let f(x)=2x+3 and g(x)=x×x-1
find a. f(g(x)) b.g(f(x))

​

Given:

Consider the below figure attached with this question.

To find:

The value of x.

Solution:

We know that, the sum of all exterior angles of a quadrilateral is always 360 degrees.

The below figure represents the four exterior angles of the quadrilateral. So,

\(65^\circ+106^\circ+78^\circ+x^\circ=360^\circ\)

\(249^\circ+x^\circ=360^\circ\)

\(x^\circ=360^\circ -249^\circ\)

\(x^\circ=111^\circ\)

Therefore, the measure of x is \(111^\circ\).

Answer:

40

Step-by-step explanation: It's 40 because 8 times 5 is 40. But if you want to find out how much water the patient drank all together including right before bed then it would be 46 ounces of water.

Answer:.

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

One is used as an enlargement of the object drawn. The image formed can either be smaller or bigger.

Answer:

It's the last option, (a-c)√x + b√y

Step-by-step explanation:

Step-by-step explanation:

\(2p + 2p + 2p + 60 = 360 \\ 6p = 360 - 60 \\ 6p = 300 \\ p = \frac{300}{6} \\ p = 50\)

Answer:

If you take the 2 smallest sides and put it in the pythagreon theorem to get the other side length.

Step-by-step explanation:

So if you have a triangle with side lengths, 3, 4, and 5, you can use the exact equation below.

\( {3}^{2} + {4}^{2} = {5}^{2} \)

Because this is true, then the triangle does have a right angle.

Translations, reflections, and rotations produce a figure that is congruent to the original figure.

When we perform translations, reflections, and rotations on a figure, the resulting figure maintains the same size, shape, and orientation as the original figure. In other words, the transformed figure is congruent to the original figure.

Here's a brief explanation of each transformation:

1. Translations: A translation involves sliding a figure in a particular direction without changing its orientation or shape. Every point of the figure moves the same distance and direction. The resulting figure is congruent to the original because all corresponding sides and angles remain the same length and measure.

2. Reflections: A reflection involves flipping a figure over a line, called the line of reflection. Each point of the figure is mirrored across the line, creating a symmetrical image. The resulting figure is congruent to the original because the distance between corresponding points remains the same, and the angles formed between intersecting lines are preserved.

3. Rotations: A rotation involves turning a figure around a fixed point, known as the center of rotation. The figure is rotated by a specific angle in a clockwise or counter clockwise direction. The resulting figure is congruent to the original because all corresponding angles and side lengths remain unchanged.

In each of these transformations, the congruency of the resulting figure to the original figure is a fundamental property. Congruent figures have the same shape and size, even though they may be positioned differently in space. This property allows us to apply the concept of congruence in geometry to establish relationships, prove theorems, and solve geometric problems.

Therefore, when we perform translations, reflections, and rotations on a figure, we produce a transformed figure that is congruent to the original figure.

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Answer:

Area: 79.25

Perimeter:33.7

Using the bisection concept, it is found that the measure of angle PQR is of 130º.

A bisection divides an angle into two equal angles. In this problem, the angles are given as follows:

Hence the value of x is given as follows:

3x + 5 = 2x + 25

x = 20º.

Hence the measure of angle PQR is given as follows:

m<PQR = 3x + 5 + 2x + 25 = 5x + 30 = 5 x 20º + 30º = 130º.

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Answer:

Step-by-step explanation:

The question is on the mensuration of solids, a cylinder

Given data

height of cylinder h= 4 cm

diameter d= 9 cm

radius = d/2= 9/2= 4.5 cm

we know that the surface area of cylinder is

\(SA= 2\pi r h+ 2\pi r^2\)

Substituting our data into the expression we have

\(SA= 2*3.142 *4.5* 4+ 2*3.142 4.5^2\)

\(SA= 113.12+ 127.25\\\\SA= 240.37 cm^2\)

Therefore the total surface area is 240.37 cm^2

The general solution to the differential equation y'' + 16y = 0 is y(x) = (c₁ + c₂) * cos(4x)

To solve the differential equation y'' + 16y = 0 using reduction of order, we'll assume a second solution of the form y₂(x) = u(x) * y₁(x), where y₁(x) is a known solution and u(x) is an unknown function.

Given y₁(x) = cos(4x), we'll differentiate it to find y₁'(x) and y₁''(x):

y₁'(x) = -4sin(4x)

y₁''(x) = -16cos(4x)

Now we substitute y₂(x) = u(x) * y₁(x) into the original differential equation:

y'' + 16y = 0

(-16cos(4x)) + 16(u(x) * cos(4x)) = 0

Simplifying the equation:

-16cos(4x) + 16u(x) * cos(4x) = 0

cos(4x)(-16 + 16u(x)) = 0

For this equation to hold for all values of x, we must have (-16 + 16u(x)) = 0.

Solving for u(x):

-16 + 16u(x) = 0

16u(x) = 16

u(x) = 1

Now we have the second solution:

y₂(x) = u(x) * y₁(x)

y₂(x) = 1 * cos(4x)

y₂(x) = cos(4x)

Therefore, the general solution to the differential equation y'' + 16y = 0 is:

y(x) = c₁ * y₁(x) + c₂ * y₂(x)

y(x) = c₁ * cos(4x) + c₂ * cos(4x)

y(x) = (c₁ + c₂) * cos(4x)

Where c₁ and c₂ are arbitrary constants.

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According to the statement the simplest pos expression of f = σw,x,y,z(0, 1, 6, 7, 8, 9, 14, 15)  = wxyz + wxy'z + wx'yz + wx'y'z

To find the simplest pos expression of f = σw,x,y,z(0, 1, 6, 7, 8, 9, 14, 15) using K-maps, we first need to create the K-map for f. The K-map for this function has four variables, w, x, y, and z, with each variable representing one column or row in the K-map. We then fill in the cells corresponding to the eight minterms given in the question, as shown below:
   z\wy 00 01 11 10
   0    1  1  1  1
   1    1  1  1  1
Next, we group the adjacent cells with the value 1 to form groups of 2, 4, or 8 cells. In this case, we have one group of 8 cells, two groups of 4 cells, and one group of 2 cells. These groups correspond to the following pos expression:
f = σw,x,y,z(0, 1, 6, 7, 8, 9, 14, 15) = wxyz + wxy'z + wx'yz + wx'y'z
This is the simplest pos expression for the given function, as it uses only four terms, which is the minimum number required to represent all eight minterms. In other words, any further simplification would result in a longer expression that does not provide any additional benefit.

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Answer:

Step-by-step explanation:

y=3x-2, plug in each for x and y on the table and they work

Answer: -48

Step-by-step explanation:

You would multiply 6 by -2 and then multiply 4 and -9 and then add the two products together

Answer:

C. AOE

Step-by-step explanation:

Supplementary means 180 degrees which is a straight line

Only angle AOE combined with DOE is a straight line

Let's begin by identifying key information given to us:

Answer:

23/36

Step-by-step explanation:

Add all the numbers

1/2 + 2/3 + 3/4 = 23/12

Divide by 3

23/12 / 3 = 23/36

answer: associative property

Step-by-step explanation:

If the length of a rectangle is 3 more than twice the width and the perimeter is 36 inches, then the area of the rectangle is equal to 65 in².

The length and width of the rectangle can be determined by using the formula for the perimeter of the rectangle,

P = ( L + W ) × 2

P = 2L + 2W

Here L is equal to the length of the rectangle and W is the width of the rectangle.

As the length is 3 more than twice the width, we can write the length of the rectangle as,

L = 3 + 2W

Putting L = 3 + 2W in the equation of perimeter,

P = 2L + 2W

As P = 36

36 = 2( 3 + 2W) + 2W

36 = 6 + 4W + 2W

6W = 30

W = 30 ÷ 6

W = 5

The length of the rectangle can be found by putting W = 5 in the equation,

L = 3 + 2W

L = 3 + 2(5)

L= 3 + 10

L = 13

Therefore, the length and width of the rectangle are equal to 13 and 5 respectively

As, area = width × length

area = 5 × 13

area = 65

Hence, the area of the rectangle is equal to 65 square inches.

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The function T(n) in terms of the number of operations is:

T(n) = 2n^3 + 3n^2 + 2n + 1 and the asymptotic complexity of the matrix multiplication algorithm is O(n^3).

To analyze the provided pseudo code for matrix multiplication and determine the function T(n) in terms of the number of operations, we need to examine the code and count the number of operations performed.

The pseudo code for matrix multiplication may look something like this:

```

MatrixMultiplication(A, B):

   n = size of matrix A

   C = empty matrix of size n x n

   for i = 1 to n do:

       for j = 1 to n do:

           sum = 0

           for k = 1 to n do:

               sum = sum + A[i][k] * B[k][j]

           C[i][j] = sum

   return C

```

Let's break down the number of operations step by step:

1. Assigning the size of matrix A to variable n: 1 operation

2. Initializing an empty matrix C of size n x n: n^2 operations (for creating n x n elements)

3. Outer loop: for i = 1 to n

- Incrementing i: n operations  

- Inner loop: for j = 1 to n

- Incrementing j: n^2 operations (since it is nested inside the outer loop)

- Initializing sum to 0: n^2 operations

- Innermost loop: for k = 1 to n

- Incrementing k: n^3 operations (since it is nested inside both the outer and inner loops)

- Performing the multiplication and addition: n^3 operations

- Assigning the result to C[i][j]: n^2 operations

- Assigning the value of sum to C[i][j]: n^2 operations

Total operations:

1 + n^2 + n + n^2 + n^3 + n^3 + n^2 + n^2 = 2n^3 + 3n^2 + 2n + 1

Therefore, the function T(n) in terms of the number of operations is:

T(n) = 2n^3 + 3n^2 + 2n + 1

To determine the asymptotic (big O) complexity of the algorithm, we focus on the dominant term as n approaches infinity.

In this case, the dominant term is 2n^3. Hence, the asymptotic complexity of the matrix multiplication algorithm is O(n^3).

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Analysis of variance is used to test for equality of several population means.

ANOVA could also be utilized to predict the dependent variable of even more with around 2 categories and seems to be compared to the general population extra influential throughout this circumstance.

Throughout addition, ANOVA variants typically include covariates that encourage somebody to manipulate numerically for confounding factors as well as to recognize interactions wherein the factor progressives the implications of some other factor.

ANOVA (Analysis of Variance) was developed by Ronald Fisher.

ANOVA means the Analysis of Variance, is collection of statistical models & linked estimation processes, like variation among & between groups. It is used in analyzing differences among various means.

Therefore, Analysis of variance is used to test for equality of several population means.

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Solution,

Principal=£ 500

Time=2 years

Interest=£40

Rate=?

Now,

R=I*100/P*T

= 40*100/500*2

=4000/1000

=4%

Hope it helps

Good luck on your assignment

Answer:

\(4\%\)

Step-by-step explanation:

\(p = 500 \\ r = x \\ t = 2\)

\(simple \ \: \: \: = \frac{prt}{100} \\ interest \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 40= \frac{500 \times x \times 2}{100} \\ \: \: \: \: \: \: \: 40 \: \: \: \: \: \: \: \: \: = \frac{1000x}{100} \\ \frac{40 \times 100}{1000} = x \\ x = 4\)

Step-by-step explanation:

IF  x-4   is a factor, then putting in x = + 4    will make the polynomial = 0

5 ( 4^3) - 20 (4^2) - 5(4)  + 20   =   0    Yes...it is a factor

\(x - 4 = 0 \\ x = 4 \\ \)

substitute value of x in the function to see if it equals to zero , if not it won't be a factor of the function

\(5 {x}^{3} - 20 {x}^{2} - 5x + 20 = 0 \\ 5(4) ^{3} - 20( {4})^{2} - 5(4) + 20 = 0 \\ 5(64) - 20(16) - 20 + 20 = 0 \\ 320 - 320 - 20 + 20 = 0 \\ 0 = 0\)

so (x-4) is a factor for the function

The Lagrange polynomial using the given points and calculate its value at x = 2.5. The expression to find the value of the Lagrange polynomial at x = 2.5.

To construct a Lagrange polynomial that passes through the given points (-2, -1), (0.1, 1.3), (14.5, -5.4), (0.3, 0), and (X, y), we can use the Lagrange interpolation formula.

The formula for the Lagrange polynomial is:

L(x) = Σ [y(i) * L(i)(x)], for i = 0 to n

Where:
- L(x) is the Lagrange polynomial
- y(i) is the y-coordinate of the ith point
- L(i)(x) is the ith Lagrange basis polynomial

The Lagrange basis polynomials are defined as:

L(i)(x) = Π [(x - x(j)) / (x(i) - x(j))], for j ≠ i

Where:
- L(i)(x) is the ith Lagrange basis polynomial
- x(j) is the x-coordinate of the jth point
- x(i) is the x-coordinate of the ith point

Now, let's construct the Lagrange polynomial step by step:

1. Calculate L(0)(x):
L(0)(x) = [(x - 0.1)(x - 14.5)(x - 0.3)(x - X)] / [(-2 - 0.1)(-2 - 14.5)(-2 - 0.3)(-2 - X)]

2. Calculate L(1)(x):
L(1)(x) = [(-2 - 0.1)(-2 - 14.5)(-2 - 0.3)(-2 - X)] / [(0.1 - (-2))(0.1 - 14.5)(0.1 - 0.3)(0.1 - X)]

3. Calculate L(2)(x):
L(2)(x) = [(x + 2)(x - 14.5)(x - 0.3)(x - X)] / [(0.1 + 2)(0.1 - 14.5)(0.1 - 0.3)(0.1 - X)]

4. Calculate L(3)(x):
L(3)(x) = [(x + 2)(x - 0.1)(x - 0.3)(x - X)] / [(14.5 + 2)(14.5 - 0.1)(14.5 - 0.3)(14.5 - X)]

5. Calculate L(4)(x):
L(4)(x) = [(x + 2)(x - 0.1)(x - 14.5)(x - X)] / [(0.3 + 2)(0.3 - 0.1)(0.3 - 14.5)(0.3 - X)]

Now, we can write the Lagrange polynomial as:

L(x) = y(0) * L(0)(x) + y(1) * L(1)(x) + y(2) * L(2)(x) + y(3) * L(3)(x) + y(4) * L(4)(x)

To calculate the value of the Lagrange polynomial at x = 2.5,

substitute x = 2.5 into the Lagrange polynomial equation and evaluate it.

It is important to note that the value of X and y are not provided, so we cannot determine the exact Lagrange polynomial without these values.

However, by following the steps outlined above, you should be able to construct the Lagrange polynomial using the given points and calculate its value at x = 2.5 once the missing values are provided.

Now, evaluate the expression to find the value of the Lagrange polynomial at x = 2.5.

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Answer:

Truck D.

Step-by-step explanation:

Below are the rates of travel of 4 shipping trucks.

Truck A: 300 miles in 4 hours Truck B: 240 miles in 3 hours Truck C: 325 miles in 5 hours Truck D: 170 miles in 2 hours.

Speed = distance/time

Speed of Truck A,

\(v_A=\dfrac{300}{4}\\\\v_A=75\ mph\)

Speed of Truck B,

\(v_B=\dfrac{240}{3}\\\\v_B=80\ mph\)

Speed of Truck C,

\(v_C=\dfrac{325}{5}\\\\v_C=65\ mph\)

Speed of Truck D,

\(v_D=\dfrac{170}{2}\\\\v_D=85\ mph\)

It can be seen that the speed of Truck D is more out of Trucks A,B and C. Hence, Truck D is moving at a faster rate.

The sum of the first 200 multiples of 3 is 60,300(B).

To find the sum of the first 200 multiples of 3, we need to calculate the arithmetic series. The formula for the sum of an arithmetic series is Sn = (n/2)(a + l), where Sn is the sum, n is the number of terms, a is the first term, and l is the last term. In this case, the first term (a) is 3, and the last term (l) is 3 * 200 = 600.

Plugging these values into the formula, we get Sn = (200/2)(3 + 600) = 100 * 603 = 60,300. Thus, the sum of the first 200 multiples of 3 is 60,300(C).

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Answer:

The original temperature was -18°F

Step-by-step explanation:

x°F + 24°F = 6°F

or, x°F = 6°F - 24°F

so, x°F = -18°F