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3 years ago

13

What is the distance between the points M (-3, 7) and N (a, b)?

1 answer:

gavmur [86]3 years ago

4 0

Answer: $\sqrt{ (-3-a)^2 + (7-b)^2 }$

Explanation:

We plug the given coordinates into the distance formula

$d = \sqrt{ (x_1-x_2)^2 + (y_1-y_2)^2 }\\\\$

There isn't much we can do from there since we don't know the values of 'a' or 'b'. You could expand out each binomial, but it's more simplified being factored like that.

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A population of mice is increasing exponentially. On Monday there were 120 most. One month later there were 132 most. Ready func

djyliett [7]

Answer:

$y=120 * 1.1^x$ --- function

The monthly rate is 10%

Step-by-step explanation:

Given

Let

$x \to months$

$y \to mice$

So, we have:

$(x_1,y_1) = (0,120)$ --- Monday

$(x_2,y_2) = (1,132)$ --- One month later

Required

The function

The function is represented as:

$y=ab^x$

In $(x_1,y_1) = (0,120)$ , we have:

$120 = a * b^0$

$120 = a * 1$

$120 = a$

$a=120$

In $(x_2,y_2) = (1,132)$ , we have:

$132 = a * b^1$

$132 = a * b$

Substitute: $a=120$

$132 = 120 * b$

Solve for b

$b = \frac{132}{120}$

$b = 1.1$

So, the function is:

$y=ab^x$

$y=120 * 1.1^x$

To calculate the monthly rate (r), we have:

$y =a(1 + r)^x$

Compare to: $y =ab^x$

$1 + r = b$

Make r the subject

$r = b-1$

Substitute $b = 1.1$

$r = 1.1-1$

$r = 0.1$

Express as percentage

$r = 0.1*100\%$

$r = 10\%$

5 0

3 years ago

You are debating about whether to buy a new computer for $800.00 or a refurbished computer with the same equipment for $640.00.

Xelga [282]

The difference
800−640
=160

160×(1+0.045)
=167.2

3 0

3 years ago

Read 2 more answers

Consider the graph of the quadratic function y = 3x2 – 3x – 6. What are the solutions of the quadratic equation 0 = 3x2 − 3x − 6

Ilya [14]

Roots of the equation 3x² -3x-6=0 are -1 and 2,
all choices are given wrong
3*2²-3*2-6=0
12-6-6=0
0=0, which is true , so root is 2

3*20²-3*20-6=0
600-60-6=0
534=0 which is wrong, so root is 2, but not 20

4 0

3 years ago

I need help I’m helping my son with a project he has to choose 2 ingredients out of his Mac and cheese recipe and tell their rat

AnnyKZ [126]

Answer:

2/3:1

fillerfillerfillerfillerfiller

7 0

3 years ago

Ella and Margaret were at a carnival. They each got a ticket for the carousel. Ella got a jumbo pretzel, and Margaret got a snow

Nikolay [14]

Carousel : 2 x $4 = $8
Snow cone: $4.50
--------------------
$8 + $4.50 = $12.50
The total amount they pay: $5 + $12.75 = $17.75
$17.75 - $12.50 = $5.25
Jumbo pretzel ticket costs $5.25

5 0

3 years ago