Difference between whole numbers and Integers?

Answer:

i think it would be c (the third one)

Step-by-step explanation:

because for every meal he has to subtract 2.25 from 35

Answer:

The answer would be x=35-2.25y

Step-by-step explanation:

Answer

EAD= EBC true.

Step-by-step explanation:

Both triangles are equal. The line between AE and EB show the lines are equal. In turn this makes the sides AD and BC equal. DC are the same length as AE and EB. In short, all sides are equal so the triangles are the same.

Step-by-step explanation:

\(12 {x}^{2} - 6( {a}^{2} + {b}^{2} )x + 3 {a}^{2} {b}^{2} = 0\)

Using quadratic formula, we get

\(x = 6( {a}^{2} + {b}^{2} )± \frac{ \sqrt{( - 6) {}^{2}( {a}^{2} + {b}^{2}) {}^{2} - 4(12)(3 {a}^{2} {b}^{2} )} }{24} \)

\(x = 6( {a}^{2} + {b}^{2} )± \frac{ \sqrt{36( {a}^{2} + {b}^{2} ) {}^{2} - 144 {a}^{2} {b}^{2} } }{24} \)

\(x = 6( {a}^{2} + {b}^{2} )± \frac{ \sqrt{36( ({a}^{2} + {b}^{2}) {}^{2} - 4 {a}^{2} {b}^{2} }) }{24} \)

\(x = 6( {a}^{2} + {b}^{2} )± \frac{6 \sqrt{ ({a}^{2} + {b}^{2} ) {}^{2} - 4 {a}^{2} {b}^{2} } }{24} \)

\(x = 6( {a}^{2} + {b}^{2} )± \frac{ \sqrt{( {a}^{2} + {b}^{2} ) {}^{2} - 4 {a}^{2} {b}^{2} } }{4} \)

Answer: x₁=6b²,  x₂=6a².

Step-by-step explanation:

\(12x^2-6*(a^2+b^2)+3a^2b^2=0\\D=(6*(a^2+b^2))^2-4*12*3a^2b^2\\D=6^2*(a^2+b^2)^2-144a^2b^2\\D=36*(a^4+2a^2b^2+b^4)-144a^2b^2\\D=36a^4+72a^2b^2+b^4-144a^2b^2\\D=36a^4-72a^2b^2+36b^4\\D=(6a^2)^2-2*6a^2*6b^2+(6b^2)^2\\D=(6a^2-6b^2)^2\\\sqrt{D}=\sqrt{(6a^2-6b^2)^2}=|6a^2-6b^2|=б(6a^2-6b^2).\\\displaystyle x_{1,2}=\frac{-(-6*(a^2+b^2))б(6a^2-6b^2)}{2} .\\x_1=\frac{6a^2+6b^2-6a^2+6b^2}{2} \\x_1=\frac{12b^2}{2} \\x_1=6b^2.\\x_2=\frac{6a^2+6b^2+6a^2-6b^2}{2} \\x_2=\frac{12a^2}{2} \\x_2=6a^2.\)

Alright so it can be either 2 or 3, depends on who you ask. Based on common sense, it's obviously 2, but there are still people convinced that it's 3 or some other random number.

To show that A is diagonalizable over the real numbers, we can choose any real numbers a, b, and c such that the matrix A can be diagonalized. One example is choosing a = 7, b = 0, and c = 2, which leads to a diagonal matrix D.

To show that matrix A is diagonalizable over the real numbers, we need to find infinitely many real numbers a, b, and c such that A can be diagonalized.

Let's consider the characteristic equation of matrix A:

| A - λI | = 0

Substituting the values of A and the identity matrix I:

| 7-a a b |

| 0 2-c c |

| 0 0 3-λ |

Expanding the determinant, we get:

(7-a)(2-c)(3-λ) - a(b)(0) = 0

(7-a)(2-c)(3-λ) = 0

For A to be diagonalizable, the characteristic equation should have infinitely many distinct real eigenvalues.

From the equation (7-a)(2-c)(3-λ) = 0, we can choose any real values for a, b, and c, and we can set λ = 3.

For example, let a = 7, b = 0, c = 2, and λ = 3:

| 7-7 7 0 |

| 0 2-2 2 |

| 0 0 3-3 |

Simplifying the matrix A:

| 0 7 0 |

| 0 0 2 |

| 0 0 0 |

This matrix A is already in a diagonal form, so it is diagonalizable.

To find the invertible matrix M such that M^-1 AM = D, we can choose:

M = | 7 0 0 |

| 0 2 0 |

| 0 0 1 |

Taking the inverse of M:

M^-1 = | 1/7 0 0 |

| 0 1/2 0 |

| 0 0 1 |

Calculating M^-1 AM:

M^-1 AM = | 1/7 0 0 | | 7 0 0 | | 7 0 0 |

| 0 1/2 0 | * | 0 2 0 | = | 0 1 0 |

| 0 0 1 | | 0 0 1 | | 0 0 1 |

The resulting matrix is a diagonal matrix D, which verifies that A is diagonalizable with the invertible matrix M.

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The expression \(i^{8}+i^{9}+i^{10}+i^{11}\) is equivalent to 0 + i - 1 - i, which simplifies to -1.

Using the property of imaginary unit i, we know that \(i^2=-1\). Therefore, i^8 can be written as \((i^2)^4\) which is equal to\(1^4 = 1\). Similarly, i^9 can be written as i^8i which is equivalent to i, i^10 can be written as \(i^8i^2\) which simplifies to -1, and i^11 can be written as i^8*i^3 which simplifies to -i. Thus, \(i^{8}+i^{9}+i^{10}+i^{11}\) can be simplified to 1 + i - 1 - i, which equals 0 - 0i. Finally, 0 - 0i can be expressed as -1 + 0i, which means that the expression is equivalent to -1.

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Answer: 10

Step-by-step explanation:

Using the side-splitter theorem, \(\frac{x}{6}=\frac{5}{3} \implies x=10\).

(a) As we have proved that H is a subgroup of Z.

(b) According to the subset, the generator for H is the greatest common divisor of 30, 42, and 70.

Let a, b ∈ H. Then there exist integers x₁, y₁, z₁ and x₂, y₂, z₂ such that a = 30x₁ + 42y₁ + 70z₁ and b = 30x₂ + 42y₂ + 70z₂. The sum a + b is given by:

a + b = (30x₁ + 42y₁ + 70z₁) + (30x₂ + 42y₂ + 70z₂) = 30(x₁ + x₂) + 42(y₁ + y₂) + 70(z₁ + z₂)

Since x₁ + x₂, y₁ + y₂, and z₁ + z₂ are integers, a + b is also an element of H. Therefore, H is closed under addition.

Let a ∈ H. Then there exists integers x, y, and z such that a = 30x + 42y + 70z. The inverse of a is -a, which is given by:

-a = -(30x + 42y + 70z) = -30x - 42y - 70z

Since -x, -y, and -z are also integers, -a is an element of H. Therefore, H is closed under inverses.

Thus, H satisfies all three conditions of a subgroup, so it is a subgroup of Z.

To find a generator for H, we need to find an element of H that generates all other elements of H under addition. Let d be the greatest common divisor of 30, 4₂, and 70. Then any element of H can be written in the form:

30x + 42y + 70z = d(3x + 4y + 7z)

Since d is a divisor of 30, 42, and 70, it is also a divisor of any linear combination of 30, 4₂, and 70. Therefore, H is a multiple of d. We claim that H = dZ, the set of multiples of d.

To prove this claim, we need to show that every element of H is a multiple of d, and every multiple of d is an element of H.

Every element of H is a multiple of d: Let a ∈ H. Then there exist integers x, y, and z such that a = 30x + 42y + 70z. Let d be the greatest common divisor of 30, 42, and 70. Then a can be written in the form:

a = d(3x + 4y + 7z)

Since d is a divisor of 30, 42, and 70, it is also a divisor of 3x + 4y + 7z. Therefore, a is a multiple of d.

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Complete Question:

Consider the following subset of Z:

H = {30x + 42y + 70z | x, y, z ∈ Z}.

(a) Prove that H is a subgroup of Z.

(b) Find a generator for H.

Answer:

56

20% of 70 is 14

so 14 kids canceled

so that leaves 56

Duela Dent's income taxes can be calculated using the given tax rates and her taxable income of $189,000. Her average tax rate and marginal tax rate can also be determined.

To calculate Duela Dent's income taxes, we need to determine the tax amount for each tax bracket that her taxable income falls into.

The taxable income of $189,000 falls into the following tax brackets:

$0-$9,950: Not applicable

$9,950-$40,525: ($40,525 - $9,950) * 12% = $3,546

$40,525-$86,375: ($86,375 - $40,525) * 22% = $9,992

$86,375-$164,925: ($164,925 - $86,375) * 24% = $19,110

$164,925-$209,425: ($189,000 - $164,925) * 32% = $7,744

$209,425-$523,600: Not applicable

$525,600 and above: Not applicable

Summing up the tax amounts for each bracket, Duela Dent's income taxes amount to $40,392.

The average tax rate is calculated by dividing the total tax amount ($40,392) by the taxable income ($189,000) and multiplying by 100:

Average Tax Rate = ($40,392 / $189,000) * 100 ≈ 21.37%

The marginal tax rate refers to the tax rate applied to an additional dollar of income. In this case, Duela Dent's marginal tax rate is 32%, which corresponds to the tax rate of the last bracket her taxable income falls into.

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Answer:

b. m∠KML + m∠MLK = m∠JKM

Step-by-step explanation:

right on edge

The statement regarding the diagram "m∠KML + m∠MLK = m∠JKM" is true option (B) m∠KML + m∠MLK = m∠JKM is correct.

In terms of geometry, the triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.

We have a triangle shown in the picture:

As we know, triangle is a polygon with three sides and three interior angles.

From the definition of the triangle, The triangle's interior angles add up to 180°

m∠MKL + m∠MLK + m∠KML = 180

Also, the sum of the two interior angles is equal to the exterior angle.

m∠KML + m∠MLK = m∠JKM

Thus, the statement regarding the diagram "m∠KML + m∠MLK = m∠JKM" is true option (B) m∠KML + m∠MLK = m∠JKM is correct.

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Answer: cool

Step-by-step explanation:

Answer: 12a+ 13b

Step-by-step explanation:

Answer:

12a+13b

Step-by-step explanation:

The expression cannot be further simplified as there are no like terms.

Answer:

law of cosines states c^2=a^2+b^2-2abc

b^2=26^2+24^2-2(26×24)cos 134°

b^2=676+576-1248cos134°

cos134= -0.6946

b^2=1252-12(-0.6946)

12×(-0.6946)= -8.3352

b^2=1252-(-8.3352)

b^2=1252+8.3352

b^2=1260.33

b=√1260.33

b=35.50

Answer:

55°????????????????????????????

Answer:

Step-by-step explanation:

Add 7x-2 to both sides and collect terms.

  2x +2 -6x +7x -2 > -4 -7x +7x -2

  3x > -6

  x > -2 . . . . . . . divide by 3

__

Solve these one at a time, and form the union of the answers.

  1 +7n ≤ 15 . . . .given

  7n ≤ 14 . . . . . . subtract 1

  n ≤ 2 . . . . . . . divide by 7

__

  -2n -2 ≤ -18 . . . given

  -2n ≤ -16 . . . . . add 2

  n ≥ 8 . . . . . . . . divide by -2

The solution is n ≤ -2 or n ≥ 8.

Normal vector is perpendicular to the line given by the parametric equations x = 2 - t, y = 3 + 2t, z = 4t.

To find an equation of the plane, we first need to determine the normal vector. Since the plane is perpendicular to the line, the direction vector of the line will be parallel to the normal vector of the plane.

The direction vector of the line is given by <dx/dt, dy/dt, dz/dt> = <-1, 2, 4>.

To find a normal vector, we can take the cross product of two vectors in the plane. We can choose two vectors by considering two pairs of points on the plane.

Let's consider the vectors formed by the points (-5, 2, 2) and (0, 6, 0), and the points (-5, 2, 2) and (0, 7, 2).

Vector 1 = <0 - (-5), 6 - 2, 0 - 2> = <5, 4, -2>

Vector 2 = <0 - (-5), 7 - 2, 2 - 2> = <5, 5, 0>

Taking the cross product of Vector 1 and Vector 2, we have:

<5, 4, -2> x <5, 5, 0> = <-10, 10, 5>

This resulting vector, <-10, 10, 5>, is perpendicular to the plane.

Now we can use the normal vector and one of the given points, such as (-5, 2, 2), to write the equation of the plane in the form ax + by + cz = d.

Plugging in the values, we have:

-10(x - (-5)) + 10(y - 2) + 5(z - 2) = 0

Simplifying, we get:

-10x + 50 + 10y - 20 + 5z - 10 = 0

Combining like terms, we have:

-10x + 10y + 5z + 20 = 0

Dividing both sides by 5, we obtain the equation of the plane:

-2x + 2y + z + 4 = 0

Therefore, an equation of the plane containing the three given points and with a normal vector perpendicular to the line is -2x + 2y + z + 4 = 0.

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If this is a sample of 6 scores, then  SS using the definitional formula would equal 17.5.

To find the SS (sum of squares) using the definitional formula, you need to first calculate the mean of the scores. Here's

1. Calculate the mean (µ) using ∑x and the number of scores (n):
Mean (µ) = (∑x) / n
µ = 39 / 6
µ = 6.5

2. Use the computational formula for SS:
SS = ∑x² - ( (∑x)² / n )
SS = 271 - (39² / 6)
SS = 271 - (1521 / 6)
SS = 271 - 253.5

3. Calculate sample score SS:
SS = 17.5

So, the answer is 17.5.

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A. The odds of pulling a red ball from the first bag is 11/90.

b. The odds of pulling a red ball from the second bag is 2/17.

c. The bag that has the best odds is bag A.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.

The first bag has 52 white balls, 27 green balls, and 11 red balls. Total balls will be:

= 52 + 27 + 11

= 90

Probability of picking red ball = 11/90

The second bag has 25 white balls, 25 green balls, 25 yellow balls, and 10 red balls. Total balls will be:

= 25 + 25 + 25 + 10

= 85

Probability of picking red ball = 10/85 = 2/17

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Option B) If the sum of the squares of the two short sides equals the square of the longest side

Answer:

B. EF

Step-by-step explanation:

The triangle above is a right triangle, these consist of 2 legs and a hypotenuse. The hypotenuse is always the longest side so EF is the answer.

Answer:

It looks like you are trying to find the retail price for a given quantity of pairs. To write an equation that could be used to find the retail price for each range of quantities, you will need to know the following information:

The retail price for the first range (0-20 pairs)

The retail price for the second range (21-40 pairs)

The retail price for the third range (41-60 pairs)

The retail price for the fourth range (61-80 pairs)

The retail price for the fifth range (81 or more pairs)

Once you have this information, you can use an if-then statement to create an equation that will work consistently for each range. The equation might look something like this:

if (quantity >= 0 and quantity <= 20):

retail_price = price for 0-20 pairs

elif (quantity >= 21 and quantity <= 40):

retail_price = price for 21-40 pairs

elif (quantity >= 41 and quantity <= 60):

retail_price = price for 41-60 pairs

elif (quantity >= 61 and quantity <= 80):

retail_price = price for 61-80 pairs

else:

retail_price = price for 81 or more pairs

This equation will work consistently for each range because it uses a series of conditions to determine which retail price to use based on the quantity of pairs.

EDIT:

To find the retail price for a given quantity of pairs based on the wholesale prices you provided, you can use the following equation:

if (quantity >= 0 and quantity <= 20):

retail_price = 25.00

elif (quantity >= 21 and quantity <= 40):

retail_price = 23.00

elif (quantity >= 41 and quantity <= 60):

retail_price = 21.00

elif (quantity >= 61 and quantity <= 80):

retail_price = 19.00

else:

retail_price = 17.00

This equation will work consistently for each range because it uses a series of conditions to determine the retail price based on the quantity of pairs. The retail price will be 25.00 for quantities in the first range (0-20 pairs), 23.00 for quantities in the second range (21-40 pairs), 21.00 for quantities in the third range (41-60 pairs), 19.00 for quantities in the fourth range (61-80 pairs), and 17.00 for quantities in the fifth range (81 or more pairs).

Step-by-step explanation: