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kow [346]
3 years ago
12

Evaluate 2 times 3 to the power of 2 minus 5

Mathematics
2 answers:
shepuryov [24]3 years ago
4 0
2* 3^2 - 5 = 18-5 = 13
the answer would be 13
bekas [8.4K]3 years ago
3 0
The answer is 13 common sense

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Verify that 2,-1 and 1⁄2 are the zeroes of the cubic polynomial
Mariulka [41]

Answer:

i) Since P(2), P(-1) and P(½) gives 0, then it's true that 2,-1 and 1⁄2 are the zeroes of the cubic polynomial.

ii) - the sum of the zeros and the corresponding coefficients are the same

-the Sum of the products of roots where 2 are taken at the same time is same as the corresponding coefficient.

-the product of the zeros of the polynomial is same as the corresponding coefficient

Step-by-step explanation:

We are given the cubic polynomial;

p(x) = 2x³ - 3x² - 3x + 2

For us to verify that 2,-1 and 1⁄2 are the zeroes of the cubic polynomial, we will plug them into the equation and they must give a value of zero.

Thus;

P(2) = 2(2)³ - 3(2)² - 3(2) + 2 = 16 - 12 - 6 + 2 = 0

P(-1) = 2(-1)³ - 3(-1)² - 3(-1) + 2 = -2 - 3 + 3 + 2 = 0

P(½) = 2(½)³ - 3(½)² - 3(½) + 2 = ¼ - ¾ - 3/2 + 2 = -½ + ½ = 0

Since, P(2), P(-1) and P(½) gives 0,then it's true that 2,-1 and 1⁄2 are the zeroes of the cubic polynomial.

Now, let's verify the relationship between the zeros and the coefficients.

Let the zeros be as follows;

α = 2

β = -1

γ = ½

The coefficients are;

a = 2

b = -3

c = -3

d = 2

So, the relationships are;

α + β + γ = -b/a

αβ + βγ + γα = c/a

αβγ = -d/a

Thus,

First relationship α + β + γ = -b/a gives;

2 - 1 + ½ = -(-3/2)

1½ = 3/2

3/2 = 3/2

LHS = RHS; So, the sum of the zeros and the coefficients are the same

For the second relationship, αβ + βγ + γα = c/a it gives;

2(-1) + (-1)(½) + (½)(2) = -3/2

-2 - 1½ + 1 = -3/2

-1½ - 1½ = -3/2

-3/2 = - 3/2

LHS = RHS, so the Sum of the products of roots where 2 are taken at the same time is same as the coefficient

For the third relationship, αβγ = -d/a gives;

2 * -1 * ½ = -2/2

-1 = - 1

LHS = RHS, so the product of the zeros(roots) is same as the corresponding coefficient

7 0
3 years ago
Someone help me with my math homework pleaseee. Find the volumes of the pyramids and the height is 7cm for the first one.
gregori [183]
\bf \textit{volume of a pyramid}\\\\
V=\cfrac{1}{3}Bh\qquad 
\begin{cases}
B=\textit{area of the base}\\
h=height
\end{cases}

now, the first one, on the far-left.... can't see the height.. but I gather you do, now as far as its Base area, well, the bottom is just a 12x12 square, so the area of its base is just 12*12


now, the middle pyramid, has a height of 6, the base is also a square, 8x8, so the Base area is just 8*8

now the last one on the far-right

has a height of 8, the Base is a Hexagon, with sides of 6

\bf \textit{area of a regular polygon}\\\\
A=\cfrac{1}{4}ns^2cot\left( \frac{180}{n} \right)\qquad 
\begin{cases}
n=\textit{number of sides}\\
s=\textit{length of one side}\\
\frac{180}{n}=\textit{angle in degrees}\\
----------\\
n=6\\
s=6
\end{cases}\\\\\\ A=\cfrac{1}{4}\cdot 6\cdot 6^2\cdot cot\left( \frac{180}{6} \right)
5 0
3 years ago
What the expression (4f-3+2g)-(4g+2)
galben [10]
For this question you can say: 
4f -3 +2g - 4g -2
so now you can simplify and find the answer:
4f -3 -2g -2 = 4f -2g -5
and that's the answer :)))
I hope this is helpful
have a nice day 
8 0
3 years ago
Which shows a correct order to solve this story problem?
ELEN [110]
C is the right answer, the product is 13.348
8 0
3 years ago
Read 2 more answers
An electrician sent Bonnie an invoice in the amount of 'a' dollars for 6 hours of work that was done on Saturday. The electricia
Mazyrski [523]

Answer:

(a-f)/6 = r

Step-by-step explanation:

The total Bonnie must pay is the weekend fee plus the hourly rate times the hours worked

Cost = weekend fee * hourly rate* hours

hours = 6

weekend fee =f

hourly rate = r

Cost = a dollars

Substituting in what we know

a = f+ 6r

We want to solve for r

Subtract f from each side

a-f =f-f +6r

a-f = 6r

Divide each side by 6

(a-f)/6 = 6r/6

(a-f)/6 = r

4 0
3 years ago
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