Which of the following is not a congruence theorem or postulate? A. SSS B. SAS C. SSA D. AAS

Answer:

Y = -½x + 3/2

Y = -3x + 5

Y = 1/4x - 3¼

Step-by-step explanation:

Parallel implies they have the same gradient

Perpendicular implies the gradient is a negative reciprocal of the other.

F and G are inverse if both of them satisfy the condition h(x)=x. f(g(x))=g(f(x))=x, as we discovered. The argument f(x) and g(x) are inverse functions is thus established.

If f (x) and g (x) are inverse functions, it can be determined using one of two ways. For more information, see the explanation.

Explanation:

Instance 1

Inverse functions of both functions can be found using the first method.

Example.

Inverse of f (x) = x + 7 is what we're looking for.

We attempt to determine x using the equation y = x + 7.

y = x + 7

Inferring that g (x) is the inverse of f (x) from the fact that x = y 7

Finding g (x inverse )'s is now necessary.

g( x ) = x − 7

y = x − 7

x = y + 7

As a result, we discovered that f (x) is the inverse function of g (x).

f and g are equal if g is inverse of f and vice versa.

The second approach entails locating the compound functions f ( g ( x ) ) and g ( f ( x ) ). In this case, f and g are inverse if they are both h (x ) = x.

Example:

f ( g ( x ) =  [ x − 7 ] + 7

G ( x ) placed as x is the expression in brackets.

f ( g ( x ) ) = x − 7  + 7 = x

g (f ( x ) =  [ x + 7 ] − 7

f ( x ) inserted as x is the expression in brackets.

g ( f ( x ) ) = x + 7 − 7 = x

The equation f ( g ( x ) ) = g ( f ( x ) ) = x was what we discovered. The argument f (x) and g (x) are inverse functions is thus established.

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The phrase that represents the algebraic expression n - 4 is option b four less than a number.

Given,

The algebraic expression; n - 4

We have to find the phrase that represents the given algebraic expression.

Algebraic expression;

In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.

An algebraic expression can be categorized into different categories depending on how many terms it contains: polynomial, quadrinomial, trinomial, monomial, and binomial.

So,

n - 4

That is,

4 is less than from a number

Therefore,

The phrase that represents the algebraic expression n - 4 is option b four less than a number.

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Answer:

the answer is b

Step-by-step explanation:

The 70 meters by 50 meters rectangular field having a path with an area of 104 m² around it indicates that the width of the path, found using the quadratic formula is about 0.43 meters.

The quadratic formula is a formula that is used to find the values of x that are the solutions to the the the quadratic equation of the form, a·x² + b·x + c = 0.

The length of the rectangular field = 70 meters

The width of the rectangular field = 50 meters

The width of the path around the field = Uniform width

Area of the path around the field = 104 m²

Let x represent the width of the path, we get;

(70 + 2·x) × (50 + 2·x) - 70 × 50 = 104

4·x² + 240·x = 104

4·x² + 240·x - 104 = 0

The quadratic formula which can be used to find the value of x in the equation a·x² + b·x + c = 0, is presented as follows;

\(x = \dfrac{-b\pm \sqrt{b^2-4\cdot a \cdot c} }{2\cdot a}\)

Comparing the equation 4·x² + 240·x - 104 = 0 to the quadratic equation for the quadratic formula; a·x² + b·x + c = 0, we get;

a = 4, b = 240, c = -104

Therefore;

\(x = \dfrac{-240\pm \sqrt{240^2-4\times 4 \times (-104)} }{2\times 4}\)

x ≈ 0.430 or x ≈ -60.4

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Answer:

The correct option - Figure A

Step-by-step explanation:

The exact question is as follows :

Given - Royce kept track of the inches of snowfall in his town over a 15-day period. Royce's data is given below.

1, 0, 0, 3, 5, 0, 0, 0, 2, 2, 1, 7, 2, 2, 3

To find - Which box plot shows this data set?

Solution -

Given the data is -

1, 0, 0, 3, 5, 0, 0, 0, 2, 2, 1, 7, 2, 2, 3

Firstly,

Arrange the data from smallest to largest

0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 3, 3, 5, 7

Now,

Find the median

Median is the middle value - i.e. (15 + 1)/2 = 8th value

So, we get Median = 2

Now,

Find the Quartile -

The first quartile is the median of the data points to the left of the median.

i.e. Median of 0, 0, 0, 0, 0, 1, 1

so, we get

Q1 = 0

The third quartile is the median of the data points to the right of the median.

i.e. Median of 2, 2, 2, 3, 3, 5, 7

so, we get

Q3 = 3

Now,

Compute the min and the max

Minimum value = 0

Maximum value - 7

So,

five number summary is -

0, 0, 2, 3, 7

And we draw the box as follows -

So,

The correct option - Figure A

Answer:

A

Step-by-step explanation:

Answer:

Step-by-step explanation:

Letter B is the correct answer

Initial population is 200, tripled every hour

200 x 3 = 600

First hour 200

Second hour = 600 + 200 = 800

Third hour 800x3 = 2400 + 800 = 3200

and so on.

Answer:

Use Desmos.com. It is a site that can graph basically anything you want.

Step-by-step explanation:

Answer:

$25-$9.9

Step-by-step explanation:

45/100

0.45*$25

$9.9

$25-$9.9

it cost 14.1

Answer:

the 4 gallon jug of 24$ is cheaper

Answer:

The company that sells 4 gallon jug of lemonade for $24 is cheaper

Step-by-step explanation:

The second company sells 8 packs of 1 quart bottles for $16 which basically means 8 quarts for $16.

There are 4 quarts in a gallon so if there are 8 quarts,  it would equal 2 gallons.

Now we know that the second company sells 2 gallons of lemonade for $16. So to find how much they will sell for 4 gallons, we just need to multiply by 2 for gallons and the price.

The second company sells 4 gallons of lemonade for $32.

This means that the first company is cheaper.

Hope this helps and pls do mark me brainliest if you can:)

===================================================

Explanation:

The set of natural numbers is {1,2,3,4,...} aka the set of positive whole numbers.

Consecutive natural numbers follow one right after another, like with that example above or something like 7,8,9,...

Since B follows right after A, this means B = A+1. Similarly, C = B+1 = (A+1)+1 = A+2 because C follows right after B.

So we have

In other words, we have the sequence A,A+1,A+2 to replace the sequence A,B,C in that order.

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

The reciprocal of A is 1/A. Taking 2/7 of this gets us 2/(7A). This result is equal to 1/3 of the reciprocal of C, so,

2/(7A) = 1/3 of 1/C

2/(7A) = 1/(3C)

2/(7A) = 1/(3(A+2))

2/(7A) = 1/(3A+6)

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

Let's cross multiply and solve for A

2/(7A) = 1/(3A+6)

2(3A+6) = 7A*1

6A+12 = 7A

12 = 7A-6A

12 = A

A = 12

Therefore, B = A+1 = 12+1 = 13 and C = A+2 = 12+2 = 14

The sequence A,B,C updates to 12,13,14.

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

Check:

A = 12

reciprocal of A = 1/A = 1/12

D = 2/7 of reciprocal of A = (2/7)*(1/12) = 2/84 = 1/42

C = 14

reciprocal of C = 1/C = 1/14

E = 1/3 of the reciprocal of C = (1/3)*(1/14) = 1/42

Items D and E are equal, so it confirms we have the correct answer.

Answer:

1376 minutes

Step-by-step explanation:

Alicia sews costumes for schools

She takes 86 minutes to sew one costume

Therefore the time taken to sew 16 costumes can be calculated as follows

86 mins= 1 costume

x= 16 costume

Cross multiply

x= 86×16

= 1376 minutes

Answer:

12 apples is the answer because 1/2 divided by 6 is 12

Step-by-step explanation:

Answer:

2 and 3/10 pints

Step-by-step explanation:

4 and 3/5= 4.6

Divide by two

2.3= 2 and 3/10

Answer:

2.3 pints or 2 3/10

Step-by-step explanation:

divide 2 to the whole number which is 4

4÷2=2

divide 2 to the remaining fraction which is 3/5

3/5÷2 turn two into a fraction

3/5÷2/1

3/5×1/2=3/10

Put them together and you have 2 3/10

The preceding polynomial equation has three solutions: z = 0, z = 3/4, and z = -1/5.

First, we can factor out a common factor of z:

z(20z² - 11z - 3) = 0

Now we need to factor the quadratic expression in the parentheses.

We can use the quadratic formula or factor by grouping to do this. Factoring by grouping yields:

z(20z² - 11z - 3) = 0

z(4z - 3)(5z + 1) = 0

Setting each of the factored terms equal to zero, we have:

z = 0, 3/4, -1/5

Therefore, the solutions to the given polynomial equation are z = 0, z = 3/4, and z = -1/5.

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The amount of money that Theresa has left is equal to £2,740.

In order to write a linear equation to describe this situation, we would assign variables to the cost of flights for each of them and the cost of accommodation for each of them respectively, and then translate the word problem into a linear equation as follows:

Let the variable a represent cost of flights for each of them.

Let the variable f represent cost of accommodation for each of them.

Since Theresa paid for herself and 11 friends to go on holiday with a flight cost of £339 and accommodation cost of £266, a linear equation to describe this situation is given by;

y = 12(a + b)

y = 12(266 + 339)

y = £7,260

For the amount of money left, we have:

Amount of money left = £10,000 - £7,260

Amount of money left = £2,740.

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Note that the parameters of the graph a and graph b are given below.

Graph A - y=2(x-1)²

See graph attached.

Graph B - y = 1/2x² + 3

Vertex: The vertex of the function is (0, 3).

Axis of symmetry: The axis of symmetry is the vertical line passing through the vertex, which is x = 0.

Y-intercept: The y-intercept is the point where the graph intersects the y-axis. It is (0, 3).

Minimum or maximum: The coefficient of x² is positive, which means the parabola opens upwards, and therefore the function has a minimum value. The minimum value is 3.

Solutions: To find the solutions or roots of the quadratic equation, we need to set y or f(x) equal to zero and solve for x.

0 = 1/2 x² + 3

Subtracting 3 from both sides, we get:

-3 = 1/2 x²

Multiplying both sides by -2, we get:

6 = -x²

Taking the square root of both sides, we get:

x = ±√(-6)

Since the square root of a negative number is not a real number, the function has no real roots.

Minimum or maximum value: The minimum value of the function is 3.

Range: The range of the function is y ≥ 3, because the function has a minimum value of 3.

Domain: The domain of the function is all real numbers, because there are no restrictions on the values of x for which the function is defined.

Stretch/Shrink/Standard: The coefficient of x^2 is positive and less than 1, which means that the graph of the function is narrower than the graph of y = x². This is an example of a standard quadratic function that has been vertically compressed by a factor of 1/2.

See graph attached.


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The expressions that are equivalent to 3^8 are:

We have to solve these out

3^8. = 6561

From the options

A. 3^2x3^4

= 9 x 81

= 729

B  3²x3^6

= 9 x 729

= 6561

C.  3^16/3^2

= 43046721/9

= 4782969

d. 3^12/3^4

= 531441 / 81

= 6561

E.  (3^4)²

= 3⁴ x 3⁴

= 3⁴⁺⁴

= 3⁸

= 6561

F. (3¹)^7

= 3⁷

= 2187

The expressions that are equivalent to 3^8 are:

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The number of minutes spent higher than 38 meters above the ground on the Ferris wheel ride is approximately 1.0918 minutes.

To solve this problem, we need to determine the angular position of the Ferris wheel when it is 38 meters above the ground.

The Ferris wheel has a diameter of 50 meters, which means its radius is half of that, or 25 meters.

When the Ferris wheel is at its highest point, the radius and the height from the ground are aligned, forming a right triangle.

The height of this right triangle is the sum of the radius (25 meters) and the platform height (4 meters), which equals 29 meters.

To find the angle at which the Ferris wheel is 38 meters above the ground, we can use the inverse sine (arcsine) function.

The formula is:

θ = arcsin(h / r)

where θ is the angle in radians, h is the height above the ground (38 meters), and r is the radius of the Ferris wheel (25 meters).

θ = arcsin(38 / 29) ≈ 1.0918 radians

Now, we know the angle at which the Ferris wheel is 38 meters above the ground.

To calculate the time spent higher than 38 meters, we need to find the fraction of the total revolution that corresponds to this angle.

The Ferris wheel completes one full revolution in 2 minutes, which is equivalent to 2π radians.

Therefore, the fraction of the revolution corresponding to an angle of 1.0918 radians is:

Fraction = θ / (2π) ≈ 1.0918 / (2π)

Finally, we can calculate the time spent higher than 38 meters by multiplying the fraction of the revolution by the total time for one revolution:

Time = Fraction \(\times\) Total time per revolution = (1.0918 / (2π)) \(\times\) 2 minutes

Calculating this expression will give us the answer in minutes.

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The value of x from the venn diagram if P(T | V) = 1/5 is 16

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

The venn diagram

From the venn diagram, we have the following probability values

P(T | V) = (x - 4)/(3x + x - 4)

Evaluate the like terms

So, we have

P(T | V) = (x - 4)/(4x - 4)

From the question, we have

P(T | V) = 1/5

This means that

(x - 4)/(4x - 4) = 1/5

When evaluated, we have

x = 16

Hence, the value of x is 16

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we know that

diameter of the base of a cylindrical can= 4 in----------> r=2 in

h=6.5 in

[surface area]=2*[pi*r²]+[2*pi*r*h]

then

[surface area]=2*[pi*2²]+[2*pi*2*6.5]=[ 25.13 ]+[ 81.68 ]=106.81 in²

the answer is 106.8 in²

a) To re-express the given differential equation as a first-order differential equation using matrix and vector notation, we can rewrite it in the form:

\(x' = Ax\)

where x is a vector and A is a square matrix.

b) To determine the stability of the system obtained in part (a), we need to analyze the eigenvalues of matrix A.

If all eigenvalues have negative real parts, the system is stable.

If at least one eigenvalue has a zero real part, the system is neutrally stable.

If at least one eigenvalue has a positive real part, the system is unstable.

c) To compute the eigenvalues and eigenvectors of matrix A, we solve the characteristic equation

\(det(A - \lambda I) = 0\),

where λ is the eigenvalue and I is the identity matrix.

By solving this equation, we obtain the eigenvalues.

Substituting each eigenvalue into the equation

\((A - \lambda I)v = 0\),

where v is the eigenvector, we can solve for the eigenvectors.

d) Once we have computed the eigenvalues and eigenvectors of matrix A, we can construct the diagonalization relationship as follows:

\(A = PDP^{(-1)}\)

where P is a matrix whose columns are the eigenvectors of A, and D is a diagonal matrix whose diagonal elements are the eigenvalues of A.

To show that this relationship is valid, we can compute \(PDP^{(-1)}\) and verify that it equals A.

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The difference in temperature between Rome and Munich is given as follows:

6ºC.

The difference in temperature between Rome and Munich is given by the subtraction of Rome's temperature by Munich's temperature.

The bar graph in the context of this problem gives the temperature for each town.

From the bar graph given by the image presented at the end of the answer, the temperatures for Rome and Munich are given as follows:

Hence the difference in temperature between Rome and Munich is given as follows:

11 - 5 = 6ºC.

The graph is given by the image presented at the end of the answer.

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The slope of the line that passes through the points (0, -6) and (0, -5)is undefined.

Slope is line's inclination with regard to the horizontal is quantified numerically. In analytical geometry, a line, ray, or line segment's slope is the ratio of the vertical to horizontal distance between any two points on the line, ray, or line segment ("slope equals rise over run").

In differential calculus, the derivative of a function yields the slope of a line tangent to its graph, which represents the function's instantaneous rate of change with respect to changes in the independent variable.

Ok so slope is the change in y over change in x.

Your why changed from 6 to -5 so you can write this as -5 - 6

Your x didn’t change it went from 0 to 0

You can write this as 0-0

Now -11/0 is what you end up with as a slope.

Any number divided by 0 is undefined so your slope is undefined.

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The missing value for the coordinate pair that lies on the graph of the function. y=5^x (2,​ 25)

The equation of the function is given as:

y = 5^x

And the x value is given as

x = 2

To determine the missing value, we start by substituting 2 for x in the function y = 5^x

So, we have:

y = 5^2

Evaluate the exponent

y = 25

So, the complete coordinate is (2, 25)

Hence, the missing value for the coordinate pair that lies on the graph of the function. y=5^x (2,​ 25)

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Step-by-step explanation:

\( \frac{2}{4} + \frac{3}{8} = \\ = \frac{4 + 3}{8} = \\ = \frac{7}{8} \)

Answer:

The answer is 0.875 in decimal form but is 7/8 in fraction form

Step-by-step explanation:

Answer:  x    =   -3

Step-by-step explanation:

3(x + 1) = -6

Divide both sides by 3:   3(x + 1) / 3 = -6 / 3

                                              x + 1 = -2

Subtract 1 from each side:   x + 1 - 1 = -2 - 1

                                                      x    =   -3

Answer:

Hope that will help you get