Write an equation in slopeintercept form for the line that passes through (6, 5) and is

For how many integers $n$ is it true that $\sqrt{n} \le \sqrt{4n - 6} < \sqrt{2n + 5}$?

ale4655 [162]

$\bf \sqrt{n}\leqslant \sqrt{4n-6}$

$\bf \sqrt{n}< \sqrt{2n+5}\implies \stackrel{\textit{squaring both sides}}{n< 2n+5}\implies 0\leqslant 2n - n + 5 \\\\\\ 0 < n+5\implies \boxed{-5 < n} \\\\\\ \stackrel{-5\leqslant n < 2}{\boxed{-5}\rule[0.35em]{10em}{0.25pt}0\rule[0.35em]{3em}{0.25pt}2}$

namely, -5, -4, -3, -2, -1, 0, 1. Excluding "2" because n < 2.

6 0

4 years ago

Please answer the question because I don’t understand can you answer please!,,

Minchanka [31]

Answer:y= 2x+7

Step-by-step explanation:

They are all pretty much want you to create the equation so the formula they want is y=mx+b format.

First problem(1,9) slope 2

Y=mx +b

Where y is 9,x is 1 and slope (m) is 2.

Now solve for b using equation

Y=mx +b

9= 2(1)+b

9=2+b

9-2=b

7=b

Now you can create equation

Y= 2x+7

Prob.4

(3,-6) and (-1,2)

First find slope

M= y2-y1/x2-x1

M= 2-(-6)/-1-3

M = 8/-4

M= -2

Your slope "m" is -2

Now do as problem 1 get one of the points and your slope to get equation .

(3,-6) slope -2

Y=mx+b

-6= -2(3)+b

-6= -6+b

-6+6=b

0=b

Y= -2x

Problem 7

(5,13) (10,14)

You solve this one as problem 4 same steps that I did above .

Problem 8 is also the same as steps in problem 4

( 2,160) and ( 2.75,220)

I hope this helps you

5 0

4 years ago

A store has a coupon for $10 off and a discount of 20%. Write a function for the coupon. Use x for the original price and C for

Ludmilka [50]

<h2>Explanation:</h2><h2></h2>

We know some facts:

x for the original price.
The store has a coupon for $10 off and a discount of 20%
C for the price after the coupon is applied.

So from the statement 2, you can realize there are two types of discounts:

The discount offered by the coupon
The discount offered by 20%

Since we need to write a function just for the coupon, then we don't include the discount offered as percentage, then we subtract the coupon from the original price:

$\boxed{C=x-10}$

8 0

3 years ago

Please help.........

Schach [20]

Answer: what the heck do you have to answer

Step-by-step explanation:

3 0

3 years ago

Toby's Tiny Toys have fixed expenses of $53,900 for the production of their tiny toys. Toby's has a variable expense of $12.50 a

ipn [44]

The total cost of the factory will be the sum of its variable costs and it's fixed costs. The factory has fixed costs of $53,900 and variable costs of $12.50 per unit produced. Let $x$ be the number of toy's produced by this Toby's Tiny Toys, then the total variable costs will be $12.50x$ . From this information we can gather that the cost function for this factory is,

$C(x)=53\,900+12.50x.$

On the other hand, if we let $x$ be the number of toys sold, we can gather that at the selling price of 16.50, the revenue function will be ,

$R(x)=16.50x.$

Toby's Tiny Toys will reach their break even point when the total costs are equal to the total revenue. At this break even point ,we have that

$R(x)=C(x)\\\implies 16.50x=12.50x+53\,900\\\implies 16.50x-12.50x=53\,900\\\implies 4x=53\,900\\\implies x=\frac{53\,900}{4} \\\implies x=134\,750.$

The company has to sell 134 750 units to break even.

6 0

3 years ago