Mary simplified the algebraic expression 2/3x + 1/4x as shown below.

Step-by-step explanation:

3 - (1/4)×(8/3 × 9)

3 - (1/4)×(8×9/3)

3 - (1/4)×(8×3)

3 - (1/4)×24

3 - 24/4

3 - 6 = -3

2 1/8 pints

2.125 pints

The solutions to the given polynomial equation are x = 1/3 and x = 1.

According to the given polynomial equation f(x)=-3x^(2)+4x-1, we can find the values of x by using the quadratic formula, which is x = (-b ± √(b^(2)-4ac))/(2a).

In this equation, a = -3, b = 4, and c = -1.

Plugging these values into the quadratic formula, we get:

x = (-(4) ± √((4)^(2)-4(-3)(-1)))/(2(-3))

Simplifying this equation, we get:

x = (-4 ± √(16-12))/(-6)

x = (-4 ± √4)/(-6)

x = (-4 ± 2)/(-6)

Therefore, the two possible values of x are:

x = (-4 + 2)/(-6) = -2/(-6) = 1/3

x = (-4 - 2)/(-6) = -6/(-6) = 1

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Answer:$18

Step-by-step explanation: Since 50% is half of a hundred and the item is half off, you multiply 36 by 0.5 and get $18. This is the price of the item with the sale and the the discount

Answer:

18$

Step-by-step explanation:

go to Safari and look it up is how I got the answer

Answer:

20° and 22°

Step-by-step explanation:

Quadrilaterals are shapes with 360°. Since we are given two known angles, we can subtract them from 360. 360 - 216 - 102 = 144 - 102 = 42

Because the others are in a ratio of 10:11, the only possible degree combination will be 20° and 22°

Answer:

Step-by-step explanation: First you do 5*5 and get 25. Then you do 25/8 and get 3 1/8.

Answer: C

Step-by-step explanation:

The correct answer is (a) (x-7)^2 / 25 + (y+2)^2 / 9 = 1.

The standard equation of an ellipse is (x-h)^2 / a^2 + (y-k)^2 / b^2 = 1, where (h,k) is the center of the ellipse, a is the distance from the center to the vertices, and b is the distance from the center to the covertices.

In this case, the center of the ellipse is the midpoint of the vertices and covertices, which is (7, -2). The distance from the center to the vertices is 5 (12-7) and the distance from the center to the covertices is 3 (1-(-2)).

Therefore, the standard equation of the ellipse is (x-7)^2 / 25 + (y+2)^2 / 9 = 1, which corresponds to answer choice (a).

So the correct answer is (a) (x-7)^2 / 25 + (y+2)^2 / 9 = 1.

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Answer: $139.00

Step-by-step explanation: 5x11 = 55
12x7 = 84

55+84=139

Given trigonometric equation is equal to 2 so the it has been proved.

what is trigonometric identity?

A trigonometric identity is a mathematical equation that expresses a relationship between trigonometric functions of an angle. These identities are true for all values of the angle, and they allow us to simplify expressions involving trigonometric functions, manipulate them algebraically, or evaluate them more easily.

Trigonometric identities include basic relationships such as [tex]sin^2(x) + cos^2(x) = 1,[/tex] as well as more complex identities involving multiple functions such as the Pythagorean identity.

According to the question:
Let us begin by applying the trigonometric identity[tex]cos^2(x) + sin^2(x) = 1,[/tex]which is true for any angle x. Solving for[tex]cos^2(x)[/tex], we get [tex]cos^2(x) = 1 - sin^2(x).[/tex]

Using this identity, we can rewrite the given equation as

[tex]1 - sin^2((1/8)^2) + 1 - sin^2(3n/8) + 1 - sin^2(5n/8) + 1 - sin^2(7n/8) = 2[/tex]

Simplifying, we get:

[tex]4 - (sin^2((1/8)^2) + sin^2(3n/8) + sin^2(5n/8) + sin^2(7n/8)) = 2[/tex]

Rearranging, we get:

[tex]sin^2((1/8)^2) + sin^2(3n/8) + sin^2(5n/8) + sin^2(7n/8) = 2[/tex]
Now, let us apply the trigonometric identity [tex]sin^2(x) + cos^2(x) = 1[/tex], which is true for any angle x. Solving for [tex]sin^2(x),[/tex] we get [tex]sin^2(x) = 1 - cos^2(x)[/tex].
2=2
Therefore, the equation is true

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The polynomial that 3x^(2)-22x+26 is divided by is x - 6.

To find the polynomial that 3x^(2)-22x+26 is divided by, we can use the formula:

Dividend = Quotient * Divisor + Remainder

In this case, the dividend is 3x^(2)-22x+26, the quotient is 3x-4, and the remainder is 2. We can plug these values into the formula and solve for the divisor:

3x^(2)-22x+26 = (3x-4) * Divisor + 2

Next, we can rearrange the equation to isolate the divisor:

Divisor = (3x^(2)-22x+26 - 2) / (3x-4)

Divisor = (3x^(2)-22x+24) / (3x-4)

Now, we can use polynomial long division to find the divisor:

```
3x - 4 | 3x^2 - 22x + 24
      - (3x^2 - 4x)
      -------------
           -18x + 24
          - (-18x + 24)
          -------------
                0
```

Therefore, the divisor is x - 6.

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When [tex]3x^{4}-x^{2}[/tex] is divided by [tex]x^{3}-x^{2}+2[/tex], the quotient is 3x and the remainder is [tex]5x^2-2x[/tex].

To see why, we perform long division as follows:    

    [tex]3x[/tex]

[tex]x^3 - x^2 + 2 | 3x^4 + 0x^3 - x^2 + 0x + 0[/tex]

                [tex]- 3x^4 + 3x^3 - 6x^2[/tex]

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

                            [tex]3x^3 - 7x^2[/tex]

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

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

                                    [tex]5x^2 - 2x[/tex]

The divisor is [tex]x^3 - x^2 + 2[/tex] and the dividend is [tex]3x^4 - x^2[/tex]. We start by dividing the highest degree term of the dividend by the highest degree term of the divisor, which gives 3x. We then multiply the divisor by this quotient and subtract the result from the dividend. We repeat this process with the resulting polynomial until the degree of the remainder is less than the degree of the divisor.

In this case, the remainder is [tex]5x^2-2x[/tex], which has a degree of 2 (less than the degree of the divisor). Therefore, we have found the quotient and remainder of the division.

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Answer: 11 1/4

Step-by-step explanation:

To multiply fractions, you must use the improper form so...

2 1/4 x 5 =

9/4 x 5 =

45/4 =

11 1/4

Hope this helps!

The mentioned relationship is an additive relationship as the total cost is not proportional to the number of games played.

To represent the relationship between the total cost, y, and the number of games played, x, we can create a table, graph, and equation as follows:

Number of games played (x) Total cost (y)

0                                                          10

1                                                          11

2                                                          12

3                                                          13

4                                                          14

5                                                          15

The equation that represents this relationship is: y = 1x + 10

Where 10 is the fixed cost to enter the arcade and 1 is the cost per game played.

To represent this relationship graphically, we can plot the points from the table on a graph. Refer to the image attached with this answer.

This graph shows that the relationship between the total cost and the number of games played is a straight line with a positive slope.

This relationship is an additive relationship because the total cost is not proportional to the number of games played. If the relationship was proportional, the cost per game played would remain constant regardless of the number of games played. In this case, the cost per game played is always $1, but the total cost increases by $1 for each additional game played.

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The complete question is :  

Sam went to play video games in Video Game Central arcade. Video Game Central charges $10 to get into the arcade and then $1 per game played. Represent the relationship between total cost, y, and number of games played, x using a table, graph and equation. Is this relationship a proportional or additive relationship? Explain.

Answer:

52.4285714286

Step-by-step explanation:

use a calculator

Answer: 52.4

Step-by-step explanation:

The equation 4(x - 2) = 2(2x + 6) has no solution.

To solve the equation 4(x - 2) = 2(2x + 6), we must first use the distributive property to expand the equations. The distributive property states that a(b + c) = ab + ac.

Using the distributive property, we can expand the equation as follows:

4(x - 2) = 2(2x + 6)

4x - 8 = 4x + 12

Next, we must isolate the variable on one side of the equation. We can do this by subtracting 4x from both sides of the equation:

-8 = 12

This equation is not true, so there is no solution to the equation 4(x - 2) = 2(2x + 6).

In conclusion, the equation 4(x - 2) = 2(2x + 6) has no solution.

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The answer of equation for the function is y=(x-2)^(2)-1.

The equation for a function that has the shape of y=x^(2), but shifted right 2 units and down 1 unit is y=(x-2)^(2)-1.

To shift a function to the right, we subtract the amount of the shift from the x variable.

In this case, we want to shift the function 2 units to the right, so we subtract 2 from x: (x-2).

To shift a function down, we subtract the amount of the shift from the entire function.

In this case, we want to shift the function down 1 unit, so we subtract 1 from the entire function: (x-2)^(2)-1.

Therefore, the equation for the function is y=(x-2)^(2)-1.

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A = |λ-6 0 0| . |0 λ 4| . |0 5 λ-1| λ 1= 4.79 λ 2= 4.79 λ3 = 4.79, as the highest value of lif it exists is 4.79. therefore X=4.79

To find the values of λ for which det(A) = 0, we need to solve the equation det(A) = 0. The matrix determinant of a 3x3 matrix A is given by:

[tex]det(A) = a11(a22a33 - a23a32) - a12(a21a33 - a23a31) + a13(a21a32 - a22a31)[/tex]

In this case, the matrix A is:
A = |λ-6 0 0|
   |0 λ 4|
   |0 5 λ-1|

So, the determinant of A is:
[tex]det(A) = (λ-6)(λ(λ-1) - 4*5) - 0(0(λ-1) - 4*0) + 0(0*5 - λ*0)[/tex]
Simplifying the equation, we get:
[tex]det(A) = (λ-6)(λ^2 - λ - 20)[/tex]
Setting det(A) = 0, we can find the values of λ:
[tex](λ-6)(λ^2 - λ - 20) = 0[/tex]
This equation has three solutions:
[tex]λ 1 = 6λ 2 = (-1 + √81)/2 ≈ 4.79λ 3 = (-1 - √81)/2 ≈ -5.79[/tex]

So, the answer is:
λ 1 = 6
λ 2 = 4.79
λ 3 = -5.79
The greater value of λ is λ 2 = 4.79.

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Answer: 55 miles per hour.

To find the unit rate, divide the miles traveled by the time taken:

275 miles ÷ 5 hours = 55 miles per hour

Step-by-step explanation:

The numeric values of the piece-wise function are given as follows:

To obtain the numeric value of a function or of an expression, we replace each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression.

A piece-wise function is a function that has different definitions, based on the input interval of the function.

For x < 2, the function is defined as follows:

h(x) = -2x + 10.

Hence the numeric values on the interval are obtained as follows:

For x >= 2, the function is defined as follows:

h(x) = x + 2.

Hence the numeric values on the interval are obtained as follows:

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Based, on the given information, the length of the ramp z, is equal to 53 inches.

A triangle is said to be right-angled if one of its internal angles is 90 degrees, or if any one of its angles is a right angle. The right triangle or 90-degree triangle is another name for this triangle. In geometry, the right triangle is significant.

A triangle is said to be right-angled if one of its edges is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the parts that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.

In a right-angled triangle, the square of the hypotenuse side is equivalent to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three edges are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposing the 90° angle, the hypotenuse in this case is the longest side. When the positive number sides of a right triangle (let's say sides a, b, and c) are squared, the result is an equation known as a Pythagorean triple.

In this question, the base, the height and the length of the ramp form a right angled triangle.

To find the length, we will use Pythagoras theorem, which states that,

(hypotenuse)² = (base)²+ (height)²

Substituting the values, we get

x²=45²+ 28²

x²= 2809

x=√2809

x=53 inches

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The x-intercept is (-3,0) and the y-intercept is (0,9).

The x-intercept of a quadratic function is the point where the function intersects with the x-axis. This point represents the value of x for which the function is equal to 0. The x-intercept can be found by setting the function equal to 0 and solving for x.

The y-intercept of a quadratic function is the point where the function intersects with the y-axis. This point represents the value of y for which the function is equal to 0. The y-intercept can be found by setting x equal to 0 and solving for y.

1. The x-intercept of the function is (-3,0) and it represents the point where the function intersects with the x-axis.
2. The y-intercept of the function is (0,9) and it represents the point where the function intersects with the y-axis.

To find the x-intercept, set the function equal to 0 and solve for x:

0 = x^2 + 6x + 9

0 = (x+3)(x+3)

x = -3

To find the y-intercept, set x equal to 0 and solve for y:

y = 0^2 + 6(0) + 9

y = 9

Therefore, the x-intercept is (-3,0) and the y-intercept is (0,9).

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Answer:

1011.00

Step-by-step explanation:

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The simplified expression of the given expression is [tex]\frac{6\sqrt{10}}{7}$.[/tex]

What is expression ?

An expression is a mathematical phrase that can contain numbers, variables, operators, and symbols. It can be a combination of terms, factors, and/or coefficients, and may involve addition, subtraction, multiplication, division, exponents, roots, and/or other mathematical operations. Expressions can be simplified, evaluated, or manipulated using algebraic rules and properties.

We can simplify the expression as follows:

[tex]\frac{\sqrt{40\cdot9}}{\sqrt{49}}=\frac{\sqrt{4\cdot10\cdot3\cdot3}}{\sqrt{7\cdot7}}\\ \\ \\=\frac{\sqrt{4}\cdot\sqrt{10}\cdot\sqrt{3}\cdot\sqrt{3}}{\sqrt{7}\cdot\sqrt{7}}\\ \\ \\=\frac{2\cdot3\sqrt{10}}{7}\\ \\ \\={\frac{6\sqrt{10}}{7}}.[/tex]

Therefore, the simplified expression of the given expression is [tex]\frac{6\sqrt{10}}{7}$.[/tex]

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Answer: EF, DF, DE

Step-by-step explanation:

The smaller the opposite angle, the smaller the side, and vice versa.

∠EDF = 85°

∠DEF = 60° (Because the total degrees in a triangle must be 180°)

∠DFE = 35°

EF, DF, DE

Hope this helps!

Answer: 7/2 + 7b

Step-by-step explanation:

When applying the distributive property, you want to start by identifying which value you are distributing. That value in this case will be 7/8.

7/8 is going to be multiplied with 4, then multiplied with 8b, and you will then find the sum of those to products:

( (7/8) * 4 ) + ( (7/8) * (8b) )

The first product simplified will be 7/2.

The second product simplified will be 7b.

The sum of those two products is: 7/2 + 7b.

Hope this helps.

The amount we would have after 40 years will be $8183.27

Exponential growth is a pattern of data that shows greater increases with passing time, creating the curve of an exponential function.

Given that, an amount increasing exponentially every two years and with a rate of 15% and the amount is $500, we need to find the amount we would have after 40 years.

Since, the amount is increasing exponentially every two years, therefore,

T = 40 / 2 = 20 years

A = P(1+0.15)²⁰

A = 500(1+0.15)²⁰

A = 500(1.15)²⁰

A = 8183.27

Hence, the amount we would have after 40 years will be $8183.27

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Answer:

The dilated image has half the dimensions of the pre-image

So the pre-image is dilated by a scale factor of 1/2 (0.5)

Step-by-step explanation:

The side lengths of the dilated image is related to the preimage by a division of 2

From the question, we have the following parameters that can be used in our computation:

The figure

Where we have

Pre-Image = PQRS

Image = P''Q'R'S'

From the figure, we can see that

The side lengths of P''Q'R'S' is half of the side lengths of PQRS

This means that

(x, y) = 1/2(x, y)

Hence, the transformation is (x, y) = 1/2(x, y)

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The whole number that is a solution for the inequality x ≥ 4 but is not a solution for the inequality x > 4 is 4.

Option B is the correct answer.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

here,

We have,

x ≥ 4 and x > 4

Now,

x ≥ 4 means that x can be 4 and greater than 4.

x > 4 mean x is greater than 4.

So,

4 is a solution to x ≥ 4 but not a solution to x > 4.

Thus,

4 is the whole number.

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Each person should pay $16.37.

If the meal was $54.55 and you should tip the waiter 20%, the total cost of the meal would be $54.55 + ($54.55 * 0.20) = $65.46.

If the bill is shared equally among 4 people, each person should pay $65.46 / 4 = $16.37.

Therefore, each person should pay $16.37 for the meal. Step-by-step explanation:

1. Calculate the tip by multiplying the cost of the meal by 20% (0.20): $54.55 * 0.20 = $10.91

2. Add the tip to the cost of the meal to get the total cost: $54.55 + $10.91 = $65.46

3. Divide the total cost by the number of people to get the cost per person: $65.46 / 4 = $16.37

4. The final answer is $16.37 per person.

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