Find the inequality represented by the graph.

The Simplification of the algebraic expression gives:

a. -2/3x² - (4/15)xy +  (11/4)y²

b. -(12/7)x³ + (20/9)y

Simplification of an algebraic expression is the process of writing an expression in the most efficient and compact form without affecting the value of the original expression

a. (1/3)x² - (2/5)xy + 2y² + (2/15)xy - 3x² + (3/4)y²

To simplify this, add or subtract like terms. That is:

(1/3)x² - (2/5)xy + 2y² + (2/15)xy - 3x² + (3/4)y²

     = (1/3)x² - 3x² - (2/5)xy + (2/15)xy + 2y²  + (3/4)y²

     = -2/3x² - (4/15)xy +  (11/4)y²

b. (2/7)x³ - (1/3)y + 2y - 2x³ + (5/9)y

To simplify this, add or subtract like terms. That is:

(2/7)x³ - (1/3)y + 2y - 2x³ + (5/9)y = (2/7)x³- 2x³ - (1/3)y + 2y + (5/9)y

                                                    = -(12/7)x³ + (20/9)y

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a) The algebraic fraction \(\frac{{x + 2}}{{(x - 1)^2}}\) is proper. b) The algebraic fraction \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\) can be expressed as \(-\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

Let's solve each part step by step and determine whether the fraction is proper or improper, and then express it accordingly.

a) \(\frac{{x + 2}}{{(x - 1)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 1 (linear term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is less than the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

\(\frac{{x + 2}}{{(x - 1)^2}} = \frac{A}{{x - 1}} + \frac{B}{{(x - 1)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 1)^2)\) to eliminate the denominators:

  (x + 2) = A(x - 1) + B.

Expand the equation and collect like terms:

  x + 2 = Ax - A + B.

Equate the coefficients of like terms:

  Coefficient of x: 1 = A.

  Constant term: 2 = -A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = 1.

Substituting A = 1 into the constant term equation: 2 = -1 + B, we find B = 3.

Therefore, the partial fraction decomposition is:

  \(\frac{{x + 2}}{{(x - 1)^2}} = \frac{1}{{x - 1}} + \frac{3}{{(x - 1)^2}}\).

b) \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 2 (quadratic term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is equal to the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = \frac{A}{{x - 4}} + \frac{B}{{(x - 4)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 4)^2)\) to eliminate the denominators:

  (4x^2 - 31x + 59) = A(x - 4) + B.

Expand the equation and collect like terms:

  4x^2 - 31x + 59 = Ax - 4A + B.

Equate the coefficients of like terms:

Coefficient of \(x^2\): 4 = 0 (No \(x^2\) term on the right side).

Coefficient of x: -31 = A.

Constant term: 59 = -4A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = -31.

Substituting A = -31 into the constant term equation: 59 = 4(31) + B, we find B = -25.

Therefore, the partial fraction decomposition is:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = -\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

The above steps provide the solution for each part, including determining if the fraction is proper or improper and expressing it in partial fractions.

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By answering the presented question, we may conclude that Therefore, 1  expressions cm on the map corresponds to a real distance of 3.2 km. 

In mathematics, an expression is a collection of integers, variables, and complex mathematical (such as arithmetic, subtraction, multiplication, division, multiplications, and so on) that describes a quantity or value. Phrases can be simple, such as "3 + 4," or complicated, such as They may also contain functions like "sin(x)" or "log(y)". Expressions can be evaluated by swapping the variables with their values and performing the arithmetic operations in the order specified. If x = 2, for example, the formula "3x + 5" equals 3(2) + 5 = 11. Expressions are commonly used in mathematics to describe real-world situations, construct equations, and simplify complicated mathematical topics.

Scale 1:

320000 means that 1 unit on the map represents his 320000 units in the real world.

To find the actual distance represented by 1 cm on the map, you need to convert the units to the same scale.

1 kilometer = 100000 cm

So,

1 unit on the map = 320000 units in the real world

1 cm on the map = (1/100000) km in the real world

Multiplying both sides by 1 cm gives:

1 cm on the map = (1/100000) km * 320000

A simplification of this expression:

1 cm on the map = 3.2 km

Therefore, 1 cm on the map corresponds to a real distance of 3.2 km. 

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Answer:

91 cm squared

Step-by-step explanation:

Find the area of the rectangle 7 x 10=70

Triangle are (6 x 7)/2=21

Add 21+70=91

Answer:

91

Step-by-step explanation:

The area of the circle with the given radius is 201.088 square units.

The area of a circle is the space occupied by the circle in a two-dimensional plane. Alternatively, the space occupied within the boundary/circumference of a circle is called the area of the circle. The formula for the area of a circle is A = πr², where r is the radius of the circle.

Given that, the radius of a circle is 8 units.

Here, area of a circle

= 3.142×8²

= 3.142×64

= 201.088 square units

Therefore, the area of the circle is 201.088 square units.

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Answer:

t=6.8

Step-by-step explanation:

t=2.01[squareroot(L)]

L=11.56

t=2.01[squareroot(11.56)]

t=2.01(3.4)

t=6.834

(round to nearest tenth)

t=6.8

Answer:

0.3 or 1/3

Step-by-step explanation:

add 4/5 + 3/15=1

then 1-2/3 = 1/3

Answer: 1/3

\(\frac{4}{5}+\frac{3}{15}-\frac{2}{3}\\\\=\frac{4}{5}+\frac{3}{3.5}-\frac{2}{3}\\\\=\frac{4}{5}+\frac{1}{5}-\frac{2}{3}\\\\=1-\frac{2}{3}\\\\=\frac{3}{3}-\frac{2}{3}\\\\=1/3\)

Step-by-step explanation:

Answer: 3 copies of 5 tenths = 3*0.5 = 1.5

Step-by-step explanation:

Ok, if we have:

"3 copies of a number B"

This is written as:

3*B

And we have that the number B is "5 tenths"

Now, a tenth is the first digit after the decimal point.

Then 5 tenths = 5*0.1 = 0.5

B = 0.5

3 copies of 5 tenths = 3*0.5 = 1.5

Answer:

200.96 units

Step-by-step explanation:

Use the formula for the volume of a cone \(V=\pi r^{2} \frac{h}{3}\)

Plug in the values (\(\pi\)=3.14) and multiply them all out

Answer:

≈ 201

Step-by-step explanation:

V= πr²h/3

V= 3.14*4²*12/3= 200.96 ≈ 201

Answer:

y= -1/2x-1

Step-by-step explanation:

Step-by-step explanation:

Just multiply the two dimensions to get m^2  area

7.2 m * 11 m = 79.2 m^2

Answer:

No they would be $100 short.

Step-by-step explanation:

Answer:

The answer will be True

Step-by-step explanation:

Because I said so

The pair of numbers that yields the maximum product when their sum is 24 is (12, 12), and the maximum product is 144. The corresponding quadratic function is P(x) = -x^2 + 24x, and the parabola opens downwards.

To find a pair of numbers whose sum is 24 and whose product is as large as possible, we can use the concept of maximizing a quadratic function.

Let's denote the two numbers as x and y. We know that x + y = 24. We want to maximize the product xy.

To solve this problem, we can rewrite the equation x + y = 24 as y = 24 - x. Now we can express the product xy in terms of a single variable, x:

P(x) = x(24 - x)

This equation represents a quadratic function. To find the maximum value of the product, we need to determine the vertex of the parabola.

The quadratic function can be rewritten as P(x) = -x^2 + 24x. We recognize that the coefficient of x^2 is negative, which means the parabola opens downwards.

To find the vertex of the parabola, we can use the formula x = -b / (2a), where a = -1 and b = 24. Plugging in these values, we get x = -24 / (2 * -1) = 12.

Substituting the value of x into the equation y = 24 - x, we find y = 24 - 12 = 12.

So the pair of numbers that yields the maximum product is (12, 12). The maximum product is obtained by evaluating the quadratic function at the vertex: P(12) = 12(24 - 12) = 12(12) = 144.

Therefore, the maximum product is 144. This quadratic function has a maximum value because the parabola opens downwards.

To graph the function, you can plot several points and connect them to form a parabolic shape. Here is an uploaded image of the graph of the quadratic function: [Image: Parabola Graph]

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Answer:

R1620

Step-by-step explanation:

1620 ×1=1620

1620×2=3240

1620×3=4860

1620×4=6480

1620×5=8100

Answer:

D. You were correct.

Step-by-step explanation:

The even numbers on a 6 sided dice are 2 4  6 or 3/6 which is 1/2

The spinner has 2 red sections out of 4. The probability of getting a red is 2/4 = 1/2

P(even and red) = 1/2 * 1/2 = 1/4

I don't know what the table is for.

The true statement is if k = - 1 there are solutions, but if k = - 3 there are no solutions

Given: |x+3|-2=k

Below are rules for solving absolute value equations:

1. If p is positive and |y| = p, then

x = p   OR    y = -p

(two equations are set up)

2. If p is negative and |y| = p, then

No solution

3. If p is zero  and |y| = p, then

One solution

Using the rules:

|x+3|-2=k

when k = -1

|x+3|-2= -1    

|x+3| = 1

Rule 1 is applicable here. Thus, there are solutions  

when k = -3

|x+3|-2 = -3

|x+3| = -1

Rule 3 is applicable here. Thus, no solution

Therefore, if k = - 1 there are solutions, but if k = - 3 there are no solutions.     The 2nd option is the true statement

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Answer:

b = sqrt(57)

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse

8^2 + b^2 = 11^2

64+ b^2 = 121

Subtract 64

b^2 = 121-64

b^2 =57

Take the square root of each side

b = sqrt(57)

Answer:

$113.75

Step-by-step explanation:

First add 70.25 to 43.50 to get 113.75

Answer:

$113.75

Step-by-step explanation:

b-70.25=43.50

add 70.25 to each side ..

b-70.25=43.50

+70.25+70.25

simpilfy...b=113.75

Answer:

9x^2 - 3x - 2,  R -7.

Step-by-step explanation:

x - 5) 9x^3 - 48x^2 + 13x + 3(9x^2 - 3x - 2 <---- Quotient.

        9x^3 - 45x^2

                  - 3x^2 + 13x

                   -3x^2 + 15x

                                -2x + 3

                                -2x + 10

                                          -7 <----- Remainder

Answer:

he bought 17 book.

Answer: f(-3) = 9

Step-by-step explanation:

Plug in -3 for x

f(-3) = (-3)^2

Square -3

(-3)^2 = 9

Answer:

f(-3)=9

Step-by-step explanation:

f(x)=\(x^{2}\)

To find f(-3) replace x in the function by -3

Therefore:

f(−3)=(−3)^2

=−1^2 × 3^2 =1 × 9 = 9

HOPE THIS HELPS

HAVE A GOOD DAY:)

Answer:

1/4

Step-by-step explanation:

1/2 ÷ 2 = 1/4

Answer:

0.25 which is 1/4.

you're welcome(:

also please give brainliest.

Step-by-step explanation:

Answer:

x-int=-40

y-int=15

Step-by-step explanation:

we have points 0,15 and -40,0 on the line.

It is as easy as the y-int being 15 and the x-int being -40!

the y-int will always be= (0,#)

the x-int will always be (#,0)

To determine when the total cost of each health club will be the same, we can set up an equation and solve for the number of months.

Let's assume the number of months is represented by 'x'.

For Club A, the total cost is given by:

Total cost of Club A = $13 (one-time fee) + $28x (monthly fee)

For Club B, the total cost is given by:

Total cost of Club B = $19 (one-time fee) + $27x (monthly fee)

To find the number of months when the total cost is the same, we set the two equations equal to each other:

$13 + $28x = $19 + $27x

Simplifying the equation, we get:

$28x - $27x = $19 - $13

$x = 6

Therefore, after 6 months, the total cost of each health club will be the same.

To find the total cost for each club after 6 months, we substitute the value of 'x' back into the equations:

Total cost of Club A after 6 months = $13 + $28(6) = $13 + $168 = $181

Total cost of Club B after 6 months = $19 + $27(6) = $19 + $162 = $181

So, the total cost for both Club A and Club B will be $181 after 6 months.

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Let "x" be the number of years it takes for the two plants to be the same height.The first plant has an initial height of 7 inches and grows at a constant rate of 3 inches each year. So, the two plants will be the same height after 5 years.

Therefore, after "x" years, its height will be:7 + 3xThe second plant also grows at a constant rate and has an initial height of 2 inches. After 3 years, its height is 14 inches.

Therefore, its rate is: Rate = (Final height - Initial height) / TimeRate = (14 - 2) / 3Rate = 12 / 3Rate = 4So, after "x" years, the second plant's height will be:2 + 4x.

To find when the plants are the same height, we can set the expressions for their heights equal to each other:7 + 3x = 2 + 4xSolving for "x":3x - 4x = 2 - 73x = -5x = -5/(-1). Therefore, x = 5, the two plants will be the same height after 5 years.

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Step-by-step explanation:

Answer:

24234221111111111111111111111

Step-by-step explanation: