△ABC has vertices A(-2, 0), B(0,8), and C(4,2). Find the coordinates of the point of congruency of the altitudes (H)

The closest point is (3.5, 1.9) and the distance is 1.96 units

The coordinate is given as:

(4, 0)

The equation of the function is

y = √x

The distance between two points is calculated using

d = √(x2 - x1)^2 + (y2 - y1)^2

So, we have the following points

(x1, y1) = (4, 0) and (x2, y2) = (x, 0)

This gives

d = √(x - 4)^2 + (√x - 0)^2

Evaluate the difference

d = √(x - 4)^2 + (√x)^2

Evaluate the exponent

d = √x^2 - 8x + 16 + x

Evaluate the like terms

d = √x^2 - 7x + 16

Next, we differentiate using a graphing calculator

d' = (2x - 7)/[2√(x^2 - 7x + 16)]

Set to 0

(2x - 7)/[2√(x^2 - 7x + 16)] = 0

Cross multiply

2x - 7 = 0

Add 7 to both sides

2x = 7

Divide by 2

x = 3.5

So, we have:

Substitute x = 3.5 in y = √x

y = √3.5

Evaluate

y = 1.9

So, the point is (3.5, 1.9)

The distance is then calculated as:

d = √(x2 - x1)^2 + (y2 - y1)^2

This gives

d = √(3.5 - 4)^2 + (1.9 - 0)^2

Evaluate

d = 1.96

Hence, the closest point is (3.5, 1.9) and the distance is 1.96 units

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Using the sample space and probability concepts, we have that:

A) All the possibilities for the sample space are: {{G,G,G}, {G,G,B}, {G,B,G}, {G,B,B}, {B,G,G}, {B,G,B}, {B,B,G}, {B,B,B}}.

B) The probability is: 7/8.

C) The probability is: 1/2.

D) The probability is: 1/4.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

The sample space is the set that contains all possible outcomes, hence in this problem, considering G for girl and B for boy, it is given by:

{{G,G,G}, {G,G,B}, {G,B,G}, {G,B,B}, {B,G,G}, {B,G,B}, {B,B,G}, {B,B,B}}.

For item B, 7 outcomes have at most two boys, hence the probability is 7/8.

For item C, 4 outcomes have at least two girls, hence the probability is 4/8 = 1/2.

For item D, 2 outcomes have all the babies with the same sex, hence the probability is 2/8 = 1/4.

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I don't know what you mean by g. and h., so I'll just skip that part.

I'm assuming you're asking about some arbitrary finite set [tex]A[/tex].

a. If [tex]A[/tex] has 64 subsets, then [tex]A[/tex] has [tex]\log_2(64) = \boxed{6}[/tex] elements. This is because a set of [tex]n[/tex] elements has [tex]2^n[/tex] subsets/elements in its power set.

b. A proper subset is a subset that doesn't contain all the elements of the parent set. This means we exclude the set [tex]A[/tex] from its power set. The power set itself would have 32 elements, so [tex]A[/tex] would have [tex]\log_2(32) = \boxed{5}[/tex] elements.

c. The empty set is a proper subset of any non-empty set. However, if [tex]A=\emptyset[/tex], then it has no proper subsets. So [tex]A[/tex] must be the empty set and have [tex]\boxed{0}[/tex] elements.

d. By the same reasoning as in part (b), if [tex]A[/tex] has 255 proper subsets, then it has a total of 256 subsets, and [tex]\log_2(256) = \boxed{8}[/tex].

Answer: 470.4 N

Step-by-step explanation:

Concept:

1 kg on Earth = 9.8 N

Given information:

Mass = 48 kg

Find the weight on Earth

1 kg = 9.8 N

48 kg = 48 * 9.8 = [tex]\Large\boxed{470.4N\\}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer: 70 and 60 degrees

Step-by-step explanation:

Angle AOB = 180 - 50 - 60 = 70 degrees so x is 70 degrees

Angle OCD = 180 - 130 = 50 so y = 180 - 70 - 50 = 60 degrees

Answer:

The answer is B if the octagon has side lengths of 8

The new monthly payment is $3,181.53

What is ARM?

ARM stands adjustable rate mortgage, which means that the interest rate applicable to the mortgage would change during the life of the mortgage, in this case, 7/1 ARM means that interest rate of 3% is applicable for the first 7 years and the rate would change in year 8 to another interest rate, which is 4.925% as hinted at in the question.

To determine the monthly payment in year 8 , we need to compute the outstanding balance at the end of year 7, which is the opening balance in year 8 using the present value formula of an ordinary annuity since monthly payments would occur at the end of each month

PV(balance at the end of year 7)=PMT*(1-(1+r)^-N/r

PMT=initial monthly payment=$2,635.03

r=initial monthly interest rate=3%/12=0.0025

N=number of monthly payments in the remaining 23 years(i.e 30-7)=23*12

N=number of monthly payments in the remaining 23 years(i.e 30-7)=276

PV=$2,635.03*(1-(1+0.0025)^-276/0.0025

PV=$2,635.03*(1-0.502008144755209)/0.0025

PV=$2,635.03*0.497991855244791/0.0025

PV=$ 524,889.39

With the balance at the end of year 7, we can now compute monthly payment in year 8 using the same formula as above where the unknown is the PMT, PV=$ 524,889.39  and r= 4.925%.

$524,889.39=PMT*(1-(1+4.925%/12)^-276/4.925%/12)

$524,889.39=PMT*(1-(1.00410416666666667

)^-276/0.00410416666666667

$524,889.39=PMT*(1-0.32289378683267300

)/0.00410416666666667

$524,889.39=PMT*164.98019407122700000

PMT=$524,889.39/164.98019407122700000

PMT=$3,181.53

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Answer:

25, 26, and 27 are the three consecutive integers.

Step-by-step explanation:

Let the numbers be represented as x, x + 1 and x + 2.

We can write the equation:

[tex]x+(x+1)+ (x+2)=78[/tex]

Opening the brackets and simplifying:

[tex]x+x+1+x+2=78[/tex]

[tex]3x+3=78[/tex]

Subtract 3 from both sides.

[tex]3x=75[/tex]

Divide both sides by 3.

[tex]x=25[/tex]

Since the three consecutive integers are x, x + 1 and x + 2, replace x with 25.

∴ 25, 26 and 27 are the three consecutive integers.

Answer:

25 , 26 and 27

Step-by-step explanation:

Solving for y:

6y - 2x = 20

6y = 2x + 20

y = [tex]\frac{2x + 20}{6}[/tex]

y = [tex]\frac{2x}{6} + \frac{20}{6}[/tex]

y = [tex]\frac{1x}{3} + \frac{10}{3}[/tex]

Hope it helps!

Answer:

Step-by-step explanation:

6y - 2x = 20

     -6      -6

-2x = 20 - 6y

divide both sides by -2

[tex]\frac{-2x}{-2}[/tex] = [tex]\frac{20 - 6y}{-2}[/tex]

Dividing by -2 undoes the multiplication by -2.

[tex]x = \frac{20 - 6y}{ -2}[/tex]

Divide 20 -6 by -2

x = 3y - 10

Or

y = [tex]\frac{10}{3}[/tex]x +[tex]\frac{x}{3}[/tex]

Answer:

A = $11; C = $7 tickets

Step-by-step explanation:

Using the given info, we can create a system of equations to find the price of adult and children tickets.

Thus, we have 5A + 7C = 104 and 7A + 3C = 98

The easiest method to solve would be elimination:

Answer:

Step-by-step explanation:

The sales on the two days can be expressed using equations that can be solved for ticket prices.

Let x and y represent the prices of adult and children's tickets, respectively. Then the sales revenue for the two days can be expressed in the equations ...

One of the easiest solution methods is to use a graphing calculator. The first attachment shows the prices are $11 for an adult ticket; $7 for children tickets.

Using the matrix functions of a calculator, the augmented matrix of the equation coefficients can be reduced to row-echelon form. This, too, shows the solution to be (adult price, children price) = ($11, $7). See the second attachment. (The solution is the right-most column of the reduced matrix.)

Yet another solution method can use the coefficients from the equations written in general form:

In this form, we define three products of "cross multiplication":

  Δ1 = (5)(3) -(7)(7) = -34

  Δ2 = (7)(-98) -(3)(-104) = -374

  Δ3 = (-104)(7) -(-98)(5) = -238

Using those, we find the variable values to be ...

  x = Δ2/Δ1 = -374/-34 = 11

  y = Δ3/Δ1 = -238/-34 = 7

(adult price, children price) = ($11, $7)

__

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\cos (\tan \left( -1\right) (\frac{x}{2}))

c

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s

(

t

a

n

(

−

1

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(

2

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Simplify

1

Combine multiplied terms into a single fraction

\cos (\tan \left( -1\right) \cdot \frac{x}{2})

c

o

s

(

t

a

n

(

−

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)

⋅

2

)

\cos (\frac{\tan \left( -1\right) x}{2})

c

o

s

(

t

a

n

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−

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)

2

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Solution

\cos \left( \frac{\tan \left( -1\right) x}{2}\right)

c

o

s

(

t

a

n

(

−

1

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2

)

Answer:

Step-by-step explanation:

[tex]cos(tan^{-1}(\frac{x}{2} ))\\put~tan^{-1}(\frac{x}{2} )=t\\\frac{x}{2} =tan~t\\sec^2t-tan^2t=1\\sec^2t=1+tan^2t=1+(\frac{x}{2} )^2=\frac{x^2+4}{4} \\sec~t=\pm\frac{\sqrt{x^2+4}}{2} \\cos ~t=\pm\frac{2}{\sqrt{x^2+4}} \\hence~cos(tan^{-1}(\frac{x}{2} ))=cos~t=\pm\frac{2}{\sqrt{x^2+4}}[/tex]

The minimum value of z is -38

The optimization equation is given as

z=−3x+5y

The constraints are given as:

x+y≥−2

3x−y≤2

x−y≥−4

Next, we plot the constraints on a graph and determine the points of intersections

See attachment for the graph

From the attached graph, the points of intersections are

(-9, -13) and (-10, -12)

So, we have:

(-9, -13)

(-10, -12)

Substitute these values in the objective function

z=−3x+5y

This gives

z= −3 * -9 +5 * -13 = -38

z= −3 * -10 +5 * -12 = -30

-38 is less than -30

Hence, the minimum value of z is -38

So, the complete parameters are:

Optimization Equation:

z=−3x+5y

Constraints:

x+y≥−2

3x−y≤2

x−y≥−4

Vertices of the feasible region

(0, -2)

(-3, 1)

(3, 7)

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Part a

The domain is the set of x-values, which is [tex](-\infty, \infty)[/tex]

Part b

The range is the set of y-values, which is [tex](-\infty, -2][/tex]

Part c

The x-intercepts is when y=0, which there are none of.

Part d

The y-intercept is when x=0, which is at (0, -2).

a. The changes in each four-month period are as follows:

Month and       Prices       Absolute      Relative

Year              in Dollars     Change       Change

Apr-20              1.841             n/a                n/a

Aug-20            2.183         $0.342        18.58%

Dec-20            2.195            0.012         0.55%

Apr-21             2.858          0.663         30.21%

Aug-21             3.158          0.300        10.50%

Dec-21            3.307           0.149          4.72%

Apr-22            4.109          0.802        24.25%

b. The change in gas prices has been relatively unstable.

c. Using the inflation calculator, the costs of gas in April 2020 in 2022 dollars terms should be $2.08.

d. The inflation-adjusted cost of gas in April 2020 when compared to April 2022 as absolute and relative changes are as follows:

Absolute change = $2.268 ($4.109 - $1.841)

Relative change = 123.2% ($2.268/$1.841 x 100)

e. The two most drastic rises in gasoline prices in April 2021 and April 2022 can be attributed to spikes in demand relative to supply.

Gasoline prices rise when there is an increased demand relative to supply.

Increasing prices in gasoline prices can also be attributed to cuts in production and supply by the oil cartel.

An absolute change is a dollar change from one period to another.

A relative change is an absolute change expressed in percentages.

The calculations of absolute change and relative change are demonstrated below.

Month and       Prices       Absolute      Relative

Year              in Dollars     Change       Change

Apr-20              1.841             n/a                n/a

Aug-20            2.183         $0.342        18.58% ($0.342/$1.841 x 100)

Dec-20            2.195           0.012         0.55% ($0.12/$2.183 x 100)

Apr-21             2.858          0.663        30.21% ($0.663/$2.195 x 100)

Aug-21             3.158          0.300        10.50% ($0.3/$2.858 x 100)

Dec-21            3.307           0.149          4.72% ($0.149/$3.158 x 100)

Apr-22            4.109          0.802        24.25% ($0.802/$3.307 x 100)

Absolute Change for Aug-20 = $0.342 ($2.183 - $1.841)

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Answer:

The original price was $30

Step-by-step explanation:

40% = 40/100 = 0.4

[tex]\frac{12}{0.4} =30[/tex]

Hope this helps

The value of the expression (a - b)² from the given equations is; 16

We are given the two equations as;

a + b = 10   -----(eq 1)

ab = 21    ------(eq 2)

From eq 1, square both sides;

(a + b)² = 10²

a² + 2ab + b² = 100

a² + b² = 100 - 2ab

We are given ab = 21. Thus;

a² + b² = 100 - 2(21)

a² + b² = 58

Now, we know that (a - b)² = a² - 2ab + b²

Thus;

(a - b)² = 58 - 2(21)

(a - b)² = 16

Complete question is;

If a + b = 10 and ab = 21, then the value of (a - b)² is?

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Step-by-step explanation:

With this question ,

The length of the rectangle is 3m longer than it's width=3 +w

then the width =w

therefore perimeter= 2L +2w

34= 2(3+w) +2w

34= 6+2w +2w

34-6 = 4w

28=4w

7= w

Area= Length x breadth

Area = (7+3) x7

Area= 10 x7

Area= 70cm square

Since we know the sequence is quadratic, we expect the [tex]n[/tex]-th term to have the general form

[tex]x_n = an^2 + bn + c[/tex]

Plug in the first 3 known values of the sequence to form a system of equations.

[tex]x_1 = 3 = a + b + c[/tex]

[tex]x_2 = 12 = 4a + 2b + c[/tex]

[tex]x_3 = 25 = 9a + 3b + c[/tex]

Eliminating [tex]c[/tex] gives

[tex](4a + 2b + c) - (a + b + c) = 12 - 3 \implies 3a + b = 9[/tex]

[tex](9a + 3b + c) - (a + b + c) = 25 - 3 \implies 8a + 2b = 22 \implies 4a + b = 11[/tex]

Eliminating [tex]b[/tex] gives

[tex](4a + b) - (3a + b) = 11 - 9 \implies a = 2[/tex]

Solving for [tex]b,c[/tex], we get

[tex]4a + b = 11 \implies b = 11-4\cdot2 = 3[/tex]

[tex]a+b+c=3 \implies c=3-2-3 = -2[/tex]

So, the [tex]n[/tex]-th term of the sequence is

[tex]x_n = \boxed{2n^2 + 3n - 2}[/tex]

Hello and Good Morning/Afternoon:

Let's take this problem step-by-step:

When we expand a function, everything must be multiplied out evenly.

      [tex](x+6)*(x+6)\\=x*x +x*6+6*x+6*6\\=x^2 + 6x + 6x+36\\x^2 +12x+36[/tex]

Answer: x² + 12x + 36

Hope that helps!

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Polynomials are mathematical expressions made up of many terms.

To simplify the polynomial to the maximum, all like terms must be grouped together and rearranged from highest to lowest power.

Distribute

Combining like terms.

The equation that represents the distance, in kilometers, Seb travels (d) based on how many hours he bikes (t) at this rate is d = 20t

The given parameter is

constant rate of 20 kilometers per hour.

This means that

Rate = 20km per hour

When Seb bikes for t hours, the distance is

d = rate * t

This gives

d = 20t

Hence, the equation that represents the distance, in kilometers, Seb travels (d) based on how many hours he bikes (t) at this rate is d = 20t

This means that

t = 5

So, we have:

d = 20 * 5

Evaluate

d = 100

Hence, Seb will travel 100 kilometers if he bikes at this rate for 5 hours

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Answer:

1. d=20t

2. 50

green balls = 83

orange balls = 19

Step-by-step explanation:

green balls = g

orange balls = r

g = 7 + 4r

g + r = 102

7 + 4r + r = 102

5r = 95

r = 19

g + 19 = 102

g = 83

Answer:

(3+3) x (3+1)

Step-by-step explanation:

free

We have give 4 numbers that are 1,3,3,3. we have to apply operations on it to make it 24.

» (1 + 3) × (3 + 3)

» (4) × (6)

» 24

Here's our answer..!!

We conclude that the starting average grade is 79.17%

There are 50 students, let's say that the grades are measured between 1% and 100%.

And the average grade of the 50 students is A.

We know that after it increased by 20%, the average of the grades is 95.

Then we just need to solve the percentage equation:

95 = A*(1 + 20%/100%) = A*(1.2)

95/1.2 = A = 79.17

We conclude that the starting average grade is 79.17%

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Answer:

75%

Step-by-step explanation:

You need to do the following equation: x+20≤95 and you will have the answer. (I am sorry if it is wrong but this is what my teacher told the answer was. I put this answer and got it correct.) Hope it helped. Have a nice day.

Trabajando con porcentajes, concluimos que la pérdida es de $4800.

Sabemos que la inversión inicial es de $60000, y de esta cantidad, se pierde un 8%.

Entonces la pérdida va a ser el 8% de $60000.

Podemos escribir las relaciones:

$60000 = 100%

x = 8%

Queremos resolver esto para x, tomando el cociente entre esas relaciones y resolviendo para x obtenemos:

x = $60000*(8%/100%) = $60000*0.08 = $4800

Así, concluimos que la pérdida es de $4800.

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Answer:

option B is the answer of given question

Answer:

D. 93.5

Step-by-step explanation:

Angle Formed by Two Chords= 1/2(SUM of Intercepted Arcs)

The lower arc is twice 52

c = 1/2( 104  +83)

c = 1/2 ( 187)

c =93.5

The conclusion for p, from the confidence interval, using an absolute value inequality is:

[tex]|p - 0.27| \leq 0.019[/tex]

A confidence interval is given by the estimate plus minus the margin of error. As an inequality, we have that the absolute value of the difference between the proportion and the estimate is of at most the margin of error, that is:

[tex]|p - E| \leq M[/tex]

For this problem, the estimate and the margin of error are:

E = 0.27, M = 0.019.

Hence the inequality is:

[tex]|p - 0.27| \leq 0.019[/tex]

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Given the measure of angle B, side b and side, the measure of angle C to the nearest whole number is 43 degrees.

From the Rule of Sine;

sinA/a = sinB/b = sinC/c

Where A,B and C are the angles of the triangle and a, b and c are the corresponding opposing sides.

Given that;

Using the rule of sine.

sinB/b = sinC/c

We substitute the given values into the equation

sin( 18° )/9 = sinC/20

We solve for C.

sin( 18° ) × 20 = sinC × 9

0.309016994 × 20 = sinC × 9

6.18033988 = sinC × 9

Divide both sides by 9

6.18033988/9 = (sinC × 9)/9

sinC = 0.686704431

C = sin⁻¹( 0.686704431 )

C = 43.3697°

C = 43°

Given the measure of angle B, side b and side, the measure of angle C to the nearest whole number is 43 degrees.

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The most efficient measurements of the box should be 4cm long, 1cm wide and 2cm high so that its cost is $129.2

To calculate the measurements of the rectangular box we must take into account the following condition:

According to the above, we can establish that the most appropriate measurement for the bottom and top should be 1cm (width) × 4cm (length). Additionally we can establish that the height of the box would be 2cm.

To find the volume of the box we must use the following formula:

The areas of this box are:

The total price of this box is as follows:

Top and bottom:

Sides:

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The number with the given properties is 17

Let the tens be x and the units be y.

So, the number is 10x + y

The relationship between the digits is

[tex]y = x + 6[/tex]

The relationship between the number and the reverse is

[tex]2(10x + y + 10y + x) = 6 + 10 * (10x + y)[/tex]

Simplify the second equation

[tex]2(11x + 11y) = 6 + 100x + 10y[/tex]

Open the brackets

[tex]22x + 22y = 6 + 100x + 10y[/tex]

Substitute y = x + 6

[tex]22x + 22(x + 6) = 6 + 100x + 10(x + 6)[/tex]

Expand

[tex]22x + 22x + 132 = 6 + 100x + 10x + 60[/tex]

Collect like terms

[tex]22x + 22x - 100x - 10x = 6 + 60 - 132[/tex]

Evaluate the like terms

[tex]-66x = -66[/tex]

Divide by -66

x = 1

Substitute x = 1 in y = x + 6

[tex]y = 1 + 6[/tex]

y = 7

Recall that the number is 10x + y

So, we have

Number = 10 * 1 + 7

Evaluate

Number = 17

Hence, the number is 17

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