help with number 4 plz i’ll give brainliest

Answer:

We know that P(x) = 30*x^3 + k*x^2 + 1

a) If (3x - 1) is a factor, let's find the value of k.

Because the degree of the original polynomial is 3, and the degree of the factor is 1, we should multiply it by a polynomial of degree 2.

Then:

30*x^3 + k*x^2 + 1 = (3*x - 1)*(a*x^2 + b*x + c)

30*x^3 + k*x^2 + 1  = 3*a*x^3 + 3*b*x^2 + 3*c*x - a*x^2 - b*x - c

30*x^3 + k*x^2 + 1 = 3*a*x^3 + (3*b - a)*x^2 + (3*c - b)*x - c

The terms with the same exponent should be equal, then:

30*x^3 = 3*a*x^3

30 = 3*a

30/3 = a = 10

k*x^2 = (3*b - a)*x^2

k = (3*b - 10)  

0*x = (3*c - b)*x

0 = (3*c - b)

b = 3*c

and

1 = -c

then:

c = -1

Replacing this in the equation: b = 3*c

we get: b = -3

Replacing this in the equation for k, we get:

k = (3*b - 10) = (3*-3 - 10) = -19

k = -19

And we can write:

P(x) = (3*x - 1)*(10*x^2 - 3*x - 1)

b) Now we want to write P(x) as a product of its linear factors.

Then we need to factorize the quadratic part:

We need to solve

10*x^2 - 3*x - 1 = 0

We can use the Bhaskara's equation to get the solutions:

[tex]x = \frac{-(-3) \pm \sqrt{(-3)^2 - 4*10*(-1)} }{2*10} = \frac{3 \pm 7}{10}[/tex]

Then the two zeros of that polynomial are

x = (3 + 7)/10 = 1

x = (3 - 7)/10 = - 4/10 = -2/5

So we can write the polynomial as:

10*(x - 1)*(x - (-2/5))

Replacing this in the equation of P(x) we get:

P(x) = (3*x - 1)*10*(x -1)*(x + 2/5)

     = 10* (3*x - 1)*(x -1)*(x + 2/5)

So P(x) is written as a product of lineal factors.

C) The zeros of the polynomial are the values of x such that one of the factors becomes equal to zero.

For the first factor, we have a zero at x = 1/3

for the second, we have a zero at x = 1

for the third one, we have a zero at  x = -2/5

Answer: the answer is 1/2

Step-by-step explanation: I just got the answer form IXL

Answer:

1/2 is the answer

Step-by-step explanation:

1/2

Answer:

255

Step-by-step explanation:

Once split up you find the are of the rectangle which is 8*17=136

Then since the bottom line is 22, you do 22-8 to find the bottom line of the triangle.

The area of the triangle is 17*14/2=238/2

Hence, 119

Hope it helps!

Answer:

63

Step-by-step explanation:

I hope

Answer:

Surface Area: 1320

Volume: 2160

Step-by-step explanation:

Before calculating Volume and Surface Area, we need to calculate the missing side of the right triangle using the Pythagoreon theorem: [tex]a^2+b^2=c^2[/tex]

where c is the hypotenuse, 26.

Substituting the values into the equation you get:

10^2 + b^2 = 26^2

100 +b^2 = 676

Subtract 100 from both sides.

b^2 = 576

b = 24

Now that we have the missing side, we can calculate the rest of the question.

Surface Area =  2([tex]\frac{1}2[/tex] × 24 × 10) + (18 × 26) + (18 × 24)  +(18 × 10)

240 + 468 + 432 + 180 = 1320 unit^2

Volume = [tex]\frac{1}2[/tex] × base × height × length

[tex]\frac{1}2[/tex] × 24 × 10 × 18 = 2160 unit^2

Brainliest if you don't mind ;)

Answer:

Use distance formula to find the length of the segments

1. H = (-3, 0), F = (3, 2)

2. E = (1, 4), G = (-1, -2)

3. We see the diagonals are congruent, opposite sides are parallel.

The above is the property of a rectangle

Answer:

D

Step-by-step explanation:

40% = [tex]\frac{40}{100}[/tex] = [tex]\frac{2}{5}[/tex] ← in simplest form

Then

[tex]\frac{2}{5}[/tex] of $120 = [tex]\frac{2}{5}[/tex] × $120 = 2 × $24 = $48

she pays $120 - $48 = $72

Answer:

Matter in living things may pass into nonliving things.

Step-by-step explanation:

Answer:

Associative property of addition. Grouping different addends does not change the sum.

Step-by-step explanation:

5 + 2 + 3 = 5 + (2 + 3)

10 = 5 + (5)

10 = 10

Answer:

6

Step-by-step explanation:

3/4

1 1/2

2 1/4

3

3 3/4

4 1/2

Sorry if this doesn't make sense, I hope I helped though!

Answer:

Difference is $3

Step-by-step explanation:

The Jones Family bought 3 adult tickets and 7 student tickets, so they spent 27+42=$69 spent.

The Smith Family bought 4 adult tickets and 5 student tickets, so they spent 36+30=$66 spent.

The difference between them is 69-66=$3.

So, the difference between how much the two families spent is $3.

Answer:

3$

Step-by-step explanation:

Smith family:

9x4=36

5x6=30

total=66$

Jones family:

3x9=27

7x6=42

total=69$

difference=3$

Answer:

The answer is 33 years.

Step-by-step explanation:

10% of 3 is .3

Just move the decimal to the left.

.3 times 33=9.9

9.9~10

Step-by-step explanation:

blue: 4x+2+7x+7+5x -4 = 16x +5

red: x+3+x+7+2x-5 = 4x -5

difference: 16x+5 - (4x -5) = 12x +10

Answer: 1,145,375cm^3

Step-by-step explanation:

Answer: Answer in photo below.

Hope this helps!

Answer:

1: 9

2: i dont know sorry

3: 21/2

Step-by-step explanation:

1: know that the bottom portion of the triangle is 18  the bottom left is 12 and the top left is 6. Now you could say that its six because they look the same size but we cant be sure, and six isnt an option. i dont know how to solve so we're using process of elimination so bare with me. we alread have 12 and 18 and theyre way bigger, it cant be 11 because it wouldnt be that small. so in my mind its 9.  

2:  n/A

3: because i said so

Answer:

#1

Option D

#2

#3

Option B

Answer:

10

Step-by-step explanation:

5*2=10

2+2+2+2+2=10

Answer:

1/8 and 1/12

Step-by-step explanation:

Answer:

the correct classification and decimal expansion of StartFraction 5 Over 8 EndFraction

=5/8=0.625[irrational number]

Answer:

The correct answer is (b) i believe

Step-by-step explanation:

   Have a great day!

The correct relation for the sea gull population is: P(t) = 5.3t^(11/7)

Answer:

d. about 66.5 hundred thousand

Step-by-step explanation:

Given that :

P(t) = 5.3t^(11/7)

Population, P is in hujdred thousand ; t = number of years

Population after 5 years ;

t = 5

P(5) = 5.3 * 5^(11/7)

P(5) = 5.3 * 5^1.5714285

P(5) = 5.3 * 12.542422

P(5) = 66.474840

P(5) = 66.5 (approximately)

Hence, population after 5 years will be about 66.5 hundred thousand.

Answer:

31%

33%

Step-by-step explanation:

I'm not 100% sure. I tried my best.

Answer:

13/4

Step-by-step explanation:

for these types of problems i recommend symbolab

Answer:

He is incorrect

Step-by-step explanation:

Given

3(x + 1) - 5 = 3x - 2 ← simplify left side

3x + 3 - 5 = 3x - 2

3x - 2 = 3x - 2

Since both sides are equal, then this indicates that the equation has infinite solutions.

Answer:

no, that's good

Step-by-step explanation:

I'm pretty sure that's a b, so it's good

Answer:

No thats good cause last year i had a 60% as my major grade but i got 92% this year

Step-by-step explanation:

Answer:

I am going to assume that D's expression is actually $2.99+$3.19+$2.59+(-$0.25)+(-$0.40)

= $6.18+$2.59-$0.25-$0.40 [Note: (+)*(-)=(-)]

=$8.77-$0.25-$0.40

=$8.52-$0.40

=$8.12

Step-by-step explanation:

The prices of the loaf bread, a jar of peanut butter and 3 pounds of apples will be added. The value of the coupons will be then reduced from the total to get the final total.

Answer:

The midpoint is (-2,14) and the slope is m=1/3

Step-by-step explanation:

Answer:

x = 61°

Step-by-step explanation:

since the triangle is isosceles the two angles opposite 58° are equal so:

x = (180° - 58°)/2 = 61°