How much work is done if an object travels 55m due to a force of 20N?​

Answer:

i) a = 2, b = - 3, c =-6

Step-by-step explanation:

4x² - 12x + 3

4x² - 6x - 6x + 9 - 6

(2x - 3)(2x - 3) - 6

(2x - 3)² - 6

(2x + (- 3) )² - 6

In form of (ax + b)² - 6

a = 2, b = - 3, c =-6

In triangle ΔGHI, with ∠I measuring 90° and ∠G measuring 82°, and GH measuring 3.4 feet, the length of HI is 24.2 feet.

To find the length of HI, we can use the trigonometric function tangent (tan). In a right triangle, the tangent of an angle is equal to the ratio of the length of the side opposite the angle to the length of the side adjacent to it. In this case, the side opposite ∠G is HI, and the side adjacent to ∠G is GH. Therefore, we can set up the equation: tan(82°) = HI / GH.

Rearranging the equation to solve for HI, we have: HI = GH * tan(82°). Plugging in the given values, we get: HI = 3.4 * tan(82°). Using a calculator, we find that tan(82°) is approximately 7.115. Multiplying 3.4 by 7.115, we find that HI is approximately 24.161 feet. Rounded to the nearest tenth of a foot, the length of HI is 24.2 feet.

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The sum of cubes identity states that a^3 + b^3 = (a+b)(a^2 - ab + b^2). To find the factors of 8x^6 + 27y^3, we can apply this identity to the expression by identifying a and b:

What is the identity of the sum of cubes?

What Does the Algebraic Sum of Cubes Formula Mean? One of the key algebraic identities is the sum of cubes formula. Its symbol is written as a3 + b3 and is interpreted as a cube plus a cube. A3 + b3 = (a + b) (a2 - ab + b2) is how the sum of cubes formula (a3 + b3) is written.

8x^6 + 27y^3 = (2x^2)^3 + (3y)^3

We can then apply the identity to get:

(2x^2)^3 + (3y)^3 = (2x^2 + 3y)((2x^2)^2 - 2x^2*3y + (3y)^2)

This gives us the factors of 8x^6 + 27y^3 as (2x^2 + 3y)(4x^4 - 6x^2y^2 + 9y^2).

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The least common multiple (LCM) of the expressions is 24x³

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

8x²

12x³

Factor each expression

So, we have

8x² = 2 * 2 * 2 * x²

12x³ = 2 * 2 * 3 * x³

Multiply all factors

So, we have

LCM = 2 * 2 * 2 * 3 * x³

Evaluate

LCM = 24x³

Hence, the LCM is 24x³

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Answer:

225 adult tickets

530 student tickets

Step-by-step explanation:

The least-squares error in the least-squares solution of ax = b is given by the equation:

\(||b - ax||^2 = (b - ax)^T(b - ax) = b^Tb - 2a^Tbx + a^Tax\)

The least-squares solution is the value of x that minimizes this error. This occurs when the derivative of the error with respect to x is equal to zero, and the second derivative is positive.

To find the least-squares solution, we take the derivative with respect to x and set it to zero:

\(-2a^T(b - ax) = 0\\a^Tb = a^Tax\)

This gives us the normal equation, which is the equation that x must satisfy in order to minimize the error. The solution of this equation is:

\(x = (a^Ta)^-1a^Tb\)

This is the least-squares solution of the equation ax = b, and it is the value of x that minimizes the least-squares error. The least-squares error is given by the equation:

\(||b - ax||^2 = b^Tb - 2a^Tbx + a^Tax = b^Tb - a^T(a(a^Ta)^-1a^Tb) = b^Tb - a^T(a^Tb)\)

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Answer:

Step-by-step explanation:

Answer:  3t - 6

Reasoning:

We multiply the outer term 3 by each term inside, which is t and -2

3 times t = 3*t = 3t

3 times -2 = 3*(-2) = -6

Add up those results to get 3t+(-6) = 3t-6

Therefore, 3(t-2) = 3t-6

This is an example of the distribution property.

Answer:

18

Step-by-step explanation:

3(t-2)

3x2=6

(t-6)

^3^

3(6)

3x6= 18

Answer: 72.97 Minutes

Step-by-step explanation: We have two cars, A and B, traveling along a straight road. Car A is moving at a constant speed of 77.0 km/h, while car B is moving at a constant speed of 114 km/h. At the starting point (t=0), car B is 45.0 km behind car A.

To figure out how long it takes for car B to catch up and overtake car A, we need to consider their relative speeds. The relative speed is the difference between the speed of car B and the speed of car A.

Relative speed = Speed of car B - Speed of car A

Relative speed = 114 km/h - 77.0 km/h

Relative speed = 37.0 km/h

So, car B is moving 37.0 km/h faster than car A. Now, we need to determine the time it takes for car B to cover the initial distance between them, which is 45.0 km.

To calculate time, we use the formula: Time = Distance / Speed. In this case, the distance is 45.0 km, and the speed is the relative speed of 37.0 km/h.

Time = 45.0 km / 37.0 km/h ≈ 1.2162 hours

Now, let's convert the time to minutes by multiplying it by 60 (since there are 60 minutes in an hour).

Time = 1.2162 hours * 60 minutes/hour ≈ 72.97 minutes

Therefore, it takes approximately 1.2162 hours or 72.97 minutes for car B to catch up and overtake car A.

Hope this helps!

F is continuous at every point x₀ ∈ I. Thus, f is continuous on an interval I.

Regarding the converse, the statement "if f is continuous on an interval I, then it is uniformly continuous on I" is not always true. There exist functions that are continuous on a closed interval but not uniformly continuous on that interval. A classic example is the function f(x) = x² on the interval [0, ∞). This function is continuous on the interval but not uniformly continuous.

To prove that if a function f is uniformly continuous on interval I, then it is continuous on I, we need to show that for any ε > 0, there exists a δ > 0 such that for any x, y ∈ I, if |x - y| < δ, then |f(x) - f(y)| < ε.

Since f is uniformly continuous on I, for the given ε, there exists a δ > 0 such that for any x, y ∈ I, if |x - y| < δ, then |f(x) - f(y)| < ε.

Now, let's consider an arbitrary point x₀ ∈ I and let ε > 0 be given. Since f is uniformly continuous, there exists a δ > 0 such that for any x, y ∈ I, if |x - y| < δ, then |f(x) - f(y)| < ε.

Now, choose δ' = δ/2. For any y ∈ I such that |x₀ - y| < δ', we have |f(x₀) - f(y)| < ε.

Therefore, for any x₀ ∈ I and ε > 0, we can find a δ' > 0 such that for any y ∈ I, if |x₀ - y| < δ', then |f(x₀) - f(y)| < ε.

This shows that f is continuous at every point x₀ ∈ I. Thus, f is continuous on interval I.

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I believe the answer is football.

Answer:

it is C i just got a 100 on the unit test review

Step-by-step explanation:

The required line representing the equation part of the constraint is go through (0, 4) and (7,0).

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

The line representing the equation 7x1 + 4x2 = 28 is a boundary line that separates the feasible solutions from the infeasible solutions in a linear programming problem.

The line passes through two points, which can be determined by substituting the x1 and x2 values into the equation. By substituting the values (4,0) and (7,0) into the equation, we can see that both points satisfy the constraint.

This means that any point on the line also satisfies the constraint, and any point above or to the right of the line would be infeasible as they would not meet the requirement of the constraint.

Understanding the position and shape of the constraint lines is important in solving linear programming problems and finding the optimal solution.

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The solution of the expression after evaluation is 24.

The solution of the expression is calculated by simplifying the expression as follows;

The given expression; [ 28 - (-18)]/2  - [15-(-2)(-6)/-3]

The expression is simplified as follows;

[ 28 - (-18)]/2 = (28 + 18)/2 = (46/2) = 23

[15-(-2)(-6)/-3] = (15 - 12)/(-3) = (3)/(-3) = -1

The final solution of the expression is calculated as follows;

[ 28 - (-18)]/2  - [15-(-2)(-6)/-3] = 23 - (-1)

= 23 + 1

= 24

Thus, the final solution of the expression is determined by applying the rule of BODMAS.

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Required standard form for given circle is \((x-2)^{2}+(y+9)^{2}=4\)

Standard form of circle is expressed as\((x-h)^{2}+(y-k)^2=r^{2}\) ,where h,k are the coordinate of the center of circle and r is radius.

Center (h, k) = (2, -9)

radius = 2 units

Using standard form of equation,

\((x-h)^{2}+(y-k)^2=r^{2}\)

Putting the given values,we get

\((x-2)^{2}+(y-(-9))^{2}=2^{2}\)

⇒ \((x-2)^{2}+(y+9)^{2}=4\)

Hence, the standard form of equation of circle is \((x-2)^{2}+(y+9)^{2}=4\) .

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Answer:

y = \(\frac{1}{5}\) x - 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ = x- intercept (10, 0) and (x₂, y₂ ) = y- intercept (0, - 2)

m = \(\frac{-2-0}{0-10}\) = \(\frac{-2}{-10}\) = \(\frac{1}{5}\)

The y- intercept c = - 2

y = \(\frac{1}{5}\) x - 2 ← equation of line

Answer:

15

Step-by-step explanation:

10+10-5=15

Answer:

It is 15

Step-by-step explanation:

Hope this helped have an amazing day!

Answer:

0.4

0.3

0.04

0.2

0.06

Step-by-step explanation:

Hope this helps :)

Answer:

58- 0.4

42- 0.3

6- 0

24- 0.2

8- 0.1

Hope this helps plz mark brainliest :)

Step-by-step explanation:

Step-by-step explanation:

$803.98 before tax

x 8.75%

_______

$ 70.35 tax to pay

$803.98 before tax

+ 70.35 tax to pay

_______

$874.33 to pay for bicycle

Answer:

1) 0.12

2) 52.5

3) 185.32

4) 77.85

5) 313.75

6) 1.536

7) 0.0167

8) 64

9) 21

10) 282.4

11) 136.64

12) 88.56

Step-by-step explanation:

Answer:

3xyz

Step-by-step explanation:

The required sum = 7xyz+(−5xyz)+9xyz+(−8xyz)

=7xyz–5xyz+9xyz–8xyz

=(7–5+9–8)xyz

=(16–13)xyz

=3xyz

In the given case, The sum of the given expressions is \(-3x2y2z2 + 19xyz2 + 10xyz - 10xyz2.\)

To add the given expressions, we combine the like terms and simplify.

To add the given expressions, we combine the like terms.

Like terms are the ones that have the same variables raised to the same powers.

In the first expression,  we have  \(-3x2y2z2, 12xyz2, and 7xyz.\)

In the second expression, we have 10xyz and -10xyz2.

Combining the like terms, we get \(-3x2y2z2 + (12 + 7)xyz2 + 10xyz - 10xyz2.\)

Simplifying further, we have \(-3x2y2z2 + 19xyz2 + 10xyz - 10xyz2.\)

So, the sum of the given expressions is \(-3x2y2z2 + 19xyz2 + 10xyz - 10xyz2.\)

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The area of the trapezoid is 30x + 42. Option C

The formula for calculating the area of a trapezoid is expressed as;

A = 1/2h(b1+b2)

Such that the parameters are enumerated as;

Now, substitute the values, we get;

Area = 1/2 × 12(2x + 3 + 3x + 4)

collect the like terms, we have;

Area = 6(5x + 7)

Expand the bracket, we get;

Area = 30x + 42

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The probability of scoring exactly four out of the given six shots is 0.311, calculated using the concept of binomial distribution in probability theory.

What is a Binomial Distribution?

Binomial Distribution in probability theory is defined as getting x number of successes on repetition of trial n times, the formula for binomial distribution is C(n,r) × (p)x × (q)n - r, where p denotes the probability of success and q denotes the probability of failure.

Calculation of the probability of scoring exactly four shots out of six

Let p denote the probability of success and q denote the probability of failure, which is equal to 1 - p.

Using Binomial Distribution, we get,

P(x = r) = C(n,x) × (p)x × (q)n - x

Taking r = 4,

P(x = 4) = C(6,4) × (0.6)4 × (0.4)2

= 6! / (4! 2!) × (0.6)4 × 0.16

= 0.31104

~ 0.311

Hence, the required probability using binomial distribution is 0.311.

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Answer:

Step-by-step explanation:

A, because more debt would build up for your credit card if you added money to a savings account since you would have to wait a whole year to get interest back. And it wouldn't be B because it simply would not be worth it to invest in stocks while in debt. Also, I just took the test and got it right!

Answer i cant read it..

Step-by-step explanation:

Answer:

y = -10/3x + 5

Step-by-step explanation:

Hi there!

We are given that a line has a slope of -10/3, and a y intercept of 5

We want to write the equation of this same line in slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept

As we are already given the slope and y intercept, we can simply substitute these values into the format for slope-intercept form to find the equation of the line!

Starting with the slope, substitute -10/3 as m in y=mx+b

y = -10/3x + b

Now for the y intercept, substitute 5 as b in the equation

y = -10/3x + 5

Hope this helps!

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