Using the graph, determine the coordinates of the vertex of the parabola.

The fully expanded and simplified expression is:

[tex]4a^12 - 24a^9 + 36a^6.[/tex]

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

To expand [tex](2a^6 - 6a^3)^2[/tex], we can use the formula:

[tex](a + b)^2 = a^2 + 2ab + b^2[/tex]

with [tex]a = 2a^6[/tex] and [tex]b = -6a^3:[/tex]

[tex](2a^6 - 6a^3)^2 = (2a^6)^2 + 2(2a^6)(-6a^3) + (-6a^3)^2[/tex]

[tex]= 4a^12 - 24a^9 + 36a^6[/tex]

Thus,

The fully expanded and simplified expression is:

[tex]4a^12 - 24a^9 + 36a^6.[/tex]

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Answer:

5

Step-by-step explanation:

AC = AB + BC

16 = x+1 + x+7

Combine like terms

16 =2x+8

Subtract 8 from each side

16-8 = 2x+8-8

8 = 2x

Divide by 2

8/2 = 2x/2

4 =x

We want to find AB

AB = x+1 = 4+1 = 5

Answer:

The answer is 3.

Step-by-step explanation:

To answer this, you have to find the total amount of cups he had to begin with. You add the cups of peanuts, cashews, chocolate chips, and raisins together, which equals 15 cups. Then, he divided it evenly into 5 bags, which means he put 3 cups of trail mix into each bag.

Answer:

El saldo de la cuenta de  Ana María es de -$16.500 , es decir, Ana María debe al banco $16.500.

Step-by-step explanation:

Ana María tiene $ 30.000 en su cuenta vista y retira $ 18.000 para un pago. Para saber la cantidad de dinero que posee en su cuenta luego de retirar el dinero debes realizar la diferencia (resta) entre lo que tiene inicialmente y la cantidad que retira:

$30.000 - $18.000= $12.000

Ahora el Banco paga un cheque de $ 26.000 con cargo a la cuenta de Ana María, por lo que debe restarse la mencionada cantidad a la suma de dinero que Ana María posee luego del retiro de dinero [un cheque con cargo a la cuenta de una persona indica que para el titular de la misma significa una salida de fondos, y por tanto, una disminución de su saldo]:

$12.000 - $26.000= - $14.000

Finalmente le descuentan una comisión por mantenimiento de la cuenta equivalente a $ 2.500, por lo que se debe realizar la diferencia entre la cantidad calculada previamente y $2.500:

- $14.000 - $2.500= -$16.500

El saldo de la cuenta de  Ana María es de -$16.500 , es decir, Ana María debe al banco $16.500.

Answer:

-12=4x-20

4x=12+20

4x=32

4 = 4

x=8

Answer:

[tex] - 12 = 4(x - 5) \\ - 12 = 4x - 4 \times 5(bracket \: multipiction) \\ - 12 = 4x - 20 \\ - 12 + 20 = 4x\\ 8 = 4x \\ x = \frac{8}{4} = 2 \\ x = 2 \\ thank \: you[/tex]

Answer: From Mustafa's perspective, there is a 47\degree47°47, degree angle between Ana and the kite.

Step-by-step explanation: Khan Academy

Answer:

A dozen is 12.

12*5 = 60 eggs

5 dozen eggs are equal to 60 eggs.

A dozen is a unit of measurement equal to 12 items. So, 5 dozen is equivalent to 5 times 12, which gives us a total of 60 items.

When referring to eggs, the term "dozen" is commonly used to represent a quantity of eggs. In this case, if we have 5 dozen eggs, it means we have 5 sets of 12 eggs each.

To calculate the total number of eggs, we multiply the number of dozens (5) by the number of eggs in a dozen (12):

5 dozen x 12 eggs/dozen = 60 eggs

Therefore, 5 dozen eggs are equal to 60 eggs. This means that if you have 5 sets of 12 eggs, you would have a total of 60 eggs.

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Answer:

B. 4:10

Step-by-step explanation:

A. 3:6 is equal to 1:2, which is our given answer for A.

B. Has no equivalent to 3:6

C. 10:20 can be simplified to 1:2 which 3:6 can also be simplified to… giving our answer.

Finally, D. You can multiply equally by 5 to get 15:30 and divide to get back to 3:6… it’s equal ;)

Hope this helps, good luck!

Answer:

$8.99

Step-by-step explanation:

14.38 ÷ 2 = 7.19

7.19 + 1.8 = 8.99

Hope this helps

Answer:

Step-by-step explanation:

LCM×HCF= Product

LCM×3=180

LCM=180/3=60

Answer:

2 x 2 x 2 x 3 x 5

Step-by-step explanation:

The first and smallest prime number that can be divisible by 120 is 2; 120/2 = 60, 60/2 = 30, 30/2 = 15; and the smallest prime number divisible by 15 is 3; 15/3 = 5; and the smallest prime number divisible by 5 is 5; 5/5 = 1.

hence, we have 2 x 2 x 2 x 3 x 5 = 2³ x 3 x 5

Answer:

f(x + 1) = -(3/4)*f(x)

(second option)

Step-by-step explanation:

Here we have the sequence:

64, -48, 36, -27, ...

First, we can notice two things:

Each term has a different sign than the previous term, so the relation is something like:

f(x + 1) = -k*f(x)

Now to find the value of k, we can just replace some of the values (for example, the first and the second one)

-48 = -k*64

48/64 = k

3/4 = k

Now, if we use any pair of consecutive terms we should get the same value of k, now let's try to use the second and third terms to see if we get the same value of k:

36 = -k*(-48)

36 = k*48

36/48 = k

3/4 = k

We got the same value, so we can conclude that k = (3/4)

Then the relation that describes this sequence is:

f(x + 1) = -(3/4)*f(x)

Answer:

a

Step-by-step explanation:

Answer:

- 18[tex]\sqrt{10}[/tex]

Step-by-step explanation:

Using the rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]

Given

(6[tex]\sqrt{2}[/tex] )(- 3[tex]\sqrt{5}[/tex] )

= 6 × - 3 × [tex]\sqrt{2}[/tex] × [tex]\sqrt{5}[/tex]

= - 18 × [tex]\sqrt{10}[/tex]

= - 18[tex]\sqrt{10}[/tex]

Answer:

62.8 mm

Step-by-step explanation:

pie = 3.14

radius = 10 mm

circumference of a circle = 2πr

=2*3.14*10

=62.8 mm

Answer:

2nd option

Step-by-step explanation:

The discriminant b² - 4ac tells us about the nature of the roots

• If b² - 4ac > 0 then 2 real and distinct roots

• If b² - 4ac = 0 then 2 real and equal roots

• If b² - 4ac < 0 then the roots are not real

Here b² - 4ac = 15 > 0

Then there are 2 real and distinct roots

x = 2 and x = - 3 are possible solutions to the equation

Answer:

option b) x = 2 and x = -3

Step-by-step explanation:

If discriminant is greater than zero, then the quadratic equation will have two solutions.

If discriminant is equal to zero, then the quadratic equation will have only one solution.

If discriminant is less than zero no solution

Here the discriminant is 15 , which is greater than zero.

Therefore we will have to solutions.

There is only one option with two solutions for x.

So option b is the answer.

Answer:

1. mode

2. median, mode, mode interval

3. stem and leaf graph

4. not sure (try using a median calculator)

5. 80 or 90 (not exactly sure)

Step-by-step explanation:

Answer:

6-1 7-3

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

5x-8 = 2x+16

Move 2x to the left side and you get 3x-8 = 16

Move -8 to the right side and you get 3x = 24

Divide 3 on both sides and you get x = 8

Answer:

44.8 cm

Step-by-step explanation:

Vertical height (h) = EM = 20 cm

Slant height (l) = 30 cm

This two heights form a right angle at the interception at the base. Thus, we have a right angle triangle.

The length of the sides of the base = 2 × the base of the right triangle

✔️Use Pythagorean theorem to find the base of the right triangle formed. Thus: c² = a² + b²

a = base of the triangle

b = h = 20 cm

c = l = 30 cm

Plug in the values

30² = a² + 20²

a² = 30² - 20²

a² = 500

a = √500

a = 22.4 cm

✔️length of the sides of the base = 2 × the base of the right triangle

= 2 × a

= 2 × 22.4

= 44.8 cm

Answer:

x = 15

Step-by-step explanation:

-3x+20+7x=80

Combine like terms

4x+20 = 80

Subtract 20 from each side

4x+20 -20 = 80-20

4x = 60

Divide by 4

4x/4 = 60/4

x = 15

Answer:

4cm

Step-by-step explanation:

first find the length of one side of the square

let x represent that

making 2x length of the rectangle

area of a rectangle=length x width

2cm²=2x×x

2cm²=2x²

2cm²/2=2x²/2

1cm²=x²

1√cm²=√x²

1cm=x

perimeter of a square=4xside

4x1cm

4cm

Answer:

[tex](x^3 + 3x^2 - x + 2)(x^2 + 6x -2) = x^5 + 9x^4+ 15x^3 + 2x^2 + 10x -4[/tex]

Step-by-step explanation:

Given

[tex](x^3 + 3x^2 - x + 2)(x^2 + 6x -2)[/tex]

Required

The equivalent expression

We have:

[tex](x^3 + 3x^2 - x + 2)(x^2 + 6x -2)[/tex]

Open bracket

[tex](x^3 + 3x^2 - x + 2)(x^2 + 6x -2) = x^5 + 6x^4 - 2x^3 + 3x^4 + 18x^3 - 6x^2 -x^3 + 6x^2 - 2x + 2x^2 + 12x -4[/tex]

Collect like terms

[tex](x^3 + 3x^2 - x + 2)(x^2 + 6x -2) = x^5 + 6x^4 + 3x^4- 2x^3 -x^3 + 18x^3 - 6x^2 + 6x^2 + 2x^2- 2x + 12x -4[/tex]

Evaluate like terms

[tex](x^3 + 3x^2 - x + 2)(x^2 + 6x -2) = x^5 + 9x^4+ 15x^3 + 2x^2 + 10x -4[/tex]

Answer:

What is 5/8 x 128? Answer: This is the same as working out 5/8 of 128. Do this by dividing by the bottom numbers, and multiplying by the top number. So 128 divided by 8 is 16, 16 times 5 is 80.

Answer:

2y

Step-by-step explanation:

2x-3=2y

2x-2y=3

Answer:

x = 3, y = 1.5

Step-by-step explanation:

Given the 2 equations

x + 2y = 6 → (1)

2x - 3 = 2y → (2)

In (2) subtract 2y from both sides and add 3 to both sides

2x - 2y = 3 → (3)

Adding (1) and (3) term by term will eliminate the y- term

3x = 9 ( divide both sides by 3 )

x = 3

Substitute x = 3 into either of the 2 equations and solve for y

Substituting into (1)

3 + 2y = 6 ( subtract 3 from both sides )

2y = 3 ( divide both sides by 2 )

y = 1.5

Answer:

79.5

Step-by-step explanation:

10^7 = 10^6 * 10

then 10*7.95 = 79.5