FRACTIONS
Understanding equivalent fractions

Answer: lol

Step-by-step explanation: same

4/4 = 1

z-1+8 = z+7

C. z+7

Where the voice rises and falls. But inflection also describes a departure from a normal or straight course.

Inflection points for the given equation x^2e^{-2x} are

f'(x) =\(2x2xe^{(-2x)}-2{(x2)} e^{(-2x)}\)

f'(x) =\(-2(x-1)xe {(^-2x)}\)

x= -b±√(b^2 - 4ac)/2a

x=4±√(16+16)4

x=4±4√2/4

x=\(\sqrt{2+2/2}\)

x=\(\sqrt{2-2/2}\)

We get,

x=\(\sqrt{(2+2)/2^{2}*\sqrt{2+2}\)

so, inflection points are,

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The values are given below,

Left Hand Limit i.e.  \(\lim_{x \to 1^-} f(x)\) = 3 ,

Right Hand Limit i.e.  \(\lim_{x \to 1^+} f(x)\) = 1 ,

Function value at x = 1  \(f(1)\) = 1 ,

Left Hand Derivative \(\lim_{x \to 1^-} f'(x)\) = -6 and

Right Hand Derivative \(\lim_{x \to 1^+} f'(x)\) = -6.

So, the function f(x) is neither continuous nor differentiable at x = 1.

Given, a piecewise function

              3㏑(3 - 2x) + 3                for x < 1

f(x) =

                    -3x² + 4                     for x ≥ 1

Now, for  \(\lim_{x \to 1^-} f(x)\) we will consider the function  3㏑(3 - 2x) + 3, as we have to find the Left Hand Limit of the function, at x = 1.

\(\lim_{x \to 1}\) 3㏑(3 - 2x) + 3 = 3㏑(3 - 2(1)) + 3

= 3 ㏑(1) + 3

= 0 + 3

= 3

Now, for \(\lim_{x \to 1^+} f(x)\) we will consider the function -3x² + 4, as we have to find the Right Hand Limit of the function, at x = 1.

\(\lim_{x \to 1}\) -3x² + 4 = -3(1)² + 4

= -3 + 4

= 1

Now, for \(f(1)\) we will consider the function -3x² + 4,

\(f(1)\) = -3(1)² + 4

= -3 + 4

= 1

Now, for \(\lim_{x \to 1^-} f'(x)\) we will consider the derivative of the function

3㏑(3 - 2x) + 3,

\(\lim_{x \to 1}\) -6/(3 - 2x) = -6/(3 - 2(1))

= -6

Now, for \(\lim_{x \to 1^+} f'(x)\) we will consider the derivative of the function

-3x² + 4,

\(\lim_{x \to 1}\) -6x = -6(1)

= -6

So, the function f(x) is neither continuous nor differentiable at x = 1.

Hence,  \(\lim_{x \to 1^-} f(x)\) = 3 ,  \(\lim_{x \to 1^+} f(x)\) = 1 ,  \(f(1)\) = 1 ,  \(\lim_{x \to 1^-} f'(x)\) = -6 and  \(\lim_{x \to 1^+} f'(x)\) = -6

The function is neither continuous nor differentiable at x = 1.

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Using the Pythagorean theorem:

BC = sqrt(13^2 - 8^2)

BC - sqrt(169 - 64)

BC = sqrt(105)

The exact dimension is sqrt105

If it needs be be in decimal format, sqrt(105) = 10.24695

Answer:

The 3rd one or C

Step-by-step explanation:

A       B

C      D

Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes

The radius of the Ferris wheel is 30 / 2 = 15 meters.

The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.

The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.

The angle between these two positions is 180 degrees.

The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.

Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.

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For the fractions, the calculation of 3/5 of 2/3 of 3/4 of 560 is equal to 168.

To calculate 3/5 of 2/3 of 3/4 of 560, break it down step by step:

Step 1: Calculate 3/4 of 560:

3/4 × 560 = (3 × 560) / 4 = 1680 / 4 = 420

Step 2: Calculate 2/3 of the result from Step 1:

2/3 × 420 = (2 × 420) / 3 = 840 / 3 = 280

Step 3: Calculate 3/5 of the result from Step 2:

3/5 × 280 = (3 × 280) / 5 = 840 / 5 = 168

Therefore, 3/5 of 2/3 of 3/4 of 560 is equal to 168.

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Answer:

C

Step-by-step explanation:

0.528 is the smallest number and C is the only one that starts with it

The first table represents y as a function of x.

If a table represents a function, each of the x-values will have only one possible y-value that corresponds to it, however, two different x-values can have the same y-value.

All the tables, except the first table, have x-values that have more than one y-value assigned to it.

The first table have exactly one y-value that corresponds to each of the x-values. Therefore, the first table represents y as a function of x.

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Answer:

\(\huge\boxed{x+y=-2}\)

Step-by-step explanation:

The standard form of an equation of a line:

\(Ax+By=C\)

The point-slope form of an equation of a line:

\(y-y_1=m(x-x_1)\)

where

\(m=\dfrac{y_2-y_1}{x_2-x_1}\)

We have two points (-2, 0) and (1, -3).

Substitute:

\(x_1=-2;\ y_1=0;\ x_2=1;\ y_2=-3\)

\(m=\dfrac{-3-0}{1-(-2)}=\dfrac{-3}{1+2}=\dfrac{-3}{3}=-1\\\\y-0=-1(x-(-2))\\\\y=-(x+2)\)

\(y=-x-2\)         add x to both sides

\(x+y=-2\)

Regression analysis will indicate about the underlying population and the model.

It is one of the most used and most powerful multivariate statistical techniques for it infers the existence and form of a functional relationship in a population. Once you learn how to use regression, you will be able to estimate the parameters { the slope and intercept } of the function that links two or more variables. With that estimated function, we  will be able to infer or forecast things like unit costs, interest rates, or sales over a wide range of conditions.

Though the simplest regression techniques seem limited in their applications, statisticians have developed a number of variations on regression that greatly expand the usefulness of the technique. And again, the t-distribution and F-distribution will be used to test hypotheses.

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Answer:

5.2 hours

Step-by-step explanation:

divide the total distance by how fast

td/speed

3250/625=5.2hrs

Answer:

about 189

Step-by-step explanation:

because out of 34 is 9 so 714 divided by 34 is 21 and 21 multiply by 9 is 189.

Answer:

A

Step-by-step explanation:

It works

The exponential retrogression equation that fits these data is

ŷ = 107.54286 X-214.06667

The link between two variables is shown by a retrogression line. It's used when the value of the dependant variable changes as a result of changes in the independent variable's value.

We've the Data,

x    y

1     4

2    8

3    27

4    85

5   250

6   600

So, Sum of X = 21

Sum of Y = 974

Mean X = 3.5

Mean Y = 162.3333

Sum of places( SSX) = 17.5

Sum of products( SP) = 1882

Regression Equation, ŷ = bX + a

b = SP/ SSX

b = 1882/17.5

b = 107.54286

and, a = MY- bMX

a = 162.33-(107.54 x3.5)

a = -214.06667

So, the retrogression line is ŷ = 107.54286 X-214.06667

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The amount of TT$ she received is TT$2,982.

The amount of BD$ she received is BD$700.

The cash price of the refrigerator is $235,008.

The solution of the pair of equations is x = 5 and y = 3.

The first step is to convert US$700 to TT.

$700 x TT$4.26 = TT$2,982

The next step is to determine how much is left after the Trinidad trip:

Amount left =  TT$2,982 = TT$1302 = TT$1680

The third step is to convert TT to BB

Amount of BD$ she received = TT$1680 / 2.10 = BD$800

The first step is to determine the price of the refrigerator after the 20% profit.

Price of the refrigerator after the profit = (1 + 0.2) x $256,000

1.02 x $256,000 = $261,120

The price after the discount = (1 - 0.1) x $261,120

The price after the discount = 0.9 x $261,120 = $235,008

3x + y = 18 equation 1

2x – y= 7 equation 2

The elimination method would be used to solve the equations.

Add equation 1 and equation 2 together

5x = 25

Divide both sides of the equation by 5

x = 25 / 5

x = 5

Substitute for x in equation 1:

3(5) + y = 18

15 + y = 18

y = 18 - 15

y = 3

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Answer:

x-7=2

Step-by-step explanation:

x + 8x = 9x

(like 1 + 8 but with x's)

Answer:  x(-2,0) y(0,1.4)

Answer:

Step-by-step explanation:

x(-2,0) y(0,1.4)

f(x) has a point of inflection at x = 0 and x = 1/2.To find the values of x where the graph of the function\(f(x) = x^4 - x^3\) has a point of inflection, we need to find where the second derivative of the function changes sign from positive to negative or vice versa.

The first derivative of the function is:

\(f'(x) = 4x^3 - 3x^2\)

The second derivative of the function is:

\(f''(x) = 12x^2 - 6x\)

Setting f''(x) equal to zero and solving for x gives:

\(12x^2 - 6x = 0\)

6x(2x - 1) = 0

This equation has two solutions:

x = 0, or x = 1/2

To determine whether these values of x correspond to points of inflection, we need to look at the sign of the second derivative on either side of each value.

When x < 0, f''(x) is positive because both \(12x^2\) and -6x are positive. When 0 < x < 1/2, f''(x) is negative because \(12x^2\)is positive but -6x is negative. When x > 1/2, f''(x) is positive again because both \(12x^2\) and -6x are negative.

Therefore, f(x) has a point of inflection at x = 0 and x = 1/2.

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Answer:

\(\angle ADC=62^\circ\)

Step-by-step explanation:

Given the circle centered on point B with points A, C and D on its circumference.

\(\angle ABC\) is the angle subtended by arc AC at the centre.

Since D is on the circumference, \(\angle ADC\) is the angle subtended by arc AC on the circumference.

Circle Theorem: The measure of the angle subtended by an arc at the center is twice the measure of the angle subtended by same arc at the circumference.

By the theorem stated above:

\(\angle ABC = 2 X \angle ADC\\Since \angle ABC=124^\circ\\124^\circ = 2 X \angle ADC\\ \angle ADC=124^\circ \div 2\\\\ \angle ADC=62^\circ\)

Answer:

The real answer is 20 its not that high of a number

Step-by-step explanation:

The ratio will remain constant. Then the value of the variable 'x' will be 2.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

The ratio will remain constant. Then the equation is given as,

9/4 = 13.5 / (x + 4)

9(x + 4) = 13.5 (4)

9x + 36 = 54

9x = 18

x = 2

The ratio will remain constant. Then the value of the variable 'x' will be 2.

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The inverse of the function f(x) = x + 4 is given as f⁻¹(x) = x - 4

An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by ‘f’ or ‘F’, then the inverse function is denoted by f-1 or F-1.

In this problem, the function given is f(x) = x + 4;

We can find the inverse of the function as;

y = x + 4;

Let's switch the variables by replacing x as y and y as x;

x = y + 4

Solving for y;

y = x - 4

f⁻¹(x) = x - 4

The graph of the function is attached below

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The sum of all a triangle's sides' lengths is the formula for calculating a triangle's perimeter.

The whole length of a shape's boundary is referred to in geometry as the perimeter of the shape. By multiplying the lengths of all the sides and edges that surround an object, the perimeter may be calculated. It is measured in measures of length that are linear, such as centimeters, meters, inches, or feet.

The sum of all a triangle's sides' lengths is the formula for calculating a triangle's perimeter.

Add the sides' lengths to find a triangle's perimeter. As an illustration, the perimeter of a triangle with sides a, b, and c is given by P = a + b + c.

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Answer:

47.1cm²

Step-by-step explanation:

diameter=15cm

circumference of circle= d×3.14

circumference=15×3.14

circumference=47.1

Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip