Distance between two points
What is the length of the line?

We cannot get further information about the dimensions of the piece since the number of variables is greater than the number of equations.

By geometry we know that the area of the piece of metal is equal to the product of its length and width, then we must find two real numbers such that:

l · w = 27.75, where l, w > 0.

Unfortunately, we cannot get further information about the dimensions of the piece since the number of variables is greater than the number of equations. We need at least one equation to find an unique solution.

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Answer: If one angle of a parallelogram is a right angle, then all other angles would also be right angles and the parallelogram would be a rectangle.

a) The future value, principal plus interest, with compound interest on a principal of $8,704.56 at a rate of 4% per year compounded 2 times per year over 8 years is $11,949.50.

b) The future value, principal plus interest, with compound interest on a principal of $8,704.56 at a rate of 4% per year compounded continuously over 8 years is $11,987.29.

The future value can be determined using an online finance calculator.

Data and Calculations:

Principal (P): $8,704.56

Annual Rate (R): 4%

Compound (n): Compounding Semi-Annually

Time (t in years): 8 years

Result:

A = $11,949.50

A = P + I where

P (principal) = $8,704.56

I (interest) = $3,244.94

First, convert R as a percent to r as a decimal

r = R/100

r = 4/100

r = 0.04 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 8,704.56(1 + 0.04/2)(2)(8)

A = 8,704.56(1 + 0.02)(16)

A = $11,949.50

Using the formula A = Pert

Principal (P):  $8,704.56

Annual Rate (R): 4%

Compound (n): Compounding Continuously

Time (t in years):   8 years

Result:

A = $11,987.29

A = P + I where

P (principal) = $8,704.56

I (interest) = $3,282.73

First, convert R as a percent to r as a decimal

r = R/100

r = 4/100

r = 0.04 rate per year,

Then solve the equation for A, using the mathematical constant, e = 2.71828

A = Pert

A = 8,704.56(2.71828)(0.04)(8)

A = $11,987.29

Thus, while the future value of $8,704.56 at a rate of 4% per year compounded semiannually over 8 years is $11,949.50,  the future value of $8,704.56 at a rate of 4% per year compounded continuously over 8 years is $11,987.29.

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Answer:

x = 52

Step-by-step explanation:

Since the inscribed angle measures 64 degrees, the minor arc is 64*2 = 128 degrees. Therefore the major arc is 180-128 = 232 degrees. Angle X is the difference of major and minor arc divided by 2, so X = (232-128)/2 = 52 degrees.

The vertices of the feasible region are (0, -2), (-3, 1) and (3, 7)

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

(-3, 1), (3, 7) and (0, -2)

So, we have:

(0, -2)

(-3, 1)

(3, 7)

Hence, the vertices of the feasible region are (0, -2), (-3, 1) and (3, 7)

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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The time taken for the smaller pipe to fill the pool by itself is 15.71 hours

1/6 = 1/x + 1/(x+6)

1/6 = (x+6)+(x) / (x)(x+6)

1/6 = (x+6+x) / x²+6x

1/6 = (2x+6)(x² + 6x)

1(x² + 6x) = 6(2x+6)

x² + 6x = 12x + 36

x² + 6x - 12x - 36 = 0

x² - 6x - 36 = 0

x = 9.71 or -3.71

The value of x cannot be negative

Therefore, the

Time taken for long pipe = x

= 9.71 hours

Time taken for small pipe = x + 6

= 9.71 + 6

= 15.71 hours

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The measure of the unknown angles are as shown below;

m<2 = 128 degrees = m<4

m<5 = 128 degrees

m<6 = 52 degrees

m<3 = 52 degrees = m<8

m<7 = 128 degrees

An angle is the point where the two lines meet. From the given diagram, the lines B and D are parallel to each other with a transversal.

Given the following parameters

m<1 = 52 degrees

From the given diagram, the following are true

m<1 = m<3 (corresponding angle)

m<3 = m<8 (vertical angles)

m<1 = m<6 (vertical angles)
m<2 = m<5 (vertical angles)

m<4 = m<7 (vertical angles)

Also;

m<1 + m<2 = 180

m<2 = 180 - m<1

m<2 = 180 - 52
m<2 = 128 degrees = m<4

m<5 = 128 degrees

m<6 = 52 degrees

m<3 = 52 degrees = m<8

m<7 = 128 degrees

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Answer:

None of these

Step-by-step explanation:

[tex]\frac{360}{n}=24 \implies n=15[/tex]

This is called a pentadecagon.

Step-by-step explanation:

x = a + 7

y = b-a

To prove

x + y = b + 7.

=a+7+b-a

=a-a+7+b

=0 + 7+b

= b+7

Proved ✅

Step-by-step explanation:

Let ABC be the equilateral triangle. Let AE, BD and CF be the medians. A meridian divides a side into two equal parts. Hence, proved that medians of an equilateral triangle are equal .

[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

The given figure shows a vertical hyperbola with its centre at origin, and as we observe the figure, we can conclude that :

Length of transverse axis is :

[tex]\qquad \sf  \dashrightarrow \: 2b = 12[/tex]

[tex]\qquad \sf  \dashrightarrow \: b = 6[/tex]

length of conjugate axis is :

[tex]\qquad \sf  \dashrightarrow \: 2a = 8[/tex]

[tex]\qquad \sf  \dashrightarrow \: a = 4[/tex]

Equation of hyperbola ~

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {y}^{2} }{ {b}^{2} } - \cfrac{ {x}^{2} }{ {a}^{2} } = 1[/tex]

plug in the values ~

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {y}^{2} }{ {6}^{2} } - \cfrac{ {x}^{2} }{ {4}^{2} } = 1[/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {y}^{2} }{ {36}^{} } - \cfrac{ {x}^{2} }{ {16}^{} } = 1[/tex]

Answer:

[tex]\dfrac{y^2}{36}-\dfrac{x^2}{16}=1[/tex]

Step-by-step explanation:

Standard form equation of a vertical hyperbola

[tex]\dfrac{(y-k)^2}{a^2}-\dfrac{(x-h)^2}{b^2}=1[/tex]

where:

From inspection of the graph:

Substitute the found values into the formula:

[tex]\implies \dfrac{(y-0)^2}{6^2}-\dfrac{(x-0)^2}{4^2}=1[/tex]

[tex]\implies \dfrac{y^2}{36}-\dfrac{x^2}{16}=1[/tex]

The  techniques that can be used to best explain for each equation that I have created are:

A)  For  graphing -  This is often used in checking if your answer is correct, if the math is known to be a little tedious, graphing is recommended

(b) For factoring:  x^2 -3x +4 '

Where: (x-4)(x+1)=0

Then x=-1, 4

(c) For  square root method:   x^2 = 64

Therefore x = + or - [tex]-\sqrt{64}[/tex] = + or - 8

(d) For  completing the square:  x^2 + 4x = 11 and x^2 +4x + 4

Note that:  x^2 +4x + 4

= x^2 + 4x = -4

= x^2 +4x + 4 = -4 + 4

= (x+2)^2 = 0

So, x = -2

(e) For quadratic formula: 6x² + 7x -19 =0  

x= [-b + or - sqr(b² - 4ac)]/2a

Note that b=7

a=6

c=-19

Therefore

x= [-7+ or - sqr(49+4(6)(9)]/2

2.  if the discriminant is said to be negative,   then the equation is one that is made up of two imaginary or complex solutions.

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See full question below

You have learned several techniques for solving quadratic equations. Create an equation that would be best for each technique listed below. Then explain why that technique would be best for each equation that you created.

a. graphing

b. factoring

c. square root method

d. completing the square

e. quadratic formula

2. What is the discriminant and what happens if you are solving and the discriminant turns out to be negative?

The probability that the battery life is  20 ± 2 hours (between 18 and 22 hours) for each of the phones is:

Using the normalcdf function on a calculator, the probability that Phone C's battery would last between 18 and 22 hours can be found by inputing the function:

normalcdf (20, IE99, 18, 2)

The result is 0.158655 or 15.9%.

For Phone T, the function is:

normalcdf (20, IE99, 20, 3)

The result is 0.5 or 50%.

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I'm not sure if the last two apostrophes are part of the quote - "Solve ... " - or if you mean the second derivative [tex]x''[/tex]. I think you mean the first interpretation, but I'll include both cases since they are both solvable.

If the former is correct, separate variables to solve.

[tex]x' = -9tx \implies \dfrac{dx}{dt} = -9tx \implies \dfrac{dx}x = -9t\,dt[/tex]

Integrate both sides to get

[tex]\ln|x| = -\dfrac92 t^2 + C[/tex]

Solve for [tex]x[/tex].

[tex]e^{\ln|x|} = e^{-9/2\,t^2 + C} \implies \boxed{x = Ce^{-9/2\,t^2}}[/tex]

If you meant the latter, then the ODE can be rewritten as

[tex]9t x'' + x' = 0[/tex]

Reduce the order of the equation by substituting [tex]y(t) = x'(t)[/tex] and [tex]y'(t) = x''(t)[/tex].

[tex]9t y' + y = 0[/tex]

Solve for [tex]y'[/tex] and separate variables.

[tex]y' = -\dfrac y{9t} \implies \dfrac{dy}{dt} = -\dfrac y{9t} \implies \dfrac{dy}y = -\dfrac{dt}{9t}[/tex]

Integrate.

[tex]\ln|y| = -\dfrac19 \ln|t| + C[/tex]

Solve for [tex]y[/tex].

[tex]e^{\ln|y|} = e^{-1/9 \,\ln|t| + C} \implies y = Ct^{-1/9}[/tex]

Solve for [tex]x[/tex] by integrating.

[tex]x' = Ct^{-1/9} \implies x = C_1 t^{8/9} + C_2[/tex]

Answer:

4900

Step-by-step explanation:

When rounding a number such as 4928 to the nearest hundred, we use the following rules:

A) We round the number up to the nearest hundred if the last two digits in the number are 50 or above.

B) We round the number down to the nearest hundred if the last two digits in the number are 49 or below.

C) If the last two digits are 00, then we do not have to do any rounding, because it is already to the hundred.

In this case, Rule B applies and 4928 rounded to the nearest hundred is:

4900

Answer:

Step-by-step explanation:

4,928, look at the last two numbers 28 if they are above 50 you round up, if below 50 round down,

The answer is 4,900

a) The probability is P = 1/9

b) The probability is P = 1/3.

First, we need to count the total number of outcomes (different cars that can be made with the given options):

Then there are 2*3*3 = 18 different cars.

a) Picking a blue hybrid car with an interior that is not leather.

There are 2 cars that meet that condition:

2 out of the 18 cars meet the condition, then the probability is:

P = 2/18 = 1/9

b) picking an electric car in a color other than blue is

The cars that meet the condition are:

So 6 out of the 18 cars meet the condition, then the probability is:

P = 6/18 = 1/3

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Answer:

eight and thirty-seven fiftyths

Step-by-step explanation:

6 and 4/100 + 2 and 5/10

6 and 1/25 + 2 and 1/2

156 / 25 + 5 / 2

312 / 50 + 125 / 50

437 / 50

400 / 50 = 8

8 and 37 / 50

Answer:

Gradient of the line is choice D.9/5

Step-by-step explanation:

Slope between two points:slope=(y₂-y₁)/(x₂-x₁)

slope(m)=

[tex] \frac{5 - ( - 4)}{3 - ( - 2)} \\ refine \: (m )= \frac{9}{5} [/tex]

See attachment for the graph of the inequality expression x + 2y > 6

The condition is given as:

{(x, y): x + 2y > 6}

This means that

x + 2y > 6

The above is an inequality expression, where the variables are x and y

So, we simply plot the graph of the inequality expression x + 2y > 6

See attachment for the graph of the inequality expression x + 2y > 6

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The experimental probability that only 2 of 4 children in a family are boys is 50%.

Experimental probability refers to the chance of an expected success being achieved in a series of experiments conducted.

Experimental probability is the number of times that the expected success occurs as a fraction of the total number of times the experiment was conducted.

Like all probabilities, the experimental probability is based on the likelihood that what the experimenter expects is achieved.

Expected number of boys = 2

The number of children in the family = 4

Experimental probability = 50% (2/4 x 100)

Thus, we can conclude, based on the experimental probability, that 50% (or 2) of the 4 children in the family are boys.

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Answer:

15%

Step-by-step explanation:

Step 1: Count samples with one H

Why; Only 1 of 4 children  in families are boys. The problem is simulated with samples.

Step 2: Count samples with only one H.

Why; The H represents the one boy in the family.

Step 3: Add the samples you counted with one H.

Answer: Your answer should be 3/20 after you change it into a percentage your final answer is 15%

The value of x^3 + 3x^2 - 2x + 7 divided by x- 2 is (x^2 + 5x + 8) + 23/(x - 2)

Quotients involve the result of dividing a dividend by a divisor.

In other words, quotient means division or the result of a division operation

The quotient expression is given as:

(x^3 + 3x^2 - 2x + 7)/x- 2

Expand the numerator in the above expression

(x^3 + 5x^2 - 2x^2 + 8x - 10x - 16 + 23)/(x - 2)

Rearrange the terms of the numerator in the above expression

(x^3 + 5x^2 + 8x - 2x^2 - 10x - 16 + 23)/(x- 2)

Factorize the numerator in the above expression

[x(x^2 + 5x + 8) - 2(x^2 + 5x + 8) + 23]/(x - 2)

Factor out x^2 + 5x + 8

[(x -2)(x^2 + 5x + 8) + 23]/(x - 2)

Split the fractions

(x -2)(x^2 + 5x + 8)/(x - 2) + 23/(x - 2)

Divide the common factors

(x^2 + 5x + 8) + 23/(x - 2)

Hence, the value of x^3 + 3x^2 - 2x + 7 divided by x- 2 is (x^2 + 5x + 8) + 23/(x - 2)

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Complete question

Evaluate (x^3 + 3x^2 - 2x + 7)/x- 2

Answer:

Step-by-step explanation:

The correct answer is D because when you divide & simplify the original question's equation, you get the results that are equivalent to answer D.

Answer:

below

Step-by-step explanation:

-14y = 28 - 10x

10x - 14y - 28 = 0.

a = 10

b = -14

c = -28

Answer:

a = 10

b = -14

c = 28

Step-by-step explanation:

Goal form: Standard form

ax + by = c

Given form: linear form (not fully simplified)

-14y = 28 - 10x

Add 10x on both sides (to move the x-value to the left-hand side of the equation)

-14y + 10x = 28 - 10x + 10x

-14y + 10x = 28

10x - 14y = 28

Determine [ a ], [ b ], [ c ]

ax + by = c

10x - 14y = 28

[tex]\Large\boxed{a=10}[/tex]

[tex]\Large\boxed{b=-14}[/tex]

[tex]\Large\boxed{c=28}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

B

Step-by-step explanation:

The area of the triangle is half the base time the height.  The height is y sub 1.  The length is the distance between the x values.

The equations of the three altitudes of triangle ABC include the following:

A triangle can be defined as a two-dimensional geometric shape that comprises three (3) sides, three (3) vertices and three (3) angles only.

A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.

Mathematically, the slope of a straight line can be calculated by using this formula;

[tex]Slope, m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope, m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

Also, the point-slope form of a straight line is given by this equation:

y - y₁ = m(x - x₁)

Assuming the following parameters for triangle ABC:

For the equation of altitude AM, we have:

Slope of BC = (2 - 8)/(4 - 0)

Slope of BC = -6/4

Slope of BC = -3/2

Slope of AM = -1/slope of BC

Slope of AM = -1/(-3/2)

Slope of AM = 2/3.

The equation of altitude AM is given by:

y - y₁ = m(x - x₁)

y - 0 = 2/3(x - (-2))

3y = 2(x + 2)

3y = 2x + 4

3y - 2y - 4 = 0.

For the equation of altitude BN, we have:

Slope of CA = (2 - 0)/(4 - (-2))

Slope of CA = 2/6

Slope of CA = 1/3

Slope of BN = -1/slope of CA

Slope of BN = -1/(1/3)

Slope of BN = -3.

The equation of altitude BN is given by:

y - y₁ = m(x - x₁)

y - 8 = -3(x - 0)

y - 8 = -3x

y + 3x - 8 = 0.

For the equation of altitude CL, we have:

Slope of AB = (8 - 0)/(0 - (-2))

Slope of AB = 8/2

Slope of AB = 4

Slope of CL = -1/slope of AB

Slope of CL = -1/4

The equation of altitude CL is given by:

y - y₁ = m(x - x₁)

y - 2 = -1/4(x - 4)

4y - 2= -(x - 4)

4y - 2= -x + 4

4y + x - 2 - 4 = 0.

4y + x - 6 = 0.

In conclusion, we can infer and logically deduce that the equations of the three altitudes of triangle ABC include the following:

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Answer:

See below

Step-by-step explanation:

Distance = rate * time

              = 65 m/hr * 2 1/4 hr = 146.25 miles

rate = distance / time

for Declan :   rate =  146.25 miles / (2 hrs + 35/60 min) = 56.61 mph

1 week = 7 days

10 weeks = 10×7 days

= 70 days

if Ellen reads 1 book in a day

Therefore,

1 day = 1 book

70 days = 70×1

= 70 books.

Thus Ellen reads 70 books in 10 weeks.

Hope helps

Answer:

70 books

Step-by-step explanation:

Ellen reads one book per day for 10 weeks.

All we need to do to know the number of books Ellen read overall is to multiply 1 (number of books he read each day) and 10 weeks (total number of days).

Each week is 7 days, so 10 weeks is equal to 70 days.

The equation will be: 1 x 70

We can conclude that Ellen read 70 books overall within 10 weeks.

The formula that shows the relationship between the distance, rate and time is t = d/r and t = 5.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.

Given that:

d = rt

Hence:

t = d/r

For d = 40, r = 8:

t = 40 / 8

t = 5

The formula that shows the relationship between the distance, rate and time is t = d/r and t = 5.

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Answer:

Step-by-step explanation:

[tex]\frac{1}{2} x=a=\frac{2}{3} y\\\frac{1}{2}x=a\\x=2a \\\frac{2}{3} y=a\\y=\frac{3}{2} a\\x+y=2a+\frac{3}{2} a=\frac{4a+3a}{2} =\frac{7}{2} a=na\\n=\frac{7}{2}[/tex]

The correct answer for the solution of  inequality  is [tex]x\geq 8[/tex].

Let the unknown number be "[tex]x[/tex]."

The statement  "a number plus four" can be written  as "[tex]x+4[/tex]."

The phrase "is greater than or equal to twelve" can be expressed as "[tex]\geq 12.[/tex]

Put these together, the inequality becomes:

[tex]x + 4\geq 12[/tex]

solve for "[tex]x[/tex],"  isolate the variable on one side of the inequality:

Subtract -[tex]4[/tex] from both side of the expression:

[tex]x + 4 - 4 \geq 12 - 4[/tex]

[tex]x\geq 8[/tex]

The correct expression for the  inequality is  [tex]x\geq 8[/tex]

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