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Charra [1.4K]
3 years ago
15

How many terms are in the expression 32g + 11 (to the third power) - 9

Mathematics
1 answer:
nika2105 [10]3 years ago
6 0
Given that an expression is given by:
32g+11^3-9
simplifying this we get:
32g+1331-9
=32g+1322
Expressions are generally classified according to number of terms:
Our expression has only 2 terms
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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
Find the slope of the line that passes through Point A $$(​−5,7) and Point B $$(2,5), using the formula $$m=
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Answer:

slope = - \frac{2}{7}

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \frac{y_{2}-y_{1}  }{x_{2}-x_{1}  }

with (x₁, y₁ ) = (- 5, 7 ) and (x₂, y₂ ) = (2, 5 )

m = \frac{5-7}{2-(-5)} = \frac{-2}{2+5} = - \frac{2}{7}

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Step-by-step explanation:

To find unit rate

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Which of the following could be the side lengths of a right triangle?
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Recall that in a right-triangle, the hypotenuse, or longest side, is √(a²+b²).

\bf \sqrt{4.1^2+6.2^2}\qquad \approx\qquad 7.43303437&#10;\\\\\\&#10;\sqrt{40^2+60^2}\qquad \approx\qquad 72.1110255&#10;\\\\\\&#10;\sqrt{3.2^2+5.4^2}\qquad \approx\qquad 6.27694193&#10;\\\\\\&#10;\sqrt{33^2+56^2}\qquad =\qquad 65

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