x 1/10 + 2 x 1/100 + 1 x 1/1000 + 9 x 1/10000

A number is divided up into its place values, then expanded to represent the value of each digit. The enlarged form of 943 is shown as an example. 9 blocks of 100s Three blocks of ones, and four blocks of tens. Nine hundred increased to 4 tens, 3 ones. Form: 900 + 40 + 3.

The accepted method for representing both integer and non-integer numbers is the decimal numeral system. It is the expansion of the Hindu-Arabic numeral system to non-integer values. Decimal notation is the term used to describe the method of representing numbers in the decimal system.

In expanded form, the odometer reading of 35,467.219 can be broken down into the value of each digit in the number.

5 stands for 5 x 1,000 miles

3 stands for 3 x 100 miles

4 stands for 4 x 10 miles

6 stands for 6 x 1 miles

7 stands for 7 x 1/10 of a mile

2 stands for 2 x 1/100 of a mile

1 stands for 1 x 1/1000 of a mile

9 stands for 9 x 1/10000 of a mile

So the expanded form of the odometer reading 35,467.219 is:

5 x 1000 + 3 x 100 + 4 x 10 + 6 x 1 + 7 x 1/10 + 2 x 1/100 + 1 x 1/1000 + 9 x 1/10000

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The additional expense brought on by reducing the quantity is known as the cost. An additional expense "at the margin" is another name for this. The extra income that results from raising the supply is known as the marginal revenue.

Profit is defined as the difference of revenue and cost (determined by deducting cost from revenue. when revenue exceeds operational expenses, the difference between them is called the operating profit.

The additional money "at the margin" is another name for this.The money left over after a corporation pays its bills and expenses is known as its profit. Costs are the out-of-pocket expenditures comes to making, producing, and marketing the company's goods and services.

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Answer:

(-2,5), refer to the step-by-step. Feel free to comment any questions you may have!

Step-by-step explanation:

Given the system of equation, [tex]\left \{ {{x+6y=28} \atop {2x-3y=-19}} \right.[/tex], solve by elimination.

[tex]\left \{ {{-2(x+6y=28)} \atop {2x-3y=-19}} \right.[/tex] , multiply the top equation by -2.

We get,  [tex]\left \{ {{-2x-12y=-56} \atop {2x-3y=-19}} \right.[/tex]

[tex]+ {{-2x-12y=-56} \atop {2x-3y=-19}} \right.[/tex], add the equations together.

We get, [tex]-15y=75[/tex], we just eliminated the variable, x, we can now solve this equation for y.

[tex]-15y=-75 = > y=\frac{-75}{-15}[/tex], [tex]y=\frac{75}{15} = > y=5[/tex]

We just found the value y, which is y=5. Now we can take this value and plug it into y for either of the two original equations and solve for x. I will take the top equation...

[tex]x+6y=28 = > x+6(5)=28 = > x+30=28[/tex], subtract the value, 30, from both sides. We get, [tex]x=-2[/tex].

We found the value x, x=-2.

Thus the solution to the given system of equations is (-2,5).

Answer:

(-2, 5)

Step-by-step explanation:

Given linear system of equations:

[tex]\begin{cases}x+6y=28\\2x-3y=-19\end{cases}[/tex]

To solve by the method of elimination, first multiply the first equation by -2:

[tex]\implies -2 (x+6y=28)[/tex]

[tex]\implies -2x-12y=-56[/tex]

Add this to the second equation to eliminate the term in x:

[tex]\begin{array}{lrcrcr}& 2x & - & 3y & = & -19\\+\vphantom{\dfrac12}&(-2x & - & 12y & = & -56\\\cline{2-6}&\vphantom{\dfrac12}&- & 15y & = &-75\end{array}[/tex]

Solve the expression for y:

[tex]\implies -15y=-75[/tex]

[tex]\implies y=5[/tex]

Substitute the found value of y into the expression for x and solve for x:

[tex]\implies x=28-6(5)[/tex]

[tex]\implies x=28-30[/tex]

[tex]\implies x=-2[/tex]

Check by substituting the found values of x and y into both equations.

Equation 1

[tex]\implies -2+6(5)=-2+30=28[/tex]

Equation 2

[tex]\implies 2(-2)-3(5)=-4-15=-19[/tex]

Hence proving that the solution (-2, 5) is true.

If the mean of 100 nummerical observations is 51.82 then the value of all 100 numbers is 5182.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Given that mean of 100 nummerical observations is 51.82

We need to find the sum of all the observations

The formula to find mean is mean=Sum of observations/ Number of observation

From given mean=51.82

Number of observations =100

Let us take x as sum of all 100 numbers

So 51.82=x/100

Now apply cross multiplication

x=51.82×100

x=5182

Hence, if the mean of 100 nummerical observations is 51.82 then the value of all 100 numbers is 5182.

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A) The ratios for 2021 are as follows:

Rate of return on total asset = (Profit for the year / Total assets) * 100 = (12,605 / 29,935) * 100 = 42%

Profit margin ratio = (Profit for the year / Revenue) * 100 = (12,605 / 55,000) * 100 = 22.9%

Current ratio = (Current assets / Current liabilities) = (17,190 / 7,700) = 2.23:1

Inventory turnover ratio = (Cost of sales / Inventory) = (35,100 / 3,675) = 9.58

Accounts receivable turnover ratio = (Revenue / Receivables) = (55,000 / 4,905) = 11.22

Debt ratio = (Total liabilities / Total assets) = (15,720 / 29,935) = 52.6%

Times interest earned = (EBIT / Interest) = (12,715 / 1,560) = 8.14

B) Based on the above industry averages:

profitability: the company's profit margin ratio of 22.9% is lower than the industry average of 40%, which suggests that the company's profitability is lower than the industry average.

liquidity: the company's current ratio of 2.23:1 is lower than the industry average of 2.5:1, which suggests that the company's liquidity is lower than the industry average.

use of financial gearing: the company's debt ratio of 52.6% is higher than the industry average of 6%, which suggests that the company is more heavily leveraged than the industry average.

In summary, the company profitability is lower than the industry average, liquidity is lower than the industry average, and the company is more heavily leveraged than the industry average.

A company's profitability refers to its ability to generate a profit and return on investment. It is a measure of how well a company is able to generate revenue, control costs, and manage its assets and liabilities. Profitability ratios are used to evaluate a company's financial performance and to compare it to other companies in the same industry. Some of the most common profitability ratios include:

Gross profit margin: measures the percentage of revenue that remains after accounting for the cost of goods sold. It's calculated by dividing gross profit by revenue.

Operating profit margin: measures the percentage of revenue that remains after accounting for all operating expenses. It's calculated by dividing operating profit by revenue.

Net profit margin: measures the percentage of revenue that remains after accounting for all expenses, including taxes and interest. It's calculated by dividing net profit by revenue.

Return on assets (ROA): measures how efficiently a company is using its assets to generate a profit. It's calculated by dividing net income by total assets.

Return on equity (ROE): measures how efficiently a company is using shareholder's equity to generate a profit. It's calculated by dividing net income by shareholder's equity.

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Answer:

Step-by-step explanation:buordjkdkeek

The amount of money that was spent is $120.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split.

In this case, the women went to Shopping and first she spent 4/5th of all money she had in her purse, and then she lost 2/3 of what was remaining.

The fraction of money left will be:

= 1 - 4/5 - (2/3 × 1/5)

= 1 - 4/5 - 2/15

= 1/15

Since she had $10 left the original amount will be:

= $10 ÷ 1/15

= $10 × 15

= $150

The amount spent will be:

= 4/5 × $150

= $120

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Answer:

Dylan should purchase the 10-lens boxes in packs of 4 for $120, as this is the better deal. This option provides 40 lenses for $120, which works out to be $3 per lens. The 8-lens boxes in packs of 2 for $52 only provides 16 lenses for $52, which works out to be $3.25 per lens Therefore, the 10-lens boxes in packs of 4 is the better deal.

Step-by-step explanation:

Answer:

he should buy the 10-lens boxes in packs of 4 for $120

Step-by-step explanation:

Answer:

The answer is zero

Step-by-step explanation:

Hope it helps

Answer:

1) Let D be the number of dimes and Q be the number of quarters. We can set up the following system of equations to represent the given information:

D + Q = 65

0.1D + 0.25Q = 10.70

The first equation represents the total number of coins Victoria has, and the second equation represents the total value of those coins in dollars. Solving this system of equations will give us the number of dimes and quarters Victoria has.

2) Let M be the number of hours Max spends mowing lawns and T be the number of hours he spends tutoring. We can set up the following system of equations to represent the given information:

M + T = 14

12M + 15T = 192

The first equation represents the total number of hours Max worked over the weekend, and the second equation represents the total amount of money he made during that time. Solving this system of equations will give us the number of hours Max spent on each job.

The length of the side CD is 5.195 cm and the Area of ΔABC is 31.17 cm²

The basic trigonometric functions are;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

From the given triangle ABC, we can see that it is a right angle triangle where ∠ACD = 60°, and as such, ∠CAD = 30°.

Thus;

BC/AC = tan 30°

6/AC = 0.5774

AC = 10.39cm

Thus;

CD/AC = cos 60

CD = 10.39 * 0.5

CD = 5.195 cm

Formula for area of a triangle is;

Area = ¹/₂ * base * height

Area = ¹/₂ * 6 * 10.39

Area = 31.17 cm²

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Answer:

Step-by-step explanation:

If Colton makes a guaranteed salary of $500 per week, and he is paid a commission of 10% on top of that for a total of $1075 in sales, he would make an additional $107.50 in commission (1075 x .1 = 107.5). In total, Colton would make 500 + 107.5 = $607.50 in a week where he made $1075 in sales.

Answer:14 a

Step-by-step explanation:

The explanation is that it is E

The three ways to purchase a vehicle include: (1) On lease  (2) On hire purchased and (3) On cash basis

A vehicle can be purchased on the following ways:

Advantages include:

Disadvantages:

Additional expenses include

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Answer:

25

Step-by-step explanation:

5x5 = 25

Answer:

25

Step-by-step explanation:

Let's go through our times tables really quick!

5x1 = 5 (5 + 0)

5x2 = 10 (5 + 5)

5x3 = 15 (5 + 5 + 5 [10 + 5])

5x4 = 20 (5 + 5 + 5 + 5 [15 (5x3) + 5)

As we can see, if we know 5x4, we can easily find 5x5! It's just 5x4 + 5

So, 5x5 is 25

Hope this helped!

Answer:

70

Step-by-step explanation:

for every 5 $20 notes is $100 70 notes is $1400 and the other 20 is $2000 which makes 3400

Answer:

Step-by-step explanation:

0.124

The line that passes through these two points is y=x-2

Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.

Given here function whose graph contains the points (9, 7) and (4, −8)

Thus using the two point formula for a line we get the equation as              y-7=(x-9)

y=x-2

Hence, The line that passes through these two points is y=x-2

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Work Shown:

area = length*width

length = area/width

length = 3162/51

length = 62 meters

a) The process to find the limit is given as follows:

b) When a function does not have any discontinuity at x = 1, the procedure is the same as calculating f(1), however in the case of a discontinuity, such as for f(x), the discontinuity first has to be removed, if possible.

The first step in calculating the limit of a function is calculating the numeric value of the function at the value of x which the function approaches.

Hence:

For the case of g(x), there is a discontinuity, meaning that the function has to be factored to remove the discontinuity.

Applying the subtraction of perfect squares, we have that:

x² - 1 = (x - 1)(x + 1).

Then:

g(x) = (x - 1)(x + 1)/(x - 1) = x + 1.

Meaning that the limit is then calculated as follows:

lim x -> 1 g(x) = lim x->1 x + 1 = 1 + 1 = 2.

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We can conclude the proof of inequality : 3 (m + n)! ≥ m! + n! below.

In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. Mathematically, we can write -

[tex]$n! = n \times (n-1) \times \dots \times 1[/tex]

Given is the inequality -

3 (m + n)! ≥ m! + n!

We have -

3 (m + n)!

3 {(m + n)(m + n - 1)(m + n - 2) ....... (3)(2)(1)}

3 {m² + mn - m + nm + n² - n}(m + n + 2) ...... (3)(2)(1)

3 {m² + n² - m - n + 2mn}(m + n + 2) ........ (3)(2)(1)

3 {m(m - 1) + n(n - 1) + 2mn}(m + n + 2) ....... (3)(2)(1)

Now, for (m! + n!) --

(m! + n!) = m(m - 1) .... (3)(2)(1) + n(n - 1) ..... (3)(2)(1)

It can be seen that -

3 {m(m - 1) + n(n - 1) + 2mn}(m + n + 2) ....... (3)(2)(1) ≥

m(m - 1) .... (3)(2)(1) + n(n - 1) ..... (3)(2)(1)

Hence, it can be seen that -

3 (m + n)! ≥ m! + n!

Therefore, we can conclude that 3 (m + n)! ≥ m! + n!.

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Answer:

y = 10

Step-by-step explanation:

given DEFG = SPQR

QR = FG

=> 2x - 4 = 12

=> 2x = 16

=> x = 8

angle PQR = EFG

=> 6y + x = 68

=> 6y + 8 = 68

=> 6y = 60

=> y = 10

Taking into account the definition of a system of linear equations, the number of sodas and hot dogs sold is 92 and 45 respectively.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

The values of the unknowns must be found, with which, when replaced, they must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that:

You know:

The system of equations to be solved is

x + y= 137

x= y + 47

To solve a system of equations by the substitution method, an unknown quantity must be solved in one of the equations. Substitute the expression of this unknown in the other equation, obtaining an equation with only one unknown and thus be able to solve it. The value obtained is substituted in the equation in which the unknown appeared. In this way, the two values obtained constitute the solution of the system.

In this case, substituting the second equation in the first one you get:

y + 47 + y= 137

Solving:

y+ y= 137 -47

2y= 90

y= 90÷2

y= 45

Replacing this value in the second equation, you get:

x= 45 + 47

x= 92

Finally, the number of sodas sold is 92 and the number of hot dogs sold is 45.

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[tex]\dfrac{s}{4} +5=13[/tex]

Simplify:

[tex]\dfrac{1}{4} s+5=13[/tex]

Subtract 5 from both sides:

[tex]\dfrac{1}{4} s+5-5=13-5[/tex]

[tex]\dfrac{1}{4} s=8[/tex]

Multiply both sides by 4:

[tex]4\times(\dfrac{1}{4} s)=4\times(8)[/tex]

[tex]\fbox{s = 32}[/tex]

s = 32.

[tex]\frac{s}{4} +5=13[/tex]

[tex]\frac{s}{4} +5-5=13-5\\ \\\frac{s}{4} =8[/tex]

[tex]\frac{s}{4}*4 =8*4\\ \\s=32[/tex]

If the result is correct, then the equation should return the same value of both sides of the equal symbol (=) when we substitute the variable "s" by it's calculated value, 32.

[tex]\frac{(32)}{4} +5=13\\ \\8+5=13\\ \\13=13[/tex]

As you can tell, the same number appears on both sides of the equal symbol, this means that the result is correct!

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A. A function that represents the attendance after t years can be written as y = 20,000(1 + 0.05t)

What does a math function mean?

a mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).

This function represents the initial attendance of 20,000, multiplied by 1 + 5% increase each year (0.05) times the number of years (t).

B. To find out about how many people will attend the festival in the fifth year, we can substitute t = 5 into the function.

y = 20,000(1 + 0.05 * 5)

y = 20,000(1 + 0.25)

y = 20,000(1.25)

y = 25,000

So, approximately 25,000 people will attend the festival in the fifth year.

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The value of x and y in equations 17x - y = 40 and 2x + 4y = 50 are x = 3 and y = 11.

What is equation ?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.

17x - y = 40  ⇒ (1)

2x + 4y = 50 ⇒ (2)

(1)* 4

68x - 4y = 160

Adding equation (1) and (2)

68x - 4y = 160

2x + 4y = 50

⇒ 70 x = 210

        x = 3

Substituting the value of x in equation (1)

17*3 - y = 40

51 - y = 40

-y = 40 - 51

-y = -11

y = 11

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Using equations, the weights of the four fish are as follows:

Equations are mathematical statements showing the equality of two mathematical expressions.

Using the equation sign (=), equations depict that expressions are equal or equivalent.

The total weight of the four fish = 1,032

Let the weight of the Amberjack = x

Weight of the Tarpon = 2x

Weight of the White Marlin = 4x (2 x 2x)

Weight of the Tuna = 5x

x + 2x + 4x + 5x = 1,032

12x = 1,032

x = 86

Amberjack = 86 pounds (x)

Tarpon = 172 pounds (2x)

White Marlin = 344 pounds (4x)

Tuna = 430 pounds (5x)

Total weight = 1,032 pounds (86 + 172 + 344 + 430)

Thus, we solved the weight of each fish using equations.

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How much did each fish weigh?