Write an algebraic equation based on the description. Two angles form a linear pair. The measure of one angle is 24° more than the measure of the other angle.

Answer:

Answer:

The area of the rectangular pasture is 768x^{11}\ unit^{2}.768x

11

unit

2

.

Step-by-step explanation:

Formula

Area of a rectangle = Length × Breadth

As given

A rectangular pasture has a fence around the perimeter. The length of the fence is 16x^{7}16x

7

and the width is 48x^{4}48x

4

.

Put all the values in the formula

Area\ of\ a\ rectangular\ pasture = 16x^{7}\times 48x^{4}Area of a rectangular pasture=16x

7

×48x

4

Now by using the exponent

x^{a}\times x^{b} = x^{a+b}x

a

×x

b

=x

a+b

Area\ of\ a\ rectangular\ pasture = 16\times 48\times (x^{7+4})Area of a rectangular pasture=16×48×(x

7+4

)

Area\ of\ a\ rectangular\ pasture = 768(x^{11})Area of a rectangular pasture=768(x

11

)

Therefore the area of the rectangular pasture is 768x^{11}\ unit^{2}.768x

11

unit

2

.

Answer:

C. 768x11

Step-by-step explanation:

Answer:

The time Jacob spent on the test represented by J = (m + 10) minutes

where m is the number of minutes spent by Mark on the test

Step-by-step explanation:

Here, we want to give an equation which represents the time taken for Jacob to finish his test compared to the time m which Mark spent on the test.

Since Jacob finished 10 minutes before Mark, it means Mark actually took longer on the test.

Now, we are told that Mark spent m minutes on the test, the time spent by Jacob on the test is thus (m + 10) minutes

Let the amount of time spent by Jacob be J minutes. This in relation to the amount of time spent by Mark will be ;

J = (m + 10) minutes

Answer:

3.4 × 10^6

Step-by-step explanation:

Answer:

9^3=729

9^2=81

9^1=9

9^0=1

The displacement of the particle from t = 0.0 s to t = 1.3 s is approximately 2.641 m, the velocity of the particle at t = 1.0 s is approximately 6.03 m/s, at t = 2.0 s is approximately 16.72 m/s, at t = 3.0 s is approximately 39.69 m/s, and at t = 4.0 s is approximately 76.68 m/s, the acceleration of the particle at t = 1.0 s is approximately 9.48 m/s², at t = 2.0 s is approximately 16.80 m/s², at t = 3.0 s is approximately 21.42 \(m/s^2\) and at t = 4.0 s is approximately 23.04 m/s².

(a) To find the displacement of the particle from t = 0.0 s to t = 1.3 s, we need to calculate the change in position.

The initial position at t = 0.0 s is\(x(0)=c(0)^3-b(0)^7=0.0\)

The final position at t = 1.3 s is \(x(1.3) = c(1.3)^3 - b(1.3)^7\).

Substituting the given values for c and b, we have:

\(x(1.3) = (2.1)(1.3)^3 - (1.6)(1.3)^7 = 2.641\) m.

Therefore, the displacement of the particle from t = 0.0 s to t = 1.3 s is approximately 2.641 meters.

(b) To find the velocity at t = 1.0 s, we need to calculate the derivative of the position function with respect to time and evaluate it at t = 1.0 s.

\(x(t) = ct^3- bt^7\)

Taking the derivative with respect to t, we get:

\(v(t) = 3ct^2 - 7bt^6\)

Substituting the given values for c and b, we have:

\(v(1.0) = 3(2.1)(1.0)^2 - 7(1.6)(1.0)^2 = 6.03 m/s\)

Therefore, the velocity of the particle at t = 1.0 s is approximately 6.03 m/s.

(c) Similarly, to find the velocity at t = 2.0 s:

\(v(2.0) = 3(2.1)(2.0)^2 - 7(1.6)(2.0)^6 = 16.72 m/s\)

Therefore, the velocity of the particle at t = 2.0 s is approximately 16.72 m/s.

(d) To find the velocity at t = 3.0 s:

\(v(3.0) = 3(2.1)(3.0)^2 - 7(1.6)(3.0)^6 = 39.69 m/s\)

Therefore, the velocity of the particle at t = 3.0 s is approximately 39.69 m/s.

(e) To find the velocity at t = 4.0 s:

v(4.0) = 3(2.1)(4.0)² - 7(1.6)(4.0)⁶ ≈ 76.68 m/s

Therefore, the velocity of the particle at t = 4.0 s is approximately 76.68 m/s.

(f) To find the acceleration at t = 1.0 s, we need to calculate the derivative of the velocity function with respect to time and evaluate it at t = 1.0 s.

\(a(t) = d(v(t))/dt = d^2x(t)/dt^2\)

Differentiating v(t) with respect to t, we get:

\(a(t) = 6ct - 42bt^5\)

Substituting the given values for c and b, we have:

\(a(1.0) = 6(2.1)(1.0) - 42(1.6)(1.0)^5= 9.48 m/s^2\)

Therefore, the acceleration of the particle at t = 1.0 s is approximately 9.48 m/s².

(g) Similarly, to find the acceleration at t = 2.0 s:

\(a(2.0) = 6(2.1)(2.0) - 42(1.6)(2.0)^5 16.80 m/s^2\)

Therefore, the acceleration of the particle at t = 2.0 s is approximately 16.80 m/s².

(h) To find the acceleration at t = 3.0 s:

\(a(3.0) = 6(2.1)(3.0) - 42(1.6)(3.0)^5 21.42 m/s^2\)

Therefore, the acceleration of the particle at t = 3.0 s is approximately 21.42 \(m/s^2\)

(i) To find the acceleration at t = 4.0 s:

\(a(4.0) = 6(2.1)(4.0) - 42(1.6)(4.0)^5=523.04 m/s^2\)

Therefore, the acceleration of the particle at t = 4.0 s is approximately 23.04 m/s².

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The correct question is:

The position of a particle moving along the x axis depends on the time according to the equation \(x(t) = ct^3- bt^7\), where x is in meters and t in seconds. Let c and b have numerical values 2.1 m/s 3 and 1.6 m/s 7, respectively. From t=0.0 s to t=1.3 s,(a) what is the displacement of the particle? Find its velocity at times (b) 1.0 s, (c) 2.0 s, (d) 3.0 s, and (e) 4.0 s. Find its acceleration at (f) 1.0 s, (g) 2.0 s, (h) 3.0 s, and (i) 4.0 s.

Answer: x=48

i know the answer bc i just did it

Y = (1/6)*e^5t  is  differential equation .

What exactly does differential equation mean?

An equation that connects one or more unknown functions and their derivatives is known as a differential equation in mathematics.  

                                     Applications typically use functions to describe physical quantities, derivatives to indicate the rates at which those quantities change, and differential equations to define a relationship between the two.

y′′−9y′+26y=e^(5t)

The characteristice equation of the differential equation is : r^2 -9r +26 =0

On solving we get the values of r=4.5 + 2.34i (z1) ,  4.5 - 2.4i(z2)--- (complex roots)

homogeneous solution is: yh = c1e^z1t + c2e^z2t

Plug  Y = Ae^5t in the ODE:

=   25Ae^5t -9*5Ae^5t +26Ae^5t =e^(5t)

25A -45A +26A =1 ;  6A = 1; A =1/6

Y = c1e^z1t + c2e^z2t  is a general solution but we wnata particular solution

So, simply Y = (1/6)*e^5t

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Answer:

Step-by-step explanation:

2tan θ+sinθcosθ=0

2 sin θ/cosθ +sin θcos θ=0

2sin θ+sin θcos²θ=0

sin θ(2+cos²θ)=0

sin θ=0=sin 0,sin π

θ=0,π

or

2+ cos²θ=0

cos² θ=-2

rejected  as

|cos θ|≤1

or cos²θ≤1

Hence θ=0,π

This would give us the coordinates for E as (1, 4).  Similarly, we can use the same method to find the coordinates for F, G, and H.  F would be (7,2), G would be (9,-5), and H would be (3,-6).

The coordinates of E can be found by taking the average of the x and y coordinates of points A and B.  This would give us the coordinates for E as (1, 4).  Similarly, we can use the same method to find the coordinates for F, G, and H.  F would be (7,2), G would be (9,-5), and H would be (3,-6).  To find the coordinates for these points, we use the formula \((x1 + x2)/2, (y1 + y2)/2\).  For example, to find the x coordinate for E, we would use (-2 + 4)/2 = 1, and for the y coordinate of E, we would use (3 + 5)/2 = 4.  We can then use this formula to find the coordinates for all of the midpoints.Step 1: Find coordinates of E, F, G, and H E: (1, 4) F: (7, 2) G: (9, - 5) H: (3, - 6) Step 2: Calculate the perimeter of the quadrilateral ABCD,Perimeter = |AB| + |BC| + |CD| + |DA = |(-2, 3) - (4, 5)| + |(4, 5) - (10, -1)| + |(10, -1) - (8, -9)| + |(8, -9) - (-2, 3)| = (6 + 14 + 18 + 10) = 48

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The value of the n for the given algebraic equation is=12.

The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added to a variable before being multiplied by it.

The given algebraic expression is

-4.3+1.2n=10.1

Add 4.3 on both sides

1.2n=10.1+4.3

1.2n=14.4

divide 1.2 into both sides

n = 14.4÷1.2

n = 12

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Answer:

It will be the 26th divided by 7

Answer:

a. x increased by three

Step-by-step explanation:

An equation has to have an equal sign.

The word "is" usually means "equals", and an equal sign is used for it.

Look at the choices:

a. x increased by three    ------->   no word is; expression; x + 3

b. Seven more than m is 15      ----> equation; m + 7 = 15

c. Three minus five is -2     ----> equation; 3 - 5 = -2

d. Twelve is half a number     ------> equation; 12 = 1/2 × n

The first choice is an expression, not an equation.

the last three choices are equations.

Answer: a. x increased by three

The range of function g would be c. (-∞, 1).

The requried range of the function is range = {y | y ≤ 1} or in interval notation, this can be written as range = (-∞, 1]. Option C is correct.

The range is the set of values that come out to an outcome for a certain mathematical operation.

Here,

First find the function g(x),
So,
g(x) = -2(10ˣ) + 1

To calculate the range of the function g(x) = -2(10ˣ) + 1, we need to determine the set of all possible output values that the function can produce.

Notice that the function f(x) is a linear function of the form y = mx + b, where m = -2 and b = 1. Since the exponent function, 10ˣ is always positive, the value of -2(10ˣ) is always negative, and adding 1 to a negative number results in a range of all real numbers less than or equal to 1.

Therefore, the range of the function is range = {y | y ≤ 1} or in interval notation, this can be written as range = (-∞, 1]

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Answer:

Here we can use the relationship:

Distance = time*speed.

When Jose walks, his speed is 4 mph.

Then if he walks for X hours, the distance that he will travel is:

D = 4mph*X

When Jose runs, his speed is 8mph.

Then if he runs for T hours, the distance that he will travel is:

D´ = 8mph*Y

And we know that he travels in total 20 miles, then we must have that:

D + D´= 20mi

This leads to:

4mph*X + 8mph*Y = 20mi

Where X is the time that he walked, and Y is the time that he runed.

Then the equation that represents the different amounts of times that Jose runs and walks  is:

4mph*X + 8mph*Y = 20mi

Where we can not really find the solutions for Y and X, because there is only one equation and two variables.

true - searching for a value in a binary search tree takes O(log n) time.

a binary search tree is a data structure where each node has at most two children, and the left child is always smaller than the parent while the right child is always larger. This structure allows for efficient searching, as we can compare the value we are searching for with the value of the current node and traverse either the left or right subtree accordingly. By doing so, we can eliminate half of the remaining nodes with each comparison, leading to a time complexity of O(log n).

searching for a value in a binary search tree takes O(log n) time, which is a relatively efficient algorithmic complexity. However, it's important to note that this assumes the tree is balanced and does not take into account worst-case scenarios where the tree may be heavily skewed.

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The three domains are the Archaea, the Bacteria, and the Eukary.

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The correct symbol used for a column alias containing spaces is C. " " (quotation marks).

In SQL, when we want to assign a column alias containing spaces, we enclose the alias within double quotation marks. This is done to differentiate the alias from other SQL keywords or to handle cases where the alias includes special characters, spaces, or is case-sensitive.

For example, consider the following SQL query:

SELECT column_name AS "Column Alias"

FROM table_name;

In this query, we are selecting a column named "column_name" from the table "table_name" and assigning it the alias "Column Alias" containing spaces. By enclosing the alias within double quotation marks, we indicate to the database that it should treat the entire string as a single identifier or alias.

Using other symbols such as '', ||, or // will not achieve the desired result of creating an alias with spaces. These symbols have different meanings in SQL.

'' (two single quotation marks) typically represents an empty string or a string literal in SQL.

|| (double vertical bars) is the concatenation operator in some SQL dialects, used to combine strings or values.

// (double forward slashes) is commonly used for comments in various programming languages and does not have any special meaning for column aliases in SQL.

Therefore, the correct symbol to use for a column alias containing spaces is C. " " (quotation marks).

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There are 12 combination ways to draw two cards of the same color from the shuffled deck, since there are 6 pairs of cards of the same color to choose from.

1. There are a total of 12 cards with 3 cards of each color (red, blue, yellow, and green).

2. To draw two cards of the same color, you must choose one of the six pairs of cards of the same color, which can be done in 6 ways.

3. Therefore, there are 6 x 1 = 6 possible ways to draw two cards of the same color from the shuffled deck.

If you draw three cards combination instead of two, there are still 6 ways to draw cards of the same color, since you must still choose one of the six pairs of cards of the same color. This can be done in 6 x 1 x 1 = 6 ways.

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Answer:

x = 10

Step-by-step explanation:

x = 10

Answer:

1

Step-by-step explanation:

listing the factors of both numbers

factors of 10 are 1, 2, ,5, 10

factors of 3 are 1, 3

the only common factor to both is 1

the greatest common factor is 1

Answer:

5x + 20 + (-20) = 5x

Step-by-step explanation:

Opposite of 20 is just -(20) which is -20.

5x + 20 + (-20) = 5x + 20 -20 = 5x

Answer:

13

Step-by-step explanation:

(n-2) +(n-1) +n =3n-3=36

n=(36+3)/3=13

Consecutive integers are 11,12 and 13

Answer: 13

Step-by-step explanation:

The easy way to do this is simply to divide 36 by three.  36/3 = 12.  Thus, 12 is the middle integer and the integers are 11,12,13, the largest of which is 13.

Answer:

0.4987

Step-by-step explanation:

What we must do is calculate the z value for each value and thus find what percentage each represents and the subtraction would be the percentage between those two values.

We have that z is equal to:

z = (x - m) / (sd)

x is the value to evaluate, m the mean, sd the standard deviation

So for 80 we have:

z = (80 - 80) / (3)

z = 0

and this value represents 0.5

for 89 we have:

z = (89 - 80) / (3)

z = 3

and this value represents 0.9987

we subtract:

0.9987 - 0.5 = 0.4987

Which means that it represents 49.87%

To complete the square for the quadratic equation x^2 + 7x - 27 = 0, we want to add a specific number to both sides of the equation in order to create a perfect square trinomial on the left side.

The coefficient of x in the equation is 7, and to complete the square, we need to take half of this coefficient and square it. Half of 7 is 7/2, and squaring it gives us (7/2)^2 = 49/4.

Therefore, the number that needs to be added to "complete the square" is 49/4.

Given:

The graph of cost of taxi with respect to number of miles.

To find:

The formula for C in terms of n.

Solution:

In the given graph x axis represents the number of miles (n) and y-axis represents the cost of taxi (C).

From the given graph it is clear that, the line passes through the points (0,3) and (5,6). So, the equation of line is

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

\(y-3=\dfrac{6-3}{5-0}(x-0)\)

\(y-3=\dfrac{3}{5}(x)\)

Adding 3 on both sides, we get

\(y=\dfrac{3}{5}x+3\)

Putting y=C and x=n, we get

\(C=\dfrac{3}{5}n+3\)

Therefore, the required formula is \(C=\dfrac{3}{5}n+3\).

Answer:

c=3/5n+3

Step-by-step explanation:

Answer:

y=4x-1 i think

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given:

Slope-intercept form:

So the equation is:

Answer:

7x+5y=-3

Step-by-step explanation:

Answer:

Hello,

answer B

Step-by-step explanation:

Vertex is (-3,-1)

The equation of the parabola should be:

y=k*(x+3)²-1

(0,8) is a point of the parabola:

8=k*(0+3)²-1

8+1=9k

k=1

Equation is y=(x+3)²-1

Answer B