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raketka [301]
3 years ago
6

The difference of the square of a number and 4 is equal to 3 times that number. Find the negative solution.

Mathematics
1 answer:
leonid [27]3 years ago
7 0

The negative solution is x = –1.

Solution:

Let the number be x.

Square of a number = x²

3 times a number = 3x

Difference of square of a number and 4 = 3 times that number

\Rightarrow x^2-4=3x

Subtract 3x from both sides of the equation, we get

\Rightarrow x^2-3x-4=0

–3x can be written as x – 4x.

\Rightarrow x^2+x-4x-4=0

\Rightarrow( x^2+x)+(-4x-4)=0

1st bracket have common term x and bracket have –4 common term.

\Rightarrow x( x+1)-4(x+1)=0

Take common term x + 1 outside.

(x+1)(x-4)=0

<em>By zero factor principle, if AB = 0 then A = 0 or B = 0.</em>

x + 1 = 0,   x – 4 = 0

x = –1,   x = 4

The negative solution is x = –1.

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Samantha just opened a new restaurant. She earned $550 on the first day and $750 on the third day that she was open for business
mr Goodwill [35]

Answer:

Step-by-step explanation:

If Samantha's earnings continue to increase at the same rate, this means that her earning is increasing arithmetically.

If she earned $550 in the first day, we can say the first term is $550

If she earned $750 on the third day, we can say the third term is $750

For us to know by how much her money is increasing, we need to find the common difference d formed by the sequence

550, x , 750

T1 = 550

T2 = x

T3 = 750

Common difference d = T2-T1 = T3-T2

x - 550 = 750 - x = d

Let's calculate the second term first i.e x

Since x - 550 = 750 - x = d

x - 550 = 750 - x

Collect like terms

x+x = 750+550

2x = 1300

x = 1300/2

x = 650

d = T2-T1

d = x - T1

d = 650-550

d = 100

Hence her money keeps increasing by $100 each day

8 0
3 years ago
At The Green House of Salad, you get a
Leto [7]

Answer:

30 salads

Step-by-step explanation:

6 0
3 years ago
The sum of two numbers is 23. Twice one number increased by 6 is the same as 4 times the other number decreased by 2. What is th
Crank

Answer:

One number is 4.2, the other is 18.8

Step-by-step explanation:

1.)  x+y=23

    (x+6y)x2=4

2.) (x+6y)x2=4   =   2x+12y=4

3.)Use elimination/substitution to solve

     2x+12y=4  =   x+6y=2  =  x=2-6y

     2-6y+y=23

4.)Solve for y

     2-5y=23 -> -5y=21 -> y=4.2.

5.)Solve for x

    x+4.2=23

    x=18.8

I may be wrong so let me know if I am

8 0
2 years ago
Find the product of (4z^2 + 7z – 8) and (–z + 3).
san4es73 [151]

Answer:

5, 29 will both blank boxes

Step-by-step explanation:

the product of (4z^2 + 7z – 8) and (–z + 3)

(4z² + 7z – 8)(–z + 3)

-z(4z² + 7z – 8) + 3(4z² + 7z – 8)

-4z³-7z²+8z+12z²+21z-24

choose like terms

-4z³-7z²+12z²+8z+21z-24

-4z³+5z²+29z-24

5, 29

8 0
3 years ago
Please help i’m so confused LMC of 9, 12 and 24
julia-pushkina [17]

Answer:

The LCM of 9, 12, and 24, is <em>72.  </em>

Step-by-step explanation:

To find the answer you must figure out the factors of <em>each number</em>, and see which factor has the <em>same number.</em>  

<u><em>Factors of 9: </em></u>         <u><em>Factors of 12:</em></u><em>        </em><u><em>Factors of 24: </em></u>

     <em>  9                            12                          24</em>

<em>        18                          24                          48</em>

<em>        27                          36                         72</em>

<em>        36                          48</em>

<em>        45                          60</em>

<em>        54                          72</em>

<em>        63</em>

<em>        72</em>

When we look at all these factors, none of them have the same number <em>except 72.</em>  Since <em>all</em> of these factors have <em>72 in them</em>, this is the<em> </em>LCM of 9, 12, and 24.

7 0
3 years ago
Read 2 more answers
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