Tyler and Gabe went to the arcade and played the same two games. Tyler played 5 rounds of one game and two rounds of the other for $24. Gabe played 4 rounds of each game for $30. Write two equations for the amounts the two boys spent. Then find the cost for one round of each game.

Answer:

1. 4[tex]x^{3}[/tex] + 26x² + 4x - 48

2. 2[tex]x^{3}[/tex] - 23x² + 60x - 32

3. [tex]x^{5}[/tex] + 7[tex]x^{3}[/tex] - 4x + 2[tex]x^{4}[/tex] + 14x² - 8

4. 2[tex]x^{7}[/tex] + [tex]x^{6}[/tex] - 28[tex]x^{5}[/tex] + 3x + 12

Step-by-step explanation:

To multiply polynomials, simply distribute whatever's outside the largest set of parenthesis, then combine like terms.

1) Distribute the parenthesis (x + 6):

x(4x² + 2x - 8)  +  6(4x² + 2x - 8)

4[tex]x^{3}[/tex] + 2x² -8x  +  6(4x² + 2x -8)

4[tex]x^{3}[/tex] + 2x² -8x + 24x² + 12x - 48

Combine like terms:

4[tex]x^{3}[/tex] + 26x² + 4x - 48

2) Distribute the parenthesis (x - 8):

x(2x² - 7x + 4)  +  (-8)(2x² - 7x + 4)

2[tex]x^{3}[/tex] - 7x² + 4x  +  (-8)(2x² - 7x + 4)

2[tex]x^{3}[/tex] - 7x² + 4x  +  -16x² + 56x - 32

Combine like terms:

2[tex]x^{3}[/tex] - 23x² + 60x - 32

3) Distribute the parenthesis (x + 2):

x([tex]x^{4}[/tex] + 7x² - 4)  +  2([tex]x^{4}[/tex] + 7x² - 4)

[tex]x^{5}[/tex] + 7[tex]x^{3}[/tex] - 4x  +  2([tex]x^{4}[/tex] + 7x² - 4)

[tex]x^{5}[/tex] + 7[tex]x^{3}[/tex] - 4x + 2[tex]x^{4}[/tex] + 14x² - 8

No like terms to combine, so:

[tex]x^{5}[/tex] + 7[tex]x^{3}[/tex] - 4x + 2[tex]x^{4}[/tex] + 14x² - 8

4) Distribute the parenthesis (x + 4):

x(2[tex]x^{6}[/tex] - 7[tex]x^{5}[/tex] + 3)  +  4(2[tex]x^{6}[/tex] - 7[tex]x^{5}[/tex] + 3)

2[tex]x^{7}[/tex] - 7[tex]x^{6}[/tex] + 3x  +  4(2[tex]x^{6}[/tex] - 7[tex]x^{5}[/tex] + 3)

2[tex]x^{7}[/tex] - 7[tex]x^{6}[/tex] + 3x + 8  [tex]x^{6}[/tex] - 28[tex]x^{5}[/tex] + 12

Combine like terms:

2[tex]x^{7}[/tex] + [tex]x^{6}[/tex] - 28[tex]x^{5}[/tex] + 3x + 12

hope this helps!

It costs $122.4 dollars before the increase.

Therefore, It costs $122.4 dollars before the increase.

Learn more about Finding the Percentage here:

https://brainly.com/question/24862040

Answer:

0

Step-by-step explanation:

[tex]\left[\begin{array}{ccc}a&b\\c&d\end{array}\right] = ad-bc[/tex]

0(4)-4(0) = 0

Answer:

[tex]\huge\boxed{\bf\:2}[/tex]

Step-by-step explanation:

[tex]\frac{4}{3 + \sqrt{7}}[/tex]

Rationalise the denominator by multiplying the numerator & denominator of the fraction with [tex](3 - \sqrt{7})[/tex].

[tex]\frac{4\left(3-\sqrt{7}\right)}{\left(3+\sqrt{7}\right)\left(3-\sqrt{7}\right)}[/tex]

Now, we  an see that the denominator is in the form of the algebraic identity: (x + y) (x - y) = x² - y². So,

[tex]\frac{4\left(3-\sqrt{7}\right)}{3^{2}-\left(\sqrt{7}\right)^{2}} \\= \frac{4\left(3-\sqrt{7}\right)}{9-7} \\= \frac{4\left(3-\sqrt{7}\right)}{2} \\[/tex]

The new denominator is 2.

[tex]\rule{150pt}{2pt}[/tex]

Answer:

Option D. 2

Step-by-step explanation:

Hello!

To rationalize the denominator, we should multiply the numerator and the denominator by the conjugate of the denominator. The conjugate simply means the same terms but with the opposite operation.

The new denominator is 2.

Answer: y = one-half x minus 4

Step-by-step explanation:

y = 1/2 x + b

-3 = 1/2 (2) + b

-3 = 1 + b

-3 - 1 = b

-4 = b

Answer: hii

Exchanged a good or service directly for a good or service

Step-by-step explanation:

Bartering was an early way that people... Exchanged a good or service directly for a good or service.

Hopefully this helps you

- Matthew

Bartering was an early way that people exchanged goods.

Let's imagine a situation between "A" and "B". Suppose "A" wants rice and have sugar. On the other hand "B" has rice and he wants sugar. So,there will be exchange between "A" and "B" where "A" will give sugar to "B" and "B" will give rice to "A".

Answer:

sorry I tried But Don't Know The Answer

Answer:

1

Step-by-step explanation:

[tex]my \: dear \: \\ to \: find \: the \: slope \: of \: a \: line \: use \: the \: formular \\ slope = \frac{y2 - y1}{x2 - x1} \\ from \: the \: question \: x1 = 5 \: \: y1 = 1\: \: x2 = - 5 \: \: y2 =- 9 \\ slope = \frac{ - 9 - 1}{ - 5 - 5} = \frac{ - 10}{ - 10} = 1 \\ therefore \: slope = 1 \\ hope \: this \: helps \\ stay \: focused \: with \: your \: studies[/tex]

We can find the distance between two points by using distance formula,

[tex] \qquad \: D = \sf \red{\sqrt{ {(x_2 -x_1)}^{2} + {(y_2 -y_1)}^{2} }}[/tex]

Here,

x₁ = -3

x₂ = 5

y₁ = -2

y₂ = 2

Therefore,

[tex] : \implies \: D = \sf \red{\sqrt{ {(x_2 -x_1)}^{2} + {(y_2 -y_1)}^{2} }} \\ \\ : \implies \: D = \sf \sqrt{ {(5-( - 3))}^{2} + {(2 -( - 2))}^{2} }

\\ \\ : \implies \: D = \sf \sqrt{ {8}^{2} + {4}^{2} } \\ \\ : \implies \: D = \sqrt{64 + 16}

\\ \\ : \implies \: D = \sqrt{80} [/tex]

Hence the √80 = 8.94 approx is the distance between the two points (-3,-2) and (5,2).

The distance between 2 points

Here we have been provided 2 points

(-3, -2) and (5, 2)

[tex] (x_1,y_1) = (-3,-2) \\ (x_2,y_2) = (5,2) [/tex]

Formula to find distance is

[tex] = \sqrt{ {(x_2 - x_1)}^{2} + {(y_2 - y_1)}^{2} } [/tex]

[tex] = \sqrt{ {(5 - ( - 3))}^{2} + {(2 - ( - 2))}^{2} } \\ = \sqrt{ {(8)}^{2} + {(4)}^{2} } \\ = \sqrt{64 + 16} \\ = \sqrt{80} \\ = 4 \sqrt{5} [/tex]

The distance between 2 points is 4√5.

[tex] \mathcal {BE \: \: BRAINLY} [/tex]

Answer:

-cos^4(x)

Step-by-step explanation:

Step 1: Use the Pythagorean identity : 1=cos^2(x) + sin^2(x)

1-sin^2(x) = cos^2(x)

-1+sin^2(x) = -cos^2(x)

cos^2(x) (-cos^2(x))

Step 2: Factor out common terms cos^2(x)

cos^2(x) (sin^2(x)-1)

Ans: -cos^4(x)

I assume the integral is

[tex]\displaystyle \int\frac{\sin(2x)}{\sin(x)} \, dx[/tex]

Simplify the integrand:

[tex]\sin(2x) = 2\sin(x)\cos(x) \implies \dfrac{\sin(2x)}{\sin(x)} = 2\cos(x)[/tex]

Then the indefinite integral is

[tex]\displaystyle \int\frac{\sin(2x)}{\sin(x)} \, dx = 2 \int \cos(x) \, dx = \boxed{2 \sin(x) + C}[/tex]

Answer:

 33800

Step-by-step explanation:

You have to multiply all the sides in order to get the answer.

13cm x 10cm = 130cm

130cm x 20cm = 2600cm

2600cm x 13cm = 33800

Answer:

divide what is on the right hand side of the equal sign by what is next to x or y

Step-by-step explanation:

e.g.

2x=3

x=3/2

fraction:3/2

decimal: 1.5

Answer:

divide what is on the right hand side of the equal sign by what is next to x or y

Step-by-step explanation:

Answer:

25 fl oz

Step-by-step explanation:

1 pint is equivalent to 16 fl oz, so we're left with 25 fl oz and 16 fl oz. As you can see, 25 is greater than 16, making 25 fl oz the correct answer.

Answer:

< –13, 4, 4 >

Step-by-step explanation:

Vector u = < –5, 6, 3 >

Vector t = < –8, –2, 1 >

  -5   6   3

+ -8  -2   1

 -13   4   4

Vector u + t = < –13, 4, 4 >

Answer:

B. <14,-3>

Step-by-step explanation:

Answer:

A=0.50

B=0.477

C=0.423<p<0.531

Step-by-step explanation:

sample size N :333

number of success X: 159

sample part of success x/n = 159/333

x=0.477 B

0.50 A Half a chance to flip a tail or head

part C:

[tex]0.477 plusminus 1.96 * \sqrt{ \frac{0.477 (1 - 0.477)}{333} } [/tex]

simplify

[tex]0.477 plusminus 1.96 * 0.0536[/tex]

expand

[tex]0.477 + 1.96 * 0.0536[/tex]

[tex]0.531[/tex]

expand minus

[tex]0.477 - 1.96 * 0.0536[/tex]

[tex]0.423[/tex]

finally answer part c

[tex]0.423 < p < 0.531[/tex]

Answer:

2x+b

Step-by-step explanation:

f(x)=x

2

+bx−21

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax

n

is nax

n−1

.

2x

2−1

+bx

1−1

Subtract 1 from 2.

2x

1

+bx

1−1

Subtract 1 from 1.

2x

1

+bx

0

For any term t, t

1

=t.

2x+bx

0

For any term t except 0, t

0

=1.

2x+b×1

For any term t, t×1=t and 1t=t.

2x+b

Your answer would be 'How thick is the thickest book in your book collection?'

Answer:

how this is the thickest book

Step-by-step explanation:

i took the quiz and got it correct your welcome

Answer:

(5,000+(132 months × 25))×0.079 = 655.7

so at the end of 11 years you have:

$8,300 + interest= 8955.7

Answer:

a) - y = 30°,x = 70°

b)- y = 105°,x = 75°

c)- x = 25°

d)- x = 116°

Step-by-step explanation:

a) =

80 + 70 + y = 180 (co-interior angles)

or, y = 180 - 150

so, y = 30°

Now,

x = 70° (alternate angles)

b) =

y + 75 = 180° (co-interior)

(y = angle which is supplement to 75)

y = 180° - 75°

so, y = 105°

Now,

x + y = 180° (co-interior angles)

or, x = 180° - 105°

so, x = 75°

c)=

180° - 5x = 55° (corresponding angles)

or, 5x = 180° - 55°

or, 5x = 125°

or, x = 125°/5

so, x = 25°

d)=

64° + x = 180° (co-interior angles)

x = 180° - 64°

so, x = 116°

Answer:

See below ~

Step-by-step explanation:

a)

b)

c)

d)

Answer:

?

Step-by-step explanation:

Answer:

68 units sq

Step-by-step explanation:

You have to find the total area of all the shapes and subtract the unshaded.

(9 + 17) * 8 / 2, formula

26 * 4 = 104

Then find the unshaded part

9 * 8 / 2

9 * 4

= 36

104 - 36 = 68

Answer:

68

Step-by-step explanation:

The formula of a trapezoid is [tex]A = \frac{a+b}{2} h[/tex]
Use the values given in the equation:
[tex]A = \frac{17+9}{2} *8[/tex]
A = 13*8

A=104 (This the area of the overal trapezoid)

To find the area of the inner unshaded triangle, simply multiply 9 (Base) times height (8) * 1/2 to get 36

Then subtract 36 from 104 and you get 68

Answer:

Yes

Step-by-step explanation:

5,000 cm = 50m

[tex]\frac{1m}{100cm} =5000cm[/tex]

[tex]\frac{1m(5000)}{100}[/tex]

[tex]\frac{5000m}{100}[/tex]

= 50 m

hope this helps :)

Answer:

x = 52, c = 87

Step-by-step explanation:

Set up and then solve this system of equations:

3c + 5x = 521--->3c + 5x = 521

c + x = 139 --->3c + 3x = 417

-------------------

2x = 104

x = 52, c = 87

Answer: the answer is 139-c

Answer:

Step-by-step explanation:

First confirm that x = 1 is one of the zeros.

f(1) = 2(1)^3 - 14(1)^2 + 38(1) - 26

f(1) = 2 - 14 + 38 - 26

f(1) = -12 + 38 = + 26

f(1) = 26 - 26

f(1) = 0

=========================

next perform a long division

x -1  || 2x^3 - 14x^2 + 38x - 26 || 2x^2 - 12x + 26

         2x^3 - 2x^2

         ===========

                   -12x^2 + 28x

                    -12x^2 +12x

                    ==========

                                 26x -26

                                 26x - 26

                                ========

                                     0

Now you can factor 2x^2 - 12x + 26

                                2(x^2 - 6x + 13)

The discriminate of the quadratic is negative. (36 - 4*1*13) = - 16

So you are going to get a complex result.

x = -(-6) +/- sqrt(-16)

    =============

                2

x  = 3 +/- 2i

f(x) = 2*(x - 1)*(x - 3 + 2i)*(x - 3 - 2i)

The zeros are

1

3 +/- 2i

Apply the long division to find that there is only 1 real root