GEOMETRY FIND LENGTH OF THIRD SIDE!!

Answer: The equation of the perpendicular bisector of AB is 3x+7y-77=0

A line equation is an algebraic representation of a set of points that together form a line in a coordinate system. Multiple points that together form a line on the coordinate axis are represented as a set of x,y variables to form an algebraic equation called a one-line equation.

Equation of line⇒[tex](y-y1)=\frac{(y2-y1)}{(x2-x1)} (x-x1)[/tex]

Midpoint of line⇒[tex]\frac{(x1+x2)}{2}, \frac{(y1+y2)}{2}[/tex]

Step-by-step explanation:

Line CD⊥AB

Equation of AB⇒ [tex]\frac{y+10}{x-4} =\frac{15-1}{10-4} \\[/tex]

                        ⇒ [tex]\frac{y+10}{x-4} =\frac{14}{6}[/tex]

                        ⇒ [tex]\frac{y+10}{x-4} =\frac{7}{3}[/tex]

                        ⇒ 3(y+10)=7(x-4)

                        ⇒ 3y+30=7x-28

                        ⇒ 7x-3y=30+28

                        ⇒ 7x-3y=58

Midpoint of AB⇒  [tex]\frac{4+10}{2} , \frac{1+15}{2}[/tex]

                         ⇒ [tex]\frac{14}{2}, \frac{16}{2}[/tex]

                         ⇒ (7, 8)

Slope of CD⇒  [tex]\frac{-1}{slope of AB}[/tex]

Slope of AB⇒ [tex]\frac{-7}{-3}[/tex]

                   ⇒ [tex]\frac{7}{3}[/tex]

Slope of CD⇒ [tex]\frac{-3}{7}[/tex]

Equation of CD⇒ [tex]y-8=\frac{-3}{7} (x-7)[/tex]

                        ⇒ 7(y-8)=-3(x-7)

                        ⇒ 7y-56=-3x+21

                        ⇒ 3x+7y-56-21=0

                        ⇒ 3x+7y-77=0

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Dwayne's percentage favorite eatery. Overall, the restaurant had 25 specials, with salmon filets accounting for 24% of those. The eatery served 6 salmon filets.

10% is a comparison number that means one tenth of any amount. The hundredth component, one percent (symbolized as 1%), is denoted by 100 percent, whereas 200 percent denotes double the quantity stated. In mathematics, a percentage is a number or ratio that may be expressed as a fraction of 100. If we want to calculate a percentage of a number, we should multiply the result by 100.

Dwayne's favorite eatery. Overall, the restaurant had 25 specials, with salmon filets accounting for 24% of those. The eatery served 6 salmon filets.

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Answer: 180°

Step-by-step explanation:

If given the bearing from B to A, the bearing from A to B can be found using interior angles. Subtract the bearing of B to A from 180° to find the missing interior angle, then use the fact that angles in a full turn add to 360° to find the bearing of A to B.

Answer:

9 years

Step-by-step explanation:

Losing 15 % means 85% remains

  so multiply each year's value by .85 to find the current value

       after 'n'  years it will be  24300 * .85^n

when will it be 5600 ?

    5600 = 24300 * .85^n

     5600/24300  = .85^n  

             now you need to take the log of both sides and solve for 'n'  years

  log ( 5600/24300) / log(.85) = n = 9.031 = ~~ 9 years

The angle theta lies in quadrant I or III.

Hence, option (C) is the correct choice.

The coordinate system's two axes, the x-axis and the y-axis, constitute an area called a quadrant. The quadrants are generated when the two axes, the x-axis and the y-axis, cross at a 90-degree angle. These areas include coordinates, or positive and negative values of the x- and y-axes.

Cosθ=(1/Sinθ)

And, Secθ = (1/Cosθ)

As we know,

In the first Quadrant.

The value of Sinθ is positive, so the corresponding value of Cosθ will be also Positive.

As, In the second case the value of Secθ should be less than 0,

We know the value of Cosθ is negative in the third Quadrant.

So, the value of the Secθ will be less than 0 in the third quadrant.

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The smallest possible integer value that 'a' could take is 6.

Perimeter is the total length of a shape's boundary.

Perimeter of equilateral triangle = 3a, where a is the side length

Perimeter of a square = 4b, where b is the side length

Let P₁ be the perimeter of equilateral triangle and P₂ be the perimeter of square.

Here,

Length of side of equilateral triangle = 4a + 2

P₁ = 3 (4a + 2)

Length of side of square = 2a + 7

P₂= 4 (2a + 7)

Given P₁ > P₂

3 (4a + 2) > 4 (2a + 7)

By distributive property,

12a + 6 > 8a + 28

12a - 8a > 28 - 6

4a > 22

a > 22/4

a > 5.5

Hence 6 is the smallest number which is an integer that 'a' could take.

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Yes, the given functions are inverses of one another.

Inverse function is represented by  with regards to the original function  and the domain of the original function becomes the range of inverse function and the range of the given function becomes the domain of the inverse function. The graph of the inverse function is obtained by swapping (x, y) with (y, x) with reference to the line y = x.

The given functions are f(x)=5x+2 and g(x)=(x-2)/5.

The function f(x)=5x+2 can be written as y=5x+2

Swap x and y positions, we get

x=5y+2

x-2=5y

y=(x-2)/5

Therefore, the function g(x) is the inverse function os f(x).

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Adam will be paying by installment, and will pay the amount of $140 of his last payment if he pays the $10 minimum monthly payment up until the last payment.

Payment by installment is when one pay small sums of money at regular intervals over a period of time, rather than paying the whole amount at once.

Adam made a down payment of $100 out from the total amount of $1,670, so he will have to pay a balance of $1570 in 12 years.

The minimum monthly payment is $10, and he will have 144 months to pay up the balance.

If Adam pays $10 for 144 months, he will pay up a total of $1440 having a balance of $130 to pay after the deadline.

Therefore, if Adam makes the minimum monthly payment up until the last payment, he would have paid up $1430 which is $10 in 143 months and will pay the amount of $140 of his last payment.

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Answer:

8v+3c

Step-by-step explanation:

2v+6v+3c

2v and 6v have similar figures so you can add them together

so it becomes 8v+3c

c and v have nothing in common so you cannot simplify them more

Benito's gross pay for the week will be $757.07.

What are work and time?

In aptitude, work and time are related concepts that are used to calculate the rate of work being done.

Benito is to be paid time and a half for every hour over 40 that he works, so for a 49-hour work week, he will be paid for 49 - 40 = 9 hours of overtime.

His regular pay for the first 40 hours is $14.15 per hour * 40 hours = $566.

His overtime pay is $14.15 per hour * 1.5 = $21.23 per hour

His overtime pay for 9 hours is $21.23 per hour * 9 hours = $191.07

his gross pay for the week will be $566 + $191.07 = $757.07.

Hence, Benito's gross pay for the week will be $757.07.

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Answer:

[tex]y=-\frac{3}{2}x+9[/tex]

Step-by-step explanation:

Parallel lines have the same slope, but different y-intercepts, so it helps to rewrite the equation in slope-intercept form:

[tex]2y+3x-4=0\\2y=-3x+4\\y=-\frac{3}{2}x+2[/tex]

Now, just simply change the y-intercept from 2 to 9 and you're done!

Answer:

28 / Ounce of wed >;)

Step-by-step explanation:

Answer:

28

Step-by-step explanation:

PEMDAS (parenthesis, exponents, multiplication, division, addition, subtraction)

Multiply 4 and 7 (28), divide 20 by 5 (4), add those together (32) and then subtract 4 which will get you 28

Base 3 logarithm of 81 equals 4 .The logarithmic form, written as log of "b" to base "a" is equal to "n," .

How many times must one "base" number be multiplied by itself in order to get another specific number is the subject of the mathematical expression known as a logarithm (or log). Mathematics includes both logarithms and logs. They share a connection with exponential functions. Logarithms are the opposite of exponentiation because they reveal the exponent (or power) required to create a given number. They were helpful in the past for splitting or multiplying huge numbers.

given

Base 3 logarithm of 81 equals 4 .

Therefore, the logarithmic form, written as log of "b" to base "a" is equal to "n," may be expressed in exponential form as  a = b.

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Answer:

A proportional graph is a straight line that goes through the origin (0,0).\

Based on this information, the only correct answers would be B and C.

Answer:

14.13

Step-by-step explanation:

Since we know the area of a circle is [tex]\pi r^2[/tex], we just need to divide it by 2 to get the semicircle's area ( [tex]\frac{\pi r^2}{2}[/tex] )

We know the radius is equal to half of the diameter, or in this case 3, and we're approximating pi to 3.14, so we just substitute on the formula:

[tex]\frac{(3.14)(3)^2}{2} = \frac{(3.14)(9)}{2} = \frac{28.26}{2} = 14.13[/tex]

Aiden can make up to 166 copies before his copy card balance reaches below $5.00 as each copy total costs $0.06.

1. 15.00 - 0.06x ≥ 5.00

2. Add 0.06x to both sides: 15.00 ≥ 0.06x + 5.00

3. Subtract 5.00 from both sides: 10.00 ≥ 0.06x

4. Divide both sides by 0.06: 166.67 ≥ x

5. Therefore, x ≤ 166.67, so Aiden can make a maximum of 166 copies.

Aiden's copy card balance is $15.00, and each copy he makes costs $0.06. To ensure that his card balance does not go below $5.00, he needs to calculate the max number of copies he can make. To do this, we set up an inequality, 15.00 - 0.06x ≥ 5.00, and solved it to get x ≤ 166.67, meaning Aiden can make a maximum of 166 copies.

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Keon scored 5 goals.

The solutions of x²=-36 are 6i and -6i.

Two or more expressions with an Equal sign is called as Equation.

X by the power of 2 is -36

This can be written as x²=-36

We need to find the value of x.

x²=-36

Take square root on both sides

x=√-36

x=√i²36

x=6i, -6i

Hence, the solutions of x²=-36 are 6i and -6i.

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The value of [tex]r[/tex] is [tex]7[/tex]

The given equation is

                        [tex]5(r-3)=20[/tex]

We will now open the bracket, [tex]5r-15=20[/tex]

Let's simplify,

                      [tex]5r=20+15\\5r=35\\r=\frac{35}{5} \\r=7[/tex]

The value of [tex]r=7[/tex]

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Vectors V1=(22,15) and v2=(-2,4) are not orthogonal.

Two vectors are said to be orthogonal if they are perpendicular

to each other. i.e. the dot product of the two vectors is zero.

Given vectors are:

V₁ = (22,15)

V₂ = (-2,4)

Dot product of V₁ and V₂ = (22,15).(-2,4) = 22×-2 + 15×4

Part 1:

Multiplying x-coordinates of vectors-

(22×-2) = -44

Multiplying y-coordinates of vectors-

(15×4) = 60

Part 2: Adding the products = -44+60 = 16

Part 3: If the dot product of two vectors is zero, then the two vectors are orthogonal.

But the dot product from the above calculation is 16 means vectors are not orthogonal.

Hence, the two vectors are not orthogonal.

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(a) Expected number of repairs per year is 0.33 (b) Standard deviation of number of repairs per year is 0.749, (c) The mean and standard deviation of annual expense are $136.55 and $26.217 respectively.

Standard deviation is a measure in statistics which measures the amount of deviation a set of data has with respect to their mean.

(a) Expected number of repairs for the freezer per year is the sum of the product of number of repairs to their probability.

E(Repairs) = (0 × 0.80) + (1 × 0.11) + (2 × 0.05) + (3 × 0.04)

                 = 0.33

(b) Standard deviation of number of repairs per year can be calculated as,

SD(Repairs) = [tex]\sqrt{[(0 - 0.33)^{2}(0.8)]+[(1-0.33)^{2}(0.11)] + [(2-0.33)^{2}(0.05)]+[(3-0.33)^{2}(0.04)] }[/tex]

= √ (0.5611)

= 0.749

(c) Mean of the restaurant's annual expense with service contract is,

Mean = Expected cost = $125 + ($35 × 0.33) = $136.55

Standard deviation of the restaurant's annual expense with service contract is,

SD = [tex]\sqrt{35^{2}(0.5611) }[/tex] = 35 × 0.759 = 26.217

Hence the expected number of repairs is 0.33, standard deviation of number of repairs is 0.749, mean and standard deviation of annual expense is $136.55 and $26.217 respectively.

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Answer:

y = 4x + 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept, where it crosses the y- axis )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (- 2, - 4) ← 2 points on the line

m = [tex]\frac{-4-0}{-2-(-1)}[/tex] = [tex]\frac{-4}{-2+1}[/tex] = [tex]\frac{-4}{-1}[/tex] = 4

the line crosses the y- axis at (0, 4 ) ⇒ c = 4

y = 4x + 4 ← equation of line

answer: 60.00

Based on the given conditions, formulate:: 4000x
((1.5%+1)12/12-1)

Evaluate the equation/expression:: 60

Round 60 to the required place rounding: 60.00

[tex]\dfrac{1}{3} x=6[/tex]

Multiply both sides by 3:

[tex]3\times(\dfrac{1}{3} x)=3\times(6)[/tex]

[tex]\fbox{x = 18}[/tex]

1/3x = 6

Multiply both sides by 3:
3 * 1/3x = 3 * 6

x = 18

x = 18 would be your answer.

Hope this helps!

The type of data expressed in the example is ordinal data.

This is an example of ordinal data, as it is data that is expressed on a scale from 1 to 5. Ordinal data is useful for comparing objects or ideas in relation to each other, and is often used to indicate levels of preference or satisfaction. In this case, the data is used to compare the reliability of two travel agents.

Ordinal data is a type of data where the values are ranked in order of magnitude. In the example given, the company has expressed their belief on a scale from 1 to 5, with higher numbers representing a higher level of reliability. Therefore, this type of data is considered ordinal.

The type of data expressed in the example is ordinal data.

Ordinal data is a type of data where the values are ranked in order of magnitude.

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a) P20 is the 20th percentile, which separates the lowest 20% of the data from the highest 80%. To find P20, you would need to put the data in numerical order and find the value at the 20th percentile.

b) P67 is the 67th percentile, which separates the lowest 67% of the data from the highest 33%. To find P67, you would need to put the data in numerical order and find the value at the 67th percentile.

c) 34 is the 34th percentile, which separates the lowest 34% of the data from the highest 66%. It is the value at the 34th percentile

d) A boxplot is a graphical representation of a dataset that shows the minimum, first quartile, median, third quartile, and maximum of the data. To create a boxplot, you would need to put the data in numerical order, then calculate the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum of the data. These values are then plotted on a graph, with the box representing the interquartile range (Q3 - Q1) and the whiskers representing the minimum and maximum values. The outliers(if any) will be plotted as dots

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In Exercises 23-26 and In Exercises 27-36 , the trigonometric function by memory and by constructing an appropriate triangle for the given special angle are mentioned below

Trigonometry is a branch of mathematics, which deals with the study of right angle triangles. Trigonometry is concerned with specified functions of angles and their applications to calculations.

There are 6 commonly used functions in trigonometry with their name and abbreviations-

sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), cosecant (cosec)

1. Exercises 23-26

23. (a) cos 60° = 0.5

24. (a) cot 45° = 0.7071

25. (a) sin 45° =  0.7071

26. (a) sin 60° = 0.8660

(b) cos 30° = 0.8660

(b) cos 45° =  0.7071

(b) cos 30° = 0.8660

(b) tan 45° = 1

27. (a) sin 10° = 0.9958

28. (a) tan 23.5° = 0.4348

29. (a) sin 16.35° = 0.2815

(c) tan 60° = 1.732

(c) cosec 45° = 1.4142

(c) tan 30° = 0.5773

(c) sec 30° = 1.1547

2.  Exercises 27-36

(b) cos 80° = 0.1736

(b) cot 66.5° = 0.4348

(b) cosec 16.35° = 3.5523

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Answer: To find the midpoint of a line segment, you can average the x-coordinates of the endpoints and average the y-coordinates of the endpoints.

The x-coordinates of the endpoints are -1 and -9, so the average of the x-coordinates is (-1 + (-9))/2 = -5

The y-coordinates of the endpoints are 3 and -7, so the average of the y-coordinates is (3 + (-7))/2 = -2

So the midpoint of the segment with endpoints (-1, 3) and (-9, -7) is (-5, -2)

Step-by-step explanation: