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4 years ago

Which of the following are solutions to the equation below 3x^2+27x+54=0

Mathematics

2 answers:

VikaD [51]4 years ago

7 0

Answer:x=6

Step-by-step explanation:Step-1 : Multiply the coefficient of the first term by the constant 1 • 18 = 18

Step-2 : Find two factors of 18 whose sum equals the coefficient of the middle term, which is -9 .

-18 + -1 = -19

-9 + -2 = -11

-6 + -3 = -9 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -6 and -3

x2 - 6x - 3x - 18

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (x-6)

Add up the last 2 terms, pulling out common factors :

3 • (x-6)

Step-5 : Add up the four terms of step 4 :

(x-3) • (x-6)

Which is the desired factorization

spin [16.1K]4 years ago

5 0

Answer:

x=-5

Step-by-step explanation:

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Multiply the following rational expressions and simplify the result

GarryVolchara [31]

Answer:

Step-by-step explanation:

We have to solve the given expression,

$\frac{9y-33y^2-3y^4}{100-49y^2}.\frac{7y^2+17y+10}{14y^2+28y}$

$\frac{9y-33y^2-3y^4}{100-49y^2}.\frac{7y^2+17y+10}{14y^2+28y}$ = $\frac{-y(-9+33y+3y^3)}{100-49y^2}.\frac{7y^2+17y+10}{14y(y+2)}$

= $\frac{-y(-9+33y+3y^3)}{(10-7y)(10+7y)}.\frac{7y^2+10y+7y+10}{14y(y+2)}$

= $\frac{-y(-9+33y+3y^3)}{(10-7y)(10+7y)}.\frac{y(7y+10)+1(7y+10)}{14y(y+2)}$

= $\frac{-y(-9+33y+3y^3)}{(10-7y)(10+7y)}.\frac{(y+1)(7y+10)}{14y(y+2)}$

= $\frac{-3y(-3+11y+y^3)}{(10-7y)}.\frac{(y+1)}{14y(y+2)}$

= $\frac{-3(-3+11y+y^3)}{(10-7y)}.\frac{(y+1)}{14(y+2)}$

= $\frac{3(3-11y-y^3)(y+1)}{(10-7y)(14(y+2)}$

3 0

3 years ago

Write each polynomial in standard form. Then give the leading coefficient. You may need to combine like terms before writing the

Bond [772]

Step-by-step explanation:

To write a polynomial in standard form, put the degree that are the greatest first

So here it would be

${x}^{5} + 4 {x}^{3} - 3 {x}^{2} + 10$

Remember constant are numbers that you learned back in elementary,

Numbers like 10,90,4,1,0,-3 etc.

Remember that constant are basically represented like this

$k \times {x}^{0}$

For example, 10 is represented like

$10 \times {x}^{0}$

Since 0 is the smallest degree possible, for a polynomial, constants are the last term of a polynomial in standard form

6 0

2 years ago

two wheels are rolled simultaneously. The radius of the smaller wheel is r feet and the radius of the larger wheel 2r feet. If b

Nuetrik [128]

The circumference of a circle is C=2πR, where R is the radius of the circle and π≈3.14.

So if we open the circumference of the circle into a straight line segment, the length of this segment is C=2πR≈2*3.14*R=6.28R

4 rotations mean 4 circumferences that is 4 segments of length 6.28R,
which makes a linear distance of 4*6.28R=25.12R

i: the radius of the smaller wheel is R=r, thus it covers a distance of 25.12r feet

ii: the radius of the smaller wheel is R=2r, thus it covers a distance of 25.12*2r=50.24r (feet)

50.24r is twice 25.12r, thus the larger wheel traveled Twice the distance of the smaller one.

Answer: the larger covered twice the distance of the smaller.

6 0

3 years ago

Which is the graph of y=3/4x-3<br><br> Graph A<br> Graph B<br> Graph C.

irina [24]

Answer:

Graph A

Step-by-step explanation:

I had this question in my class and got it right with answer A :')

8 0

3 years ago

In order to determine the average price of hotel rooms in Atlanta, a sample of 64 hotels was selected. It was determined that th

kow [346]

Answer:

Step-by-step explanation:

6 0

3 years ago