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OverLord2011 [107]
3 years ago
8

Decide which is the better value based on the unit prices. ( show your work).

Mathematics
1 answer:
alexdok [17]3 years ago
3 0

The questions are asking about unit prices (price per 1 unit of thing)

we want to find out which is the better deal

we want to find out which price/1item is least (you want to pay as little as possible per item)

so to solve each problem, divide price by number of things to get the unit price (price per unit)


1) $25.00 for concert tickets for 2 people or $36.00 for concert tickets for 3 people.

$25 for 2 people is $25/2=$12.50/person

vs

$36 for 3 people is $36/3=$12.00/person

12<12.5 so better value is the $36 for 3 people


2) $380 for a bus for 32 people or $420 for a bus for 38 people.

$380 for 32 people is $380/32=$11.875/person

vs

$420 for 38 people is $420/38=$11.05/person

11.05<11.875

$420 for 38 people is better value


3) $4.25 for 4 liters of milk or $2.55 for 2 liters of milk.

$4.25 for 4 lieter is $4.25/4=$1.06/liter

vs

$2.55 for 2 lieter is $2.55/2=$1.27/liter

1.06<1.27 so $4.25 for 4 liter is better value


4) 35 grams of mixed nuts for $0.99 or 59 grams of mixed nuts for $1.49

$0.99 for 35 grams is $0.99/35=$0.02828/gram

vs

$1.49 for 59 grams is $1.49/59=$0.02525/gram

0.02525<0.02828 so $1.49 for 59 grams is better value


5) inline skate rentals for fat $30.00 for 4 hours or $54.00 for 7 hours.

$30 for 4hrs is $30/4=$7.50/hr

vs

$54 for 7hrs is $54/7=$7.71/hr

7.50<7.71 so $30 for 4hr is better value


6) 500 sheets of paper for $9.45 or 4500 sheets of paper for $49.00

$9.45 for 500 sheets is $9.45/500=$0.0189/sheet

vs

$49.00 for 4500 sheets is $49.00/4500=$0.0108/sheet

0.0108<0.0189 so $49.00 for 4500 is better value


7) 25 liters of gas for $21.50 or 35 liters of gas for $40.00

$21.50 for 25 liters is $21.50/25=$0.86/liter

vs

$40 for 35 liters is $40/35=$1.41/liter

0.86<1.41 so $21.50 for 25 liters is better value

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4.
zubka84 [21]

Answer:

See Explanation Below

Step-by-step explanation:

Given

(sin x - cos x)^2 = sec^2x - tan^2x - 2sinx.cos x.

Required

Prove

To start with; we open the bracket on the left hand side

(sin x - cos x)^2 = (sin x - cos x)(sin x - cos x)

(sin x - cos x)^2 = (sin x )(sin x - cos x)- (cos x)(sin x - cos x)

(sin x - cos x)^2 = sin^2 x -sinx cos x - sin xcos x + cos^2 x

(sin x - cos x)^2 = sin^2 x -2sinx cos x + cos^2 x

Reorder

(sin x - cos x)^2 = sin^2 x + cos^2 x - 2sinx cos x

From trigonometry;

sin^2x + cos^2x = 1

So;

(sin x - cos x)^2 = sin^2 x + cos^2 x - 2sinx cos x

becomes

(sin x - cos x)^2 = 1 - 2sinx cos x

Also from trigonometry;

sec^2x - tan^2x = 1

So,  

(sin x - cos x)^2 = 1 - 2sinx cos x

becomes

(sin x - cos x)^2 = sec^2x - tan^2x  - 2sinx cos x

Proved

3 0
3 years ago
Simple math help?<br> Solve for x<br> √x+12 = √x+2
lozanna [386]
This is an impossible equation. If sqrt(x) = sqrt(x), and sqrt(x) + 2 = sqrt(x) + 12, then that would mean that 2=12, which is incorrect.
3 0
2 years ago
How many roots does this has?<br>x^2+(2√5x)+2x=-10​<br>find Discriminant
Alexxandr [17]

Given:

The equation is

x^2+(2\sqrt{5})+2x=-10

To find:

The number of roots and discriminant of the given equation.

Solution:

We have,

x^2+(2\sqrt{5})x+2x=-10

The highest degree of given equation is 2. So, the number of roots is also 2.

It can be written as

x^2+(2\sqrt{5}+2)x+10=0

Here, a=1, b=(2\sqrt{5}+2), c=10.

Discriminant of the given equation is

D=b^2-4ac

D=(2\sqrt{5}+2)^2-4(1)(10)

D=20+8\sqrt{5}+4-40

D=8\sqrt{5}-16

D\approx 1.89>0

Since discriminant is 8\sqrt{5}-16\approx 1.89, which is greater than 0, therefore, the given equation has two distinct real roots.

3 0
3 years ago
Find the final cost of an item that was originally price at $245 with a 15% discount and a 6% tax. Please help this is My last q
Soloha48 [4]

Answer:

12

Step-by-step explanation:

8 0
2 years ago
Kate father is 50 years old and kate is 24 years old now. How many years ago was kates father three times as old as her
patriot [66]

Answer:

11

Step-by-step explanation:

50-x=3(24-x)

50-x=72-3x

2x=22

x=11years ago when kate's father was 3 times as old as kate=11

8 0
2 years ago
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