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2 years ago

6

Destiny's class packs school lunches for the local homeless shelter. They pack the same number of lunches each minute. In 6 minu

tes, the class packs 18 lunches.
At this rate, how many lunches does the class pack in 28 minutes?

1 answer:

Leno4ka [110]2 years ago

8 0

Make is a proportion
6/18=28/x
Cross multiply
18•28=6•x
504=6x
x=84

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Find all points on the circle (x^2) + (y^2) = 676 where the slope is 5/12

borishaifa [10]

Implicit defferentation

remember that dy/dx y= dy/dx

so
take derivitive of both sides
$2x+2y \space\ \frac{dy}{dx}=0$
solve for $\frac{dy}{dx}$
minus 2x both sides
$2y \space\ \frac{dy}{dx}=-2x$
divide both sides by 2y
$\frac{dy}{dx}=\frac{-2x}{2y}$
$\frac{dy}{dx}=\frac{-x}{y}$

when is the slope equal to $\frac{5}{12}$
solve for $\frac{dy}{dx}=\frac{5}{12}$
$\frac{dy}{dx}=\frac{5}{12}$
$\frac{5}{12}=\frac{-x}{y}$
$5y=-12x$
$y=\frac{-12}{5}x$
find where the circle and this line intersects

substitute $\frac{-12}{5}x$ for y
$x^2+(\frac{-12}{5}x)^2=676$
$x^2+\frac{144}{25}x^2=676$
$\frac{25}{25}x^2+\frac{144}{25}x^2=676$
$\frac{169}{25}x^2=676$
times both sides by $\frac{25}{169}$
$x^2=100$
sqrt both sides, take positive and negative roots
x=+/-10

sub back

$y=\frac{-12}{5}x$
$y=(\frac{-12}{5})(10) \space\ or \space\ (\frac{-12}{5})(-10)$
$y=\frac{-120}{5} \space\ or \space\ \frac{120}{5}$
$y=-24 \space\ or \space\ 24$

the points are (10,-24) and (-10,24)

8 0

2 years ago

Determine the value of base x if (211)x = (6A)16

igor_vitrenko [27]

$211_x=2x^2+x+1$
$6A_{16}=106_{10}$

$\implies 2x^2+x+1=106\iff 2x^2+x-105=(x-7)(2x+15)=0$

This has two solutions, $x=7$ and $x=-\dfrac{15}2$ .

4 0

2 years ago

Paula has a dog that weighs 3 times as much as Carla's dog

ivanzaharov [21]

Answer:

The weight of Paula's dog is 36 pounds.

Step-by-step explanation:

SO we would draw one box for the weight of Carla's dog. Then we would draw 3 boxes for the weight of Paula's dog.

To find how much does Paula's dog weigh we divide the total weight of the dogs by the total number of boxes.

So then you would calculate 48 divided by 4.

The weight of Carla's dog is 12 pounds.

Therefore the weight of Paula's dog is 3x12=3x10+3x2=30+6=36 pounds.

4 0

2 years ago

There are five envelopes on a table. Four of the envelopes are marked 8, 2, 4 and 1. You are told that the mean of the numbers o

Lostsunrise [7]

Answer: 16

Step-by-step explanation:

3 0

1 year ago

The cost in dollars of making x items is given by the function C(x)=10x+800. a. The fixed cost is determined when zero items are

deff fn [24]

Answer:

1. Fixed cost is $800

2.Cost of 25 bags is $1025

3. (170,2300)

Step-by-step explanation:

Given

$c(x) = 10x + 800$

Solving (a): Fixed cost

From the question, fixed cost is when x = 0;

Substitute 0 for x in $c(x) = 10x + 800$

$c(0) = 10 * 0 + 800$

$c(0) = 0 + 800$

$c(0) = 800$

<em>Hence, the fixed cost is $800</em>

Solving (b): Cost of making 25 items

Here; x = 25

Substitute 25 for x in $c(x) = 10x + 800$

$c(25) = 10 * 25 + 800$

$c(25) = 250 + 800$

$c(25) = 1025$

<em>Hence, the cost of 25 bags is $1025</em>

<em></em>

Solving (c): Domain and Range where Maximum cost = $2300

Here; c(x) = 2500

Substitute 25 for c(x) in $c(x) = 10x + 800$

$2500 = 10x + 800$

Subtract 800 from both sides

$10x = 2500 - 800$

$10x = 1700$

Divide both sides by 10

$x = 170$

The domain and range of a function is in form of (x,c(x))

<em>Hence, the domain and range is (170,2300)</em>

4 0

2 years ago