4.01 ESSENTIAL QUESTIONS
How do you use the distance formula and slope formula to classify a
quadrilateral?
How do you use the distance formula and slope formula to classify a triangle?
How do you use the distance formula and slope formula to prove properties of
polygons?

4.02 ESSENTIAL QUESTIONS
How do you use the slope to prove lines are parallel or perpendicular?
How do you write an equation of a line so that it is parallel or perpendicular to a
given point?
How do you use parallel and perpendicular lines to solve real-world problems?
4.03 ESSENTIAL QUESTIONS
How do you divide a segment into given ratios?

How do you use coordinates to find the perimeter and area of polygons?

Answer:

19 or √145 ≈ 12.04

Step-by-step explanation:

Use the distance formula to determine the distance between the two points.

Distance  =  √ ( x ₂  −  x ₁ )²  +  ( y ₂  −  y ₁ ) ²

Substitute the actual values of the points into the distance formula.

√ ( 4  −  (  −  5 )) ²  +  ( ( − 5 ) − 3 ) ²

Simplify:  

√ 145

The result can be shown in multiple forms.

Exact Form:

√ 145

Decimal Form:

12.04159457  … ≈ 12.04

Answer:

A is the correct answer .

Step-by-step explanation:

Hope this helps .

The equation that allows you to solve the given equation is (x-3)(2x+5).

Any equation of the form [tex]ax^{2} +bx+c=0[/tex] is called a quadratic equation where a is non-zero.

The given quadratic equation is:

[tex]2x^{2} -15=x[/tex]

[tex]2x^{2} -x-15=0[/tex]

[tex]2x^{2} -6x+5x-15=0[/tex]

[tex]2x(x-3)+5(x-3)=0[/tex]

[tex](x-3)(2x+5)=0[/tex].......(1)

So, the required equation is equation(1).

Hence, the equation that allows you to solve the given equation is (x-3)(2x+5).

To get more about quadratic equations visit:

https://brainly.com/question/1214333

Answer:

The graph shows the solution set of the equality √x < -1

(No Solutions)

Answer:

60

Step-by-step explanation:

this uses the distribution property

first plug in 2 for d

5(10+2)

then distribute the 5 to both numbers in the parentheses

50+10=60

Answer:

The answer is 60

Step-by-step explanation:

First you have to plug in the 2 in place of the variable in the equation. Then add 10+2 first. After you add you will get 12, now you do 5x12 and get 60

Answer:

it will be 300 feet tall and 1000 feet wide

Step-by-step explanation:

The height and width of the arch which support of a bridge and modeled by the provided function is 1000 ft and 300 ft long respectively.

Exponential function is the function in which the function growth or decay with the power of the independent variable. The curve of the exponential function depends on the value of its variable.

The exponential function with dependent variable y and independent variable x can be written as,

[tex]y=ba^x+c[/tex]

Here, a,b and c are the real numbers.

The arch support of a bridge can be modeled by the following function,

[tex]y=-0.0012x^2+300[/tex]

Here, x and y are measured in feet.

The height and width of the arch has to be found out. First, find the x intercept of the function. As at the x intercept, the y equal to zero. Therefore,

[tex]0=-0.0012x^2+300\\0.0012x^2=300\\x=\sqrt{25000}\\x=500[/tex]

As, the graph is symmetric around the y-axis. Thus, the -500 can also be a solution. Now, the width of the arch can be given as,

[tex]w=500-(-500)\\w=1000\rm ft[/tex]

Now similarly at x equal to zero, the function will be,

[tex]y=300[/tex]

Hence, the height and width of the arch which support of a bridge and modeled by the provided function is 1000 ft and 300 ft long respectively.

Learn more about the exponential function here;

https://brainly.com/question/15602982

Answer:

because cfd eaquls a+b lllllllllll

Answer:

Step-by-step explanation:

IT is either the same as 7x+4 because it is infront of each other or you add 8x+6 and 6x+2 then you substract that from 180 to find out the remaining angle. Of course you have to subtitute the amount of x first.

Answer:

12.0 units is the answer

Step-by-step explanation:

Pythagorean theorem can be written as,

[tex]d=\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} \\\\d=\sqrt{(6-(-2))^2 + (1-(-8))^2}\\\\d=\sqrt{(8\\)^2+(9)^2} \\\\d=\sqrt{64+81} \\\\d=\sqrt{145} \\\\d=12.041...[/tex]

Rounding off,

d = 12.0 units

9514 1404 393

Answer:

Step-by-step explanation:

Given:

  daily cost function c(x) = x +11

  price-demand function p(x) = -0.15x +20.8

Find:

  daily profit function

  maximum daily profit

  quantity sold for maximum profit

  price for maximum profit

Solution:

The revenue is the product of price and demand:

  x·p(x) = -0.15x^2 +20.8x

The profit is the difference between revenue and cost:

  f(x) = x·p(x) -c(x) = -0.15x^2 +20.8x -x -11

  f(x) = -0.15x^2 +19.8x -11 . . . . . daily profit function

__

The maximum profit will be had a the vertex of the curve, found where ...

  x = -(19.8)/(2(-0.15)) = 66

  f(66) = (-0.15·66 +19.8)66 -11 = 9.9·66 -11 = 642.40

The maximum profit is $642.40, when 66 gallons of ice cream are sold.

__

The price that will result in demand of 66 gallons of ice cream is ...

  p(66) = -0.15(66) +20.8 = 10.9

The price to charge per gallon to maximize profit is $10.90.

Answer:

9 inches ; 0.7 units ; m units

Step-by-step explanation:

The area of a square is give as :

The square of the side length of the square ; that is ;

Area of square = s² ;

Where s =! Side length of the square

Hence ;

A square with area = 81 in²

Length of its side = sqrt(81) = 9 inches

Area of square = 0.49 unit²

Length of its side = sqrt(0.49) = 0.7 units

Area of square = m² unit²

Length of its side = sqrt(m²) = m units

Answer: True

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Rearrange the data set in numerical order: 1, 2, 2, 3, 5 and take the number in the middle.

Answer:

It would be 6 miles per hour

Step-by-step explanation:

the points are right above of 5 so it would have to be 6.

Answer:

3a-b/(x-b)=1/(x+1)Doing criss cross multiplication

3a(x+1)-b(x+1)=x-b

3ax+3a-bx-b=x-b

3ax-bx-x=b-3a-b

x(3a-b-1)=-3a

x=3a/(3a-b-1)

Answer:

D

Step-by-step explanation:

They are trying to see how long it takes people to complete the writing portion of the test.

Answer:

The Answer is C

Step-by-step explanation:

2.00/5= C

can i have brainlist please :)

9514 1404 393

Answer:

  te, tm, (m-e), t

Step-by-step explanation:

The problem statement tells you how to interpret the expressions and their parts.

Swap the top two expressions on the right and the list will be in the appropriate order:

Answer:

it's 423.4 miles

Step-by-step explanation:

sotry for taking a while I didn't get your notification

Answer:

$53.70 per gram

Step-by-step explanation:

Just divide the price (123.51) by the amount of grams (2.3) to get your answer, which should be $53.70 per gram

Hopefully this helps - let me know if you have any questions!

Answer:

12 dimes and 2 quarters

Step-by-step explanation:

12 dimes is 120 cents and 2 quarters is 50 cents that perfectly gives us 170 cents. As worded if he has 11 Dimes and the rest is quarters and we want 170 cents then it's impossible. 11 dimes is going to be 110 cents plus 2 quarters is 160 cents or plus 3 quarters is going to be 185 cents. therefore you are either short or over the money.

Answer:

=

Step-by-step explanation:

Because |-4| is basically 4 since its the absolute value of that..

Answer:

second one

Step-by-step explanation:

Because when you try to remove the brackets then you should multiply coefficient of x and coefficient of y by 2

So it will be 2x+18y

2*9=18

I believe it's 4 as 32 fluid ounces is 1 quart

Answer:

ok so you said 40 points but theres only 5 points....xD anyways,

we know that 4 would be as 32 fluid ounces.

that would equal 1 quart.

hope this helps! best of luck!!!!

Answer:

Its D because 2×2×2 equals 8 and they are both minus and knowing - times - makes + so it becomes 8

Answer:

B.) -1/8

Step-by-step explanation:

You flip the problem because of the negative exponent

[tex]\frac{1}{-2^3}[/tex]

This makes the exponent positive

Expand the denominator

(-2) * (-2) * (-2) = 4*(-2) = -8

1/-8 = -1/8

We have proved that the Newton-Raphson iteration formula for solving the equation[tex]x^k e^x = 0[/tex] is given by [tex]x_{n+1} = (k - 1) x_n + x_n^2 / k + x_n.[/tex]

To prove that the Newton-Raphson method for solving the equation [tex]x^k e^x = 0[/tex], where k is a constant, is given by the formula

[tex]x_{n+1} = (k - 1) x_n + x_n^2 / k + x_n,[/tex]

we can start by considering the iterative process of the Newton-Raphson method.

Given an initial guess [tex]x_n[/tex], we want to find a better approximation [tex]x_{n+1}[/tex]that is closer to the root of the equation [tex]x^k e^x = 0.[/tex]

The Newton-Raphson method involves the following steps:

Calculate the function value [tex]f(x_n) = x_n^k e^x_n[/tex] and its derivative [tex]f'(x_n) = k x_n^(k-1) e^x_n.[/tex]

Find the next approximation x_{n+1} by using the formula:

[tex]x_{n+1} = x_n - f(x_n) / f'(x_n)[/tex]

Let's apply these steps to our equation [tex]x^k e^x = 0[/tex]:

Calculate the function value and its derivative:

[tex]f(x_n) = x_n^k e^x_n\\f'(x_n) = k x_n^(k-1) e^x_n[/tex]

Find the next approximation x_{n+1} using the formula:

[tex]x_{n+1} = x_n - f(x_n) / f'(x_n)[/tex]

Substituting the function value and its derivative:

[tex]x_{n+1} = x_n - (x_n^k e^x_n) / (k x_n^(k-1) e^x_n)\\= x_n - (x_n^k / k)[/tex]

Simplifying the expression by combining like terms:

[tex]x_{n+1} = x_n - (x_n^k / k)\\= x_n - x_n^k / k\\= (k - 1) x_n + x_n^2 / k + x_n[/tex]

Therefore, we have proved that the Newton-Raphson iteration formula for solving the equation[tex]x^k e^x = 0[/tex] is given by [tex]x_{n+1} = (k - 1) x_n + x_n^2 / k + x_n.[/tex]

for such more question on Newton-Raphson iteration

https://brainly.com/question/17150870

#SPJ8

Answer:

80 miles for the .9 one.

Step-by-step explanation:

Answer:

b = -108

Step-by-step explanation:

Step-by-step explanation:

Given

[tex] - 6 = \frac{b}{18} \\ cross \: multiply \\ b = - 6 \times 18 \\ b = - 108[/tex]

Hope it will help :)❤