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Olenka [21]
3 years ago
11

Solve this system of equations: y = x2 – 3x + 12 y = –2x + 14 1.Isolate one variable in the system of equations, if needed. y =

x2 – 3x + 12 y = –2x + 14 2.Use substitution to create a one-variable equation. –2x + 14 = x2 – 3x + 12 3.Solve to determine the unknown variable in the equation. What are the values of x?

Mathematics
2 answers:
gladu [14]3 years ago
4 0
The values of x are 2 and -1.

Solving the equation created by substitution listed in the question:

-2x+14=x²-3x+12

Add 2x to both sides:
-2x+14+2x=x²-3x+12+2x
14=x²-1x+12

Subtract 14 from both sides:
14-14=x²-1x+12-14
0=x²-1x-2

Factoring this, we want factors of -2 that sum to -1; -2(1) = -2 and -2+1=-1:
0=(x-2)(x+1)

Using the zero product property, we know that either x-2=0 or x+1=0:
x-2=0
x-2+2=0+2
x=2

x+1=0
x+1-1=0-1
x=-1
marishachu [46]3 years ago
3 0

Answer:

Step-by-step explanation:

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3 months, 96 plus 78x3 = 330 (78x3=234+96) 110X3=330 meaning it is 3 months
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Consider the expression √(√625).
const2013 [10]

Answer:

5

Step-by-step explanation:

Square Root - Finding a number that multiplies itself twice into the number within the square root

With this meaning, we need to find a number that multiplies itself into 625.

Finding calculations using exponents will help,

25^2 is equal to 625. Therefore \sqrt{25}

We are not finished, as there is another square root right after, empowering the parenthesis, so what number multiplies itself equals 25?

This would be 5, therefore \sqrt{(\sqrt{625}) } is equal to 5.

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2 years ago
A bakery specializes in cupcakes. Each day, one dozen cupcakes are randomally selected to test for freshness. Which statement be
ziro4ka [17]

Answer:

b) all of the cupcakes in the bakery

Explanation:

in statistics, the population is a group of people/things that are in the same category for collecting data. c) and d) are thus wrong since no data is collected about the other goods or the employees, while a) is wrong because that is just a sample (which helps to test for a large population) and not the actual population.

i hope this helps! :D

3 0
2 years ago
7+4(r+3)=9r-6<br> show work pls AND HELP ASAP
ivanzaharov [21]

\:  \:  \:  \:  \:  \:

=  \:  \:  \:  \: r = 5

Step-by-step explanation:

7 + 4(r + 3) = 9r - 6

  • <em><u>distribute</u></em><em><u> </u></em>4 through the parentheses

7 + 4r + 12 = 9r - 6

  • add numbers

19 + 4r = 9r - 6

  • move the <em><u>variable</u></em><u> </u>to the left hand side and change its sign

19 + 9r =  - 6

  • move the <em><u>constant </u></em>to the right hand side and change its sign

4r - 9 =  - 6 - 19

  • collect<em><u> like</u></em><em><u> terms</u></em>

<em><u>- 5r =  - 6 - 19</u></em>

  • calculate the difference

- 5r =  - 25

  • divide both sides of the equation by <em>-</em><em>5</em>

<em>=  \:  \:  \:  \: r = 5</em>

<h2><em><u>hope</u></em><em><u> it</u></em><em><u> helps</u></em></h2>
7 0
2 years ago
Twenty different books are to be put on five book shelves, each of which holds at least twenty books.
olya-2409 [2.1K]

Answer:

(a) 10,626 different arrangements

(b) 95,367,431,640,625 different arrangements

(c) 2.5852017 × 10²² different arrangements

Step-by-step explanation:

(a) How many different arrangements are there if you only care about the number of books on the shelves (and not which book is where)?

We use the combination formula for this

C(n , r) = n + r - 1C r - 1

n = 20

r = 5

= 20 + 5 - 1 C 5-1

= 24C4

= 24!/4 ! × (24 - 4)

= 24!/4! × 20!

= 10,626 arrangements

(b) How many different arrangements are there if you care about which books are where, but the order of the books on the shelves doesn't matter?

Since the order of the books on the shelves does not matter,

The calculation is given as

5²⁰ = 95,367,431,640,625 arrangements

(c) How many different arrangements are there if the order on the shelves does matter?

Since order matters now

Step 1

We use the combination formula for this

C(n , r) = n + r - 1C r - 1

n = 20

r = 5

= 20 + 5 - 1 C 5-1

= 24C4

= 24!/4 ! × (24 - 4)

= 24!/4! × 20!

= 10,626

Step 2

We find the factorial of the number books

= 20!

= 2,432,902,008,176,640,000

Step 3

The different arrangements there are if the order on the shelves does matter is calculated

= 10,626 × 2,432,902,008,176,640,000

= 2.5852017 × 10²² different arrangements

8 0
3 years ago
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