The length of a rectangular lot is 7 yards less than twice its width. If the length was increased by 11 yards and the width decreased by 6 yards, the area would be decreased by 40 square yards. Find the original dimension of the lot.

Answer:

Step-by-step explanation:

Since we don't have the information we need to fit this into an exponential equation, we will do it the simple way, using recursion.  We will take the value of the car and subtract from it the depreciation, using the value at the end of one calculation as the initial value of the one following.  Here's where it gets tricky, though.  If the car's value at the end of a calculation is 80% of its initial value, then it depreciates 20%.  Here is what the equation looks like after one year:

2,700,000 - .2(2,700,000) = 2,160,000

We subtracted away 20% of the initial to get the new initial.  Now we use that value in the next recursion.

2,160,000 - .2(2,160,000) = 1,728,000

This is the value of the car after 2 years.

If we continue this process, we would find that after the 8th year, the car's value drops below 500,000 (namely, $452,984.83)

Answer:

8

Step-by-step explanation:

one sixth of 48 is 8 therefore you have eight tomato plants

Answer:

Step-by-step explanation:

The second equation tells you ...

  y = 8 -3x

Using this expression in the first equation gives you ...

  2x +3(8 -3x) = 3

  2x +24 -9x = 3 . . . . . eliminate parentheses

  21 = 7x . . . . . . . . . . .  add 7x -3

  3 = x . . . . . . . . . . . . . . divide by 7

  y = 8 -3×3 = -1 . . . . . . use the second equation to find y

The solution is (x, y) = (3, -1).

Answer:

the correct answers for edu are 2x+3(8-3x)=3 than 3 and last -1

Step-by-step explanation:

Answer:

C. X= -2.01 and x= 1.67

Step-by-step explanation:

[tex]3x {}^{2} + x + 10 = 0 \\ 3x {}^{2} + 6x - 5x + 10 = 0 \\ 3x(x + 2) - 5(x + 2) \\ (x + 2)(3x - 5 )\\ x + 2 = 0 \: \: or \: \: 3x - 5 = 0 \\ x = - 2 \: \: or \: \: x = \frac{5}{3} [/tex]

ANSWER

B. No real solutions

EXPLANATION

The given equation is

[tex]3 {x}^{2} + x + 10 = 0[/tex]

By comparing to

[tex]a {x}^{2} + bx + c= 0[/tex]

We have a=3,b=1 and c=10.

We substitute these values into the formula

[tex]D = {b}^{2} - 4ac[/tex]

to determine the nature of the roots.

[tex]D = {1}^{2} - 4(3)(10)[/tex]

[tex]D = 1 - 120[/tex]

[tex]D = - 119[/tex]

The discriminant is negative.

This means that the given quadratic equation has no real roots.

Answer:

Ballistic motion is usually modeled by a quadratic function.

Step-by-step explanation:

The usual assumption is that the only force acting on the object is that due to gravity, and that it is constant and directed downward. With this assumption, along with the assumption of a flat Earth, the resulting model is a downward-opening quadratic function.

Answer:

quadratic function.

Step-by-step explanation: "

ballistic motion is modeled with a quadratic function"

Answer:

[tex]\theta=\frac{\pi}{2},\frac{3\pi}{2},\frac{2\pi}{3},\frac{4\pi}{3}[/tex]

Step-by-step explanation:

If I'm interpreting that correctly, you are trying to solve this equation:

[tex]sin(\theta )+1=cos(2\theta)[/tex]

for theta.  To do this, you will need a trig identity sheet (I'm assuming you got one from class) and a unit circle (ditto on the class thing).

We need to solve for theta.  If I look to my trig identities, I will see a double angle one there that says:

[tex]cos(2\theta)=1-2sin^2(\theta)[/tex]

We will make that replacement, then we will have everything in terms of sin.

[tex]sin(\theta)+1=1-2sin^2(\theta)[/tex]

Now get everything on one side of the equals sign to solve for theta:

[tex]2sin^2(\theta)+sin(\theta)=0[/tex]

We can factor out the common sin(theta):

[tex]sin\theta(2sin\theta+1)=0[/tex]

By the Zero Product Property, either

[tex]sin\theta=0[/tex] or

[tex]2sin\theta+1=0[/tex]

Now look at your unit circle and find that the values of theta where the sin is 0 are located at:

[tex]\theta=\frac{\pi }{2},\frac{3\pi}{2}[/tex]

The next one we have to solve for theta:

[tex]2sin\theta+1=0[/tex] simplifies to

[tex]2sin\theta=-1[/tex] and

[tex]sin\theta=-\frac{1}{2}[/tex]

Look at the unit circle again to find the values of theta where the sin is -1/2:

[tex]\theta=\frac{2\pi}{3},\frac{4\pi}{3}[/tex]

Those ar your values of theta!

Final answer:

To find the vertices of the system of inequalities x ≤ 3, -x + 3y ≤ 12, and 4x + 3y ≥ 12, we can solve each pair of inequalities to find the intersection points. The vertices are the points where the lines intersect. The coordinates of the vertices are (3, 0), (0, 4), and (3, 5). For the function f(x, y) = x - 2y, the point where the maximum value is found in the system of inequalities is (5, 3).

Explanation:

To find the coordinates of the vertices formed by the system of inequalities x ≤ 3, -x + 3y ≤ 12, and 4x + 3y ≥ 12, we can solve each pair of inequalities to find the intersection points. The vertices are the points where the lines intersect.

The solution is (3, 0), (0, 4), and (3, 5), so the correct answer is B.

For the second question, to find the point where the maximum value is found for the function f(x, y) = x - 2y in the system of inequalities graphed below, we need to locate the highest point on the graph. From the given options, (5, 3) is the point where the maximum value is found, so the correct answer is D.

 The maximum error on volume = 270cm³

The relative error on the volume =0.08

The percentage error on volume = 8%.

How to calculate the volume of a given cube?

To calculate the volume of a given cube, the following steps should be taken as follows:

Formula for volume of a cube = a³

where;

a = 15 cm

Volume(V) = 15³ = 3375cm³

The maximum error on volume(dV);

= 3×side²×dx

= 3×15²×0.4cm

= 270cm³

The relative error on the volume;

= dV/V

= 270/3375

= 0.08

The percentage error on volume;

=Relative error × 100

= 0.08× 100

= 8%

Answer:

  -x + y > -4; x + y < 3 . . . . . last choice

Step-by-step explanation:

The boundary lines are both dashed, so there will be no "or equal to" as part of the inequality symbols (eliminates the second choice).

The downward sloping line has x- and y-intercepts that are both 3, so it will have the equation in intercept form ...

  x/3 + y/3 = 1

Multiplying by 3 gives x+y=3. The shading is below it, so the inequality with that line as the boundary is ...

  x + y < 3

This inequality is only part of the last choice.

__

The upward sloping line has x- and y- intercepts of 4 and -4, so its equation in intercept form is ...

  x/4 + y/-4 = 1

Multiplying by -4 gives -x+y=-4. The shading is above it, so the inequality with that boundary line is ...

  -x + y > -4

This inequality is included in the last choice.

The graph represents a system of inequalities that define a region satisfying all inequalities simultaneously. The relationship between variables on the axes gives the inequalities' data points, and quadratic equations' solutions provide boundaries if they're relevant and positive.

To identify the system of inequalities that the graph represents, you need to consider the relationships between the variables represented on the x-axis and the y-axis. This is an exercise in two-dimensional graphing. The values on the x-axis (independent variable) and the y-axis (dependent variable) provide the data points for the inequalities.

It's essential to note that in a system of inequalities, the solution is the region that satisfies all of the inequalities simultaneously. Depending on the inequality, the graphical representation could either be above or below a certain line, or within a particular region of the graph.

Quadratic equations sometimes provide a boundary for these inequalities, particularly when we are only interested in the real and positive root solutions. So, considering these aspects, it's possible to define a system of inequalities that match the graph provided.

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Answer: 2.85

Step-by-step explanation:

Given : A​ 90% confidence interval for the mean percentage of airline reservations being canceled on the day of the flight is ​(1.4​, 4.3​) .

We know that the the confidence interval for population mean [tex]\mu[/tex] is given by :-

[tex]\mu\pm E[/tex], where E is the margin of error.

Lower limit of confidence interval = [tex]\mu-E=1.4[/tex]          (1)

Upper limit of confidence interval =  [tex]\mu+E=4.3[/tex]        (2)

Adding (1) and (2), we get

[tex]2\mu=5.7\\\\\Rightarrow\ \mu=2.85[/tex]

Hence, the point estimator of the mean percentage of reservations that are canceled on the day of the​ flight = 2.85

The point estimator for the mean percentage of airline reservations being canceled on the day of the flight is 2.85%, found by averaging the lower and upper bounds of the given 90 percent confidence interval.

The point estimator of the mean percentage of reservations that are canceled on the day of the flight can be determined from the confidence interval given as (1.4, 4.3).

The point estimator is simply the mean of the lower and upper bounds of the confidence interval. To find this, we add the lower and upper limits together and divide by two.

The calculation is as follows:

[tex]\frac{1.4 + 4.3}{2} = 2.85[/tex]

Therefore, the point estimator for the mean percentage of airline reservations being canceled on the day of the flight is 2.85%.

The midpoint can be defined using formula,

[tex]M(x_m=\dfrac{x_1+x_2}{2},y_m=\dfrac{y_1+y_2}{2})[/tex]

So by knowing [tex]x_m, x_1[/tex] and [tex]y_m, y_1[/tex] we can calculate [tex]x_2, y_2[/tex]

First we must derive two equations,

[tex]x_m=\dfrac{x_1+x_2}{2}\Longrightarrow x_2=2x_m-x_1[/tex]

and

[tex]y_m=\dfrac{y_1+y_2}{2}\Longrightarrow y_2=2y_m-y_1[/tex]

Then just put in the data,

[tex]x_2=2\cdot(-2)-3=-7[/tex]

[tex]y_2=2\cdot(-3)-0=-6[/tex]

So the other endpoint has coordinates [tex](x,y)\Longrightarrow(-7, -6)[/tex] therefore the answer is D.

Hope this helps.

r3t40

To work out the mid point of two points you, add the x coordinates and divide by 2, and you take the y coordinates and divide by two:

So:

[tex]midpoint = \frac{sum.of.x-coords}{2},  \frac{sum.of.y-coords}{2}[/tex]

------------------------------------

So the x-coords of the midpoint is:

[tex]\frac{sum.of.x-coords}{2}[/tex]

and

y -coords of midpoint is:

[tex]\frac{sum.of.y-coords}{2}[/tex]

------------------------------------

However, in this question we are trying to work out one of the endpoints.

First let's say that the coordinates of the missing endpoint is:

(x , y)

_____________________________________________

That means that the x-coords of the midpoint of (x, y) and the other endpoint (3, 0) is :

[tex]\frac{3 + x}{2}[/tex]

However, we already know the x-coord of the midpoint ( it's -2). So we can form an equation to workout x:

[tex]\frac{3 + x}{2} = -2[/tex]                (multiply both sides by 2)

[tex]3 + x = -4[/tex]                      (subtract 3 from both sides)

[tex]x = -7[/tex]

This is the x-coord of the other endpoint

_______________________________________________

Let's do the same for the y coordinates:

We know y coords for the midpoint of (x, y) and (3, 0) is:

[tex]\frac{0 + y}{2}[/tex]

But we also know the ycoord is -3. So we can form an equation and solve for y:

[tex]\frac{0+y}{2} = -3[/tex]

[tex]\frac{0 + y}{2} = -3[/tex]   (multiply both sides by 2)

[tex]0 + y = -6[/tex]                (simplify)

[tex]y = -6[/tex]

This is the y-coord of the other endpoint

___________________________________

Now we just put these coords together to get the coordinate of the other endpoint:

Endpoint is at:

(x, y)                           (substitute in values that we worked out)

=  (-7, -6)

_________________________________________________

D. (-7, -6)

________________________________________________

Note:

If there is anything you don't quite understand or was unclear

- please don't hesitate to ask below in the comments.

Answer:

The width the asymptote rectangle is 8 units

The height the asymptote rectangle is 4 units

Step-by-step explanation:

* Lets explain how to solve this problem

- The equation of the hyperbola is x² - 4y² - 2x + 16y - 31 = 0

- The standard form of the equation of hyperbola is

  (x - h)²/a² - (y - k)²/b² = 1 where a > b

- The length of the transverse axis is 2a (the width of the rectangle)

- The length of the conjugate axis is 2b (the height of the rectangle)

- So lets collect x in a bracket and make it a completing square and

  also collect y in a bracket and make it a completing square

∵ x² - 4y² - 2x - 15 = 0

∴ (x² - 2x) + (-4y²) - 15 = 0

- Take from the second bracket -4 as a common factor

∴ (x² - 2x) + -4(y²) - 15 = 0

∴ (x² - 2x) - 4(y²) - 15 = 0

- Lets make (x² - 2x) completing square

∵ √x² = x

∴ The 1st term in the bracket is x

∵ 2x ÷ 2 = x

∴ The product of the 1st term and the 2nd term is x

∵ The 1st term is x

∴ the second term = x ÷ x = 1

∴ The bracket is (x - 1)²

∵  (x - 1)² = (x² - 2x + 1)

∴ To complete the square add 1 to the bracket and subtract 1 out

   the bracket to keep the equation as it

∴ (x² - 2x + 1) - 1 = (x - 1)² - 1

- Lets put the equation after making the completing square

∴ (x - 1)² - 1 - 4(y²) - 15 = 0 ⇒ simplify

∴ (x - 1)² - 4(y)² - 16 = 0 ⇒ add the two side by 16

∴ (x - 1)² - 4(y)² = 16 ⇒ divide both sides by 16

∴ (x - 1)²/16 - y²/4 = 1

∴ (x - 1)²/16 - y²/4 = 1

∴ The standard form of the equation of the hyperbola is

  (x - 1)²/16 - y²/4 = 1

∵ The standard form of the equation of hyperbola is

  (x - h)²/a² - (y - k)²/b² = 1

∴ a² = 16 and b² = 4

∴ a = 4 , b = 2

∵ The width the asymptote rectangle is 2a

∴ The width the asymptote rectangle = 2 × 4 = 8 units

∵ The height the asymptote rectangle is 2b

∴ The height the asymptote rectangle = 2 × 2 = 4 units

Answer:

[tex]w=8\\h=4[/tex]

Step-by-step explanation:

The given equation is

[tex]x^{2} -4y^{2}-2x-15=0[/tex]

First, we complete squares for each variable to find the explicit form of the hyperbola.

[tex]x^{2} -2x-4y^{2}=15\\x^{2} -2x+(\frac{2}{2} )^{2} -4y^{2} =15+1\\ (x-1)^{2}-4y^{2}=16\\\frac{(x-1)^{2} }{16} -\frac{4y^{2} }{16} =\frac{16}{16}\\\frac{(x-1)^{2} }{16} -\frac{y^{2} }{4}=1[/tex]

Now that we have the explicit form, you can observe that [tex]a^{2}=16 \implies a=4[/tex] and [tex]b^{2}=4 \implies b=2[/tex].

On the other hand, the width of the asymptote rectangle is [tex]2a[/tex] and the height is [tex]2b[/tex].

Therefore, the dimensions are 8 by 4.

[tex]2(4)=8\\2(2)=4[/tex]

Answer:

v = 1.45 × 10⁷ m/s

Step-by-step explanation:

Given:

Inner radius of the cylinder, r₁ = 20 mm = 0.2 m

outer  radius of the cylinder, r₂ = 80 mm = 0.8 m

Potential difference, ΔV = 600V

Now, the work done (W) in bringing the charge in to the inner conductor

W = [tex]\frac{1}{2}mv^2[/tex]

where, m is the mass of the electron = 9.1 × 10⁻³¹ kg

v is the velocity of the electron

also,

W = qΔV

where,

q is the charge of the electron = 1.6 × 10⁻¹⁹ C

equating the values of work done and substituting the respective values

we get,

qΔV =  [tex]\frac{1}{2}mv^2[/tex]

or

1.6 × 10⁻¹⁹ × 600 = [tex]\frac{1}{2}\times 9.1\times 10^{-31}v^2[/tex]

or

[tex]v = \sqrt\frac{2\times 600\times 1.6\times 10^{-19}}{9.1\times 10^{-31}}[/tex]

or

v = 14525460.78 m/s

or

v = 1.45 × 10⁷ m/s

Final answer:

The speed of the electron as it reaches the inner conductor is calculated using conservation of energy, giving a final speed of approximately 1.46 × 107 m/s.

Explanation:

Electron Velocity in Coaxial Conductors

An electron released from the outer conductor will be accelerated towards the higher potential inner conductor due to the electric field between them. To calculate the speed of the electron as it reaches the inner conductor, we use the concept of conservation of energy. The electrical potential energy lost by the electron as it moves from the outer to the inner conductor is converted into kinetic energy.

The initial potential energy (Ui) of the electron can be given by:

where q is the charge of the electron (q = -1.6 × 10-19 C) and V is the potential difference (V = 600 V).

The final kinetic energy (Kf) when the electron reaches the inner conductor is:

where m is the mass of the electron (m = 9.11 × 10-31 kg) and v is the final speed we want to find.

Using conservation of energy (Ui + Ki = Kf + Uf and noting that both the initial kinetic energy Ki and the final potential energy Uf are zero), we get:

Solving for v gives us the final speed of the electron:

This is the speed of the electron when it reaches the inner conductor.

Answer: C

Step-by-step explanation: The numerator is the angle measure, and the denominator is the side length. For angle B, the angle is 47 degrees. The opposite side is b, which is 85. We are finding the angle A, which is the numerator. The side 94 is opposite of angle A.

Answer:

The answer is A(3.5,7)

Point of partition refers that a point intersect a particular line or curve at a fixed ratio. The coordinates of P so that P partitions the segment AB in the ratio 1:3 if A(5,8) and B(−1,4) is (3.5,7).

The coordinates of the A is (5,8).

The coordinates of the B is (-1,4).

P partitions the segment AB in the ratio 1:3.

Point of partition refers that a point intersect a particular line or curve at a fixed ratio.

When a point [tex]p(x,y)[/tex] intersect a line which has the coordinates [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] at a ratio l and m then this point can be represent as,

[tex]p(x,y)=\left ( \dfrac{lx_2+mx_1}{l+m} , \dfrac{ly_2+my_1}{l+m} \right )[/tex]

Put the values,

[tex]p(x,y)=\left ( \dfrac{1\times(-1)+3\times 5}{1+3} , \dfrac{1\times 4+3\times8}{1+3} \right )[/tex]

[tex]p(x,y)=\left ( \dfrac{-1+15}{4} , \dfrac{4+24}{4} \right )[/tex]

[tex]p(x,y)=\left ( \dfrac{14}{4} , \dfrac{28}{4} \right )[/tex]

[tex]p(x,y)=(3.5,7)[/tex]

Hence the coordinates of P so that P partitions the segment AB in the ratio 1:3 if A(5,8) and B(−1,4) is (3.5,7).

Learn more about the point of partitions of a line here;

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Answer:

3

Step-by-step explanation:

the missing no is 3

I have answered ur question

Answer:

3

Step-by-step explanation:

Answer:

  24,000(0.908)^t > 15,000; no

Step-by-step explanation:

The multiplier each year is 100% - 9.2% = 90.8% = 0.908. There is only one answer choice with this as the yearly multiplier.

_____

In order to answer the yes/no question, we chose to rewrite the inequality as ...

  24000·0.908^t -15000 > 0

The graph shows that is true for t < 4.87. In 5 years, the forest area will be below the minimum.

Answer:

40oz glycol and water

10% is glycol

4oz is glycol

36oz is water

if glycol is to be added to make glycol 25% of all then

note: water does not change

100-25=75

water does not change so

36oz=75%

12=25%

there should be 12 oz of glycol total

4 now

12-4=8

8 oz should be added

sorry, I just wrote what I was thinking

answer is 8oz

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Step-by-step explanation:

Answer:

A real Even integers

Step-by-step explanation:

Answer:

A.

Step-by-step explanation:

It's all down the the double parentheses. They mean 'round down to the nearest integer'. Also because of the 2 the integer will be even.

Answer:

22π

Step-by-step explanation:

The area formula for a sector is

[tex]A=\frac{\theta }{360}*\pi  r^2[/tex]

The angle theta is to be the angle that is a part of the sector for which we are trying to find the area.  If we are looking for the area of the larger sector, we are not using 140 as our angle theta, we are using 360 - 140 = 220 as our angle theta since that is the angle for the larger of the 2 sectors.  Filling in our formula using r = 6:

[tex]A=\frac{220}{360}*36\pi[/tex]

The easiest way to handle this math is to multiply the 220 by the 36, hit enter on your calculator, then divide that product by 360.  When you do that your answer, in terms of pi, is 22π

Answer:

20

Step-by-step explanation:

Given that Tristan records the number of customers who visit the store each hour on a Saturday.

His data representing the first seven hours are 15, 23, 12, 28, 20, 18, and 23.

There are 7 entries and if written in ascending order 12,15,18,20,23,23,28

Median = middle entry -20

If one more entry is added then we have two middle entries and median would be the average of the two.

Hence if median is to remain the same, eighth hour no of customers visited should be 20

Answer is 20

Answer:

(6^⅕) (cos(-24°) + i sin(-24°))

Step-by-step explanation:

First, we convert from Cartesian to polar:

r = √((-3)² + (-3√3)²)

r = √(9 + 27)

r = 6

θ = atan( (-3√3) / (-3) ), θ in the third quadrant

θ = atan(√3)

θ = 240° + 360° k

Notice that θ can be 240°, 600°, 960°, etc.

Therefore:

-3 − 3√3 i = 6 (cos(240° + 360° k) + i sin(240° + 360° k))

Now we take the fifth root:

[ 6 (cos(240° + 360° k) + i sin(240° + 360° k)) ]^⅕

(6^⅕) [ (cos(240° + 360° k) + i sin(240° + 360° k)) ]^⅕

Applying de Moivre's Theorem:

(6^⅕) (cos(⅕ × 240° + ⅕ × 360° k) + i sin(⅕ × 240° + ⅕ × 360° k))

(6^⅕) (cos(48° + 72° k) + i sin(48° + 72° k))

If we choose k = -1:

(6^⅕) (cos(-24°) + i sin(-24°))

Answer:

a)  N = 1.06S +2000

b)  the old salary is scaled by a factor of 1.06 and translated upward by 2000.

Step-by-step explanation:

a) a 6% raise means the new salary is 100% + 6% = 106% of the old one. A raise of an additional dollar amount simply adds to the scaled salary.

__

b) The translations are "math speak" for the English description of "increased by 6% and then raised by 2000". "Increased by 6%" means that .06 of the amount is added to the amount, effectively multiplying it by 1.06. "Raised by 2000" means 2000 is added.

Answer: The following statements is not applicable to typologies, "They may be used effectively as independent or dependent variables."

Typology is a complex measurement that affect the categorization of observations in terms of their property on multiple variables.They are typically nominal composite measures.They involve a set of categories or types. They are often used when researchers wish to summarize the intersection of two or more variables.

Answer:

90°, 75°, and 15°

Step-by-step explanation:

In a right triangle, one of the angles is 90°.

           Let x = the smallest angle

Then 60 + x = the third angle

The sum of the three angles is 180°.

90 + 60 + x + x = 180

          150 + 2x = 180

                    2x =  30

                      x =   15

      Measure of right angle              = 90°

Measure of smallest angle = x         =  15°

     Measure of third angle = 60 + x = 75°  

The measures of the angles are 90°, 75°, and 15°.

Answer:

84.4 gallons to the nearest tenth.

Step-by-step explanation:

Average usage = miles travelled  / gallons used  so:

6.3 = 532 / gallons used

Gallons used  =   532 / 6.3

= 84.44.

Final answer:

To find the gallons of gasoline used, divide the total miles (532) by the average miles per gallon (6.3). This calculation results in approximately 84.4444 gallons, which can be rounded to 84.4 gallons of gasoline used.

Explanation:

To calculate the amount of gasoline used by the boater who traveled 532 miles averaging 6.3 miles per gallon, you need to divide the total miles traveled by the average miles per gallon. The formula to use is:

Gallons used = Total miles traveled ÷ Average miles per gallon
Plugging in the values given:

Gallons used = 532 miles ÷ 6.3 miles/gallon
This gives us:

Gallons used = 84.4444... gallons
To round to the nearest tenth of a gallon, we would round 84.4444... to 84.4 gallons. Thus, the boater used approximately 84.4 gallons of gasoline.

Answer:

0.36

Step-by-step explanation:

z is inversely proportional to x:

z = k / x

When x is 16, z has the value 0.5625.

0.5625 = k / 16

k = 9

What is the value of z when x= 25?

z = 9 / 25

z = 0.36

Answer:

The answer is 9/25 or .36 if you prefer it in decimal form.

Step-by-step explanation:

inversely proportional means there is a constant that we are going to divide by.

So z is inversely proportional to x means z=k/x where k is a constant.

We are given when x=16, z=0.5625.  This information will be used to find our constant value k.

0.5625=k/16

Multiply both sides by 16:

16(0.5625)=k

Simplify:

9=k.

This means no matter what (x,z) pair we have the constant k in z=k/x will always be 9.

The equation we have is z=9/x.

Now we want to find z when x=25.

z=9/25

z=.36

Answer:

So (5,1) is the orthocenter.

Step-by-step explanation:

So we have to find the slopes of all three lines in burgundy (the line segments of the triangle). We also need to find the equations for the altitudes with respect from all sides of the triangle (we are looking for perpendicular lines).

The vertical line there is just going to be x=a number so that line is x=3 because all the points on that line are of the form (3,y).  x=3 says we don't care what y is but x will always be 3.  So the line for AY is x=3.

So the altitude of the triangle with respect to that side (that line segment) would be a line that is perpendicular to is which would be a horizontal line y=1.  I got y=1 because it goes through vertex B(9,1) and y=1 is perpendicular to x=3.  

So we now need to find the equations of the other 2 lines.

One line has points A(3,5) and B(9,1).

To find the slope, you may use [tex]\frac{y_2-y_1}{x_2-x_1}[/tex].

Or you could just line up the points vertically and subtract then put 2nd difference over 1st difference.

Like this:

(9 , 1)

-(3  ,5)

----------

6     -4

So the slope is -4/6=-2/3.

So a line that is perpendicular will have opposite reciprocal slope.  That means we are looking for a line with 3/2 as the slope.  We want this line from segment AB going to opposite point Y so this line contains point (3,-2).

Point slope-form is

[tex]y-y_1=m(x-x_1)[/tex] where [tex](x_1,y_1)[/tex] is a point on the line and [tex]m[/tex] is the slope.

So the line is:

[tex]y-(-2)=\frac{3}{2}(x-3)[/tex]

[tex]y+2=\fac{3}{2}x-\frac{9}{2}[/tex]

Subtract 2 on both sides:

[tex]y=\frac{3}{2}x-\frac{9}{2}-2[/tex]

Simplify:

[tex]y=\frac{3}{2}x-\frac{13}{2}[/tex].

Let's find the the third line but two lines is plenty, really. The othorcenter is where that perpendicular lines will intersect.

Now time for the third line.

BY has points (9,1) and (3,-2).

The slope can be found by lining up the points vertically and subtracting, then put 2nd difference over 1st difference:

(9  ,1)

-(3,-2)

---------

6     3

So the slope is 3/6=1/2.

A perpendicular line will have opposite reciprocal slope. So the perpendicular line will have a slope of -2.

We want this line segment to go through A(3,5).

We are going to use point-slope form:

[tex]y-5=-2(x-3)[/tex]

Add 5 on both sides:

[tex]y=-2(x-3)+5[/tex]

Distribute:

[tex]y=-2x+6+5[/tex]

Combine like terms:

[tex]y=-2x+11[/tex]

So the equation of the 3rd altitude line is y=-2x+11.

So the equations we want to find the intersection to is:

y=(3/2)x-(13/2)

y=1

y=-2x+11

I like the bottom two equations so I'm going to start there and then use my third line to check some of my work.

y=1

y=-2x+11

Replacing 2nd y with 1 since y=1:

1=-2x+11

Subtract 11 on both sides:

1-11=-2x

Simplify:

-10=-2x

Divide both sides by -2:

5=x

The point of intersection between y=1 and y=-2x+11 is (5,1).

Let's see if (5,1) is on that third line.

y=(3/2)x-(13/2)

1=(3/2)(5)-(13/2)

1=(15/2)-(13/2)

1=(2/2)

1=1

So (5,1) is the intersection of all three lines.

So (5,1) is the orthocenter.

Answer:

336.7 yards away from the cabin....

Step-by-step explanation:

The angle 30.7° is also the angle of the upper interior angle of the triangle (near the cabin)

Use the tan function:

opposite = 200 yards

adjacent = x

tan(30.7°) = (opposite / adjacent)

tan(30.7°) = 200 yards/x

x * tan(30.7°) = 200 yards

x = 200 yards/ tan(30.7°)

x= 200/ 0.594

x = 336.7 yards.

336.7 yards away from the cabin....

Answer: 337

Step-by-step explanation: you have to round up

Answer:

The required expression is [tex]m=\frac{-15}{-3-4}[/tex].

Step-by-step explanation:

The general form of the equation is

[tex]gm=cm+rg[/tex]             .... (1)

We need to solve this equation for m.

Subtract cm from both the sides.

[tex]gm-cm=rg[/tex]

Taking out the common factor.

[tex]m(g-c)=rg[/tex]

Divide both sides by (g-c).

[tex]\frac{m(g-c)}{g-c}=\frac{rg}{g-c}[/tex]

[tex]m=\frac{rg}{g-c}[/tex]               ..... (2)

The given equation is

[tex]-3m=4m-15[/tex]            ..... (3)

From (1) and (3), we get

[tex]g=-3,c=4,rg=-15[/tex]

Substitute g=-3, c=4, rg=-15 in equation (2).

[tex]m=\frac{-15}{-3-4}[/tex]

Therefore the required expression is [tex]m=\frac{-15}{-3-4}[/tex].

Answer:

the corect answer on edge is c

Step-by-step explanation: