What inequality matches this graph?
A} x > -5

B} x ≥ -5

C} x < -5

D} x ≥-5

To find the factors of the polynomial function g(x) = x^3 + 2x^2 - x - 2, we can use different methods such as long division, synthetic division, or grouping.

Using long division, we can divide g(x) by (x-1), which is a factor by the factor theorem:

            x^2 + 3x + 2

    ___________________________

x - 1 | x^3 + 2x^2 - x - 2

    - (x^3 - x^2)

      --------

          3x^2 - x

      - (3x^2 - 3x)

        ----------

                 2x - 2

        - (2x - 2)

          --------

                   0

Therefore, we have factored g(x) as:

g(x) = (x - 1)(x^2 + 3x + 2)

We can further factor the quadratic term using factoring or quadratic formula to obtain the complete factorization of g(x).

The factors of polynomial function g(x) = x³ + 2x² - x - 2 are (x-1), (x+1), and (x+2).

This can be obtained by factoring the polynomial using the grouping method.

Using this method, we group the first two terms together and the last two terms together, resulting in (x²{2 + 2)(x-1) = 0. This gives us two possible roots, x = 1 and x = ±√2i.

However, as we are only interested in real factors, we only consider the real root of x = 1.

G(x) can then be divided by (x-1) using linear long division, yielding the quotient x² + 3x + 2. This quotient can then be factored as (x+1)(x+2). Therefore, the factors are (x-1), (x+1), and (x+2).

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Answer:

Step-by-step explanation:

You want the union and the intersection of the given sets D and E.

The union of the two sets is the list of elements in either set. It will contain all of the elements of D along with all of the elements of E, with duplicate values removed so that each element is only listed once.

The intersection of the two sets is the list of elements that appear in both sets. Any element that only appears in one of the sets is not part of the union.

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The maximum grazing area for the cow is approximately 53,343.08 square feet.

The maximum grazing area for the cow can be found by imagining a circle with radius equal to the length of the rope (130 feet) centered at the corner of the barn where the cow is tethered. The grazing area is the portion of the circle that lies outside the barn.

Since the barn is 8 feet by 8 feet, it covers a square area of 64 square feet. The radius of the circle is 130 feet, so the area of the circle is π(130)^2 square feet.

To find the maximum grazing area, we need to subtract the area of the barn from the area of the circle.

Area of circle = π(130)^2 square feet = 53,407.08 square feet

Area of barn = 64 square feet

Maximum grazing area = Area of circle - Area of barn

= 53,407.08 - 64

= 53,343.08 square feet (rounded to two decimal places)

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The maximum value of the sequence is [tex]1/6[/tex], the minimum value is 0, the supremum is [tex]1/2[/tex], and the infimum is 1/6.

The given sequence is: [tex]{1/(2 ^ n) + ((- 1) ^ n)/(n + 1) / n * N}[/tex]

When [tex]n = 1,[/tex] the sequence evaluates to: [tex]1/2 + (-1)^1 / 2 * 2 = 0[/tex]

When [tex]n = 2,[/tex] the sequence evaluates to: [tex]1/4 + (-1)^2 / 3 * 2 = 1/6[/tex]

When [tex]n = 3,[/tex] the sequence evaluates to: [tex]1/8 + (-1)^3 / 4 * 2 = 7/96[/tex]

When [tex]n = 4,[/tex] the sequence evaluates to: [tex]1/16 + (-1)^4 / 5 * 2 = 17/240[/tex]

It appears that the sequence oscillates between positive and negative values, with the negative values getting smaller as n increases.

Therefore, the minimum value of the sequence is at n = 1, where it evaluates to 0.

The maximum value occurs at n = 2, where it evaluates to 1/6.

The term [tex]1/(2 ^ n)[/tex] has a lower bound of 0 and an upper bound of 1.

The term [tex]((- 1) ^ n)/(n + 1) / n * N[/tex] has a lower bound of [tex]-1/4[/tex] and an upper bound of [tex]1/4[/tex].

Therefore, the supremum of the sequence occurs when [tex]n = 1[/tex], where the sequence evaluates to [tex]1/2[/tex].

The infimum of the sequence occurs when [tex]n = 2[/tex], where the sequence evaluates to [tex]1/6.[/tex]

In summary, the maximum value of the sequence is [tex]1/6[/tex], the minimum value is 0, the supremum is [tex]1/2[/tex], and the infimum is [tex]1/6.[/tex]

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Answer:

-2 1/3 - (-5) = -2 1/3 + 5

To add these two numbers, we need to find a common denominator. The common denominator of 3 and 1 is 3.

-2 1/3 can be written as -7/3 using the rule that a mixed number is equal to the sum of the whole number and the fraction.

So, we have:

-7/3 + 5

To add these two fractions, we need to find a common denominator. The common denominator of 3 and 1 is 3.

-7/3 can be written as -7/3 x 1/1 = -7/3.

So, we have:

-7/3 + 15/3 = 8/3

Therefore, -2 1/3 - (-5) = 8/3.

Answer: 135

Step-by-step explanation:

Answer:

5 [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

[tex]\frac{4}{1}[/tex] x [tex]\frac{4}{3}[/tex] = [tex]\frac{16}{3}[/tex]

You can re-write [tex]\frac{16}{3}[/tex] as

[tex]\frac{3}{3}[/tex] + [tex]\frac{3}{3}[/tex] + [tex]\frac{3}{3}[/tex] + [tex]\frac{3}{3}[/tex] + [tex]\frac{3}{3}[/tex] + [tex]\frac{1}{3}[/tex]  I wrote it like this because every [tex]\frac{3}{3}[/tex] is equal to 1.

1 + 1 + 1 + 1 + 1 + [tex]\frac{1}{3}[/tex] = 5[tex]\frac{1}{3}[/tex]

Helping in the name of Jesus.

Answer:

Step-by-step explanation:

(-50, -20), (-60, 40)

(40 + 20)/(-60 + 50) = 60/-10= -6

y - (-20) = -6(x - (-50))

The statement, "t is not less than 7" as an inequality is E. t ≥ 7.

The statement, " the negative of z is not greater than 8" is A. - z ≤ 8 .

The statement "t is not less than 7" means that t can be equal to 7 or greater than 7, so we can write this as:

t ≥ 7

Therefore, the correct inequality for the statement is t ≥ 7.

Similarly, the statement "the negative of z is not greater than 8" means that the opposite of z, which is -z, can be equal to -8 or less than -8, so we can write this as:

-z ≤ 8

Multiplying both sides of the inequality by -1 gives:

z ≥ -8

Therefore, the correct inequality for the statement is z ≥ -8.

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Answer:

e) The correct option is: t≥7

The phrase "t is not less than 7" means that t can be equal to 7 or any value greater than 7, but it cannot be less than 7. Therefore, we use the greater than or equal to a symbol (≥) to represent this statement.

here's an explanation of each option:

t * 7a^2 ≥ 7 * 7a^2

49a^2

t * 7a^2 ≥ 49a^2

Note that this inequality is equivalent to t ≥ 7, which is what we started with.

f) The correct option is:-z ≤ 8

The phrase "the negative of z is not greater than 8" means that -z cannot be greater than 8. In other words, -z is less than or equal to 8. To express this as an inequality, we use the less than or equal symbol (≤) and write "-z ≤ 8".
here's an explanation of each option:

Note that only the first option (-z ≤ 8) accurately represents the original statement "The negative of z is not greater than 8". The other options either represent a different statement or contradict the original statement.

The statement "the negative of z is not greater than 8" can be expressed as an inequality in terms of 7a^2 as follows:

-z ≤ 8

z ≥ -8

7a^2 * z ≥ -8 * 7a^2

-56a^2

7a^2 * z ≥ -56a^2

So, the statement "the negative of z is not greater than 8" can be expressed as the inequality 7a^2 * z ≥ -56a^2.

The equation representing the relationship between the number of weeks (w) and the number of books collected (b):

b = 10w + 0

b = 10w

We can observe from the table that the number of books collected increases by 10 for each week.

Thus, there is a linear relationship between the number of weeks (w) and the number of books collected (b). We can represent this relationship using the equation:

b = mw + c

where b is the number of books collected, w is the number of weeks, m is the slope (rate of change), and c is the y-intercept (number of books collected at week 0).

The slope (m) is the change in the number of books collected per week, which is 10. We can now find the y-intercept (c) by substituting one of the points from the table into the equation. Let's use the point (1, 10):

10 = 10 * 1 + c

c = 0

Now we have the equation representing the relationship between the number of weeks (w) and the number of books collected (b):

b = 10w + 0

b = 10w

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the data in the form of a table, which shows the total number of books collected (b) for different number of weeks (w).

Weeks (w) Books Collected (b)

1 10

2 20

3 30

4 40

Trisha is collecting books to donate. The table below shows the total number of books collected, b, for different number of weeks, w. Which equation represents the relationship between the number of weeks, w, and the number of books collected, b?

Answer:

The distance from home to second base is approximately 84.85 feet in a slow pitch softball diamond that is 60 feet on each side.

Step-by-step explanation:

In a softball diamond that is 60 feet on each side, the distance from home to second base is approximately 84.85 feet. This is based on the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the distance from home to second base forms the hypotenuse of a right triangle with legs that are each 60 / sqrt(2) feet long. Using the Pythagorean theorem, we can calculate that the distance from home to second base is approximately 84.85 feet.

Hence, a person on a 2000 calorie diet  should eat more calories approximate ratio of 200-300 calories from  vegetables and 900-1300 calories from carbohydrates.

A calorie is a measurement,  just like a teaspoon or an inch.  Calories are the amount of energy released when your body breaks down (digests and absorbs) food.  The more calories a food has, the more energy it can provide to your body

The  number of calories a person  should consume from vegetables versus carbohydrates depends on various factors  such as age, gender, activity level, body composition, and overall health status. However, in general, it is recommended that a person on a  2000 calorie diet should  consume more calories from vegetables than from carbohydrates.

The United States Department of Agriculture (USDA) recommends  that adults consume 2.5 to 3 cups of vegetables per day, depending on their age, gender, and level  of physical activity. On a 2000 calorie diet, this would amount to approximately 200-300  calories from vegetables.

For carbohydrates, the recommended  intake varies depending on the individual's energy needs,  but it generally accounts for 45-65% of their total calorie intake. This  equates to 900-1300 calories from carbohydrates on a 2000 calorie diet.

Therefore, a person on a 2000 calorie diet  should eat more calories  from vegetables than from carbohydrates, with an approximate ratio of 200-300 calories from  vegetables and 900-1300 calories from carbohydrates.

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In the ratio, the odds that are less generous is C) 19:1 and D)18:1.

What is ratio?

When two numbers are compared, the ratio between them shows how often the first number contains the second. As an illustration, the ratio of oranges to lemons in a dish of fruit is 8:6 if there are 8 oranges and 6 lemons present.

Here odds for bets are 11:1.

That means if for every $1  you bets, you may wins $11.

There are [tex]\frac{1}{1+11}=\frac{1}{12}=8.33\%[/tex] chance of this happens.

If the friends thinks odds are too generous , then the odds that less than generous are,

=> for 4:1 then [tex]\frac{1}{1+4}=\frac{1}{5}= 20\%[/tex]

=> For 6:1 then [tex]\frac{1}{6+1}=\frac{1}{7}= 14\%[/tex]

=> For 19:1 then [tex]\frac{1}{19+1}=\frac{1}{20}=5\%[/tex]

=> For 18:1 then [tex]\frac{1}{18+1}=\frac{1}{19}=5.2\%[/tex]

Hence the odds that are less generous is C) 19:1 and D)18:1.

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The angles on the Unit Circle that make the equation -√3 csc(2θ) = 2 true are θ = π/6 + 2πn and θ = 5π/6 + 2πn, where n is an integer.

From the information, the following can be deduced:

-√3 csc(2θ) = 2

csc(2θ) = -2/√3

sin(2θ) = -√3/2

We know that sin(2θ) = 2sin(θ)cos(θ) by the double-angle identity for sine,

2sin(θ)cos(θ) = -√3/2

2sin(θ)cos(θ) = -√3/2

sin(θ)cos(θ) = -√3/4

sin(θ)cos(θ) = sin(π/3)sin(θ)

cos(θ) = sin(π/3)

θ = π/6 + 2πn, 5π/6 + 2πn

Therefore, the angles on the Unit Circle that make the equation -√3 csc(2θ) = 2 true are θ = π/6 + 2πn and θ = 5π/6 + 2πn, where n is an integer

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La probabilidad de obtener entre 400 y 500 veces un 6 en 1000 lanzamientos es de 0.

Este es un problema de distribución binomial con una probabilidad de éxito del evento (obtener un 6 en un lanzamiento de un dado de 6 caras) de 1/6.

Podemos utilizar una aproximación normal para la distribución binomial si el número de ensayos es grande y la probabilidad de éxito es moderada.

La aproximación normal para una distribución binomial se define como:

Z = (X - μ) / σ

El valor esperado de X es:

μ = n * p = 1000 * 1/6 = 166.67

La desviación estándar de X es:

σ = √(n * p * (1-p)) = √(1000 * 1/6 * 5/6) = 11.79

x = 400: z = (X - μ) / σ = (400 - 166.67) / 11.79 = 19.79

x = 500: z = (X - μ) / σ = (500 - 166.67) / 11.79 = 28.27

La probabilidad de obtener entre 400 y 500 éxitos se puede calcular utilizando la tabla de distribución normal estándar o una calculadora de probabilidad normal.

P(400 ≤ X ≤ 500) = P(19.79 ≤ z ≤ 28.27) = 0

Por lo tanto, la probabilidad de obtener entre 400 y 500 veces un 6 en 1000 lanzamientos es de aproximadamente 0.

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As a result, angle B has a 24 degree measure as the total of the two angles, which are along a straight line, is 180 degrees.

Thus according their size or measurement, angles can be categorised. An oblique angle is larger than 90 degrees but far less than 180 degrees, a straight angle is exactly 90 degree, a right angle is turned 90 degrees, and an acute angle is less than 90 degrees. Reflex angles are angles that are higher than 180o but a little less than 360 degrees, and complete angles are angles that measure exactly 360 degrees. Geometry, trigonometry, physics, engineering, and many other branches of mathematics and science all make use of angles.

given

The total of the two angles, which are along a straight line, is 180 degrees. Let's refer to the angle B's measurement as x.

The information provided in the problem can then be used to create an equation as follows:

m∠A = 5(m∠B + 7.2°)

Due to the fact that the two angles are perpendicular to one another, we may replace mA with 180 - mB:

180 - m∠B = 5(m∠B + 7.2°)

The right side is being widened:

180 - m∠B = 5m∠B + 36

Simplifying and putting all the mB words to one side:

6m∠B = 144

m∠B = 24

As a result, angle B has a 24 degree measure as the total of the two angles, which are along a straight line, is 180 degrees.

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1) The graph of function g is graph W because it is result of a vertivcal compression applied to graph f.

2)  The graph of function g is graph X because it is result of a horizontal shift applied to graph f.

3)  The graph of function g is graph Y because it is result of a reflection over y-axis applied to graph f.

4)  The graph of function g is graph Z because it is result of a horizontal compression applied to graph f.

Here, a transformation applied to function f where f(x) = (1/2)^x

Consider graph W. We can observe that when the the graph of f(x) is compressed vertically then it will results in the graph of g(x)

Consider graph X. We can observe that if the the graph of f(x) is shifted horizontally right by 2 units then it will results in the graph of g(x)

Consider graph Y. We can observe that the the graph of g(x) is nothing but the reflection of f(x) over x-axis.

Consider graph Z. We can observe that when the the graph of f(x) is compressed horizontally then it will results in the graph of g(x)

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Answer:

125

Step-by-step explanation:

50 refrigerators are 40% of all the refrigerators in the store.

5 refrigerators are 4% of refrigerators in the store

125 refrigerators are 100% of refrigerators in the store

therefore there are 125 refrigerators at the store.

First of all, radius is half the diameter.  Radius is from the center-most point of a circle straight to the edge.

Answer:

The area of the whole object is 1,237.68 m^2 (meters squared).

Step-by-step explanation:

The circles are equal to:

π * d = a

3.14 * 12 = a

37.68 = a.

Now, since the circles are half in the rectangle, it would be easier to calculate the rectangle using these halves, so the total of the half-circles outside the rectangle is equivalent to a whole circle, or 37.68.  Now, let's calculate the rectangle:

20 * (30 * 2) = a

20 * 60 = a

1200 = a.

The whole area is equivalent to the area of the two half-circles and the area of the rectangle:

37.68 + 1200 = a

1237.68 = a

According to the information, the horizontal distance traveled by the ball is 443.404 feet.

We can use the kinematic equations of motion to solve for the hang time, maximum height, and horizontal distance traveled by the golf ball.

First, we need to resolve the initial velocity vector into its horizontal and vertical components. The vertical component will determine the maximum height and hang time, while the horizontal component will determine the horizontal distance traveled.

The initial velocity can be represented as:

where v0 is the initial velocity, theta is the angle of elevation, v0x is the horizontal component of the initial velocity, and v0y is the vertical component of the initial velocity.

Now we can use the kinematic equations to solve for the hang time, maximum height, and horizontal distance traveled.

Hang time (time in air):

We can use the vertical motion equation to solve for the time when the ball reaches its maximum height:

Since the ball will be in the air for twice the time it takes to reach its maximum height, the hang time is:

Maximum height:

We can use the vertical motion equation to solve for the maximum height reached by the ball:

Therefore, the maximum height of the ball is 64 feet.

Horizontal distance traveled:

We can use the horizontal motion equation to solve for the horizontal distance traveled by the ball:

x = v0x t

x = 110.851(4)

x = 443.404 ft

Therefore, the horizontal distance traveled by the ball is 443.404 feet.

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As a result, the square office's carpet replacement would cost $786.69 in total as where a square meter costs $87.41.

The geometric shape of a square has 4 equal ends and four equal, right-angled angles (90 degrees). It is an unusual instance of a rectangle with equal sides. The symbol "" is frequently used to denote a square, which is a two-dimensional figure. A square's area is equal to the sum of its sides doubled, or s2, where s denotes the width of a side. The circumference of a square, or 4s, where s is the height of a side, is the total of the lengths among all four sides. Many real-world uses for squares can be found in the fields of mathematics, architecture, construction, and design.

given

The square office's area is:

[tex]C = 9 \times $87.41 = $786.69[/tex]

A = s2 = 3 2 = 9 metres square

To completely replace the carpet, it would cost:

Cost per square meter equals C = A.

where a square meter costs $87.41. When we change the values, we obtain:

As a result, the square office's carpet replacement would cost $786.69 in total as where a square meter costs $87.41.

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Step-by-step explanation:

You are looking for the hypotenuse of a right triangle with legs of 12 and

 11 feet

Using Pthagorean theorem

hypot^2 = 12^2 + 11^2

hypot^2 = 265

hypot = sqrt (265) = 16.28 ft

Answer:

I'm sorry, but I'm not sure what you are trying to convey with the string of characters "C 17 39 511 -U D 28 4 10 6". It doesn't appear to be a meaningful sentence or question. Could you please provide me with more information or context so I can better understand what you are trying to communicate?

Step-by-step explanation:

We discard the negative solution, so EF = 8.725. Now we can substitute this value into the

How to solve the question?

To solve this problem, we can use the fact that if two triangles are similar, their corresponding sides are proportional.

We are given that triangle ABC is similar to triangle DEF. Therefore, we can set up the following proportion:

AB/DE = BC/EF = AC/DF

We are given the lengths of AB, AC, and BC, so we can substitute those values into the proportion:

11/DE = 7.9/EF = 7.6/DF

We are asked to find the length of DF, so we can isolate DF by cross-multiplying:

11EF = 7.9DE

7.6EF = 11DF

Now we can set the two expressions for EF equal to each other and solve for DF:

11EF = 7.9DE

11EF/7.9 = DE

1.39EF = DE

7.6EF = 11DF

DF = 7.6EF/11

Substitute the value of DE into the expression for EF:

DF = 7.6(1.39EF)/11

DF = 1.52EF

Now we need to find the value of EF. We can use the fact that the sum of the angles in a triangle is 180 degrees to find the measure of angle E:

angle E = 180 - angle D - angle F

We are not given the measures of angle D or angle F, so we cannot find angle E directly. However, we do know that triangles ABC and DEF are similar, so their corresponding angles are congruent. Therefore, we can use the measures of angles A, B, and C to find the measure of angle D:

angle D = angle A

angle D = 180 - angle B - angle C

Substitute the given values for angles A, B, and C:

angle D = 56.1 degrees

angle D = 116.9 degrees

We can use the Law of Cosines to find the length of EF:

EF²= DE² + DF²- 2(DE)(DF)cos(D)

EF²= 2.2² + (1.52EF)² - 2(2.2)(1.52EF)cos(D)

Substitute the two possible values for angle D:

EF²= 2.2²+ (1.52EF)² - 2(2.2)(1.52EF)cos(56.1)

EF²= 2.2²+ (1.52EF)² - 2(2.2)(1.52EF)cos(116.9)

Simplify both expressions:

EF²= 3.2596 + 2.3104EF²- 5.7024EF

EF²= 3.2596 + 2.3104EF² + 5.7024EF

Solve for EF using either equation:

-0.3104EF² + 5.7024EF - 3.2596 = 0

-0.3104EF² - 5.7024EF + 3.2596 = 0

Solve for EF using the quadratic formula:

EF = (-b ± √(b² - 4ac))/(2a)

EF = (-5.7024 ± √(5.7024² - 4(-0.3104)(-3.2596)))/(2(-0.3104))

EF = 8.725 or EF = -4.185

We discard the negative solution, so EF = 8.725. Now we can substitute this value into the

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Answer:

a. df = 1.52

Step-by-step explanation:

11 / 5 = 2.2

so... you divide the other number by 5

7.6 / 5 = 1.52

making the length of df, 1.52

hope this helps!!! :))))

Answer:

m∠B=63 degrees

AC≈23.6 units

AB≈26.4 units

Step-by-step explanation:

since the measures of ∠A and ∠C are given, we add 90 (∠C) to 27 (∠A) and x (∠B) which equals 180 by triangle angle sum theorem.

after isolating the variable, m∠B=63 degrees

we then use law of sin to find AC and AB

since [tex]\frac{sin(A)}{a}[/tex] is already given, use that to find both AC and AB

the equation for AC would be: [tex]\frac{sin(27)}{12} =\frac{sin(63)}{AC}[/tex]

the equation for AB would be: [tex]\frac{win(27)}{12} =\frac{sin(90)}{AB}[/tex]

after isolating the variables, AC≈23.6 units and AB≈26.4 units

The value of x which is the hypotenuse of the triangle is 107.48

[tex]\dfrac{\text{Opposite}}{\text{Hypotenuse}}[/tex]

[tex]\text{Hyp = x}[/tex]

[tex]\text{opp} = 76\sqrt{2}[/tex]

[tex]\text{adj} = \text{x}[/tex]

[tex]\text{x}^2 = (76\sqrt{2})[/tex]

[tex]\text{x}^2 = 11552[/tex]

[tex]\text{x}^2 = \sqrt{11552}[/tex]

[tex]\text{x} = 107.48[/tex]

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