What is the next numbere 11 13 16 21 28 39

Suppose that receiving stations X, Y, and Z are located on a coordinate plane at the points (4,5), (-6,-6), and (-14,2

Lilit [14]

Answer:

(-2, -3)

Step-by-step explanation:

A careful graph shows the point (-2, -3) is at the intersection of the circles whose radii are the given distances from the receiving stations.

_____

The simultaneous equations for the circles can be solved algebraically.

The epicenter is 10 units from X, so lies on the circle ...

(x -4)^2 +(y -5)^2 = 10^2

x^2 -8x +16 +y^2 -10y +25 = 100

x^2 +y^2 -8x -10y = 59

__

The epicenter is 5 units from Y, so lies on the circle ...

(x +6)^2 +(y +6)^2 = 5^2

x^2 +12x +36 +y^2 +12y +36 = 25

x^2 +y^2 +12x +12y = -47

__

The epicenter is 13 units from Z, so lies on the circle ...

(x +14)^2 +(y -2)^2 = 13^2

x^2 +28x +196 +y^2 -4y +4 = 169

x^2 +y^2 +28x -4y = -31

__

Subtracting the second equation from each of the other two, we get ...

(x^2 +y^2 -8x -10y) -(x^2 +y^2 +12x +12y) = (59) -(-47)

-20x -22y = 106 . . . . eq1 -eq2

(x^2 +y^2 +28x -4y) -(x^2 +y^2 +12x +12y) = (-31) -(-47)

16x -16y = 16 . . . . . . . .eq3 -eq2

These simultaneous linear equations can be solved a variety of ways. We might use substitution:

x = y+1 . . . . . from eq3 -eq2 divided by 16

10(y +1) +11y = -53 . . . . . from eq1 -eq2 divided by -2

21y = -63 . . . . . . . . . . . . simplify, subtract 10

y = -3

x = y+1 = -2

The epicenter is located at (x, y) = (-2, -3).

8 0

3 years ago

Enzel goes online to buy a graphing calculator. He finds a site that currently has a promotion of 15% off on all orders over $50

maw [93]

<h2>Steps</h2>

So firstly, we need to find the discounted price. Since this is going to be a <em>decrease by percentage</em>, we will be using this format:

(1 - p)m
<em>(p = percentage in decimal form and m = original price)</em>

In this case:

$15\% = 0.15\\\\(1-0.15)*83\\0.85*83\\70.55$

Now that we have the discounted price, we must apply the 4.5% sales tax. Since this is going to be an <em>increase by percentage</em>, we will be using this format:

(1 + p)m

In this case:

$4.5\%=0.045\\\\(1+0.045)*73.55\\1.045*70.55\\73.72$

Now we have the discounted price with the sales tax. Now all we have to do is add the shipping fee:

$73.72+6.35=80.07$

<h2>Answer</h2>

<u>The total price of Enzel's purchase is $80.07.</u>

8 0

3 years ago

Read 2 more answers

A map of a park says its scale is 1 to 100. What do you think that means? help I'm confused on this one??????

Nuetrik [128]

Answer:

Ratio scales

If the scale of the plan is 1 : 100 this means the real measurements are 100 times longer than they are on the plan

8 0

3 years ago

Find the degree of the polynomial: <br> 8xyz^7-8x^3yz^4+2x^3y^3

Nuetrik [128]

Answer:

The degree of the polynomial is 9

Step-by-step explanation:

Recall that the degree of a polynomial is given by the degree of its leading term (the term with largest degree). Recall as well that the degree of a term is the maximum number of variables that appear in it.

So, let's examine each of the terms in the given polynomial, and count the number of variables they contain to find their individual degrees. then pick the one with maximum degree, and that its degree would give the actual degree of the entire polynomial.

1) term $8\,x\,y\,z^7$ contains one variable "x" , one variable "y", and seven variables "z", so a total of nine. Then its degree is: 9

2) term $-8\,x^3\,y\,z^4$ contains three variables "x" , one variable "y", and four variables "z", so a total of eight. Then its degree is: 8

3) term $2\,x^3\,y^3$ contains three variables "x" and three variables "y", so a total of six variables. Then its degree is : 6

Therefore, the leading term of this polynomial is the first one, and it gives its degree to the entire polynomial. the polynomial is of degree 9.

7 0

3 years ago

Hat expression is equivalent to (5z^2+3z+2)^2

Lelechka [254]

25z^4+30z^3+29z^2+12z+4

8 0

3 years ago

Read 2 more answers

What is the next numbere 11 13 16 21 28 39​

What is the next numbere 11 13 16 21 28 39