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Stella [2.4K]
3 years ago
14

The product of x and 6 is greater than or equal to 25

Mathematics
1 answer:
Helen [10]3 years ago
5 0

Answer:

x+6 ≥ 25

Step-by-step explanation:

The product means the sum of <em>x</em> + 6. In this question, <em>x</em> + 6, is greater than or equal to the number 25 which is what  ≥ means. Meaning, <em>x</em> can be replaced by a number that when added to <em>6</em>, <u>will equal to </u><u><em>25</em></u><u> or more</u>. For example, <em>x </em>can equal <em>19, 20, 21 </em>and so on.

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Determine the number of real solutions for each of the given equations. Equation Number of Solutions y = -3x2 + x + 12 y = 2x2 -
rosijanka [135]

Answer:

Step-by-step explanation:

Our equations are

y = -3x^2 + x + 12\\y = 2x^2 - 6x + 5\\y = x^2 + 7x - 11\\y = -x^2 - 8x - 16\\

Let us understand the term Discriminant of a quadratic equation and its properties

Discriminant is denoted by  D and its formula is

D=b^2-4ac\\

Where

a= the coefficient of the x^{2}

b= the coefficient of x

c = constant term

Properties of D: If D

i) D=0 , One real root

ii) D>0 , Two real roots

iii) D<0 , no real root

Hence in the given quadratic equations , we will find the values of D Discriminant  and evaluate our answer accordingly .

Let us start with

y = -3x^2 + x + 12\\a=-3 , b =1 , c =12\\D=1^2-4*(-3)*(12)\\D=1+144\\D=145\\D>0 \\

Hence we have two real roots for this equation.

y = 2x^2 - 6x + 5\\

y = 2x^2 - 6x + 5\\a=2,b=-6,c=5\\D=(-6)^2-4*2*5\\D=36-40\\D=-4\\D

Hence we do not have any real root for this quadratic

y = x^2 + 7x - 11\\a=1,b=7,-11\\D=7^2-4*1*(-11)\\D=49+44\\D=93\\

Hence D>0 and thus we have two real roots for this equation.

y = -x^2 - 8x - 16\\a=-1,b=-8,c=-16\\D=(-8)^2-4*(-1)*(-16)\\D=64-64\\D=0\\

Hence we have one real root to this quadratic equation.

7 0
3 years ago
Simplify by combining like terms -17+2(6x-1)+5
earnstyle [38]

\huge\boxed{12x-14}

Start with the original expression.

-17+2(6x-1)+5

Use the Distributive Property — multiply 2 by both 6x and -1.

-17+12x-2+5

Combine the like terms — add up all the constants.

-14+12x

Reorder the terms.

\large\boxed{12x-14}

5 0
3 years ago
Read 2 more answers
A. ?? <br> B. ?? <br> C. ??<br> Please help me!!!
patriot [66]
Bonjour!

For A, the two angles are congruent by the Corresponding Angles are Congruent Theorem/Postulate.

For B, the two angles are congruent by the Vertical Angels are Congruent Theorem/Postulate.

As for C, the two angles are congruent by the Same Side Exterior Theorem/Postulate.(Though I am uncertain if that is the correct name for this one)

Hope that helps :)
4 0
3 years ago
45/8 = <br> When you get the answer convert it to fraction form <br> I need it please
Lana71 [14]

Answer:

Exact Form:

45/8

Decimal Form:

5.625

Mixed Number Form:

5 5/8

8 0
2 years ago
Read 2 more answers
If I want to make 12 pillows from the same fabric from 16 yards how much fabric will I use to make each pillow
Georgia [21]
The amount of material/ number of pillows made
16/12 = 4/3 =  1  1/3 
So the answer lies between integers 1 & 2
4 0
3 years ago
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