2. Using the ruler below, construct a triangle that has side lengths of 3 cm, 4 cm, and 5 cm.
triangle does this appear to be? Verify by using your protractor to measure angles.
What type of

Answer:

a

Step-by-step explanation:

Answer:

\(BD = 12\ cm\)

Step-by-step explanation:

Given

Shape: Rectangle

Diagonals: AC and BD

\(AC = 12\ cm\)

Required

Determine BD

From the question, we understand that the shape is a rectangle and its diagonals are AC and BD

Every rectangle has 2 diagonals, both of which are equal.

This implies that:

\(BD = AC\)

Recall that:

\(AC = 12\ cm\)

Hence,

\(BD = 12\ cm\)

The runner slides a distance of approximately 0.255 meters or 25.5 centimeters, and the mechanical energy lost due to friction is 140.29 J.

What is the coefficient?

A coefficient is a number multiplied by a variable. Examples of coefficients: In the term 14 c 14c 14c, the coefficient is 14. In the term g, the coefficient is 1.

A) The mechanical energy lost due to friction can be calculated as follows:

Initial kinetic energy of the runner: KE = 0.5 * m * v² = 0.5 * 80 kg * (4.7 m/s)² = 140.29 J

The force of friction acting on the runner is given by:

\(friction_{force} = friction_{coefficient} * normal_{force}\)

where,

\(friction_{coefficient} = 0.70\)

\(and normal_{force} = m * g (g = 9.8 m/s^{2} )\)

The normal force is given by:

\(normal_{force} = m * g = 80 kg * 9.8 m/s^{2} = 784 N\)

Therefore, the force of friction acting on the runner is: \(friction_{force} = 0.70 * 784 N = 548.8 N\)

The work done by friction is given by:

\(W = friction_{force} * distance\)

Since the speed of the runner is reduced to zero, the work done by friction is equal to the change in kinetic energy:

\(W = KE_{final} - KE_{initial}\)

= 0 - 140.29 J = -140.29 J

So, the mechanical energy lost due to friction is 140.29 J.

B) The distance the runner slides can be calculated using the work-energy theorem, which states that the work done on an object is equal to its change in kinetic energy.

The work done by friction is given by: W = friction_force * distance

Since the friction force is constant, the work done by friction is equal to the change in kinetic energy:

\(W = KE_{final} - KE_{initial}\)

= 0 - 140.29 J = -140.29 J

Rearranging this equation and substituting in the known values, we get:

\(distance = -W / friction_{force}\)

= -140.29 J / 548.8 N = 0.255 m or 25.5 cm

Hence, the runner slides a distance of approximately 0.255 meters or 25.5 centimeters, and the mechanical energy lost due to friction is 140.29 J.

To learn more about the coefficient visit,

https://brainly.com/question/26250153

#SPJ4

Using graphical method to find the solution to the system of linear equation, x = -7/2, y = 1/2

The system of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1.

The equations given are

Using graphical method, the solution to the system of linear equation is the point of intersection between the two lines.

Using a graphing calculator;

The point of intersection (x, y) are ( - 3.54, 0.494) which can be estimated as x = -7/2, y = 1/2

Learn more on system of linear equation here;

https://brainly.com/question/13729904

#SPJ1

Answer:

Step-by-step explanation:

https://brainly.com/question/28299043

I answered it here.

Answer:

x^7+x^6+x^5-x^4-x^3-x^2-x+1

Step-by-step explanation:

Answer:

37

Step-by-step explanation:

x=-4

=2(5-(-4)2+1

=2(5+4)2+1

=2(9)2+1

=18(2)+1

=36+1

=37

Answer:

y=43, m=0, b=43

Step-by-step explanation:

Answer:

37.5%

Step-by-step explanation:

Calculation for the probability that washing dishes tonight will take me between 10 and 13 minutes

Probability of washing dishes=(13minutes-10minutes)/(15minutes-7minutes)

Probability of washing dishes=3 minutes/8 minutes

Probability of washing dishes=0.375*100

Probability of washing dishes=37.5%

Therefore the probability that washing dishes tonight will take me between 10 and 13 minutes is 37.5%

old version of which the answer may be

Answer:

The answer is

x is 0

y is 2

Step-by-step explanation:

2x-y=-2

-2x-4y=-8

 -5y=-10

y=2

2x-2=-2

2x=0

x=0

Answer:

The length of the lake is 1.8 miles.

Step-by-step explanation:

These are similar triangles.

When the matrices A and B commute, or when they fulfill AB=BA, this is a significant exception.

A matrix is a rectangular array or table of numbers, symbols, or formulae used to represent mathematical objects or qualities of such things. It is often arranged in rows and columns. For instance, a matrix contains two rows and three columns. a group of integers organized in a rectangular array in rows and columns. Matrix elements or entries refer to numbers. In several disciplines of engineering, physics, economics, statistics, and mathematics, matrices have a wide range of applications.

The eigenvalues and eigenvectors of the sum of two matrices are typically not the same as the sums of the eigenvalues and eigenvectors of the individual matrices. In actuality, there is no way to separate the eigenvalues of A and B from one another.

When a vector v is an eigenvector of both A and B, it is also an eigenvector of A+B, with an eigenvalue equal to the sum of its eigenvalues for A and B, respectively. There is, however, no reason to anticipate that two matrices will share an eigenvector in general. There is no method to create an eigenvector of A+B from two random eigenvectors of A and B alone.

When the matrices A and B commute, or when they fulfill AB=BA, this is a significant exception. In this situation, their invariant spaces coincide, and if both of them are diagonalizable, they are concurrently diagonalizable, which means that their eigenvectors do as well. As was already noted, in this specific instance, the eigenvectors of A+B are likewise the same.

To know more about matrix visit:
https://brainly.com/question/29132693

#SPJ4

Answer:

The triangles are similar.

Explanation:

Similar triangles have 3 pairs of congruent angles. In this diagram, we can see that the triangles WXP and WYZ share angle W, which is congruent to itself; therefore, they have at least 1 pair of congruent angles. We are given that angle X is congruent to angle Y, so that is a second pair of congruent angles. Finally, we know that angle P is congruent to angle Z because if two pairs of corresponding angles are congruent, then the third pair must also be congruent because the measures of the interior angles of both triangles have to add to 180°.

The statements that are true about the function are

A. The function is concave down for the interval (-∞, 3)

B. The function has a maximum value at (4, 0)

F. The function is decreasing on the interval (3, 4)

G. The function is decreasing on the interval (-∞, 1)

So, the statements that are true about the function are

A. The function is concave down for the interval (-∞, 3)

B. The function has a maximum value at (4, 0)

F. The function is decreasing on the interval (3, 4)

G. The function is decreasing on the interval (-∞, 1)

Learn more about functions here:

https://brainly.com/question/10439235

#SPJ1

Answer:

Not a triangle

Step-by-step explanation:

Not a triangle.

The sum of the lengths of any two sides of a triangle has to be greater than the length of the third side.

40 + 60 is not greater than 100

therefor it is not a triangle

y = 1/4x + 1 is parallel to line a

-4x + y = -8 is neither parallel nor perpendicular to line a

4x + y = -3 is perpendicular to line a

From the question, we are to determine how the given equations compare to line a.

From the given information,

Line a is -x + 4y = 32

First, we will determine the slope of line a

To do this, we will compare the equation to the slope-intercept form of a line

The slope-intercept form of a line is

y = mx + b
Where m is the slope

and b is the y-intercept

Writing -x + 4y = 32 in the slope-intercept form

-x + 4y = 32

4y = x + 32

Divide through by

y = 1/4 x + 8

By comparison, the slope of line a is 1/4

NOTE: If two lines are parallel, their slopes will be equal

and

If two lines are perpendicular, their slopes will be the negative reciprocal of each other

Now, we will determine the slopes of each of the lines

For y = 1/4x + 1

By comparing with the slope-intercept form of a line, y = mx + b

The slope of the line is 1/4

Thus, the line is parallel to line a

For -4x+y=-8

Rewrite in the slope-intercept form of a line

-4x + y = -8

y = 4x - 8

By comparing with the slope-intercept form of a line, y = mx + b

The slope of the line is 4

4 is not equal to 1/4 and 4 is not the negative reciprocal of 1/4.

Thus, the line is neither parallel nor perpendicular to line a.

For 4x+y=-3

Rewrite in the slope-intercept form of a line

4x + y = -3

y = -4x - 3

By comparing with the slope-intercept of a line, y = mx + b

The slope of the line is -4

-4 is the negative reciprocal of 1/4.

Thus, the line is perpendicular to line a.

Learn more on Parallel and Perpendicular lines here: https://brainly.com/question/7396586

#SPJ1

Answer:

Exact Form:

32 /3

Decimal Form:

10. 6

Mixed Number Form:

10

2 /3

Step-by-step explanation:

Answer: there you go :)

Car 1 consumes 30 gallons of gas.

Car 2 consumes 20 gallons of gas.

Step-by-step explanation:

Let x = gallons consumed by car 1

Let y = gallons consumed by car 2

We set up our equations:

35x+40y = 1850        eq1

x+y = 50                   eq2

Substituting eq 2 into eq 1,

35x+40(50-x) = 1850

35x+2000-40x = 1850

-5x+2000 = 1850

-5x = -150

  x = 30

Substitute value of x into eq 2.

x+y = 50

30+y = 50

     y = 20

Car 1 consumes 30 gallons of gas.

Car 2 consumes 20 gallons of gas.

Answer:

200 sheets

Step-by-step explanation:

Divide 5,000 by 25 to get 200 sheets of paper per box.

Answer:

750 pieces of paper

Step-by-step explanation:

can't

m∠2 = 68°, m∠3 = 112°, m∠4 = 112°, m∠5 = m∠7  = m∠8 = 68°

and m∠6 = 112°.

We know when a transversal intersects two parallel lines at two distinct points,

Two pairs of interior and alternate angles are formed such that the measure of interior angles are same and the measure of alternate angles is also the same.

We also know that sum of all the interior angles in a triangle equals 180°.

Given, m∠1 = 90°.

∴ 90° + 22° + ∠2 = 180°.

m∠2 = 68°.

We know m∠2 + m∠3 = 180°. (linear pair angles)

∴ 68° + m∠3 = 180°.

m∠3 = 112°.

So, m∠4 = 112° (pair of alternate interior angles).

m∠5 = 180° - m∠4.

m∠5 = 68°.

m∠7 = m∠5 and m∠8 = m∠7 = 68° (pair of alternate interior angles)

m∠6 = 180° - m∠7 as it is an isosceles triangle = 180° - 68° = 112°

learn more about transversal here :

https://brainly.com/question/17432060

#SPJ1

The volume of the composite figure is 6,330.24 in^3

We know that the volume of half a sphere of radius R is:

V = (2/3)*pi*R^3

Here we know that pi = 3.14 and R = 12 inches, then the volume is:

V = (2/3)*3.14*(12 in)^3 = 3,617.28 in^3

And the volume of a cone of height H and radius R is:

v = (1/3)*pi*R^2*H

So here the volume is:

v = (1/3)*3.14*(12in)^2*18in = 2,712.96 in^3

Then the total volume is:

3,617.28 in^3 +  2,712.96 in^3 = 6,330.24 in^3

Learn more about volume at:

https://brainly.com/question/1972490

#SPJ1

The solution by substituting 15 for b in the Original equation. The answer is true.

The steps needed to solve the equation b + 6 = 21 are:

Subtract 6 from both sides of the equation: b + 6 - 6 = 21 - 6, which simplifies to b = 15.

Check the solution by substituting 15 for b in the original equation: 15 + 6 = 21, which is true.

Therefore, the correct steps to solve the equation are:

Subtract 6 from both sides of the equation. The answer is b = 15

the solution by substituting 15 for b in the original equation. The answer is true.

To know more about Original .

https://brainly.com/question/27960093

#SPJ11

9514 1404 393

Answer:

  5.607

Step-by-step explanation:

5 and six hundred seven thousandths = 5 607/1000 = 5.607

Answer:

5.607

Step-by-step explanation:

The equations of the composite functions are (h o h)(x) = (x² + 3)² + 3 and (f o f)(x) = x

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

h(x) = x² + 3

f(x) = 3/4x

From the above, we have

(h o h)(x) = h(h(x))

So, we have

(h o h)(x) = (x² + 3)² + 3

Also, we have

(f o f)(x) = 3/[4(3/4x)]

Evaluate

(f o f)(x) = x

Hence, the composite functions are (h o h)(x) = (x² + 3)² + 3 and (f o f)(x) = x

Read more about composite functions at

brainly.com/question/33401202

#SPJ1

Answer:

k=21

Step-by-step explanation:

Find the slope of MN which is 1/5 (use the slope formula)

Use the slope formula for AB using k as y_2

Substitute and you get k=21

21-2.25/-2.25-1.5=-5

The lines are perpendicular because the slopes are the negative reciprocal of one another.

Answer:

Step-by-step explanation:

The slope of the straight line passing through the two given points is undefined which means the line is parallel to the y-axis.

Let us consider the two points A(x₁,y₁) and B(x₂,y₂) be the two points (7,-6) and (6,-6) on the cartesian coordinates.

Let the slope of the line joining A (7,-6)  and B(6,-6)  be m.

We know that the slope of a line is given by:

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

Slope of the line

= (6-7) / (-6+6)

= -1 / 0

= undefined

Since the slope is undefined we can say that the straight line is parallel to the y axis.

we know that tan 90° = ∞

So any line parallel to this line will have the same slope as the y axis.

Hence the slope of the given line is undefined or infinity.

To learn more about slope visit:

https://brainly.com/question/11559942

#SPJ1

a) To find the average life of the ten batteries, we need to calculate the mean, which is the sum of all the values divided by the number of values.Sum of all values = 10.8 + 10.6 + 11.4 + 8.9 + 10.1 + 10.6 + 9.9 + 12.6 + 10.5 + 11.9 = 106.2

Number of values = 10

Average life = Sum of all values / Number of values = 106.3 / 10 ≈ 10.63

Therefore, the average life of the ten batteries, rounded to the nearest tenth of an hour, is approximately 10.6 hours.

b) Comparing the two advertisements:

i) The first advertisement claims that Atlas batteries are guaranteed to last 10 hours. This means that all Atlas batteries are expected to last at least 10 hours. However, based on the data provided, we can see that the average life of the batteries is approximately 10.6 hours, which is higher than the guaranteed 10-hour minimum

ii) The second advertisement claims that Atlas batteries have an average life of over 10 hours. This statement aligns with the data we have, as the average life of the batteries is indeed over 10 hours.

Based on the information provided, the second advertisement claiming that Atlas batteries have an average life of over 10 hours is more accurate, as the average life calculated from the given data is 10.6 hours.

In summary, the average life of the ten batteries is approximately 10.6 hours, and the second advertisement stating an average life of over 10 hours is more accurate based on the data provided.

For more such questions on average.

https://brainly.com/question/20118982

#SPJ8