Stephen is making a map of his neighborhood. He knows the following information: His home, the bus stop, and the grocery store are all on the same street. His home, the park, and his friend's house are on the same street. A street map is shown. The streets form a triangle comprised of the locations of home, friends house, and the grocery store. The triangle is intersected by a line formed by the park and the bus stop. Stephen wants to use the Triangle Proportionality Theorem to determine the relationships on his map. He knows the angle between the park, the bus stop, and his home. Which other angle does he need to know

let's keep in mind that a conjugate is no more than the same "pair" but with a different sign between, so the conjugate of meow + quack is simply meow - quack, and so on, let's also recall that i² = -1.

[tex]\textit{difference of squares} \\\\ (a-b)(a+b) = a^2-b^2 \\\\[-0.35em] ~\dotfill\\\\ -1-\sqrt{5}i\hspace{5em}\stackrel{conjugate}{-1+\sqrt{5}i} \\\\\\ (-1-\sqrt{5}i)(-1+\sqrt{5}i)\implies (-1)^2~~ - ~~(\sqrt{5}i)^2\implies (-1)^2~~ - ~~(\sqrt{5})^2 i^2 \\\\\\ 1~~ - ~~(\sqrt{5^2})i^2\implies 1~~ - ~~(5)(-1)\implies 1-(-5)\implies 1+5\implies \text{\LARGE 6}[/tex]

Answer:

12

Step-by-step explanation:

1) FInd the sides of small triangle. Since it has 2 congruent angles it also has to congruent sides opposite those angles. So the sides adjacent (connected to) the right angle are both 6.

2) Find the hypotenuse (side opposite the right angle) in the small triangle

a^2 +b^2 = c^2

6^2 +6^2 = c^2

36+36 = c^2

72 = c^2

c = [tex]\sqrt{72}[/tex]

In simplified radical form  [tex]\sqrt{72\\[/tex] = 6[tex]\sqrt{2}[/tex]

3) Now find the sides of big triangle. It has 2 congruent angles therefore it has two congruent side opposite those angles. We know that one of the sides is 6[tex]\sqrt{2}[/tex] because it is also the hypotenuse of the small triangle. The other side adjacent to the right angle is also 6[tex]\sqrt{2}[/tex].

4) Now find x which is the hypotenuse of the big triangle.

[tex](6\sqrt{2} )^{2}[/tex]+                    [tex](6\sqrt{2} )^{2}[/tex]= [tex]c^{2}[/tex]

(36*2)+(36*2) = [tex]c^{2}[/tex]

144 = [tex]c^{2}[/tex]

c = 12

so x = 12

Solving the quadratic equation, it is found that the company needs to sell 8 products for the net income to be equal $0.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

It is given by:

f(x) = 9x² - 54x - 144.

It can be simplified as follows:

f(x) = 9(x² - 6x - 16)

Then:

f(x) = 9[(x + 2)(x - 8)]

It has a net income equals to 0 when:

f(x) = 0,

hence:

x + 2 = 0 -> x = -2.

x - 8 = 0 -> x = 8.

The amount of products sold is positive, hence, the company needs to sell 8 products for the net income to be equal $0.

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Answer:

500 > 40 + 5t

Step-by-step explanation:

At least 500

40 intro = initial, constant

t = time in seconds

5 words per second

Please mark as brainliest

Answer:

A) 4x4 – 3x3y + 8x2y2 – 7xy3

Step-by-step explanation:

The polynomial written in standard form is: 4x4 + 8x2y2 - 3x3y - 7xy3. Option C

In standard form, a polynomial is written with the highest exponents first and positive numbers in front of each term.

This means that the term with the greatest power comes first, followed by the terms in decreasing order of powers.

The polynomial is organized in option C like this.

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Answer:

54 loaves of bread

Step-by-step explanation:

45:5=9 (45 divided by 5 equals 9)

9x6=54 (9 times 6 equals 54)

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$1230\\ r=rate\to 3.19\%\to \frac{3.19}{100}\dotfill &0.0319\\ t=years\dotfill &3 \end{cases} \\\\\\ A = 1230[1+(0.0319)(3)] \implies \stackrel{balance}{\boxed{A \approx 1347.71}}~\hfill \underset{interest}{\stackrel{1347.71~~ - ~~1230}{\boxed{117.71}}}[/tex]

Answer:

1) 33.422

2) 0.37

3) 34.034567

4) 19.501

5) 38.07

6) 51.02

7) 65.38

8) 0.072

Cheers

Answer:

$7

Step-by-step explanation:

Got it right on a test

A. The total number of points of intersection of the graphs of the equations y = 5e^x and xy = 20 is two.

To find the points of intersection, we must solve the two equations for x and y.

For the first equation, y = 5e^x, we can solve for x by taking the natural logarithm of both sides and getting x = ln(y/5).

For the second equation, xy = 20, we can solve for y by dividing both sides by x and getting y = 20/x.

We can then substitute the expression for x in terms of y into the expression for y in terms of x and solve for y to get y = 20/(ln(y/5)). This is a nonlinear equation that must be solved numerically.

By using numerical methods, we can solve the equation and find the two points of intersection, which are (x, y) = (3.68, 4.64) and (x, y) = (0.87, 22.95).

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The domain of the given rational function R(x) = 6x/(x + 1) include the following: A. the domain of R(x) is {x|x ≠ 1}.

In Mathematics, a domain can be defined as the set of all real numbers for which a particular function is defined.

This ultimately implies that, a domain is the set of all possible input numerical values or numbers (x-values) to a function and the domain of a graph comprises all the input numerical values (real numbers) which are located on the x-coordinate.

In order to determine the domain of this rational function, we would use an online graphing calculator to plot it and then write its domain in interval notation based on the graph as follows:

Domain = (-∞, 1) U (1, ∞)

By using set builder notation, the domain of this rational function R(x) = 6x/(x + 1) can be re-written as follows;

Domain = {x|x ≠ 1}.

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Answer: 15/2

Step-by-step explanation: -5/2 + 1/4W = -5/8

-    1/4W = -5/8 + 5/2

-    1/4W = 15/8

-     W = 15/8 × 4

-      W = 15/2

We may apply the simple interest formula to find the due date for repayment from Mikos is 5 months.

I = P*r*t, where I represents interest, P the principal (initial sum), r the interest rate, and t the period of time in years.

The maturity value formula can be used to calculate interest given that the loan's principal is $100,000 and its maturity value is $104,375:

Where MV is the maturity value, P is the principal, and I is the interest, the formula is: MV = P + I.

With the above data, we obtain: 104,375 = 100,000 + I

  I = 4,375.

Now we can use this value of I to find the time t in years:

I = P*r*t

4,375 = 100,000 (0.105) t

t = 4.375 / (100,000 x 0.105)

t = 4.375 / 10,500

t = 0.417 years or approximately 5 months

 So, it takes approximately 5 months to repay the pay back amount .

Therefore, Mike must repay the amount by April 14, which is around five months after the day he took out the loan.

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The equation in slope-intercept form of a line whose slope is 9 and whose y-intercept is -3 is equals to the y = 9x-3.

Slope intercept form of an equation : The slope intercept form is one of method to determine the equation of a straight line in the coordinate plane. The equation of a straight line is a relation which:

Let us assume a straight line of slope 'm' and y-intercept 'b'. The equation of slope intercept form for a straight line with slope, say, 'm', and the y-intercept, 'b', is

y = mx + b

Now, the slope of line , m = 9

y-intercept of line, b = - 3

As we know slope intercept form of a line is, y = mx + b , so plugging the known values of slope and y-intercept in it,

=> y = 9x - 3

So, required equation in slope intercept form of line is y = 9x - 3.

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Answer:

Step-by-step explanation:

1. Identify the equation and its variables.

The equation can be any type of equation, such as a linear equation, quadratic equation, or polynomial equation. Identify the variables in the equation and label them.

2. Find a strategy for solving the equation.

Depending on the type of equation, there are various strategies for solving the equation. For example, a linear equation can be solved using the addition-subtraction method, a quadratic equation can be solved using the quadratic formula, and a polynomial equation can be solved using the synthetic division method.

3. Use the strategy to solve the equation.

Follow the steps of the chosen strategy to solve the equation. This may involve expanding the equation, factoring, or rearranging the equation.

4. Check the solution.

Once the equation is solved, check the solution by plugging the answer back into the equation and verifying that it works.

5. Review and summarize the steps.

Review the steps taken to solve the equation and summarize them in a few sentences. This will help with understanding and remembering the steps.

A type I error, also known as a false positive, is when a test incorrectly rejects the null hypothesis. In this context, a type I error would mean that the test incorrectly concludes that the proportion of water bottles that are recycled is more than 23% after the program, when in reality it is still 23%.

1. Calculate the means of the two samples.

2. Calculate the standard deviation of the two samples.

3. Calculate the degrees of freedom (df) by subtracting 1 from the total

number of samples.

4. Calculate the t-statistic by subtracting the means of the two samples, dividing the result by the standard deviation, and then dividing that result by the square root of the degrees of freedom.

5. Calculate the critical value of t from the t-distribution table for the degrees of freedom and the chosen level of significance.

6. Compare the calculated t-statistic with the critical value of t.

7. Make a decision – accept or reject the null hypothesis.

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The best estimate of the average change in rent each year include the following: C. $40.

Mathematically, the rate of change is also referred to as slope or gradient and it can be calculated by using this formula;

Rate of change, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Rate of change, m = (y₂ - y₁)/(x₂ - x₁)

Next, we would determine the rate of change of the value of y with respect to the value of x on the scatter plot, which represents a line that is passing through the points (0, 800) and (10, 1200):

Rate of change, m = (1200 - 800)/(10 - 0)

Rate of change, m = 400/10

Rate of change, m = 40.

Based on the scatter plot, we can reasonably infer and logically deduce that the average rate of change in rent each year is equal to 40 dollars.

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Complete Question:

The scatter plot below shows the average rent (in dollars per month) for a 1-bedroom apartment in New York City each year between 2000 and 2013.

Which of the following is the best estimate of the average change in rent each year?

answer choices

$0.5

$1

$40

$400

Therefore , the solution of the given problem of linear equation comes out to be 550 minutes she can use her cell phone.

A linear regression model is one that conforms to the algebraic equation y=mx+b. The slope is B, and the y-intercept is m. The previous clause is usually referred to as an "mathematical equation having two variables because both y and x are unique parameters. Two variables make up bivariate linear equations. Linear equations have a variety of applications, all of which have a zero outcome. Y=mx+b, where m stands for the gradient and b for the y-intercept, is the formula for a linear equation.

Here,

Given : 55=0.1(m-500)+50

where m is the number of minute

=> 55=0.1(m-500)+50

=> 55=0.1m-50+50

=>55=0.1m-0

=>55-0=0.1

=>55=0.1

=>0.1=0.1

=>550=m

Therefore , the solution of the given problem of linear equation comes out to be 550 minutes she can use her cell phone.

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Answer:

4 km wide and 6 km long.

Step-by-step explanation:

Let the width be x, then the length is x+2 km.

Area = width * length

Substituting the given values:

24 = x(x + 2)

24 = x^2 + 2x

x^2 + 2x - 24 = 0

(x + 6)(x - 4) = 0

x = -6, 4

As x must be positive, then x = 4.

So, the dimensions are 4 and 4+2

= 4, 6,

Answer:

width = 3.46 km and length = 6.93 km

Step-by-step explanation:

let the width be : X km

then the length would be: 2X km

as area is length x width

therefore:

2X x X = 24

2X² = 24

X² = 24/2

X² = 12

X = [tex]\sqrt{12}[/tex]

X=  3.46

the width would be 3.46 km while the length would be 2X = (93.46) = 6.93 km

The sides given as 16cm , 12cm and 20cm  forms a right triangle because the sides satisfies the condition of Pythagoras Theorem .

What is Pythagoras Theorem ?

The Pythagoras Theorem states that the square of the longest side (hypotnuse) is equal to the sum of the square of the other two sides .

The sides of the triangle are given as ⇒ 16cm , 12cm and 20cm ;

here the hypotnuse (longest side) is = 20 cm ;

According to Pythagoras theorem ,

⇒ [tex]20^{2} =12^{2} +16^{2}[/tex] ;

⇒ [tex]400 =144+256[/tex] ;

⇒ [tex]400=400[/tex] ;

So , The condition of Pythagoras theorem is satisfied .

Therefore , the given sides can form a Right Triangle .

The given question is incomplete , the complete question is

Does the sides 16cm , 12cm and 20cm form a right triangle ?

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Answer:

  see attached

Step-by-step explanation:

You want the steps in order for constructing a perpendicular to a line through an external point.

Essentially, the procedure identifies two points on the line (P and Q) that are equidistant from the external point (R), then proceeds to draw a perpendicular bisector of the segment between those two points. The external point is already equidistant from P and Q, so we only need to find another equidistant point (S) to complete the construction.

See the attachment for the ordering of the instruction steps. (Note the step numbers are not in order on the left.)

For Sydney with $100 at 5%, monthly, for 10 year we get 229050.

Annual percentage rate (APR) refers to the yearly interest generated by a sum that's charged to borrowers or paid to investors. APR is expressed as a percentage that represents the actual yearly cost of funds over the term of a loan or income earned on an investment.

The interest rate is the amount a lender charges a borrower and is a percentage of the principal—the amount loaned. The interest rate on a loan is typically noted on an annual basis known as the annual percentage rate (APR).

Let the equation be

A = [ p(1 + r/n)nt ] + [ PMT ((( 1 + r/n)nt - 1) / (r / n)) ]

For Sydney with $100 at 5%, monthly, for 10 year

A = [ 100(1 + 0.05/12)(12)(10) ] + 100 (((1 + 0.05/12)(12)(10) - 1) / (0.05 / 12)) ]

= 229050

Therefore, the correct answer is 229050.

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If a figure can be transformed into another figure by a sequence of translations, rotations, and reflections, and the size and shape remain the same, the figures are congruent.

A congruence transformation is a type of transformation that preserves the size and shape of a figure. The most common congruence transformations are translations, rotations, and reflections.

Translations involve moving a figure a certain distance in a certain direction without changing its size or orientation.

Rotations involve rotating a figure around a certain point without changing its size or shape.

Reflections involve flipping a figure over a certain line without changing its size or shape.

In order to show that two figures are congruent, you can use a combination of these congruence transformations to match one figure to the other. By using these transformation you can map each point of one figure to a corresponding point on the other figure and if the size and shape of figures remain the same, that means that the figures are congruent.

It's important to notice that Congruence is an equivalence relation and it's reflexive, symmetric, and transitive.

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The dimensions of the rectangular plot that require the least amount of fencing is :

A(17.32, 17.32) = 600

P(17.32, 17.32) = 121.24

Now, According to the question:

600 [tex]u^2[/tex] of land to be enclosed by fence

Area inside plot should be maximized, amount of fence should be minimized

If we draw a quick sketch, we get something like this:

_____ _____

|        |         |

|        |         |

|        |         |

|        |         |

The two rectangles could be different sizes but if one rectangle size maximizes area then it would make sense to use that some rectangle for both sides.

Let's put some variables into our picture so we can define our constraints.

       y        y  

  |         |        |

x |      x |      x |

  |         |        |

  |         |        |

Now we just need an equation to connect our unknowns (how much fence to use) to our constraint (it has to have an exact area of 600 u^2.

A = x × 2y = area = 600

P = 3x + 4y = perimeter = a minimum

First we solve the area equation for y:

y = [tex]\frac{600}{2x}[/tex] = [tex]\frac{300}{x}[/tex]  

and then we substitute that result into our perimeter equation:

P = 3x + 4 (300/x)

P = 3x + 1200/x

Our perimeter equation is: P(x) = 3x + 1200/x OR P(x) = 3x +1200[tex]x^-^1[/tex]

We can find what value of x makes our perimeter as small as possible (a minimum) by graphing or by using Calculus.

In Calculus we know that maximums and minimums always occur when the derivative is zero. This is because the slope (rate of change) at these points in a graph are always flat or zero. Our derivative is

P'(x) = 3 - 1200[tex]x^-^2[/tex]

When set equal to zero, we can solve for x:

3 - 1200[tex]x^-^2[/tex]= 0

1 - 400[tex]x^-^2[/tex] = 0

1 = 400/[tex]x^{2}[/tex]

[tex]x^{2}[/tex] = 400

x = ± 20

Our fence length can't be a negative number so our answer must be 20u.

If our x length is 20, then our y length must be 300/x to ensure our area is 600 u^2.

The y length is 300/(20) = 15

Let's put all of our numbers into our picture to see if it make sense.

      15      15    

    |        |         |

20 |    20 |    20 |

    |        |         |

    |        |         |

       15      15

Sure enough our area is 600.

Here's what we have right now:

A(20, 15) = 600

P(20, 15) = 120

How about we try something a little bigger like 20.5 for x and 14.63 for y?

A(20.5, 14.63) = 600

P(20.5, 14.63) = 120.02

How about we try something a little smaller like 19.5 for x and 15.38 for y?

A(19.5, 15.38) = 600

P(19.5, 15.38) = 120.02

It looks like if we try to change x, even a little, to make it bigger or smaller the perimeter only gets bigger.

You might have guessed at the beginning that a square is the best shape to use to maximize area, so let's try that as well.

Each rectangle is 300 u^2. We want a square so each side would be √(300) = 17.32

              17.32         17.32    

        |                |                 |

17.32 |       17.32 |        17.32 |

        |                |                 |

             17.32          17.32

A(17.32, 17.32) = 600

P(17.32, 17.32) = 121.24

Hence, The dimensions of the rectangular plot that require the least amount of fencing is :

A(17.32, 17.32) = 600

P(17.32, 17.32) = 121.24

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Answer:

1000 mitre=1km

1.25 ×1000

Answer:

DIGIT FORM = 13km

DECIMAL FORM: 12.5km

Step-by-step explanation:

DIGIT Form: A digit can only be a whole number, so round 12 and a half (12/5 or 12.5) to the nearest whole number.

DECIMAL Form: It cannot be a whole number and must consist of a number followed by a decimal point (a period) and then another number.

DON'T FORGET TO ADD KILOMETERS (km) AFTER YOUR ANSWER.

Answer:

a. Leslie must pay the first $500 of the repair costs, as that is her comprehensive insurance policy's deductible.

b. The insurance company must pay the remaining $1,266 of the repair costs, as that is the total cost of the repairs ($1,766) minus Leslie's portion of the cost (the $500 deductible).

Therefore , the solution of the given problem of combination comes out to be  479001.6.

Combinations are mathematical procedures that count the number of possible configurations from a set of items, where the selection direction is immaterial. You can select any arrangement of the parts in any combination. It's possible to mix together combinations and permutations.

Here,

Given : four ambassadors and one advisor for each of them are to be seated at a round table with 12 chairs numbered in order 1 to 12..

and n ways for seating 8 people.

Thus , to find this permutation- combination arrangement .

So,

nPr => 6 P 6 and * 12P6

nPr =>  665280 * 720

nPr = > 47,90,01,600

and divide it by 1000 .

So ,

=> 479001600/1000

=> 479001.6

Therefore , the solution of the given problem of combination comes out to be  479001.6.

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Answer:

real number, in mathematics, a quantity that can be expressed as an infinite decimal expansion. Real numbers are used in measurements of continuously varying quantities such as size and time, in contrast to the natural numbers 1, 2, 3, …, arising from counting

Step-by-step explanation:

The quotient of any two integers is an integer.

A real number is a number that can be measured and represented on a number line; this includes fractions, decimals, irrational numbers, rational numbers, and basically every number you encounter. With that in mind, the quotient of 2 real numbers is not necessary an interger as 2.01/ 1 is not an integer

Yes, the set of all real numbers is uncountably infinite but "infinity" is not   a member of the set of real numbers.

Basically, The real numbers R is the set of "all the numbers" on the number line that  includes the rationals and irrationals together.

The real numbers are an uncountably infinite set – there actually are far more real numbers than there are natural numbers, and there is no way to line up the reals and the naturals so that we are assigning exactly one real number to each natural number. Hence there is no possible way of counting the number it can be considered in the category of uncountably infinite. If the domain of a function is all real numbers, you can represent this using interval notation as (−∞,∞), however "infinity" is not a member of the set of real numbers.

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