The product of x and 6 is less than or equal to -17.

Answer:

Step-by-step explanation:

y4−

(y2−9)(y2+9)

9

Distribute:

=y4+

−1

9

y4+9

Combine Like Terms:

=y4+

−1

9

y4+9

=(y4+

−1

9

y4)+(9)

=

8

9

y4+9

Answer:

=

8

9

y4+9

The polynomial expression is divisible by 9

Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the polynomial be represented as A

Now , A = y⁴ - (y² - 9)(y² + 9)

To prove that the expression y⁴ - (y² - 9)(y² + 9) is divisible by 9 for any value of y, we can use algebraic manipulation and factorization.

First, we can simplify the expression inside the parentheses:

y² - 9 = (y - 3)(y + 3)

y² + 9 = (y + 3i)(y - 3i)

where i is the imaginary unit, i.e., i² = -1.

Substituting these expressions back into the original equation, we get:

y⁴ - (y² - 9)(y² + 9) = y⁴ - (y - 3)(y + 3)(y + 3i)(y - 3i)

Now, we can factor out (y − 3)(y + 3) from the second term:

y⁴ - (y² - 9)(y^2 + 9) = y⁴ - (y² - 9)(y² + 9) + 9(y - 3)(y + 3)

= y⁴ - (y² - 3^2)(y² + 3²)

= (y²)² - (3²)²

= (y² + 3²)(y² - 3²)

= (y² + 9)(y² - 9)

= (y + 3i)(y - 3i)(y + 3)(y - 3)

Now, we can see that the expression is equal to the product of four factors: (y + 3i), (y - 3i), (y + 3), and (y - 3). Note that either (y + 3i) and (y - 3i) or (y + 3) and (y - 3) must have the same residue modulo 3, since there are only three residues modulo 3 (0, 1, and 2) and four factors. In either case, the product of the two factors that have the same residue modulo 3 is divisible by 3, and therefore the entire expression is divisible by 3.

Moreover, since (y + 3) and (y - 3) are both odd or both even, the product of (y + 3) and (y - 3) is divisible by 8, which implies that the entire expression is also divisible by 8.

Hence , the expression y⁴ - (y² - 9)(y² + 9) is divisible by both 3 and 8 for any value of y, and therefore it is also divisible by their least common multiple, which is 9

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Answer:

The loan was $28184.81

Step-by-step explanation:

Let the loan amount be x

Rate of interest on Loan = 9%

Time = 8 years

Amount of loan over 8 years = $56160

Formula : [tex]A=P(1+r)^t[/tex]

Where A = Amount =56160

P = Principal = x

r = rate of interest = 9% = 0.09

t = time = 8 years

Substitute the values in the formula :

So,[tex]56160=x(1+0.09)^8[/tex]

[tex]\frac{56160}{(1+0.09)^8}=x[/tex]

$28184.81=x

Hence The loan was $28184.81

Answer:

100

Step-by-step explanation:

Answer:

125

Step-by-step explanation:

8x-41+9x+17=180

17x-24=180

17x=204

x=12

9(12)+17

125

Answer:

I would have got the same answers so probably yea

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

According to my understanding I believe you are correct!

Answer:

152 fluid ounces

Step-by-step explanation:

there are 128 fluid ounces in 1 gallon. there are 24 fluid ounces in 3 cups. 128+24 is 152. :)

Answer:

Larry=X

Barry=112x

Terry=113x

L+B+T=322

x+112x++113x=322

226×=322

Larry saved $1.42

Answer:

$84

Step-by-step explanation:

I did it before.

Answer:

95 is the answer!

The measure of the angle  ∠JHN will be 45°. Then the correct option is B.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360 °.

Vertically opposite angle - When two lines intersect, then their opposite angles are equal.

Angle ∠MHL and angle ∠JHK are equal because the angles are opposite angles.

∠MHL = ∠JHK

3x + 20 = x + 20 + x + 25

x = 25

Then the measure of the angle  ∠JHN is calculated as,

∠JHN = x + 20

∠JHN = 25 + 20

∠JHN = 45°

The measure of the angle  ∠JHN will be 45°. Then the correct option is B.

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The missing diagram is given below.

Answer:

Yes they are like terms.

Step-by-step explanation:

As like terms are those who has same variables or powers.Here,we have same variables for both the terms and both have the power 1.

hope it helps!

Step-by-step explanation:

r = onion rings amount

s = sliders amount

system of equations

2s = r

r(70) + s(200) = 1020

(for deltamath)

This question is based on the system of equations. Therefore, the system  of equations 2s = r and r(70) + s(200) = 1020 are  that could be used to determine the number of onion rings in the combination meal and the number of sliders in the combination meal.

Given:

At a particular restaurant, each onion ring has 70 calories and each slider has 200 calories. A combination meal with onion rings and sliders is shown to have 1020 total calories and twice as many onion rings as there are sliders.

According to the question,

Let the amount of onion rings be r and the amount of sliders be s.

Now, it is provided in question that, amount of sliders is twice as the onion rings. In mathematically expressed as,

⇒ 2s = r is the first system of equation.

Then, it is also give that, each onion ring has 70 calories and each slider has 200 calories. A combination meal with onion rings and sliders is shown to have 1020 total calories. This representing as,

⇒ r(70) + s(200) = 1020 is the second system of equation.

Therefore, the system  of equations 2s = r and r(70) + s(200) = 1020 are  that could be used to determine the number of onion rings in the combination meal and the number of sliders in the combination meal.

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Answer:

Step-by-step explanation:

(-4,0) ; (-7, -14)

[tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\\\\ =\sqrt{(-7-[-4])^{2}+(-14-0)^{2}}\\\\ =\sqrt{(-7+4)^{2}+(-14)^{2}}\\\\=\sqrt{(-3)^{2}+(-14)^{2}}\\\\=\sqrt{9+196} \\\\=\sqrt{205} \\\\=14.3178[/tex]

Answer:

The answer is 36 squared centimeters

Answer:

25/64

Step-by-step explanation:

Answer:

It's 20 because 5ft times 4ft gives you 20ft

Answer:

Make headway with these volume of a composite 3D figure worksheet pdfs featuring figures made up of 2 or 3 solid shapes. Add the volume of each geometric ...

Step-by-step explanation:

Answer:

x > 3

Step-by-step explanation:

8x - 6 > 12 + 2x

1. add 6 to both sides.

8x > 12 + 2x + 6

2. Simplify 12 +2x + 6 to 2x + 18.

8x > 2x + 18

3. Subtract 2x from both sides.

8x - 2x > 18

4. Simplify 8x - 2x to 6x.

6x > 18

5. Divide both sides by 6.

x > 18/6

6. Simplify 18/6 to 3.

x > 3

Answer:

1600 ft

Step-by-step explanation:

The cross section that is formed is A. a rectangle

Answer:

a.) a rectangle

Step-by-step explanation:

Answer:

A) 0.5

B) 0.375

C) 0.375

D) 0.167

Step-by-step explanation:

Let's call

a: Ariel

b: Bob

c: Chris

d: Diana

There are 4*3*2*1 = 24 total combinations to order the 4 children

A) Ariel is older than Diana in the following 12 cases:

a b c d

a b d c

a c b d

a c d b

a d b c

a d c b

b a c d

b a d c

b c a d

c a b d

c a d b

c b a d

Then, the probability is 12/24 = 0.5

B) The condition "Ariel is older than Diana, if it is given that Ariel is older than Bob" is satisfied in the six first cases and last three cases of before.

Then, the probability is 9/24 = 0.375

C) Ariel is older than Diana, if it is given that Chris is older than Diana, in the following cases:

a b c d

a c b d

a c d b

a d c b

b a c d

b c a d

c a b d

c a d b

c b a d

Then, the probability is 9/24 = 0.375

D) Ariel is older than Diana, if it is given that Diana is older than Bob, in the following cases:

a c d b

a d b c

a d c b

c a d b

Then, the probability is 4/24 = 0.167

Answer:

jesus

Step-by-step explanation:

Answer:

First, let's work out the V of container A and B

V_A = pi x (diameter/2)^2 x height = pi x (26/2)^2 x 14 = 2366 pi (ft3)

V_B = pi x (diameter/2)^2 x height = pi x (18/2)^2 x 15 = 1215 pi (ft3)

After pumping water from container A to container B until B is full:

The empty space inside container A would be:

V_empty = V_A - V_B = 2366 pi (ft3) - 1215 pi (ft3) = 1151 pi (ft3) = ~3615.97 (ft3)

Answer:

3,815.1 feet³

Step-by-step explanation:

Volume filled in B = Volume emptied from A

pi × r² × h

3.14 × (18/2)² × 15

3815.1 feet³

Answer: first one is a the second one is b

Step-by-step explanation:

the bottom is the total amount and the top should relate to the bottom

Answer:

i used calculator and got 1

Step-by-step explanation:

Answer:

[tex]AC=13.5[/tex]

Step-by-step explanation:

Use the Law of Sines as follows:

[tex]\frac{sinA}{a} =\frac{sinB}{b}[/tex]

Insert the values (use the steps from the last problem):

[tex]\frac{sin25}{14} =\frac{sin24}{b}[/tex]

Isolate b. Multiply both sides by b:

[tex]b*(\frac{sin25}{14} )=b*(\frac{sin24}{b})\\\\b*\frac{sin25}{14}=sin24[/tex]

Multiply both sides by 14:

[tex]14*(b*\frac{sin25}{14})=14*(sin24)\\\\b*sin25=14*sin24[/tex]

Isolate b. Divide both sides by sin 25:

[tex]\frac{b*sin25}{sin25} =\frac{14*sin24}{ysin25} \\\\b=\frac{14*sin24}{sin25}[/tex]

Insert the equation into a calculator and round to the nearest tenth:

[tex]b=13.5[/tex]

The length of AC is 13.5 units.

:Done

Step-by-step explanation:

x2 - x - 6 = 0

x2 - 3x + 2x - 6 = 0

x(x - 3) + 2(x - 3) = 0

x - 3 = 0. x + 2 = 0

x = 3 x = - 2

Option no 2 and 5 are the correct answer

Answer: Find the area of all figures and then add it together

Step-by-step explanation:

Answer:

Five times the difference of n and four plus seven

Step-by-step explanation:

Five times the difference of n and four plus seven

Answer:

five multiplied by the difference of N and four plus seven

Answer:

x= 112

Step-by-step explanation:

(n-2)180

n is the number of sides

(7-2)180

(5)180

900

900-130-132-130-130-128-138=x

rules of pemdas

x=112

Answer:

Step-by-step explanation:

the first one is D

Answer:

first one is 180

Step-by-step explanation: