Select the correct answer.

Which pair of functions is not a pair of inverse functions?

O A.

6

=

f(x)=** 1 and g()=63–1

=

1 x

OB.

f(x)=-124 and g(I) =197+4

1 x)

O c. f(x)= 35 and g(x)=57

OD. f(x)=1 7 20 and g(x)= 1-1

-

19

=

I +

205

=

t

Answer:

2108.53 I think it's that lol

Answer:

2 nonreal solutions

Step-by-step explanation:

given a quadratic equation in standard form

ax² + bx + c = 0 (a ≠ 0 )

then the nature of the roots are determined by the discriminant

b² - 4ac

• if b² - 4ac > 0 then 2 real and irrational solutions

• if b² - 4ac > 0 and a perfect square then 2 real and rational solutions

• if b² - 4ac = 0 then 2 real and equal solutions

• if b² - 4ac < 0 then no real solutions

5x² - 2x + 6 = 0 ← in standard form

with a = 5 , b = - 2 , c = 6

b² - 4ac

= (- 2)² - (4 × 5 × 6)

= 4 - 120

= - 116

since b² - 4ac < 0

then there are 2 nonreal solutions to the equation

Answer:

The answer should be -156-61i

The equations given are x - 5y = 3 and 3x - 2y = -4. To find the solution to this system of equations, we need to find the values of x and y that satisfy both equations simultaneously.

One way to solve this system of equations is by substitution. We can solve one equation for x or y, and then substitute that expression into the other equation to eliminate one variable. Let's solve the first equation for x:

x - 5y = 3

x = 5y + 3

Now we can substitute this expression for x into the second equation:

3x - 2y = -4

3(5y + 3) - 2y = -4

15y + 9 - 2y = -4

13y = -13

y = -1

We can now substitute this value for y back into either equation to find the value of x:

x - 5y = 3

x - 5(-1) = 3

x + 5 = 3

x = -2

Therefore, the solution to the system of equations x - 5y = 3 and 3x - 2y = -4 is (-2, -1). This is the point where the solid line and dotted line intersect, as shown in the image.

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The measure of line segment FB is 5 inches and the measure of FG is 14 inches.

Diameter of Circle A = 8 inches

Diameter of Circle B  = 18 inches

Diameter of Circle C  = 11 inches

The measure of FB and FG.

Let's first find the radius of each circle:

Radius of Circle A (A F) = 1/2 × Diameter of Circle A

= 1/2 × 8 inches

= 4 inches

Radius of Circle B (A G) = 1/2 × Diameter of Circle B

= 1/2 × 18 inches

= 9 inches

Now, let's find the measure of FB using the radius of the big circle (AB) and the radius of the small circle (A F)

FB = AB - A F

AB = A G = 9 inches

Substituting the values into the equation

FB = 9 inches - 4 inches = 5 inches

Therefore, the measure of FB is 5 inches.

FG = A G - A F

= 18 - 4

= 14 inches

Therefore, the measure of FG is 14 inches.

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1. the solutions to the equation are x = π/3 and x = 2π/3.

2. the solutions to the equation are: x = (π/2 + nπ)/6, 2π/3, 4π/3        (n is an integer)

3. Dividing both sides by 3:

x = π/9 + (2nπ)/3, 5π/9 + (2nπ)/3        (n is an integer)

1. Solving the equation 16cos^2(x) - 4 = 0:

Let's rewrite the equation in terms of the double-angle formula for cosine:

16(1 - sin^2(x)) - 4 = 0

Simplifying the equation:

16 - 16sin^2(x) - 4 = 0

12 - 16sin^2(x) = 0

16sin^2(x) = 12

sin^2(x) = 12/16

sin^2(x) = 3/4

Taking the square root of both sides:

sin(x) = ±√(3/4)

sin(x) = ±√3/2

Now, we can find the values of x by considering the unit circle and the quadrants where sin(x) is positive or negative.

In the first quadrant (0 < x < π/2):

sin(x) = √3/2

x = π/3

In the second quadrant (π/2 < x < π):

sin(x) = √3/2

x = π - π/3 = 2π/3

Note: Since we're using radians, we don't need to consider the angles in the third and fourth quadrants.

Therefore, the solutions to the equation are x = π/3 and x = 2π/3.

Answer: π/3, 2π/3

2. Solving the equation cos(6x)(2cos(x) + 1) = 0:

We have two possibilities for this equation to be true:

1) cos(6x) = 0

2) 2cos(x) + 1 = 0

For the first possibility, cos(6x) = 0, we know that cosine is equal to zero at odd multiples of π/2.

6x = π/2 + nπ        (n is an integer)

Solving for x:

x = (π/2 + nπ)/6        (n is an integer)

For the second possibility, 2cos(x) + 1 = 0, we can solve for cos(x):

2cos(x) + 1 = 0

2cos(x) = -1

cos(x) = -1/2

We know that cosine is equal to -1/2 at 2π/3 and 4π/3.

Therefore, the solutions to the equation are:

x = (π/2 + nπ)/6, 2π/3, 4π/3        (n is an integer)

Answer: (π/2 + nπ)/6, 2π/3, 4π/3

3. Solving the multiple-angle equation sec(3x) - 2 = 0:

To solve this equation, we need to isolate the secant function.

sec(3x) - 2 = 0

sec(3x) = 2

Taking the reciprocal of both sides:

1/cos(3x) = 2

Now, we can solve for cos(3x):

cos(3x) = 1/2

We know that cosine is equal to 1/2 at π/3 and 5π/3.

Now, we can solve for x:

3x = π/3 + 2nπ, 5π/3 + 2nπ        (n is an integer)

Dividing both sides by 3:

x = π/9 + (2nπ)/3, 5π/9 + (2nπ)/3        (n is an integer)

Answer: π/9 +(2nπ)/3, 5π/9 + (2nπ)/3 (n is an integer)

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A sequence of transformation that would move ΔABC onto ΔDEF is: D. a dilation by a scale factor of 1/2, centered at the origin, followed by a 90° clockwise rotation about the origin.

In Geometry, a dilation is a type of transformation which typically changes the size of a geometric object, but not its shape.

In this scenario an exercise, we would dilate the coordinates of the pre-image by applying a scale factor of 1/2 that is centered at the origin as follows:

Ordered pair B (-4, 2) → Ordered pair B' (-4 × 1/2, 2 × 1/2) = Ordered pair B' (-2, 1).

In Mathematics and Geometry, a rotation can be defined as a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction;

(x, y)                               →            (y, -x)

Ordered pair B' (-2, 1)   →          E (1, 2)

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Marco would spend $13.50 on 3 bags of dog food.

What is basic arithmetic operations?

Basic arithmetic operations are the foundation of mathematics and include addition, subtraction, multiplication, and division. These operations are used to perform mathematical calculations and are necessary for solving a wide range of problems, from simple arithmetic problems to more complex mathematical equations.

To find the cost of 3 bags of dog food, we can first find the cost of one bag of dog food by dividing the cost of 5 bags by 5. That is, $22.50 ÷ 5 = $4.50. So, one bag of dog food costs $4.50.

To find the cost of 3 bags, we can multiply the cost of one bag by 3. That is, $4.50 × 3 = $13.50.

Hence, Marco would spend $13.50 on 3 bags of dog food.

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Answer:

36

Step-by-step explanation:

All angles are right angles here. You know one is 54 so the other unknown side in that quadrant has to be 90 - 54.

As angle B is going to be the same as the angle that you just located in that quadrant, the answer is 36

Answer:

x = 4

Step-by-step explanation:

Given the equation:

\(\displaystyle{4^x - 4^0 - 255=0}\)

We know that \(\displaystyle{a^0 = 1}\) where a ≠ 0. Therefore,

\(\displaystyle{4^x - 1 - 255=0}\\\\\displaystyle{4^x - 256=0}\)

Add both sides by 256, so we have:

\(\displaystyle{4^x=256}\)

Factor 256 out:

256 = 2 x 128 = 2 x 2 x 2⁶ = 2⁸

Therefore, 256 = 2⁸.

\(\displaystyle{4^x=2^8}\)

Convert to the same base:

\(\displaystyle{\left(2^2\right)^x=2^8}\\\\\displaystyle{2^{2x} = 2^8}\)

When two sides have same base, solve the equation through exponents:

\(\displaystyle{2x=8}\)

Divide both sides by 2, so we have:

\(\displaystyle{x=4}\)

Answer:

the answer to the first one is 118 the value of x is 113

Step-by-step explanation:

SOMEONE DELETED MY ORIGINAL ANSWER

The two angles will be linear pairs if the sum is 180° therefore,linear pair of 62° is 118° so option [A] is correct.

The value of x in the figure is 113° so option [C] is correct.

The m∠EXD and m∠AXE are the supplementary angles so option (B) is correct.

An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.

The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.

01)

Two angles will be linear pairs if their sum is 180°.

If the first angle is 62° then the second will be 180° - 62° = 118°

Hence "The two angles will be linear pairs if the sum is 180° therefore, linear pair of 62° is 118°".

02)

The angle x is in the same line with supplementary angle 67° so

x = 180 - 67 = 113°.

Hence "The value of x in the figure is 113°".

03)

In the figure, AXD is a straight line, therefore,

m∠EXD +  m∠AXE  = 180°

Since the sum of two angles is 180° then they are called supplementary angles.

Hence "The m∠EXD and m∠AXE are the supplementary angles".

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The probability of both events occurring is P(A ∩ B) = P(A)P(B) = 0.16^2 = 0.0256.

The event of getting a "2" and the event of getting a "5" on the first roll of a die are mutually exclusive events because they cannot both occur in the same trial. The probability of either of these events occurring is P(A) = 0.16, and the probability of both events occurring at the same time is P(A ∩ B) = 0.00.

The event of getting a "2" on the first roll and the event of getting a "5" on the second roll of a die are independent events. This can be confirmed using the formula P(A ∩ B) = P(A)P(B). The probability of getting a "2" on the first roll is P(A) = 0.16 and the probability of getting a "5" on the second roll is P(B) = 0.16. Thus, the probability of both events occurring is P(A ∩ B) = P(A)P(B) = 0.16^2 = 0.0256.

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Answer:

Step-by-step explanation:

we do first the multiplication 3*6=18

-2+18=16

16/5 is your answer or 3.2

The mean of the sampling distribution of the sample proportions is 0.67.

The standard deviation of the sampling distribution of the sample proportions is 0.052.

Population = Large

Household with cable TV = 67%

Sample size (n) = 81

The mean of sampling distribution (μx) = p = 67% = 67/100 = 0.67

The standard deviation of the sampling distribution,

Standard deviation (σ) :

                        σ = \(\sqrt{( p*(1 - p)) /n }\)

                      ⇒σ  = \(\sqrt{( 0.67*(1 - 0.67)) /81 }\)

                     ⇒ σ= \(\sqrt{( 0.67 * 0.33) /81 }\)

                     ⇒σ= \(\sqrt{( 0.2211 /81 }\)

                     ⇒ σ= \(\sqrt{0.002729}\)

                     ⇒σ = 0.052

Therefore,

The mean of the sampling distribution of the sample proportions is 0.67.

The standard deviation of the sampling distribution of the sample proportions is 0.052.

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Answer:

-30

Step-by-step explanation:

I hope this helps!

Answer:

exact form- 61/8

mixed number form-7 5/8

?

Step-by-step explanation:

Answer:

Convert the mixed numbers to improper fractions, then find the LCD and combine.

Exact Form:

61 /8

Decimal Form:

7.625

Mixed Number Form:

7

5/8

Step-by-step explanation:

Work Shown:

r = 6 = radius

V = volume of a sphere of radius r

V = (4/3)*pi*r^3

V = (4/3)*pi*6^3

V = 904.77868423386

V = 904.8

I used my calculator's stored version of pi (instead of something like pi = 3.14)

The units "cubic meters" can be abbreviated to m^3 or \(m^3\)

The volume of the given sphere is 904.8 cubic meters. Thus, option B is the answer.

         The volume of a sphere can be calculated using the formula:

V = \(4/3 * \pi * r^3\),

Where V is the volume and r is the radius of the sphere.

\(\pi\) = 3.14

The radius of the sphere (r) = 6m

Plugging in the given radius of 6m into the formula, we get:

V = (4/3) * \(\pi\) * (6^3)

V = 1.333 * \(\pi\) * 216

V = 1.333 * 3.14 * 216

V = 4.1866 * 216

V = 904.8 cubic meters

Therefore, when the radius of the sphere is 6m, the volume of the sphere is 904.8  cubic meters.

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The equations for the coordinates of the endpoint F should be x = 2 · 35 - 15 and y = 2 · (- 3) - 26.

In this problem we know the coordinates of the endpoint E and the midpoint M of the line segment EF and we need to derive expressions of the coordinates of the endpoint F by the midpoint formula:

M(x, y) = 0.5 · E(x, y) + 0.5 · F(x, y)

2 · M(x, y) = E(x, y) + F(x, y)

F(x, y) = 2 · M(x, y) - E(x, y)

If we know that M(x, y) = (35, - 3) and E(x, y) = (15, 26), then the coordinates of the endpoint F are:

F(x, y) = 2 · (35, - 3) - (15, 26)

F(x, y) = (70, - 6) + (- 15, - 26)

F(x, y) = (55, - 32)

The equations should be x = 2 · 35 - 15 and y = 2 · (- 3) - 26.

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The endpoint F's coordinates should be given by the formula

x = 2×35 - 15 and y = 2×(- 3) - 26.

In order to solve this problem, we need to derive expressions for the coordinates of the endpoint F using the midpoint formula.

We know the coordinates of the endpoint E and the midpoint M of the line segment EF.

M(x, y) = 0.5×E(x, y) + 0.5×F(x, y).

2×M(x, y) = E(x, y) + F(x, y).

F(x, y) = 2×M(x, y) - E(x, y).

Given that M(x, y) = (35, -3) and E(x, y) = (15, 26), the endpoint F's coordinates are,

F(x, y) = 2×(35, - 3) - (15, 26).

F(x, y) = (70, - 6) + (- 15, - 26).

F(x, y) = (55, - 32).

The equations should be x = 2×35 - 15 and y = 2×(- 3) - 26.

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The sets of linearly independent vectors are A), C), and E).

To determine whether a set of vectors is linearly independent or not, we can form a matrix with the vectors as columns, and then row reduce the matrix to see if any rows of zeros are produced. If there are no rows of zeros, then the vectors are linearly independent; otherwise, they are linearly dependent.

A)

| 8 -1 |

| 1 -5 |

| -6 -4 |

Performing row operations, we get:

| 1 0 |

| 0 1 |

| 0 0 |

Since there are no rows of zeros, the vectors are linearly independent.

B)

| 9 -7 -8 |

| 3 5 6 |

| 0 0 0 |

Performing row operations, we get:

| 1 0 -1 |

| 0 1 1 |

| 0 0 0 |

Since there is a row of zeros, the vectors are linearly dependent.

C)

| -1 9 |

| -7 -1 |

Performing row operations, we get:

| 1 0 |

| 0 1 |

Since there are no rows of zeros, the vectors are linearly independent.

D)

| 2 -9 7 |

| 4 -2 -2 |

| 7 -3 -4 |

Performing row operations, we get:

| 1 0 1 |

| 0 1 -1 |

| 0 0 0 |

Since there is a row of zeros, the vectors are linearly dependent.

E)

| 7 -2 -4 |

| -9 -3 -6 |

Performing row operations, we get:

| 1 0 2 |

| 0 1 1 |

Since there are no rows of zeros, the vectors are linearly independent.

F)

| -4 4 |

| -6 6 |

Performing row operations, we get:

| 1 -1 |

| 0 0 |

Since there is a row of zeros, the vectors are linearly dependent.

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Answer:

the mark-up is $10 or 20% of the original price.

Step-by-step explanation:

This is because 60-50 is 10. And 20% or 1/5 of 50 is 10.

Step-by-step explanation:

John's rent is   1325 - 820 = 505  MORE per month

  this is   505 / 217 = + 2.327 standard deviations above the mean

                      z - score = + 2.327

b)  not an outlier.....it under the bell curve 3 standard deviation limits

c)  > 3 S.D. would be an outlier   3 x 217 = 651 above the mean

     would be 820 + 651 = $1471

The equivalence class [a] consists of all integers of the form 5n + (3a - 2k)/2, where n and k are integers such that 5 divides 3a - 2k. In other words, [a] consists of all integers that differ from a by a multiple of 5 and an even integer.

To prove that R is an equivalence relation, we need to show that it satisfies three properties: reflexivity, symmetry, and transitivity.

Reflexivity: For any integer a, we have 3a - 5a = -2a, which is even. Therefore, aRa for all integers a, and R is reflexive.

Symmetry: If aRb, then 3a - 5b is even. This means that there exists an integer k such that 3a - 5b = 2k. Rearranging this equation, we get 5b - 3a = -2k, which is also even. Therefore, bRa, and R is symmetric.

Transitivity: If aRb and bRc, then 3a - 5b is even and 3b - 5c is even. This means that there exist integers k and m such that 3a - 5b = 2k and 3b - 5c = 2m. Adding these equations, we get 3a - 5c = 2k + 2m + 3(5b - 3a), which simplifies to 3a - 5c = 2(k + m + 5b) - 9a. Since k + m + 5b and 9a are both integers, this means that 3a - 5c is even, and aRc. Therefore, R is transitive.

Since R is reflexive, symmetric, and transitive, it is an equivalence relation.

To describe the equivalence classes, we need to find all integers that are related to a given integer under R. Let's consider the integer 0 as an example.

For an integer b to be related to 0 under R, we need to have 3(0) - 5b = -5b be even. This means that b must be odd. Therefore, the equivalence class [0] contains all even integers.

For an integer a ≠ 0, we can rearrange the equation 3a - 5b = 2k as b = (3a - 2k)/5. This means that b is uniquely determined by a and k, as long as 5 divides 3a - 2k.

Therefore, the equivalence class [a] consists of all integers of the form 5n + (3a - 2k)/2, where n and k are integers such that 5 divides 3a - 2k. In other words, [a] consists of all integers that differ from a by a multiple of 5 and an even integer.

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Answer:

Im pretty sure its 4 divided by (4/5 wrong)

Step-by-step explanation:

Answer:

4/5 ÷ 1.5  (C)

Step-by-step explanation:

4 sections out of 5 are shaded, this represents 4/5

1 section not shaded represents 1/5

4/5 ÷ 1/5   is the same as 4/5 · 5/1  which equals 4 (the amount shaded)

Read the left colum top to bottom then the right column top to bottom, hope this helps

Answer:

Step-by-step explanation:

2{5x²-15+(-9xy²)}-(2y²+4x-xy²)+3x²

=2{5x²-15-9xy²}-(2y²+4x-xy²)+3x²

=10x²-30-18xy²-2y²-4x+xy²+3x²

=13x²-2y²-17xy²-4x-30

Answer:

angle U ( the third option down)

Step-by-step explanation: