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Lelechka [254]
3 years ago
5

Michael is an avid reader, his generous grandparents gave him money for his birthday, and he decided to spend at most $150 on bo

oks. Barnes and Noble is running a special: all paperback books are $8.00 and hard back books are $12.00. Michael wants to purchase at least 12 books.
Write a system of inequalities to represent the situation.
Mathematics
1 answer:
Andrews [41]3 years ago
5 0

Answer:

The system of inequality to represent the situation is

p + h \geq 12  

8 p + 12 h = 150

Step-by-step explanation:

Given as :

Total money to be spend on books = $150

The cost of each paperback book = $8

The cost of each hard back book = $12

The total number of books to be purchased = 12

Let The number of paperback books = p

Let The number of hard back books = h

<u>According to question</u>

Total number of books to be purchased =  number of paperback book + number of hard back book

i.e p + h \geq 12            ...........A

<u>Again</u>

Total money to be spend on books =  number of paperback books × cost of each paperback book  +  number of hard back books × cost of each hard back book

i.e p × $8 + h × $12 = $150

Or, 8 p + 12 h = 150         .........B

So, The system of inequality to represent the situation =

p + h \geq 12     and  8 p + 12 h = 150

Hence, The system of inequality to represent the situation is

p + h \geq 12 and  8 p + 12 h = 150  . Answer

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11Alexandr11 [23.1K]

Answer:

13

Step-by-step explanation:

6 + 7 = 13

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6 0
3 years ago
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Which of the following are measurements of the sides of a right triangle?
mojhsa [17]

sides of right angle triangle follows Pythagoras theroem

which states

a^2 +b^2 = c^2

where a , b and c are sides of right angle triangle.

here none of options do not follow this.

so answer is option D

4 0
3 years ago
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Cynthia Besch wants to buy a rug for a room that is 21 ft wide and 34 ft long. She wants to leave
Daniel [21]

Answer:

Dimensions of the rug = 13 ft × 26 ft

Step-by-step explanation:

Dimensions of the room = 21 ft × 34 ft

Area of the room = 21 × 34 = 714 ft²

Cynthia wants to leave a uniform strip of floor around the rug.

Let the width of the rug = x ft

Then the dimensions of the rug will be = (21- 2x)ft × (34 - 2x)ft

Area of the rug = (21 - 2x)×(34 - 2x) square feet

338 = (21 - 2x)×(34 - 2x)

338 = 714 - 68x - 42x + 4x²

4x² - 110x + 714 - 338 = 0

4x² - 110x + 376 = 0

2x² - 55x + 188 = 0

2x² - 47x - 8x + 188 = 0

x(2x - 47) - 8(x - 47) = 0  

(x - 4)(2x - 47) = 0

x = 4, \frac{47}{2}

For x = 23.5 area of the rug will be negative.

Therefore, x = 4 ft will be the width of the rug.

Dimensions of the rug will be 13 ft × 26 ft. 

7 0
3 years ago
Which of the following represents 4x^5/6 in radical form
mash [69]
Remember, order of operations
exponent before multiply

so 4x^5/6=4 times x^5/6
simplify the x^5/6 first

remember
x^\frac{m}{n}=\sqrt[n]{s^m}

so
x^\frac{5}{6}=\sqrt[6]{x^5}

so
4x^\frac{5}{6}=4\sqrt[6]{x^5}
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6 0
3 years ago
Verify the identity. 4 csc 2x = 2 csc2x tan x
vlada-n [284]

Step-by-step explanation:

4csc(2x) = 2csc^2(x) tan(x)

We start with Left hand side

We know that csc(x) = 1/ sin(x)

So csc(2x) is replaced by 1/sin(2x)

4 \frac{1}{sin(2x)}

Also we use identity

sin(2x) = 2 sin(x) cos(x)

4 \frac{1}{2sin(x)cos(x)}

4 divide by 2 is 2

Now we multiply top and bottom by sin(x) because we need tan(x) in our answer

2\frac{1*sin(x)}{sin(x)cos(x)*sin(x)}

2\frac{sin(x)}{sin^2(x)cos(x)}

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We know that sinx/ cosx = tan(x)

Also  1/ sin(x)= csc(x)

so it becomes 2csc^2(x) tan(x) , Right hand side

Hence verified



6 0
3 years ago
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