mark has a board that is 12 feet long he cuts the board into 8 peices that are the same lenght. how long is each peice

Answer:

  (3, -6)

Step-by-step explanation:

The orthocenter is the point of intersection of the altitudes of the triangle. That is, each altitude goes through the orthocenter. Hence, the line from any given vertex through the orthocenter is perpendicular to the opposite side.

The attached figure shows the given points labeled A and B. Point A lies on the x-axis, as does the orthocenter, so the side opposite will be a vertical line (perpendicular to the x-axis).

The remaining side of the triangle will be perpendicular to the line from B through the origin. The line through B has slope 4/3, so the line containing side AC will have slope -3/4 and will go through point A. Its point-slope equation will be ...

  y -0 = -3/4(x +5)

We already know the x-coordinate of vertex C is the same as that of vertex B, so is x=3. Using this in the equation for side AC, we find the y-coordinate to be ...

  y = -3/4(3 +5) = -6

The coordinates of point C, the third vertex, are (3, -6).

_____

Additional comments

The slope of a line is given by ...

  m = (y2 -y1)/(x2 -x1)

When (x1, y1) = (0, 0), this reduces to ...

  m = y2/x2 . . . . . . the relation we used for the slope of line OB

__

The slope of a perpendicular line is the opposite reciprocal of the slope of a line. The line perpendicular to the one with slope 4/3 will be -1/(4/3) = -3/4.

__

The point-slope form of the equation of a line is ...

  y -k = m(x -h) . . . . . line with slope m through point (h, k)

Answer:

The answer is 4.2,

Hope that helped. x

Step-by-step explanation:

3 x 7 (3*7) = 21

21 divided by 5 = 4.2.

Answer:

4.2

Step-by-step explanation:

Using PEMDAS,

We know that to solve (3*7) divided by 5, we will need to solve what is in the parenthesis.

So, we need to figure out what is 7*3, which is 21.

This is what we have right now:

21 divided by 5

The next step is dividing,

In the end, the answer is 4.2, hope this helped!

Answer:

-1.4 m/sec  [backwards]

Step-by-step explanation:

The energy of the cannon moving should be equal to the energy contained in the cannonball.  Kinetic energy for each is calculated using KE = (1/2)m[tex]v^{2}[/tex]

Let x be the speed of the cannon.

Cannonball:  

KE = (1/2)m[tex]v^{2}[/tex]

KE = (1/2)(1kg)(45 m/sec)^2

KE = 22.5   kg*m/sec^2

Cannon:      [The cannon will have the reverse energy]

KE = - (1/2)m[tex]v^{2}[/tex]

22.5 kg*m/sec^2 = -(1/2)(67 kg)x^2

22.5 kg*m/sec^2 = -(33.5 kg)x^2

x^2 = (33.5 kg)/(22.5 kg*m/sec^2)

x^2 = -1.4 m/sec  [backwards]

ITS SQAURE 6

6 SQAURE OFTHE 6

Using the t-distribution, it is found that:

a)

The null hypothesis is: [tex]H_0: \mu \geq 60[/tex]

The alternative hypothesis is: [tex]H_1: \mu < 60[/tex]

b) t = -1.47

c) 0.0878.

d) Do not reject the null hypothesis.

e) Not enough evidence to conclude that the average maximum amount of time people can hold their breath is less than 60 seconds.

Item a:

At the null hypothesis, it is tested if the mean is not less than 60 seconds, that is:

[tex]H_0: \mu \geq 60[/tex]

At the alternative hypothesis, it is tested if the mean is less than 60 seconds, that is:

[tex]H_1: \mu < 60[/tex]

Item b:

We can find the standard deviation for the sample, hence, the t-distribution is used to solve this question.

The test statistic is given by:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

The parameters are:

With the help of a calculator to find the sample mean and the standard deviation, the values of the parameters are:

[tex]\overline{x} = 55.8, \mu = 60, s = 9.04, n = 10[/tex]

Hence, the value of the test statistic is:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{55.8 - 60}{\frac{9.04}{\sqrt{10}}}[/tex]

[tex]t = -1.47[/tex]

Item c:

The p-value is found using a left-tailed test, as we are testing if the mean is less than a value, with 10 - 1 = 9 df and t = -1.47.

Item d:

The p-value is of 0.0878 > 0.05, hence, we do not reject the null hypothesis.

Item e:

Since the null hypothesis is not rejected, there is not enough evidence to conclude that the average maximum amount of time people can hold their breath is less than 60 seconds.

A similar problem is given at brainly.com/question/24826023

Answer:

9

Step-by-step explanation:

5 x 3 = 15  and 5 x H = 45

45 / 5 = 9

Answer:

Step-by-step explanation:

The net income reported on the income statement for the current year was $135,500 depreciation recorded on store equipment for the year amounted to $22,400 balances of the current asset and current libaility accounts at the beginning and end of the year are as follows

Answer:

Image below!

Step-by-step explanation:

Plotting [tex]\underline{y=2x+3}[/tex]

Step 1: determine the y-intercept

[tex](0,3)[/tex]

Step 2: Move 2 units up, and 1 unit left (keep repeating this process until you have reached the limit of the graph)

Step 3: Go to the other side of the graph of the first point (y-intercept)

When you've completed this process, it should look like this:

Answer:

First Option, log 3x is equivalent to the expression shown

The measure for angle W is 80 degree.

A unrestricted polygon or figure with four sides, four corners, and four angles is called a trapezium. Each brace of a trapezium's opposing sides is resemblant to the other.

Similar to other quadrilaterals, the trapezium's four angles add up to 360°. Two of the sides of a trapezium are parallel, and the other two are not. Regular trapezium diagonals cut each other in half.

Given:

We have angles <X= 100, <Y = 130 and <Z= 66.

As, we know that in Trapezium the sum of adjacent angle is 180.

So, <X + <W = 180

100 + <W =180

<W= 180- 100

<W = 80 degree.

Learn more about Trapezium here:

https://brainly.com/question/22607187

#SPJ2

The exact values of the remaining five trigonometric functions of theta are

Since tanθ = -√3.

The remaining five trigonometric functions of theta are sinθ, cosecθ, cosθ, secθ and cotθ.

The next trigonometric function of θ is cotθ.

cotθ = 1/tanθ

= 1/-√3

= -1/√3.

Also, tan²θ + 1 = sec²θ

Substituting tanθ = -√3 into the equation, we have

(-√3)² + 1 = sec²θ

3 + 1 = sec²θ

sec²θ = 4

secθ = ±√4

secθ = ±2

Since θ is in the quadrant II,

secθ = -2

Also, cosθ = 1/secθ

= 1/-2

= -1/2

Also, cot²θ + 1 = cosec²θ

Substituting cotθ = -1/√3 into the equation, we have

(-1/√3)² + 1 = cosec²θ

1/3 + 1 = cosec²θ

cosec²θ = 4/3

cosecθ = ±√(4/3)

cosecθ = ±2/√3

Since θ is in the quadrant II,

cosecθ = +2/√3

Also, sinθ = 1/cosecθ

= 1/2/√3

= √3/2

So, the exact values of the remaining five trigonometric functions of theta are

Learn more about trigonometric functions here:

https://brainly.com/question/4515552

Answer:

84

Step-by-step explanation:

7 Sizes * 3 Lengths * 4 Colors = 84

Answer:

kanye west

Step-by-step explanation:

Answer:

Step-by-step explanation:

65%

Step-by-step explanation:

Given: Full capacity= 200000 litres

          Amount of fuel used during flight= 130000 litres

Now, finding percentage of fuel used on the flight.

∴ Percentage of fuel used=  

Solving it, we will get  

∴ 65% of fuel capacity been used in this flight.

Answer:

65%.

Step-by-step explanation:

(130,000/200.000) * 100

= 0.65 * 100

= 65%.

Answer:

60

Step-by-step explanation:

Answer:

5 tacos for 2 guests would mean more for each person, while 2 tacos for 5 guests would mean less for each person

Answer:

225 children tickets, 450 adult tickets and 500 student tickets were sold

Answer:

66 degrees.

Step-by-step explanation:

angle 4 is 124, and angle 1 and 4 make 180 degrees. that means angle 1 is 56 degrees (180-124). and the total angle in a triangle is also 180 degrees.

Add 56 and 58, you'd get 114.

180-114=66

angle 2=66 degrees.

Answer:

66

Step-by-step explanation:

1. The exterior angle theorem states that the measure of an exterior angle of a triangle is congruent to the sum of the two opposite interior angles.

2. Now, let's see what information we have so far, and what we don't have.

3. Now, let's set up the equation and solve it.

Step 1: Set up the equation.

Step 2: Subtract 58 from both sides.

Step 3: Check if solution is correct.

Therefore, the answer is 66.

Answer:

x

Step-by-step explanation:

Since the x- terms are opposites , that is 3x and - 3x , then when the 2 equations are added the x- term will be eliminated.

Answer:

a-2=a-2

Step-by-step explanation:

Here it is, you just have to notice that the numerator has common factors alternated. You will then collect the same parentheses and simplify with the denominator.

Answer:

Step-by-step explanation:

Parentheses are missing in your problem statement if you intend to simplify ...

  [tex]\dfrac{3a^2-ac+2c-6a}{3a-c}\\\\=\dfrac{a(3a-c) -2(3a-c)}{3a-c}\qquad\text{factor pairs of terms}\\\\=\dfrac{(a-2)(3a-c)}{(3a-c)}\\\\=\boxed{a-2}\qquad\text{cancel common factors}[/tex]

The "steps" are ...

Answer:

-20.54 C

Step-by-step explanation:

Form an equation

-12.94 C = initial temperature

changes -1.9 per hour = -1.9h

h = hour

x = temperature after 4 hours

-12.94 -1.9h = x

substitute 4 for "h"

-12.94-1.9(4) = x

x = -20.54C

Answer:

Step-by-step explanation:

Just multiply -1.9 by 4 then add it to 12.94

Answer:

if you can only pick one it's e

Step-by-step explanation:

Im 90% sure a and c are both true answers while 70% sure that b and d are both true answers so unless someone says otherwise e is your best bet

Number 1.

[tex]5^x=2[/tex], first we will take the [tex]log[/tex] of both of these numbers getting us,

[tex]x=\frac{log(2)}{log(5)}[/tex], which then gives us that [tex]x=0.4306777777....[/tex]

Number 2

[tex]e^x=10[/tex], solve for our exponent, [tex]2.718282^x=10[/tex], use the logarithmic formula, and we get,

[tex]x=\frac{log(10)}{log(2.718282)}[/tex], which then we get that [tex]x=2.302585[/tex]

if we can assume the ball is being thrown from the ground upwards, then we can say that the inital height of it is 0, whilst its initial velocity is 80 ft/s, thus

[tex]~~~~~~\textit{initial velocity in feet} \\\\ h(t) = -16t^2+v_ot+h_o \quad \begin{cases} v_o=\textit{initial velocity}&80\\ \qquad \textit{of the object}\\ h_o=\textit{initial height}&0\\ \qquad \textit{of the object}\\ h=\textit{object's height}\\ \qquad \textit{at "t" seconds} \end{cases} \\\\\\ h(t)=-16t^2+80t+0\implies h(t)=-16t^2+80t[/tex]

ΔPQR has:  PM is a median

So: MR = QM = 3 cm

ANSWER:  MR = 3 cm

Ok done. Thank to me :>

Answer:

1000

Step-by-step explanation:

So the taken chocolate weight equals to the original 1 box of chocolate.

Thus there are 200 x 5 = 1000g.

The orginal chocolate has 1000g each.

Answer:

9 kg per 3 weeks = 3 kg per week

Therefore, after 4 weeks it is (4 * 3) kilograms or 12 kilograms

Step-by-step explanation:

x^2-10x+25

=x^2-5x-5x+25

x(x-5)-5(x-5)

=(x-5)(x-5)

x=5 , x=5

hope it's helpful to you

[tex]x^2 -10x +25\\\\=x^2 -2 \cdot 5 \cdot x +5^2\\\\=(x-5)^2\\\\=(x-5)(x-5)[/tex]