Two hikers are walking along the Appalachian Trail. The first hiker is 2 miles ahead of the second hiker. Both hikers are traveling in the same direction at the same speed, 1 mile per hour. Let x represent the distance traveled by the first hiker after a certain time period.


Several students wrote equations for this situation. Which student is correct?


A.

Alex said, “The equation y = 2x + 1 represents the total distance traveled by both hikers.”



B.

Brenda said, “The equation y = 3x represents the total distance traveled by both hikers.”



C.

Chris said, “The equation y = x – 2 represents the distance traveled by the second hiker.”



D.

Drake said, “The equation y = x + 2 represents the distance traveled by the second hiker.”

Answer:

m < EJB = half of m < OBE.

m < BDE = 180 minus m < BOE.

m < OED = m<OBD.

Step-by-step explanation:

First part :  Because  angled subtended by an arc at the circumference = half of angle at the center.

Second: Because  The 2 angles OBD and OED = 90 degrees.

Third: DB and DE are both tangents to the circle, and OE and OB are both radii. So m < OED = m<OBD = 90 degrees.

Answer:

1. B. one-half

2. D. 180 minus

3. A. equal to

Answer:

49.2 miles

Step-by-step explanation:

The distance remains the same.                        d

The time spent on the outbound trip is t1 = -------------

                                                                         35 mph

and that on the inbound (return) trip is

                                                                              d

                                                                t2 = -------------

                                                                         45 mph

We combine these two fractions and set the sum = to 2.5 hours:

d(1/35 + 1/45) = 5/2

We wish to solve for d, the distance between home and work.

The LCD of 35, 45 and 2 is 630.

1/35 becomes 18/630; 1/45 becomes 14/630, and 5/2 becomes 1575/630.  Then we have the simpler equation   d(18 + 14) = 1575, or

d(32) = 1575, and d is then

d = 1575/32 = 49.2 miles

Answer: So the final answer would be width is 6x + 6

Step-by-step explanation: The formula for Area is Length x width.

So A = (2x + 6)(3x) and the result is: 6x^2 + 18x

Now, let y be the width of rectangle B.

(x+2) (y) = 6x^2 + 18x + 12

(x+2) y = 6(x+1)(x+2)

y = 6(x+1)

Answer: she will be done by 8:50

Step-by-step explanation:

45 minutes

Answer:

  7.  $8123.79

  8.  0.012 g

Step-by-step explanation:

It often pays to follow directions. The attachment shows the use of a TI-84 graphing calculator to find the answers.

___

You will notice that the answer to problem 8 does not agree with any of the offered choices. The time period of 22.8 years is 12 times the half-life of the substance, so there will be (1/2)^12 = 1/4096 of the original amount remaining. The time periods corresponding to the amounts shown range from 1.37 years to 16.4 years.

For half-life problems, I find it convenient to use the decay factor (0.5^(1/half-life)) directly, rather than convert it to e^-k. If you do convert it to the form ...

  e^(-kt)

the value of k is (ln(2)/half-life), about 0.3648143056.

_____

For multiple choice problems where the choices make no sense, I like to suggest you ask your teacher to show you how to work the problem. (Alternatively, use the "Report this question" or "Ask a tutor" button sometimes provided.)

Answer:

7. 8123.79

8. 0.012

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

y-intercept is defined as the point where the graph crosses the y-axis. The value of x coordinate at this point is zero, as along entire y-axis, the value of x coordinate is always zero. So substituting x = 0 in the function will give us the y-coordinate of the y-intercept of the given function.

[tex]f(x)=x^{3}-x^{2} -x+1[/tex]

Substituting x = 0 in this function, we get:

[tex]f(0)=0^{3}-0^{2}-0+1=1[/tex]

Thus, the y-coordinate of the y-intercept is 1. Therefore the y-intercept of the function in ordered pair will be: (0, 1)

The answer is:

The equation D  will produce the shown circle.

[tex]6x^{2}+6y^{2}=144[/tex]

Since the graph is showing a circle, we need to find the equation of a circle that has a radius which is between 0 and 5 units, and has a center located at the origen (0,0).

Also, we need to remember the standard form of a circle:

[tex](x+h)^{2} +(y+k)^{2}=r^{2}[/tex]

Where,

x, is the x-coordinate of the x-intercept point

y, is the y-coordinate of the y-intercept point

h, is the x-coordinate of the center.

k, is the y-coordinate of the center.

r, is the radius of the circle.

So, discarding each of the given options, we have:

First option:

A.

[tex]\frac{x^{2} }{20}+ \frac{y^{2} }{20}=1\\\\\frac{1}{20}(x^{2}+y^{2})=1\\\\x^{2}+y^{2}=20*1\\\\x^{2}+y^{2}=20[/tex]

Where,

[tex]radius=\sqrt{20}=4.47=4.5[/tex]

Now, can see that even the center is located at the point (0,0), the radius of the circle is equal to 4.5 units and from the graph we can see that the radius of the circle is more than 4.5 units but less than 5 units, the option A is not the equation that produces the shown circle.

Second option:

B.

[tex]20x^{2} -20y^{2}=400\\\\\frac{1}{20}(x^{2} -y{2})=400\\\\x^{2} -y{2}=400*20[/tex]

Where,

[tex]radius=\sqrt{8000}=89.44units[/tex]

We can see that even the center is located at the point (0,0), the radius of the circle is 89.44 units, so, the option B is not the equation that produces the shown circle.

Third option:

C.

[tex]x^{2}+y^{2}=16[/tex]

Where,

[tex]radius=\sqrt{16}=4units[/tex]

We  can see that even the center is located at the point (0,0), the radius of the circle is 4 units, which is less than the radius of the circle shown in the graph, so, the option C is not the equation that produces the shown circle.

D.

[tex]6x^{2}+6y^{2}=144\\\\6(x^{2} +y^{2})=144\\\\x^{2} +y^{2}=\frac{144}{6}=24\\\\[/tex]

Where,

[tex]radius=\sqrt{24}=4.89units[/tex]

Now, we have that the radius of the circle is 4.89 units, which is approximated equal to 0, also, the center of the circle is located at (0,0) so, the equation D will produce the shown circle.

[tex]6x^{2}+6y^{2}=144[/tex]

Have a nice day!

The equation that represents the given graph is:

              [tex]6x^2+6y^2=144[/tex]

By looking at the given graph we observe that the graph is a circle with center at (0,0) and the radius is close to 5.

Now, we know that:

The general equation of a circle with center (h,k) and radius r is given by:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Here (h,k)=(0,0)

Hence, the equation of the circle is:

            [tex]x^2+y^2=r^2[/tex]

A)

[tex]\dfrac{x^2}{20}+\dfrac{y^2}{20}=1\\\\i.e.\\\\x^2+y^2=20[/tex]

i.e.

[tex]x^2+y^2=(2\sqrt{5})^2[/tex]

This equation is a equation of a circle with center at (0,0)

and radius is: [tex]2\sqrt{5}\ units[/tex]

i.e. the radius is approximately equal to 4.5 units.

But the radius is close to 5.

Hence, option: A is incorrect.

B)

[tex]20x^2-20y^2=400\\\\i.e.\\\\x^2-y^2=20[/tex]

This is not a equation of a circle.

This equation represents a hyperbola.

Hence, option: B is incorrect.

C)

[tex]x^2+y^2=16[/tex]

which could be represented by:

[tex]x^2+y^2=4^2[/tex]

i.e. the radius of circle is: 4 units

which is not close to 5.

Hence,option: C is incorrect.

D)

[tex]6x^2+6y^2=144[/tex]

On dividing both side of the equation by 6 we get:

[tex]x^2+y^2=24[/tex]

i.e.

[tex]x^2+y^2=(\sqrt{24})^2[/tex]

i.e.

Radius is: [tex]\sqrt{24}\ units[/tex]

which is approximately equal to 4.9 units which is close to 5 units.

Answer: Option 'C' is correct.

Step-by-step explanation:

Since we have given that

The expression is defined as

[tex]f(x)=12(1.035)^x------------------------(1)[/tex]

As we know the general form of exponential function:

[tex]f(x)=a(1+r)^x--------------------------(2)[/tex]

Here, a denotes the initial amount.

r denotes the growth rate.

On comparing, we get that

[tex]1+r=1.035\\\\r=1.035-1\\\\r=0.035\\\\r=0.035\times 100\%\\\\r=3.5\%[/tex]

Hence, option 'C' is correct.

Answer:

C) 3.5%

Step-by-step explanation:

Answer:

The area of a sector GHJ is [tex]36.3\ cm^{2}[/tex]

Step-by-step explanation:

step 1

we know that

The area of a circle is equal to

[tex]A=\pi r^{2}[/tex]

we have

[tex]r=8\ cm[/tex]

substitute

[tex]A=\pi (8)^{2}[/tex]

[tex]A=64\pi\ cm^{2}[/tex]

step 2

Remember that the area of a complete circle subtends a central angle of 360 degrees

so

by proportion find the area of a sector by a central angle of 65 degrees

[tex]\frac{64\pi}{360}=\frac{x}{65}\\ \\x=64\pi (65)/360[/tex]

Use [tex]\pi =3.14[/tex]

[tex]x=64(3.14)(65)/360=36.3\ cm^{2}[/tex]

Answer: B

Step-by-step explanation: You have no more than $65 which means you will want to spend equal to or less. Since you have $65, you will be able to spend up to that amount but you will not be able to spend any more than that. So, you will need to make sure the final price remains under or equal to your amount.

The approximate value of P(z>-1.25) from the normal table is 0.8944

Z score is used to determine by how many standard deviations the raw score is above or below the mean.

It is given by:

z = (raw score - mean) / standard deviation

P(z > -1.25) = 1 - P(z < -1.25) = 1 - 0.1057 = 0.8944

The approximate value of P(z>-1.25) from the normal table is 0.8944

Find out more on z score at: https://brainly.com/question/25638875

For this case we have that by definition, the slope of a line is given by:

[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}[/tex]

Two points are needed through which the line passes:

[tex](x_ {1}, y_ {1}): (- 1.75; 14.5)\\(x_ {2}, y_ {2}}: (- 1; 4.4)[/tex]

Substituting:[tex]m = \frac {4.4-14.5} {- 1 - (- 1.75)}\\m = \frac {-10.1} {0.75}\\m = -13.46666666[/tex]

Rounding:

[tex]m = -13.47[/tex]

Answer:

[tex]m = -13.47[/tex]

Answer:

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

Two points are needed through which the line passes:

(x_ {1}, y_ {1}): (- 1.75; 14.5)\\(x_ {2}, y_ {2}}: (- 1; 4.4)

Substituting:m = \frac {4.4-14.5} {- 1 - (- 1.75)}\\m = \frac {-10.1} {0.75}\\m = -13.46666666

Rounding:

m = -13.47

Step-by-step explanation:

The answer is:

It will take 20.5 months to the populations to be equal.

Since from the statement we know that both populations are growing, we need to use the formula to calculate the exponential growth.

The exponential growth is defined by the following equation:

[tex]P(t)=StartPopulation*e^{\frac{growthpercent}{100}*t}[/tex]

Now,

Calculating for the rabbits, we have:

[tex]StartPopulation=20\\GrowthPercent=5\\[/tex]

So, writing the equation for the rabbits, we have:

[tex]P(t)=20*e^{\frac{5}{100}*t}[/tex]

[tex]P(t)=20*e{0.05}*t}[/tex]

Calculating for the fox, we have:

[tex]StartPopulation=30\\GrowthPercent=3\\[/tex]

So, writing the equation for the fox, we have:

[tex]P(t)=30*e{\frac{3}{100}*t}[/tex]

[tex]P(t)=30*e^{0.03}*t}[/tex]

Then, if we want to calculate how long does it takes for these populations to be equal, we need to make their equations equal, so:

[tex]20*e^{0.05}*{t}=30*e^{0.03}*{t}\\\\\frac{20}{30}=\frac{e^{0.03}*{t}}{e^{0.05}*t}}\\\\0.66=e^{0.03t-0.05t}=e^{-0.02t}\\\\0.66=e^{-0.02t}\\\\ln(0.66)=ln(e^{-0.02t})\\\\-0.41=-0.02t\\\\t=\frac{-0.41}{-0.02}=20.5[/tex]

Hence, we have that it will take 20.5 months to the populations to be equal.

To find out how long it takes for the populations to be equal, set up and solve an equation using the growth rates of the rabbit and fox populations.

To find out how long it takes for the rabbit population and the fox population to be equal, we can set up and solve an equation. Let's start by setting up an equation for each population growth:

Rabbit population: P(t) = 20 * (1 + 0.05)^t

Fox population: P(t) = 30 * (1 + 0.03)^t

We want to find the value of t when the two populations are equal, so we set the equations equal to each other and solve for t:

20 * (1 + 0.05)^t = 30 * (1 + 0.03)^t

Divide both sides by 20:

(1 + 0.05)^t = 1.5 * (1 + 0.03)^t

Now take the natural logarithm of both sides:

t * ln(1 + 0.05) = ln(1.5 * (1 + 0.03)^t)

Divide both sides by ln(1 + 0.05):

t = ln(1.5 * (1 + 0.03)^t) / ln(1 + 0.05)

Using a calculator, we can approximate the value of t to the nearest tenth of a month.

https://brainly.com/question/18415071

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Answer:

2118 dollars

Step-by-step explanation:

His capital gain is the difference in the (sell - buy) prices multiplied by the number of shares (120).

120 * (85.89 - 68.24) = 120 * 17.65 = 2118

The capital gain is a short term gain (held under a year)

The amount is 2118 dollars.

Answer:

y+3= -6(x+9) is the answer

Step-by-step explanation:

Answer:

[tex]y+3=-6(x+9)[/tex]

Step-by-step explanation:

We are given that

Slope of a line=-6

Given point =(-9,-3)

We have to find the equation which represents the line.

The equation of line passing through the given point [tex](x_1,y_1)[/tex] with slope m is given by

[tex]y-y_1=m(x-x_1)[/tex]

Substitute the values then we get

The equation of line passing through the point (-9,-3) with slope -6 is given by

[tex]y-(-3)=-6(x-(-9))[/tex]

[tex]y+3=-6(x+9)[/tex]

Hence, the equation of line that passes through (-9,-3) and has  a slope -6 is given by

[tex]y+3=-6(x+9)[/tex]

Answer:

  40π/3 cm^2

Step-by-step explanation:

The centerline of the shaded region has a radius of 3 +4/2 = 5 cm. Its length is 1/3 of a circle with that radius, so is ...

  length of centerline = (1/3)(2π·5 cm) = (10/3)π cm

The shaded region is 4 cm wide, so the area is the product of that width and the centerline length:

  (4 cm)(10/3 π cm) = 40π/3 cm^2

Answer:

D. y = 10000 - 750x

Step-by-step explanation:

The answer is D. y = 10000 - 750x, where:

y = the current value of the car,

10000 is the initial value of the car

750 is the depreciation it has every year

x is the number of years.

The 10000 has to be fixed and not multiplied by anything (unlike answer A or C) because that's the initial value of the car.  Then it has to be reduced (meaning we take value of out it, so a subtraction), so that excludes A and B.  The devaluation occurs every year, so it has to be multiplied by the number of years (excluding answers A and C again).  So, only answer D remains.

Final answer:

The equation that best models the depreciation of the car is: y = 10000 - 750x. This equation represents the value of the car decreasing by $750 each year.

Explanation:

The equation that best models the depreciation of the car is: y = 10000 - 750x.

This equation is derived from the given information that the car depreciates by $750 each year, which is a constant amount. The equation represents the value of the car, denoted by 'y', decreasing by $750 for each year, denoted by 'x'.

For example, if we plug in x = 1 into the equation, we get y = 10000 - 750(1) = 9250, which means the car is worth $9250 after the first year.

Move the 5 to the other side:

[tex]2\sec(x)=1-5=-4[/tex]

Divide both sides by 2:

[tex]\sec(x) = -2[/tex]

Recall the definition:

[tex]\sec(x)=-2 \iff \dfrac{1}{\cos(x)}=-2[/tex]

Invert both sides

[tex]\cos(x) = -\dfrac{1}{2}[/tex]

This is true when

[tex]x=\pm \dfrac{\pi}{3}[/tex]

If you need both angles to be in [0,2pi], you can recall

[tex]\cos\left(-\dfrac{\pi}{3}\right) = \cos\left(-\dfrac{\pi}{3}+2\pi\right) = \cos\left(\dfrac{5\pi}{3}\right)[/tex]

So, the solutions are

[tex]x=\dfrac{\pi}{3},\quad x=\dfrac{5\pi}{3}[/tex]

Answer:

2pi/3 and 4pi/3

Step-by-step explanation:

this is the answer according to apex

Answer:

It's answers 1 and 3

Step-by-step explanation:

The meeting is not mandatory and only volunteers are participating in the task he wanted, this shows bias and doesn't correctly represent the whole team.

Let [tex]a[/tex] be the number of hours worked at Job A and [tex]b[/tex] the number of hours at Job B. Then

[tex]a+b=30[/tex]

and

[tex]7.5a+8b=234.50[/tex]

From the first equation,

[tex]b=30-a[/tex]

and substituting this into the second gives

[tex]7.5a+8(30-a)=234.50\implies-0.5a+240=234.50[/tex]

[tex]\implies0.5a=5.50[/tex]

[tex]\implies\boxed{a=11}[/tex]

Answer:

Its called Omae Wa Mou Shindeiru.....then NANI?!

Step-by-step explanation:

and 11 is your answer....

____________________________________________________

Answer:

Your answer would be 3/7 or [tex]\frac{3}{7}[/tex]

____________________________________________________

Step-by-step explanation:

In this type of question, we would need to find out the chances of getting something as an outcome, and that would be expressed as a fraction.

In order to find out the chance (or likeliness) of an outcome, we would need o use the information provided in the question.

Let's give you some key information that was given to us.

Key information:

4 animal characters

3 Human characters

With the information above, we can figure out what would be the probability of an outcome.

The question is saying "what is the probability of the computer picking a human character." That means that the amount of human characters would go on our numerator.

There's not only human characters, but there are 4 animal characters too, so that would be used to give us our total. the "4" will be added to our denominator.

Now, let's write it in a fraction.

Fraction: [tex]\frac{numerator}{denominator}[/tex]

We know that we are trying to find the probability of getting a human character, so "3" would go on our numerator.

For our denominator, we would add up both numb ers since it would have to be the total amount of options in order to find the probability, and that would be "7" since 4 + 3 = 7.

When you put those into a fraction. Your FINAL answer would be:

3/7 or [tex]\frac{3}{7}[/tex]

____________________________________________________

then jeans will cost $38.25

Answer:

the answer would be $35.70

Step-by-step explanation:

0.70 x $60 = $42

0.85 x $42 = $35.70

This is using multipliers so the amount off will be taken away from 1 and that answer times amount needed to found from will give the answer you are looking for

Answer:

Conjugate radicals.

Step-by-step explanation:

The two roots a+√b and a-√b are called Conjugate radicals.

Just like in the complex number system where we have complex conjugates such as of 4+7i and 4 - 7i, the radicals also have their conjugate radicals. The conjugate radical of a+√b is simply obtained by changing the sign of the radical part of the expression to obtain a-√b. Therefore, the two expressions given are conjugate radicals

Answer:

Conjugate.

Step-by-step explanation:

The difference is in the signs. They are conjugate radicals.

Answer:

18% reduction leaves 82% remaining. 82% of $2150 = .82(2150) = $1763.

Answer:

Retail Price = $1763

Step-by-step explanation:

List price of article = $2150

Percentage discount given = 18%

Then value of discount on the list price = 18% of $2150

                                                                 = [tex]\frac{(2150)(18)}{100}[/tex]

                                                                 = $387

Now the retail price of the article = List price - discount given

                                                       = $2150 - $387

                                                       = $1763

Therefore, Retail price of the article will be $1763

Explaining the quadratic formula application in solving an equation.

The quadratic formula:

Answer: Option B

[tex]y=0.5x +0.75[/tex]

Step-by-step explanation:

The equation modeling this situation is a linear equation of the form

[tex]y = mx + b[/tex]

Where x is the slope and b is the intercept with the y axis.

To find the equation of a line we need two points that belong to the line.

We know that when it is empty the jug weighs 0.75 lib.

This is:

When x = 0, y = 0.75

Then when the jug contains 3 cups of water it weighs 2.25 pounds.

This is:

When x = 3, y = 2.25

We already have the two points

Then we find the slope of the straight

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]y_2 = 2.25\\\\y_1=0.75\\\\x_2=3\\\\x_1=0[/tex]

[tex]m=\frac{2.25-0.75}{3-0}[/tex]

[tex]m = 0.5[/tex]

The equation is:

[tex]y=0.5x +b[/tex]

We substitute the point (0, 0.75) in the equation and solve for b

[tex]0.75=0.5(0) +b[/tex]

[tex]b=0.75[/tex]

Finally the equation is:

[tex]y=0.5x +0.75[/tex]

Answer:

no freaking way, is the state test? because if it is, then wow, you need to do your work

Step-by-step explanation:

Answer:

Part 1) [tex]9x-7y=-25[/tex]

Part 2) [tex]2x-y=2[/tex]

Part 3) [tex]x+8y=22[/tex]  

Part 4) [tex]x+8y=35[/tex]

Part 5) [tex]3x-4y=2[/tex]

Part 6) [tex]10x+6y=39[/tex]

Part 7) [tex]x-5y=-6[/tex]

Part 8)

case A) The equation of the diagonal AC is [tex]x+y=0[/tex]

case B) The equation of the diagonal BD is [tex]x-y=0[/tex]

Step-by-step explanation:

Part 1)

step 1

Find the midpoint

The formula to calculate the midpoint between two points is equal to

[tex]M=(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]

substitute the values

[tex]M=(\frac{2-6}{2},\frac{-3+5}{2})[/tex]

[tex]M=(-2,1)[/tex]

step 2

The equation of the line into point slope form is equal to

[tex]y-1=\frac{9}{7}(x+2)\\ \\y=\frac{9}{7}x+\frac{18}{7}+1\\ \\y=\frac{9}{7}x+\frac{25}{7}[/tex]

step 3

Convert to standard form

Remember that the equation of the line into standard form is equal to

[tex]Ax+By=C[/tex]

where

A is a positive integer, and B, and C are integers

[tex]y=\frac{9}{7}x+\frac{25}{7}[/tex]

Multiply by 7 both sides

[tex]7y=9x+25[/tex]

[tex]9x-7y=-25[/tex]

Part 2)

step 1

Find the midpoint

The formula to calculate the midpoint between two points is equal to

[tex]M=(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]

substitute the values

[tex]M=(\frac{1+5}{2},\frac{0-2}{2})[/tex]

[tex]M=(3,-1)[/tex]

step 2

Find the slope

The slope between two points is equal to

[tex]m=\frac{-2-0}{5-1}=-\frac{1}{2}[/tex]

step 3

we know that

If two lines are perpendicular, then the product of their slopes is equal to -1

Find the slope of the line perpendicular to the segment joining the given points

[tex]m1=-\frac{1}{2}[/tex]

[tex]m1*m2=-1[/tex]

therefore

[tex]m2=2[/tex]

step 4

The equation of the line into point slope form is equal to

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=2[/tex] and point [tex](1,0)[/tex]

[tex]y-0=2(x-1)\\ \\y=2x-2[/tex]

step 5

Convert to standard form

Remember that the equation of the line into standard form is equal to

[tex]Ax+By=C[/tex]

where

A is a positive integer, and B, and C are integers

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

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

Part 3)

In this problem AB and BC are the legs of the right triangle (plot the figure)

step 1

Find the midpoint AB

[tex]M1=(\frac{-5+1}{2},\frac{5+1}{2})[/tex]

[tex]M1=(-2,3)[/tex]

step 2

Find the midpoint BC

[tex]M2=(\frac{1+3}{2},\frac{1+4}{2})[/tex]

[tex]M2=(2,2.5)[/tex]

step 3

Find the slope M1M2

The slope between two points is equal to

[tex]m=\frac{2.5-3}{2+2}=-\frac{1}{8}[/tex]

step 4

The equation of the line into point slope form is equal to

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=-\frac{1}{8}[/tex] and point [tex](-2,3)[/tex]

[tex]y-3=-\frac{1}{8}(x+2)\\ \\y=-\frac{1}{8}x-\frac{1}{4}+3\\ \\y=-\frac{1}{8}x+\frac{11}{4}[/tex]

step 5

Convert to standard form

Remember that the equation of the line into standard form is equal to

[tex]Ax+By=C[/tex]

where

A is a positive integer, and B, and C are integers

[tex]y=-\frac{1}{8}x+\frac{11}{4}[/tex]

Multiply by 8 both sides

[tex]8y=-x+22[/tex]

[tex]x+8y=22[/tex]  

Part 4)

In this problem the hypotenuse is AC (plot the figure)

step 1

Find the slope AC

The slope between two points is equal to

[tex]m=\frac{4-5}{3+5}=-\frac{1}{8}[/tex]

step 2

The equation of the line into point slope form is equal to

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=-\frac{1}{8}[/tex] and point [tex](3,4)[/tex]

[tex]y-4=-\frac{1}{8}(x-3)[/tex]

[tex]y=-\frac{1}{8}x+\frac{3}{8}+4[/tex]

[tex]y=-\frac{1}{8}x+\frac{35}{8}[/tex]

step 3

Convert to standard form

Remember that the equation of the line into standard form is equal to

[tex]Ax+By=C[/tex]

where

A is a positive integer, and B, and C are integers

[tex]y=-\frac{1}{8}x+\frac{35}{8}[/tex]

Multiply by 8 both sides

[tex]8y=-x+35[/tex]

[tex]x+8y=35[/tex]

Part 5)  

The longer diagonal is the segment BD (plot the figure)  

step 1

Find the slope BD

The slope between two points is equal to

[tex]m=\frac{4+2}{6+2}=\frac{3}{4}[/tex]

step 2

The equation of the line into point slope form is equal to

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=\frac{3}{4}[/tex] and point [tex](-2,-2)[/tex]

[tex]y+2=\frac{3}{4}(x+2)[/tex]

[tex]y=\frac{3}{4}x+\frac{6}{4}-2[/tex]

[tex]y=\frac{3}{4}x-\frac{2}{4}[/tex]

step 3

Convert to standard form

Remember that the equation of the line into standard form is equal to

[tex]Ax+By=C[/tex]

where

A is a positive integer, and B, and C are integers

[tex]y=\frac{3}{4}x-\frac{2}{4}[/tex]

Multiply by 4 both sides

[tex]4y=3x-2[/tex]

[tex]3x-4y=2[/tex]

Note The complete answers in the attached file

Answer:

1. There is a negative correlation between time (in days) and the number of push-ups Juan does.

Step-by-step explanation:

The slope of the regression line (0.631) is positive, so the correlation between days and pushups is positive.

Answer: first option.

Step-by-step explanation:

Given the right triangle shown in the figure, to calculate the measure of the angle m∠C, you can use the inverse function of the cosine:

[tex]\alpha=arccos(\frac{adjacent}{hypotenuse})[/tex]

You can identify in the figure, that, for the angle ∠C:

[tex]\alpha=\angle C\\adjacent=7\\hypotenuse=15[/tex]

Then, since you know the lenght of the adjacent side and the lenght of the hypotenuse, you can substitute these values into  [tex]\alpha=arccos(\frac{adjacent}{hypotenuse})[/tex].

Therefore, the measure of the angle ∠C is:

[tex]\angle C=arccos(\frac{7}{15})\\\\\angle C=62.2\°[/tex]

Andy earns $8.50 per hour by dividing the total amount he earns ($34).

To find out how much Andy earns for each hour he works, you need to divide the total amount he earns by the number of hours he works on Saturday morning. If Andy earns $34 over 4 hours, his hourly wage is calculated as follows:

Divide $34 by 4 hours.

$34 / 4 hours = $8.50 per hour.

So, Andy earns $8.50 per hour.

Related Scenarios

At an hourly wage of $10 per hour, a similar worker like Marcia Fanning is willing to work 36 hours per week.

With increased hourly wages between $30 and $40, Marcia decides to work 40 hours per week.

When offered $50 per hour, she chooses to reduce her hours to 35 per week, likely to balance her work and leisure time in a way that maximizes her utility.

These examples illustrate how an increase in hourly wage can influence the number of hours a person is willing to work to balance overall life satisfaction and economic benefits