MATHEMATICS HIGH SCHOOL

What is the distance between point A and point B? Round to nearest tenth.

Answers

Answer 1

Answer:

Answer:

$d \approx 12.6$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra II

Distance Formula: $d = √((x_2-x_1)^2+(y_2-y_1)^2)$

Step-by-step explanation:

Step 1: Define

Find points from graph.

Point A (-4, 2)

Point B (8, 6)

Step 2: Find distance d

Simply plug in the 2 coordinates into the distance formula to find distance d.

Substitute [DF]: $d = √((8+4)^2+(6-2)^2)$
Add/Subtract: $d = √((12)^2+(4)^2)$
Exponents: $d = √(144+16)$
Add: $d = √(160)$
Simplify: $d = 4√(10)$
Evaluate: $d = 12.6491$
Round: $d \approx 12.6$

Related Questions

Solve x2 + 12x = –11 by completing the square. Which is the solution set of the equation?
If y=-8 when x=-2, find x when y=32
What is one of the solutions to the following system of equations?y^2+x^2=53y-x=5a)(-10,-5)b)(-7,-2)c)(7,2)d)(5,10)
Two same-sized triangular prisms are attached to a rectangular prism as shown below.If a = 20 cm, b = 13 cm, c = 12 cm, d = 5 cm, and e = 8 cm, what is the surface area of the figure?a 1,208 square centimetersb 1,592 square centimetersc 1,004 square centimetersd 1,400 square centimeters
What is 0.000000986 in scientific notation?____x10---

Jill is building a wooden raised bed garden for her vegetable she wants the frame to have dimension X feet by X +3 feet if she wants the garden to have a maximum area of 50 ft.² what are the possible values of X

Answers

Answer: 0ft < X ≤ 5.73ft

Step-by-step explanation:

In this case, we have a rectangle.

For a rectangle of length L and width W, the area is:

A = L*W.

And we have:

L = X

W = X + 3ft.

Then the area will be:

A = X*(X + 3ft) = X^2 + 3ft*X.

And we want to have a maximum area of 50ft^2.

Then we can write:

A = X^2 + 3ft*X ≤ 50ft^2

Now let's solve this for X.

Now, the first thing we can see is that both coefficients in our quadratic equation are positive, so as the absolute value of X increases, also does the whole equation.

Then makes sense start for the upper limit of X, this is when:

X^2 + 3ft*X = 50ft^2.

Now we can solve the quadratic equation:

X^2 + 3ft*X - 50ft^2 = 0

Applying the Bhaskara formula, the solutions are:

$X = (-3ft +- √((3ft)^2 - 4*1*(-50ft^2)) )/(2) = (-3ft +-14.46ft )/(2)$

Then we have two solutions:

X = (-3ft - 14.46ft)/2 = -8.73 ft.

X = (-3ft + 14.46ft)/2 = 5.73 ft

Because X represents a distance, it can only be positive, then we must select the option X = 5.73ft.

This is the maximum value of X, and we will have:

0ft < X ≤ 5.73ft

Where the lower limit is there because we can not have X = 0ft, as this does not have physical meaning.

There are 5 performers who will present their comedy acts this weekend at a comedy club. One of the performers insists on being the first stand-up comedy of the evening. If this performer's request is granted, how many different ways are there to schedule the appearances?

Answers

We have to use basic combinatorics to solver his problem. We first have to determine what kind of problem this is.

Does order matter in this question? Yes it does. So it is a permutation.

Is is a permutation with repetition? No, because once a performer goes, they cannot perform again. Hence, we have defined this problem as a permutation without repetition. The formula for this kind of question is:

$(n!)/((n-r)!)$

Where n is the number of things we choose from, and p is the number of places we want to put them in.

There are 4 places for 4 performers, because 1st performer, lets call him Joe, has already taken the 1st spot. Hence, we substitute our values:

$(4!)/((4-4)!)$

= $4!$

= $24$

There are 24 different ways to schedule this performance.

Hope this helped!

Sincerely,

~Cam943, Junior Moderator

Find the area of a regular octagon with an apothem 9.7 meters long and a side length of 8 meters.

Answers

The area of a regular octagon is:
A = a * P / 2, where a is an apothem and P is a perimeter.
P = 8 * 8 m = 64 m
A = 9.7 m * 64 m / 2
A = 620.8 / 2 m²
A = 310.4 m²
Answer:
The area of a regular octagon is 310.4 m².

Victoria has some money from her birthday and the amount is modeled by the function h(x) = 200. She read about a bank that has savings accounts that accrue interest according to the function s(x) = (1.05)x − 1. Victoria is thinking about putting her money into the savings account to gain interest. Using complete sentences, explain to Victoria how she can combine her functions to create a new function, and explain what this new function means.

Answers

so h(x) is total she has

the other function is interest
if she uses her money to gain interest then she puts in 200 for x in second equation

so subsitute 200 for x
the combined function would be
s(h(x))=(1.05)^(200-1)
basically she put in her savings/gifts and got interst

s(200)=(1.05)^(200-1)
s(200)=(1.05)^(199)
s(200)=16469.1

how is the number of lines of symmetry for a regular polygon connected to the number of sides of the polygon

Answers

Excluding some quadrilaterals, some polygons like a hexagon or square have the same amount of lines of symmetry as they do sides.

Which equation is represented by the table?x y (x, y)
0 –1 (0, –1)
1 4 (1, 4)
2 9 (2, 9)

A.
y = 5x – 1

B.
y = –3x + 3

C.
y = 3x – 4

D.
y = 3x + 3

Answers

1) Find the gradient of the line by using two of the points given.
2) Find the y-intercept by using either one of the points into y=mx+c
3) The eq. is, y=5x-1

Other Questions

HELP? (Simplify in radical form)

An average football field has the dimensions of 160 ft by 360 ft. If the expressions to find these dimensions were (3x + 7) and (7x + 3) what value of would give the dimensions of the football field ?

A rectangular prism has a length of 11.8 meters, a width of 4 meters, and a height of 5 meters. What is the volume of the prism?

Diego parakeet is 13 centimeter 4 millimeters tall how tall is his parakeet In Millimeters