Prove the transitive property of congruent segments.​

The ordered pair lie on the inverse of the function is (62,−3).

Option A is the correct answer.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = -(x - 1)³ - 2

The inverse of f(x).

y = -(x - 1)³ - 2

interchange x and y and solve for y.

x = -(y - 1)3 - 2

(y - 1)³ = -2 - x

(y - 1)³ = -(2 + x)

Cuberoot on both sides.

y - 1 = ∛-(2 + x)

y = ∛-(2 + x) + 1

Now,

Substitute in the inverse of g(x).

(62, -3) = (x, y)

(−4, 123) = (x, y)

(3, 1) = (x, y)

(3,−6) = (x, y)

So,

y = ∛-(2 + x) + 1

y = ∛-(2 + 62) + 1

∛-1 = -1

y = -1∛64 + 1

y = -1 x 4 + 1

y = -4 + 1

y = -3

So,

(62, -3) ______(1)

And,

y = ∛-(2 + x) + 1

y = ∛-(2 - 4) + 1

∛-1 = -1

y = ∛(-2 + 4) + 1

y = ∛2 + 1

y =  1.26 + 1

y = 2.26

So,

(-4, 2.26) _______(2)

And,

y = ∛-(2 + x) + 1

y = ∛-(2 + 3) + 1

∛-1 = -1

y = -1∛5 + 1

y = -1 x 1.71 + 1

y = -1.71 + 1

y = -0.71

So,

(3, -0.71) _______(3)

And,

y = ∛-(2 + x) + 1

y = ∛-(2 + 3) + 1

∛-1 = -1

y = -1∛5 + 1

y = -1 x 1.71 + 1

y = -1.71 + 1

y = -0.71

So,

(3, -0.71) ______(4)

Thus,

From (1), (2), (3), (4) we see that,

(62, -3) is the solution to the inverse of g(x).

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The average score of all students, calculated by taking a weighted average based on the number of students in each group, is 38. The overall performance is slightly below the group averages.

The average score of students in the first, second, and third groups are 39, 32, and 43, respectively. There are 24 students in the first group, 26 students in the second group, and 27 students in the third group.

To find the average score of all students, we need to take a weighted average of the scores in each group, with the number of students in each group as the weights.

Here's how to do it: First, we calculate the total number of students:24 + 26 + 27 = 77. Then, we calculate the total score across all students: 39*24 + 32*26 + 43*27 = 936 + 832 + 1161 = 2929

Finally, we divide the total score by the total number of students to get the average score:2929/77 = 38. The average score of all students is 38.

This means that the overall performance of all the students is slightly below the average of the scores in each group.

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1/28561 is the probability that all four cards are kings

Hearts, clubs, spades, and diamonds make up the four suites of a normal deck of cards. thirteen cards total—aces, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, and king—make up each suite. Thus, there are 52 cards in all in the deck.

The four French suits—clubs, diamonds, hearts, and spades—each have 13 ranks. King, Queen, and Jack are the three court cards (face cards) in each suit, and their pictures are reversed (double-headed). The ten numerical cards, or pip cards, in each suit range in value from one to 10.

In a pack of cards, there are 52 cards and 4 Kings.

Probability of picking a King is:  4/52 = 1/13 .

Since a card is being replaced before picking up the next card, the probability of picking a King is always  1/13 .

Picking a subsequent King is independent of picking a King previously and thus we multiply the individual probabilities to arrive at the combined probability.

Thus, the required probability is:

= 1/13 × 1/13 × 1/13 × 1/13

= 1/28561

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Answer: The one on the left.

Step-by-step explanation:

There is no file, but the panda on the left is bigger.

Answer:

24 is the number of b

Step-by-step explanation:

b=24

Answer:

$90

Step-by-step explanation:

To find commission, you multiply the amount made by the rate of which they can earn.

300*.3 (As this is a 30 percent commission)

Thus, the surface area with the dimensions of a rectangular prism as 6m by 4 m by 15 m is found as: S = 348 sq. m.

A rectangular prism is a 3 solid that is surrounded by 6 rectangular faces, 2 of which are the bases (the top face and bottom face), and the remaining 4 are lateral faces. It likewise has 12 edges and 8 vertices.

A rectangular prism is sometimes known as a cuboid because of its shape. A shoe box, an ice cream bar, or a matchbox are some instances of rectangular prisms in everyday objects.

Dimensions of rectangular prism :

surface area of a rectangular prism:

S = 2(lw + wh + hl)

S = 2(6*4 + 4*15 + 15*6)

S = 348 sq. m.

Thus, the surface area with the dimensions of a rectangular prism as 6m by 4 m by 15 m is found as: S = 348 sq. m.

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Answer: 50

Step-by-step explanation:

2*6+2*4+2*15=12+8+30=50

The length of AC to 1 decimal place in the trapezium would be = 14.93cm

To determine the missing length of the trapezium, CD should first be determined and it's given below as follows;

Using the Pythagorean formula;

c² = a²+b²

where,

c = 16

a = 11-4 = 7

b = CD= x

That is;

16² = 7²+x

X = 256-49

= 207

=√207

= 14.4

To determine the length of AC, the Pythagorean formula is equally used;

C = AC = ?

a = 14.4cm

b = 4cm

C² = 14.4²+4²

= 207+16

= 223

c = √223

= 14.93cm

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The initial number of bacteria in the culture was approximately 116. We can solve this using differential equation.

Let N(t) be the number of bacteria present at time t, and let k be the constant of proportionality for the growth rate. Then the differential equation that describes the growth of bacteria is:

dN/dt = kN

We can solve this differential equation to get:

N(t) = N0e\(^({kt)}\)

Where N0 is the initial number of bacteria at time t=0.

Using the given information, we can set up a system of two equations:

500 = N0e\(^{(3k)}\)

5000 = N0e\(^{(10k)}\)

Dividing the second equation by the first equation, we get:

10 = e\(^{(7k)}\)

Taking the natural logarithm of both sides, we get:

ln(10) = 7k

Solving for k, we get:

k = ln(10)/7

Substituting this value of k into either of the two equations above, we can solve for N0:

500 = N0e\(^{(3ln(10)/7)}\)

N0 = 116 (rounded to the nearest integer)

Therefore, the initial number of bacteria in the culture was approximately 116.

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By SAS similarity, ΔKML and ΔRTL are similar triangles. Therefore, option A is the correct answer.

From the given figure, KR=9 units, RL=15 units, MT=7.5 units and TL=12.5 units.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

Consider ΔKML and ΔRTL, we get

RL/KL =15/(15+9)

= 15/24

= 5/8

TL/ML =12.5/(12.5+7.5)

= 12.5/20

= 5/8

Here, RL/KL=TL/ML

Here, ∠KLM≅∠RLT

By SAS similarity, ΔKML and ΔRTL are similar triangles

So, ∠KMT≅∠RTL

By SAS similarity, ΔKML and ΔRTL are similar triangles. Therefore, option A is the correct answer.

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Answer:

a

Step-by-step explanation:

got it right in edmentum

The solutions to the equation -30x² + 9x + 60 = 0 are x = 5/2 and x = -4/5.

To solve the equation, we can start by bringing all the terms to one side to have a quadratic equation equal to zero. Let's go step by step:

-5/3 x² + 3x + 11 = -9 + 25/3 x²

First, let's simplify the equation by multiplying each term by 3 to eliminate the fractions:

-5x² + 9x + 33 = -27 + 25x²

Next, let's combine like terms:

-5x² - 25x² + 9x + 33 = -27

-30x² + 9x + 33 = -27

Now, let's bring all the terms to one side to have a quadratic equation equal to zero:

-30x² + 9x + 33 + 27 = 0

-30x² + 9x + 60 = 0

Finally, we have the quadratic equation in standard form:

-30x² + 9x + 60 = 0

Dividing each term by 3, we get:

-10x² + 3x + 20 = 0

(-2x + 5)(5x + 4) = -10x² + 3x + 20

So, the factored form of the equation -30x² + 9x + 60 = 0 is:

(-2x + 5)(5x + 4) = 0

Now we can set each factor equal to zero and solve for x:

-2x + 5 = 0 --> x = 5/2

5x + 4 = 0 --> x = -4/5

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The scalar k for which u and v are orthogonal is either k = 5 or k = -2.

The scalar k for which the vectors u and v are orthogonal are as follows:

Given vectors are u = [k, k, -2] and v = [-5, k+2, 5].

Then the dot product of u and v must be 0 as they are orthogonal.

Let's find the dot product of u and v:

u.v = k(-5) + k(k+2) + (-2)(5)

u.v = -5k + k² + 2k - 10

u.v = k² - 3k - 10

Now equate the dot product of u and v to 0 and solve for k:

k² - 3k - 10 = 0(k - 5)(k + 2) = 0

Therefore, the scalar k for which u and v are orthogonal is either k = 5 or k = -2.

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Answer:

Frequency of wave = 3 Hertz

Step-by-step explanation:

Given that:

Wavelength of wave = 20 meters

Velocity of wave = 60m/s

We know that:

v = fλ

Here,

v = velocity , f = frequency and λ = wavelength

Putting values in formula

60 = f(20)

20f = 60

Dividing both sides by 20

\(\frac{20f}{20}=\frac{60}{20}\)

f = 3 Hertz

Hence,

Frequency of wave = 3 Hertz

the volume of the solid that lies between the paraboloid 2 2 zx y and the sphere 2 22 xyz 2 is (4/15)π.

To find the volume of the solid between the paraboloid and the sphere, we can use cylindrical coordinates. In cylindrical coordinates, the equation of the paraboloid is 2z = r^2 and the equation of the sphere is x^2 + y^2 + z^2 = 2r^2.

We can rewrite the sphere equation as z = (2-r^2)/2 and set it equal to the equation of the paraboloid, giving us:

2r^2 = r^2 + y^2

Simplifying this expression, we get:

y^2 = r^2

This means that the solid lies within the cylinder y^2 + z^2 = 2r^2.

To find the limits of integration, we need to determine the range of r, theta, and z that define the solid. The sphere has a radius of √2, so we know that r must be less than or equal to √2. For theta, we can integrate from 0 to 2π.

To find the limits of integration for z, we need to determine the range of z values for a given r and theta. Substituting r^2/2 for z in the equation of the sphere, we get:

x^2 + y^2 + (r^2/2)^2 = 2r^2

Simplifying this expression, we get:

x^2 + y^2 = (3/4)r^2

This means that for a given r and theta, z can vary from r^2/2 to √(2 - (3/4)r^2).

To find the volume of the solid, we can integrate the function r from 0 to √2, theta from 0 to 2π, and z from r^2/2 to √(2 - (3/4)r^2), using the formula for volume in cylindrical coordinates:

V = ∫∫∫ r dz dr dθ

Evaluating this integral, we get the volume of the solid as (4/15)π.

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The expression which is equivalent to -10 is the option b, -3 - 7.

Explanation:

We can use subtraction and addition of integers to get the value of the given expression. We can write the given expression as;

-3 - 7 = -10 (-3 - 7)

The addition of two negative integers will always give a negative integer. When we subtract a larger negative integer from a smaller negative integer, we will get a negative integer.

If we add -3 and -7 we will get -10. This makes the option b the correct answer.

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Answer:

r=8mm

h=13mm

V= 3820.176...\(mm^{3}\)

V= 2144.660...\(mm^{3}\)

Step-by-step explanation:

r=8mm

h=13mm

V= 3820.176...\(mm^{3}\)

V= 2144.660...\(mm^{3}\)

Answer: n=40

Step-by-step explanation:

let me know if i got this right for you broski

now dance

(1.25 x 12)/ 0.6=

25

Hope this helps :)

Answer:

if you're trying to find the x and y intercepts x is (-4/5,0)

Answer:

Slope: -1

y intercept: -3

equation: y=-1x-3

Step-by-step explanation:

The y intercept is when x is zero.

Answer:

The answer is B

Step-by-step explanation:

the ans has to be 36 or more. so A and D can't B the answer. amongst B and C the lowest possible value is B - 36. so 36 is the answer

Answer:

Your answer would be C (8,15,17) and E (15, 20,25)

Step-by-step explanation:

:)

Answer:

R'T = 28

Step-by-step explanation:

Dilation is one of the methods used in transformation. It is a process in which the size of a given object or shape is either increased or decreased by a scale factor.

In the given question, the length of RT was increased by the scale factor, so that;

R'T = RT x scale factor

      = 8 x 3.5

      = 28

R'T = 28

Therefore, the length of R'T is equal to 28.

Answer:

D

Step-by-step explanation:

'angle 1 + angle 2 + angle 6 = 180', as that is how triangles work. We can readjust this mathematical sentence into 'angle 6 = 180 - angle 1 - angle 2'

'angle 4 + angle 6 = 180', as the angles are a linear pair. We can readjust this mathematical sentence into 'angle 6 = 180 - angle 4.

Because angle 6 is angle 6, we know that '- angle 1 - angle 2 = - angle 4', and 'angle 1 + angle 2 = angle 4'. That knowledge lets us know that Angle 1 and 2 are the remote interior angles of exterior angle 4.

The remote interior angle of the ∠4 in the given figure are ∠1 and ∠2.

What is remote interior angle?

An exterior angle of a triangle or any polygon is formed by extending one of the sides. Each exterior angle has two remote interior angles which are inside the triangle and opposite from the exterior angle.

The given figure has five angle. The angles ∠1 , ∠2, ∠6 are interior angles and ∠3, ∠4, ∠5 are the exterior angles. Since the angle ∠1 and ∠2 are interior and opposite to the angle ∠4. So the remote interior angles of ∠4 are  ∠1 and ∠2. The remote interior angles of ∠5 are also  ∠1 and ∠2. The remote interior angles of ∠3 are ∠1 and ∠6.

Hence the remote interior angles of the angle∠4 are ∠1 and ∠2.

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Answer:

Turkey Trot

Pumpkin Pie

Family Dinner

Mashed Potatoes

Football

Wish bone

Carve the Turkey

Green Beans

Cornucopia

Black Friday Shopping

Thanks Giving

Table Clothes

November

Drumsticks

Thanksgiving Parade band

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Answer:

JK = 72

Step-by-step explanation:

JL = JK + KL = (4x+8) + (6x-6) = 10x + 2 = 162

--> x = (162-2)/10 = 16

JK = 4x + 8 = 4 . 16 + 8 = 72

Answer: Multiply the centimeters number by 10.

Step-by-step explanation: There are 10 millimeters in every centimeter.

Answer:

7) 1

8) -2

9) undefined (no slope)

10) 4/3

11) -2/7

12) 0

Step-by-step explanation:

to find the slope when given to points ... minus the y values and x values

formula :

y - y

------  =  slope

x - x

Answer:

q= 5

Step-by-step explanation:

Geometric mean of two term p and q is = \(\sqrt{pq}\)

we have

p = √7​

geometric mean = √35

Thus, using the formula of geometric mean

√35 = √7​*q

\(\sqrt{35} = \sqrt{7q} \\\)

squaring both sides

\(\sqrt{35}^2 = \sqrt{7q} ^2\\=>35 = 7q\\=> q = 35/7 = 5\)

Thus, q= 5