Find the value of z such that 0.516 of the area lies between -z and z

The result of dividing the polynomial (m² + 10m + 18) by (m + 5) using long division is a quotient of m + 5 and a remainder of -7.

To divide the polynomial (m² + 10m + 18) by (m + 5) using long division, we follow these steps:

Step 1: Arrange the polynomial in descending order of powers of m. So, we have:

m² + 10m + 18

Step 2: Divide the first term of the dividend (m²) by the first term of the divisor (m). The result is m.

Step 3: Multiply the entire divisor (m + 5) by the result obtained in Step 2 (m), and write the result below the dividend, aligning like terms:

m² + 5m

__________________

m + 5 | m² + 10m + 18

Step 4: Subtract the result obtained in Step 3 from the dividend:

m² + 10m + 18

- (m² + 5m)

__________________

5m + 18

Step 5: Bring down the next term from the dividend, which is 18.

Step 6: Divide the new polynomial (5m + 18) by the divisor (m + 5). The result is 5.

Step 7: Multiply the entire divisor (m + 5) by the result obtained in Step 6 (5), and write the result below the previous subtraction:

m² + 5m

__________________

m + 5 | m² + 10m + 18

m² + 5m

______________

5m + 18

- (5m + 25)

______________

-7

Step 8: Since we have no more terms to bring down, the remainder is -7.

Therefore, the result of dividing (m² + 10m + 18) by (m + 5) using long division is:

Quotient: m + 5

Remainder: -7

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Radius: 6√3 inches. Perimeter: 72 inches.

The exact length of the perimeter of regular hexagon ABCDEF:

To find the perimeter of a regular hexagon, we need to multiply the length of one side by 6 since a hexagon has six equal sides. The length of one side can be determined using the formula:

Side length = 2 * apothem * tan(π/6)

Substituting the given apothem length of 6√3 inches, we have:

Side length = 2 * (6√3) * tan(π/6)

Simplifying the equation:

Side length = 12√3 * √3/3

Side length = 12 inches

Now, we can calculate the exact length of the perimeter:

Perimeter = Side length * 6

Perimeter = 12 inches * 6

Perimeter = 72 inches

Therefore, the exact length of the perimeter of regular hexagon ABCDEF is 72 inches.

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Using elimination method, we can find the constants a = 3 and b = 2 make (8, -7) the solution to the system of linear equations:

{3x + 2y = 10

{2x + 3y = -5

To solve for a and b, we can substitute the values of x and y into the system of linear equation.

Plugging the values of x = 8 and y = -7 into the first equation:

a(8) + b(-7) = 10

8a - 7b = 10

Substituting x = 8 and y = -7 into the second equation:

b(8) + a(-7) = -5

8b - 7a = -5

We now have a system of two equations with two variables:

8a - 7b = 10

8b - 7a = -5

Using elimination method, we can solve for the unknown;

Let's eliminate the variable a, we can proceed as;

(7)(8a - 7b) = (7)(10)

(8)(8b - 7a) = (8)(-5)

Simplifying:

56a - 49b = 70

64b - 56a = -40

Adding the two equations:

56a - 49b + 64b - 56a = 70 - 40

15b = 30

Dividing both sides by 15:

b = 2

Substituting b = 2 into the first equation:

8a - 7(2) = 10

8a - 14 = 10

8a = 24

Dividing both sides by 8:

a = 3

Therefore;

{3x + 2y = 10

{2x + 3y = -5

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There is an 8/12 or a 2/3 (66.6%) chance of choosing either a green or a white bulb.

Las cantidades de bolitas para cada una de las tres personas son las siguientes:

Amanda: 19 bolitas

Rodrigo: 15 bolitas

Patricio: 69 bolitas

En este problema tenemos a tres personas (Amanda, Rodrigo y Patricio) que se reparten 103 bolitas, en términos algebraicos, cada persona es representada por las siguientes ecuaciones:

Amanda

x = y + 4

Rodrigo

y

Patricio

z = 2 · (x + y) + 1

Total

x + y + z = 103

A continuación, determinamos la cantidad de bolitas asociada con Rodrigo:

x + y + 2 · (x + y) + 1 = 103

3 · x + 3 · y = 102

x + y = 34

y + 4 + y = 34

2 · y = 30

y = 15

Luego, determinamos las cantidades de bolitas de Amanda y Patricio:

x = 15 + 4

x = 19

z = 2 · (19 + 15) + 1

z = 2 · 34 + 1

z = 68 + 1

z = 69

El enunciado se encuentra escrito en español y el lenguaje de la respuesta es el mismo del enunciado.

The statement is written in Spanish and the language used in the answer is the same of the statement.

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The probability that either event A or B will occur is equal to 0.88 to the nearest hundredth

The probability of an event occurring is the fraction of the number of required outcome divided by the total number of possible outcomes.

The total possible outcome = 5 + 15 + 20 = 40

probability of event A = P(A) = 15/40

probability of event B = P(B) = 20/40

probability that either event A or B will occur = 15/40 + 20/40

probability that either event A or B will occur = (15 + 20)/40

probability that either event A or B will occur = 35/40

probability that either event A or B will occur = 0.875

Therefore, the probability that either event A or B will occur is equal to 0.88 to the nearest hundredth

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The length, in units, of the rectangle is 8

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

Width = Length - 5

So, we have

Area = 24

Represent the length with x

So, we have

Area = x(x - 5)

Recall that

Area = 24

So, we have

x(x - 5) = 24

When evaluated, we have

x = 8

Hence, the length, in units, of the rectangle is 8

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The calculated measure of x in the circle is 2

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

The circle

The measure of x in the circle can be calculated using the angle intersected by arc theorem

So, we have

1/2(69x + 2) = 70

Multiply both sides by 2

69x + 2 = 140

So, we have

69x = 138

Divide both sides by 69

x = 2

Hence, the measure of x in the circle is 2

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112 hooded sweatshirts and 138 crewneck sweatshirts were sold during the first week of school.

Let's assume that the number of hooded sweatshirts sold is represented by the variable "h," and the number of crewneck sweatshirts sold is represented by the variable "c."

According to the given information, the price of a hooded sweatshirt is $39.50, and the price of a crewneck sweatshirt is $34.50. In the first week, a total of 250 sweatshirts were sold, so we can write the following equation based on the number of sweatshirts sold:

h + c = 250 ---(1)

Additionally, the total value of the sweatshirts sold in the first week was $9185. We can express this information in terms of the prices and quantities of each type of sweatshirt:

39.50h + 34.50c = 9185 ---(2)

To solve this system of equations, we can use the substitution method or the elimination method. Let's use the elimination method:

Multiply equation (1) by 34.50 to match the coefficients of "c" in both equations:

34.50h + 34.50c = 8625 ---(3)

Now, subtract equation (3) from equation (2) to eliminate "c":

(39.50h + 34.50c) - (34.50h + 34.50c) = 9185 - 8625

5h = 560

h = 560 / 5

h = 112

Substitute the value of h back into equation (1) to find the value of c:

112 + c = 250

c = 250 - 112

c = 138

Therefore, 112 hooded sweatshirts and 138 crewneck sweatshirts were sold during the first week of school.

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The equality of angle A and angle C is proved by Side-Angle-Side theorem (SAS).

The proof of similarity of the triangles is determined by applying angle - angle (AA) theorem as shown below.

angle A will be equal to angle C if the following condition is met;

triangle BAG ≅ triangle DCG

From the given diagram, by reflexive similarity;

line BG = line DG

line BA = line DC

line GA = line GC

Since all the side lengths are congruent to each other and ΔBGA is equal to ΔDGC, then angle A must be equal to angle C.

Thus, the equality of angle A and angle C is proved by Side-Angle-Side theorem.

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Answer:

Step-by-step explanation:

Question

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What is the domain of the function on the graph?

O all real numbers

O all real numbers greater than or equal to-2

O all real numbers greater than or equal to-5

O all real numbers greater than or equal to 0

Help please

The polygons that can be regarded as similar polygons are A and D.

Similar polygons are those whose sizes may vary but whose shapes are the same. To put it another way, they have proportional sides and corresponding angles that are equivalent. The geometric likeness or resemblance between them is referred to as being "similar".

Similar polygons have corresponding angles with the same measurements. For instance, if a right angle exists in one polygon, another polygon with a comparable angle will likewise have a right angle. Similar to this, if an angle in one polygon is 60 degrees, the comparable angle in a related polygon will also be 60 degrees.

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You will pay the lending company approximately $4,701.12 at the end of 6 years.

1. Convert the interest rate to decimal form: 16.13% = 0.1613.

2. Calculate the total interest paid over the 6-year period:

  Total interest = Principal amount × Interest rate × Time

                = $2200 × 0.1613 × 6

                = $2121.12 (rounded to the nearest cent).

3. Add the total interest to the principal amount to get the total repayment amount:

  Total repayment amount = Principal amount + Total interest

                        = $2200 + $2121.12

                        = $4321.12 (rounded to the nearest cent).

4. Therefore, you will pay the lending company approximately $4,701.12 (rounded to the nearest cent) at the end of 6 years.

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The converses, inverses, and contrapositives of the given statements have different truth values. In statement (a), the converse and inverse are both false, while the contrapositive is true. In statement (b), all three statements are true.

Conditional Form:

a) If someone is 18 years old, then they may vote in federal elections.

b) If a quadrilateral has opposite angles congruent, then it is a parallelogram.

Converses, Inverses, and Contrapositives:

a) Statement: If each side of a triangle has a length of 10, then the triangle's perimeter is 30.

Converse: If the triangle's perimeter is 30, then each side of the triangle has a length of 10.

Inverse: If the triangle's perimeter is not 30, then each side of the triangle does not have a length of 10.

Contrapositive: If each side of the triangle does not have a length of 10, then the triangle's perimeter is not 30.

Truth of the new statements:

The converse is false.

The inverse is false.

The contrapositive is true.

b) Statement: If an angle is acute, then it has a measure greater than 0 and less than 90.

Converse: If an angle has a measure greater than 0 and less than 90, then it is acute.

Inverse: If an angle is not acute, then it does not have a measure greater than 0 and less than 90.

Contrapositive: If an angle does not have a measure greater than 0 and less than 90, then it is not acute.

Truth of the new statements:

The converse is true.

The inverse is true.

The contrapositive is true.

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Answer:

ok, here is your answer

Step-by-step explanation:

If the sales tax is 3%, then the tax amount Lucy will pay on the silver coat rack priced at $69 would be:

Tax amount = 3% of $69

Tax amount = (3/100) * $69

Tax amount = $2.07

Therefore, Lucy will pay $2.07 in tax.

Answer:

The final purchase price is 71.07

Step-by-step explanation:

First step is to determine the amount of tax:

69*3%

69 * .03

2.07

Now add the tax to the purchase price:

69+2.07

71.07

The final purchase price is 71.07

Answer:

A) sin 59° = cos 31°

Step-by-step explanation:

The interior angles of a triangle sum to 180°. Therefore, the measure of the missing angle is:

[tex]180^{\circ}-90^{\circ}-31^{\circ}=\boxed{59^{\circ}}[/tex]

Trigonometric ratios are mathematical relationships that define the ratios between the sides of a right triangle and the angles within that triangle. The sine and cosine trigonometric ratios are:

[tex]\boxed{\begin{minipage}{9.4 cm}\underline{Sine and Cosine trigonometric ratios} \\\\$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

The legs of the given right triangle are labelled "x" and "17". The hypotenuse is not labelled. Therefore, as both the sine and cosine ratios include the hypotenuse, sin 59° and cos 31° cannot equal x/17.

Let the hypotenuse be "H". Therefore, using the sine and cosine ratios, we can say that:

[tex]\sin 59^{\circ}=\dfrac{x}{H}[/tex]

[tex]\cos 31^{\circ}=\dfrac{x}{H}[/tex]

Therefore, the only correct equation from the given answer options is:

[tex]\large\boxed{\sin 59^{\circ}=\cos 31^{\circ}}[/tex]

Answer:

A) sin 59 = cos 31

Step-by-step explanation:

hypotenuse² = x² + 17²

⇒ hypotenuse = √(x² + 17²)

The other angle is 180-90-31 = 59

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

sin 59 = x / √(x² + 17²)

cos 31 = x / √(x² + 17²)

so sin 59 = cos 31

1. Image 4:

A. In image 4, the main change from the previous image (image 3) is the addition of two squares.

B. If we choose figure 5 in image 4, we can see that its lengths are related to the figure in image 1.

C. The length of figure 5, which corresponds to 'a', and the length of figure 6, which corresponds to 'b', relate to the Pythagorean Theorem.

2. The visual proof demonstrates the Pythagorean Theorem by showing how the figures labeled 5 through 9 in image 4 are related to figures 2 and 10. Figure 5 represents side 'a' and figure 6 represents side 'b'.

1. Image 4:

A. In image 4, the main change from the previous image (image 3) is the addition of two squares. One square is attached to the side of the triangle with length 'a', and the other square is attached to the side of the triangle with length 'b'. These squares are constructed by transforming the previous image, specifically by adding the squares and adjusting their positions accordingly.

B. If we choose figure 5 in image 4, we can see that its lengths are related to the figure in image 1. The length of the bottom side of figure 5 is equal to 'a' (the length of the side of the triangle in image 1), and the length of the right side of figure 5 is equal to 'b' (the length of the other side of the triangle in image 1).

C. The length of figure 5, which corresponds to 'a', and the length of figure 6, which corresponds to 'b', relate to the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a^2 + b^2). In this case, figure 5 represents side 'a' and figure 6 represents side 'b'. So, their lengths squared (a^2 and b^2) added together equal the length of figure 7 squared (c^2).

2. The visual proof demonstrates the Pythagorean Theorem by showing how the figures labeled 5 through 9 in image 4 are related to figures 2 and 10. Figure 5 represents side 'a' and figure 6 represents side 'b'. When we combine these two figures and the square attached to the hypotenuse (c), we see that they perfectly fill the large square in figure 10. This shows that the area of the square on the hypotenuse (c^2) is equal to the sum of the areas of the squares on the other two sides (a^2 + b^2). This visual representation provides a clear and tangible demonstration of the Pythagorean Theorem.

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Answer: First row: 6,12,15

              Second row: 15

Step-by-step explanation:

For first row: 3*1, 3*2, 3*3, 3*4, 3*5

Second row: 5*1, 5*2, 5*3, 5*4, 5*5

Answer:

The mean increases by 3.5°.

Step-by-step explanation:

To determine how the mean changes when a value of 120.5° is added to the data, we need to recalculate the mean before and after the addition.

Given the average high temperatures:

58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57

To find the original mean, we sum up all the temperatures and divide by the number of data points:

(58 + 61 + 71 + 77 + 91 + 100 + 105 + 102 + 95 + 82 + 66 + 57) / 12 = 904 / 12 = 75.33°

Now, let's add the value of 120.5° to the data:

58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57, 120.5

To find the new mean, we sum up all the temperatures (including the added value) and divide by the number of data points:

(58 + 61 + 71 + 77 + 91 + 100 + 105 + 102 + 95 + 82 + 66 + 57 + 120.5) / 13 = 1025.5 / 13 ≈ 78.88°

The mean has increased from 75.33° to 78.88°.

Therefore, the mean increases by approximately 3.55° (rounded to the nearest tenth).

The correct answer is: The mean increases by 3.5°.

Answer:

The mean increases by 3.5°.

Step-by-step explanation:

The amount that Miguel originally put into the bank is given as follows:

$728.

The equation that gives the balance of an account after t years, considering simple interest, is modeled as follows:

A(t) = P(1 + rt).

Then the interest accrued is given as follows:

I(t) = Prt.

In which the parameters of the equation are listed and explained as follows:

The interest accrued from the first year to the second year is of $30.28, hence the rate is given as follows:

30.28 = 757.12r

r = 30.28/757.12

r = 0.04.

Then the principal is obtained as follows:

1.04P = 757.12

P = 757.12/1.04

P = $728.

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The options that represent arithmetic sequences are A) 2n - 1, C) 3n + 4, and D) 5n - 2.

To determine which of the given general terms represents an arithmetic sequence, we need to check if the difference between consecutive terms is constant. Let's evaluate each option:

A) 2n - 1

To find the difference between consecutive terms, we subtract the general term for the (n+1)th position from the general term for the nth position:

[(2(n+1)) - 1] - (2n - 1) = 2n + 2 - 1 - 2n + 1 = 2

Since the difference between consecutive terms is 2, option A) 2n - 1 represents an arithmetic sequence with a common difference of 2.

B) n^2 + 3

Let's calculate the difference between consecutive terms:

[(n+1)^2 + 3] - (n^2 + 3) = n^2 + 2n + 1 + 3 - n^2 - 3 = 2n + 1

The difference between consecutive terms is 2n + 1, which is not a constant value. Therefore, option B) n^2 + 3 does not represent an arithmetic sequence.

C) 3n + 4

Calculating the difference between consecutive terms:

[(3(n+1)) + 4] - (3n + 4) = 3n + 3 + 4 - 3n - 4 = 3

The difference between consecutive terms is 3, which is a constant value. Therefore, option C) 3n + 4 represents an arithmetic sequence with a common difference of 3.

D) 5n - 2

Finding the difference between consecutive terms:

[(5(n+1)) - 2] - (5n - 2) = 5n + 5 - 2 - 5n + 2 = 3

The difference between consecutive terms is 3, which is a constant value. Therefore, option D) 5n - 2 represents an arithmetic sequence with a common difference of 3.

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Question

which one of the following general term of sequence is arithmetic?​

A) 2n - 1

B) n^2 + 3

C) 3n + 4

D) 5n - 2

The correct Option is A. Equation that can be used to find the number of dogs in the shelter is StartFraction 60 divided by 2 Over 100 divided by 2 EndFraction = StartFraction 30 Over 50 EndFraction.

In order to do that, we first need to determine the number of dogs in the shelter.

We can do that by multiplying the total number of animals by 60% (0.60):60% of 50 = (60/100) × 50 = 30

Therefore, there are 30 dogs in the shelter.

Now, we can look at the answer choices to see which equation can be used to find the number of dogs in the shelter.

A. (60/2 ÷ 100/2) = 30/50This equation simplifies to (30 ÷ 50) = 0.6, which is the decimal equivalent of 60%. T

his equation is correct.

B. (100 × 2 ÷ 50 × 2) = 200/100

This equation simplifies to 1, which is not the correct answer.

C. (50 ÷ 1 ÷ 60 ÷ 1) = 50/60

This equation simplifies to 5/6, which is not the correct answer.

D. (60 × 2 ÷ 50 × 2) = 120/100

This equation simplifies to 6/5, which is not the correct answer.

Therefore, the equation that can be used to find the number of dogs in the shelter is A. (60/2 ÷ 100/2) = 30/50.

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Answer:

A = -5

B = -2

C = 3

Step-by-step explanation:

[tex](A) = (-3)^{2} +4(-3)-2\\(A) = 9+(-12)-2\\(A) = -5\\\\\\(B) = (0)^{2} +4(0)-2\\(B)=0+0-2\\(B)=-2\\\\\\(C)=(1)^{2} +4(1)-2\\(C)=1+4-2\\(C)=3[/tex]

The set of ordered pairs that represents a function is:

{(−1,6),(0,−3),(5,−9),(−1,3)}

In a function, each input value (x-coordinate) must be paired with only one output value (y-coordinate). In the given set, there are no repeated x-coordinates, meaning that each input value is associated with only one output value. Therefore, it satisfies the definition of a function.

Multiplying by 2 on both sides: x+y = 98.We are asked to find the third number, which is z. To do that, we can substitute x+y = 98 in the equation x+y+z = 174. Doing so, we get: 98+z = 174Therefore, z = 174-98 = 76Hence, the third number is 76.Therefore, the third number is 76.

Let us suppose the three numbers to be x, y, and z. From the question, we know that:Average of the three numbers = 58Therefore, (x+y+z)/3 = 58. Multiplying by 3 on both sides: x+y+z = 174.The question also states that the average of two of the numbers (let's say x and y) is 49. Therefore, (x+y)/2 = 49.

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Answer:

V = 1/3 π r^2 h

Step-by-step explanation:

V = 1/3 area base*height

1. work out the area

2. base*height

3. area*answer

4. you get full answer

Answer:

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

Solve the given equation in below steps:

Answer:

Thomas' age is 26

Step-by-step explanation:Set Whelan to A and Thomas to B  B=2A  2A+A=39 3A=39 A=13 13*2=26

We can conclude that ∠AOM ≅ ∠MOD.

Given that AC, MN, and DB intersect at point O, we can prove that ∠AOM ≅ ∠NOC and ∠MOD ≅ ∠BON. This can be shown using the vertical angles theorem.

By the given information, we know that ∠BON ≅ ∠NOC. Using the transitive property of congruence, we can conclude that ∠AOM ≅ ∠MOD.

In other words, since AC, MN, and DB intersect at point O, we have the following angle relationships: ∠BON ≅ ∠NOC and ∠AOM ≅ ∠MOD.

The given information states that ∠BON ≅ ∠NOC. Using the vertical angles theorem, we can infer that ∠AOM ≅ ∠NOC. Furthermore, since ∠AOM ≅ ∠NOC and ∠BON ≅ ∠NOC, we can apply the transitive property of congruence to conclude that ∠AOM ≅ ∠MOD.

Therefore, we have successfully proved that ∠AOM ≅ ∠MOD based on the given intersecting line segments and angle relationships.

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Therefore, if the time is between 8:00 a.m. and 3:00 p.m., then people may make withdrawals or deposits.

Based on the given statements, we can make the following inference:

If the time is between 8:00 a.m. and 3:00 p.m., then the bank is open.

If the bank is open, then people may make withdrawals or deposits.

Therefore, if the time is between 8:00 a.m. and 3:00 p.m., then people may make withdrawals or deposits.

The inference follows the logical flow of the given statements.

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