Create a quadratic polynomial function f(x) and a linear binomial in the form (x − a).Show all work to evaluate f(a) using the function you created.

Answers

Answer 1

Answer: our quadratic polynomial function is:

f(x) = 4x^2 + 2x + 5

our linear binomial form is:
x - a = -2
hence:
a = x + 2

and so we have:
f(x) = 4x^2 + 2x + 5
f(a) = 4(x + 2)^2 + 2(x + 2) + 5
= 4(x^2 + 4x + 4) + 2x + 4 + 5
f(a) = 4x^2 + 18x + 25

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What polynomial identity should be used to prove that 16^2=(10+6)^2? (A. Difference of Cubes; B. Difference of Squares; C. Square of Binomial; D. Sum of Cubes)

Answers

Answer:

C. Square of Binomial

Step-by-step explanation:

To prove the identity you should use square of Binomial that states the following:

$(a+b)^(2)=a^(2)+2ab+b^(2)$

Lets prove it, so first take the equation to solve:

$(10+6)^(2)$

Then square the first term:

$(10+6)^(2)=10^(2)$

Then multiply by 2 the first and second terms:

$(10+6)^(2)=10^(2)+2(10)(6)$

Finally square the second term:

$(10+6)^(2)=10^(2)+2(10)(6)+6^(2)$

Solve the values:

$(10+6)^(2)=100+2(10)(6)+6^(2)$

$(10+6)^(2)=100+120+6^(2)$

$(10+6)^(2)=100+120+36$

$(10+6)^(2)=256$

And prove the polynomial identity:

$16^(2)=256$

not difference of cubes since it is 2nd degree
not difference of squares since it is plus
not sum of cubes because 2nd degreee

answer is square of binomial (why do we even need this property, oh well)

C

Find the surface area of a rectangular prism with base 5 m by 2 m and height 8 m. a. 15 m² b. 80 m² c. 30 m² d. 132 m²

Answers

Answer:

Total area = 2 * base area + side area

Lateral area = base perimeter * height

Total area = 2*(5*2)+2(5+2)*8

2*10 + 2*7*8=

20+112=132m²

Is negative 5 a rational number

Answers

its a rational number but also a integer and could never be a whole number because its a negative and whole numbers are always positive

Find an exact value cos(19pi/12)

Answers

$cos\left ( (9\pi)/(12)\right )=\frac{\sqrt{2-√(3)}}{2}$

Step-by-step explanation:

We know that

cos 2x = 2cos²x - 1

So we have

$cosx=\sqrt{(1+cos2x)/(2)}$

Substituting $x=(19\pi)/(12)$

$cos\left ( (19\pi)/(12)\right )=\sqrt{(1+cos2\left ( (19\pi)/(12)\right ))/(2)}\n\ncos\left ( (19\pi)/(12)\right )=\sqrt{(1+cos\left ( (19\pi)/(6)\right ))/(2)}\n\ncos\left ( (9\pi)/(12)\right )=\sqrt{(1+cos570)/(2)}\n\ncos\left ( (9\pi)/(12)\right )=\sqrt{(1-(√(3))/(2))/(2)}\n\ncos\left ( (9\pi)/(12)\right )=\sqrt{(2-√(3))/(4)}\n\ncos\left ( (9\pi)/(12)\right )=\frac{\sqrt{2-√(3)}}{2}$

$cos\left ( (9\pi)/(12)\right )=\frac{\sqrt{2-√(3)}}{2}$

19 π / 12 = 19 * 180° / 12 = 285 °
cos ( 19 π / 12 ) = cos 285° = cos ( - 75° ) = cos 75°
cos 75° = cos ( 45° + 30° ) = cos 45° cos 30° - sin 45° sin 30° =
= ( √2 / 2 · √3/2 ) - ( √2 / 2 · 1/2 ) = √6/4 - √2/4 =
= ( √6 - √2 )/ 4

Divide 42 in a ratio of 1:2:3

Answers

the ratio in which 42 should be divided is 1:2:3

the sum of the parts of the ratio is - 1 + 2 + 3 = 6

this means that there's a sum of 6 parts

so we need to find how much 1 part is equivalent to

if 6 parts are equivalent to 42

then 1 part is equivalent to - 42/6 = 7

so the ratio should be 1:2:3

1 part - 7

2 parts - 7 x 2 = 14

3 parts - 7 x 3 = 21

therefore 42 divided into 1:2:3 ratio is as follows

7 : 14 : 12

I guessed and check since it is a small number and found that 7+14+21 adds up 42 matching your ratio.

Is anyone can help me????

Answers

Answer:

216c³

Step-by-step explanation:

8 yellow = 2³ (sides = 2 cubes)

Green added to cover yellow, making it (2+2)³ = 4³

Red added to cover green, making it (4+2)³ = 6³

Total cubes = 6³ = 216 cubes

Each cube has a volume = c³

Volume of the final cube = 216c³ units³

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