What is a correct first step in solving the inequality-4(3-5x)>-6x+9

Answer:

Mean Absolute Deviation (MAD): 8.5

Step-by-step explanation:

Xmean = (28 + 32 + 47 + 16 + 40 + 35 + 38 + 54)/8  = 290/8

Xmean = 36.25

MAD =

(28 - 36.25) + (32 - 36.25) + (47 - 36.25) + (16 - 36.25) + (40 - 36.25) + (35 - 36.25) + (38 - 36.25) + (54 - 36.25)  divided by 8

a break down of each ( )

(8.25) + (4.25) + (10.75) + (20.25) + (3.75) + (1.25) + (1.75) + (17.75)  divided by 8  =  68

then you take 68/8 = Mean Absolute Deviation  8.5

Answer:

Mean Absolute Deviation (M.A.D): 8.5

Step-by-step explanation:

1. To find the mean absolute deviation of the data, start by finding the mean of the data set.

2. Find the sum of the data values, and divide the sum by the number of data values.

3. Find the absolute value of the difference between each data value and the mean: |data value – mean|.

4. Find the sum of the absolute values of the differences.

5. Divide the sum of the absolute values of the differences by the number of data values.

Hope that helped! :)

Answer:

Part 1) ∠ABD=23.9°

Part 2) ∠ADB=119.1°

Part 3) AB=506.7 ft

Part 4) ∠BDE=60.9°

Part 5) ∠BED=77.1°

Part 6) DE=239.6 ft

Part 7) BE=312.8 ft

Part 8) ∠BEC=102.9°

Part 9) ∠EBC=36.1°

Step-by-step explanation:

Let

A-----> Zebra house

B ----> Entrance

C ----> Tiger house

D ---> Giraffe house

E ----> Hippo house

see the attached figure with letters to better understand the problem

step 1

In the triangle ABD

Find the measure of angle ABD

Applying the law of sines

sin(37°)/349=sin(ABD)/235

sin(ABD)=235*sin(37°)/349

sin(ABD)=0.4052

∠ABD=arcsin(0.4052)=23.9°

step 2

In the triangle ABD

Find the measure of angle ADB

Remember that the sum of the internal angles of a triangle must be equal to 180 degrees

so

∠ADB+23.9°+37°=180°

∠ADB+23.9°+37°=180°-60.9°

∠ADB=119.1°

step 3

In the triangle ABD

Find the measure of side AB

Applying the law of sines

sin(37°)/349=sin(119.1°)/AB

AB=349*sin(119.1°)/sin(37°)

AB=506.7 ft

step 4

In the triangle BDE

Find the measure of angle BDE

we have

∠BDE+∠ADB=180° ----> by supplementary angles

∠ADB=119.1°

substitute

∠BDE+119.1°=180°

∠BDE=180°-119.1°

∠BDE=60.9°

step 5

In the triangle BDE

Find the measure of angle BED

Remember that the sum of the internal angles of a triangle must be equal to 180 degrees

so

∠BED+60.9°+42°=180°

∠BED=180°-102.9°

∠BED=77.1°

step 6

In the triangle BDE

Find the measure of side DE

Applying the law of sines

sin(77.1°)/349=sin(42°)/DE

DE=349*sin(42°)/sin(77.1°)

DE=239.6 ft

step 7

In the triangle BDE

Find the measure of side BE

Applying the law of sines

sin(77.1°)/349=sin(60.9°)/DE  

BE=349*sin(60.9°)/sin(77.1°)

BE=312.8 ft

step 8

In the triangle BEC

Find the measure of angle BEC

we have

∠BEC+∠BED=180° ----> by supplementary angles

∠BED=77.1°

substitute

∠BEC+77.1°=180°

∠BEC=180°-77.1°

∠BEC=102.9°

step 9

In the triangle BEC

Find the measure of angle EBC

Remember that the sum of the internal angles of a triangle must be equal to 180 degrees

so

∠EBC+102.9°+41°=180°

∠EBC=180°-143.9°

∠EBC=36.1°

Answer:

b² = 2bx - 2by

Step-by-step explanation:

2x + b = y + 2b

b = 2x - y

b² = (2x - y)²

b² = (2x - y)(2x - y)

b² = 4x² - 2xy - 2xy + y²

b² = 4x² - 4xy + y²

Answer:

600 feet

Step-by-step explanation:

I am assuming that the park is rectangular, and the together, the length, with and diagonal form a right triangle.

In this case, we are given

Diagonal = 750 ft = hypotenuse

Width = 450 feet

Find length L

Using the Pythagorean theorem,

L² + 450² = 750²

L² = 750² - 450² = 360,000

L= √360,000 = 600 feet

Answer:

C, 600 ft.

Step-by-step explanation:

a^2+b^2=c^2

C is always the hypotenuse/diagonal. Let A represent length and B represent width.

A^2+450^2=750^2

A^2+202500=562500

562500-202500=360000=A^2

take the square root of both sides to solve for A and the value of A is 600.

Answer:

Step-by-step explanation:

Point slope form is y-y1=m(x-x1)

(x1,y1) is (-9,-3)

m is -6

Plug in!

y-(-3)=(-6)(x-(-9)) The answer could look like this.

y+3=-6(x+9)    Or this.

y=-6(x+9)-3     Or this

y=-6x-54-3     Even this but unlikely...

y=-6x-57         Or this.

I will change my answer after choices are posted.

Answer:

y+3 = -6(x+9)  point slope form

y = -6x-57  slope intercept form

Step-by-step explanation:

We can use the point slope equation of a line

y-y1 = m(x-x1)

y--3 = -6(x--9)

y+3 = -6(x+9)

If we want the equation in point slope form

Distribute the -6

y+3 = -6x -54

Subtract 3 from each side

y+3-3 = -5x-54 -3

y = -6x-57

Answer:

a) y=1/3 sqrt(x+1)

b) 2/3

c) 224

Step-by-step explanation:

a) y varies directly to sqrt(x+1)

means there is some constant k such that y=ksqrt(x+1)

y=1 when x=8  (plug this in and find k)    1=ksqrt(8+1)

                                                                 1=ksqrt(9)

                                                                 1=k(3)

                                                                 1/3=k

So the equation is y=1/3 * sqrt(x+1)

a)  y=1/3 *sqrt(x+1)

b) what is y when x=3 if you have y=1/3 * sqrt(x+1)

Plug in 3 for x            

y=1/3 *sqrt(3+1)

y=1/3 *sqrt(4)

y=1/3 *2

y=2/3

b) 2/3

c) what is x when y=5

Plug in 5 for y

5=1/3 *sqrt(x+1)

multiply both sides by 3

15=sqrt(x+1)

square both sides

225=x+1

subtract 1 on both sides

224=x

c) 224

The length of the sunken ship is 28.56m

To calculate the length of the sunken ship , we have to calculate the distance between the beneath of the ship to the front and to the back.

distance between the beneath of the ship to back of the sunken ship

Tan 62 = 200/x

x = 200/tan 62

x = 106.34m

distance between the beneath of the ship to front of the sunken ship

Tan 56 = 200/y

y = 200/tan 56

y = 134.90m

The length of the sunken ship = 134 .90 - 106.34

= 28.56m

your correct it is 240

lengthxwidthxheight

8x6x5=240

Answer:

2 hours 18 minutes (to the nearest minute)

Step-by-step explanation:

6.5 / 0.5 hours

--> Multiply the whole equation by 4.61538461538 so that 6.5 becomes 30

= 30 papers in 2.30769230769 hours = 02:18:28

Mrs. Bell will take 2 hrs 18 mins approximately.

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

Given that 6.5 students' papers can be checked in 0.5 hours

1 student's paper can be checked in 0.5/6.5 hours

30 students' paper can be checked in (0.5 /6.5)*30 hours = 2.307 hours

Therefore, Mrs. Bell will take 2 hrs 18 mins approximately.

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Answer:

A.) an algebraic expression

Step-by-step explanation:

Note that there are only integers (whole numbers) and the usage of algebraic operations. Also note that there is no "equal" sign (which would make it an equation), making the problem a expression.

~

Answer:

∠QPR must be an acute angle

Step-by-step explanation:

Given : ∠MPR is an acute angle and PQ is in the interior of ∠MPR.

To Find :∠QPR must be?

Solution:

Acute Angle : An angle whose measure is less than 90°

Since ∠MPR is an acute angle

This means ∠MPR is less than 90°

Now PQ is in the interior of ∠MPR

So, referring the attached figure

∠QPR should be less than ∠MPR

So, the measure of ∠QPR should be less than ∠MPR

So,  the measure of ∠QPR is also less than 90°

So, ∠QPR must be an acute angle

So, Option D is correct.

Answer: D. Acute

Step-by-step explanation:

We are given that : ∠MPR is an acute angle and PQ is in the interior of ∠MPR.

Definition :

Acute Angle : An angle having measure is less than 90°

.

Obtuse angle : An angle having measure is greater than 90° but less than 180

°.

Right angle : An angle whose measure exactly 90°

.

Straight angle : An angle whose measure exactly 180°

.

∵∠MPR is an acute angle  ,

Then ∠MPR must be less than 90°

.

Also, PQ is in the interior of ∠MPR

.

⇒∠QPR should be less than ∠MPR

.

⇒ the measure of ∠QPR is also less than 90°

⇒∠QPR must be an acute angle  . [By definition of Acute angle.]

Hence, the correct answer is option D.

Answer: Third option.

Step-by-step explanation:

Given the expression [tex]\frac{2x+4}{x+1}+\frac{-x+5}{x+1}[/tex] you need to make the addition indicated.

First, it is important to remember the multiplication of signs:

[tex](+)(+)=+\\(-)(-)=+\\(-)(+)=-[/tex]

Therefore, since both fractions have equal denominator, you can rewrite the same denominator and add the numerators. Then you get that the sum is:

 [tex]\frac{2x+4}{x+1}+\frac{-x+5}{x+1}=[/tex][tex]\frac{(2x+4)+(-x+5)}{x+1}=\frac{2x+4-x+5}{x+1}=\frac{x+9}{x+1}[/tex]  

Answer:

The correct answer is third option

(x + 9)/(x + 1)

Step-by-step explanation:

It is given an expression,

(2x + 4)/(x + 1)  + (-x + 5)/(x + 1)

To find the sum

The given expression shows the sum of two fractions,

The denominators are same

(2x + 4)/(x + 1)  + (-x + 5)/(x + 1)

 = [2x + 4 + -x + 5]/(x + 1)

 = (x + 9)/(x + 1)

Therefore the correct answer is third option

(x + 9)/(x + 1)

Answer:

(16,-12)

Step-by-step explanation:

To find where these lines intersect, we must first know their slope. If the slope is equal, then the lines don't intersect and they are parallel.

The best formula for knowing slope is slope-intercept form, y=mx+b whereas m is the slope and b is the y-intercept (where the line crosses x=0)

The first equation is already in slope-intersect form so we can substitute the section that is equal to y into the second equation where y is.

x + 2(-x + 4) = -8

x + -2x + 8 = -8

-x + 8 = -8

-x = - 16

x = 16

Now we can use this known variable to find y.

y = -(16) + 4

y = -16 + 4

y = -12

How many points are there total? (3*100)+250 = 550

So far, he has 72 + 85 + 78, or 235

He needs 0.80 * 550 for a B, or 440 points

440 - 235 = 205 points on the final to get a B

Percentage-wise, he needs 205/250, or 0.82

Answer:

40%

Step-by-step explanation:

2 out of 5 of the rectangles are shaded. With a ratio of 2/5 this represented as a percent is 40%

Answer:

40%.

Step-by-step explanation:

2 out of 5 rectangles are shaded.

As a percentage that is 2/5 * 100 = 40%.

Answer:

8%

Step-by-step explanation:

[tex]4 \div 50 \times 100 \: = \: 8[/tex]

Hello There!

[tex]\frac{4}{50}[/tex] as a percentage is 8%

You can first reduce this fraction by dividing both the numerator and denominator by the Greatest Common Factor of 4 and 50 using 2.

4 ÷ 2 ≈ 2

50 ÷ 2 ≈ 25

We now have a fraction [tex]\frac{2}{25}[/tex]

We now divide 2 by 25 and we get a quotient of 0.08

Finally we multiply 0.08 by 100 and we get 8 so 4/50 as a percentage is 8%

Answer:

13.9 is the right answer :)

Step-by-step explanation:

For this case we have to define trigonometric relations of rectangular triangles, that the tangent of an angle is given by the leg opposite the angle on the leg adjacent to the angle.

Then, according to the figure we have:

[tex]tg (60) = \frac {y} {8}\\y = 8 * tg (60)\\y = 8 * 1.73205081\\y = 13,85640648[/tex]

Rounding the value we have that [tex]y = 13.9[/tex]

ANswer:

Option B

I will assume that line 4 bisect line x exactly in half. This means that if we solve the last side of the triangle like seen in the pic below we will know what half of line x is

To find the length of the last side of the triangle (let's call this y) you must use Pythagorean theorem

[tex]a^{2} +b^{2}=c^{2}[/tex]

a and b are the legs (the sides that form a perpendicular/right angle)

c is the hypotenuse (the side opposite the right angle)

In this case...

a = 4

b = y

c = 6

^^^Plug these numbers/variables into the theorem

[tex]4^{2} +y^{2} =6^{2}[/tex]

solve for y

16 + [tex]y^{2}[/tex]  = 36

[tex]y^{2}[/tex] = 20

x = √20

x ≈ 4.472

^^^This is only half of x so if you double it then it will get you the full length of x

4.472 * 2 = 8.944

8.9 (D)

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

Answer will be: Jeremy is looking at the rate for renting a bike for 2 hours. To find the rate for one hour divide 7 by 2. The rate for renting a bike for one hour is $3.50.

The mistake that jeremy made is that the cost renting is not $7.00 for hour, it is $7.00 for two hours.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value

Given:

The table is attached below

Jeremy said the cost bike renting for an hour is $7.00. But looking at the table the difference between two consecutive cost is $7.00 not in the gap of 1 hour in fact in gap of 2 hours.

It means that the the cost of bike renting $7.00 is for 2 hours.

For an hour the cost for renting bike will be,

=7/2

=3.5 hours.

Hence, the cost of bike renting is 3.5 hours per hour.

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Answer:

b and d

Step-by-step explanation:

The figure has 12 peaks. A full circle has 360 degrees.

(360 degrees)/12 = 30 degrees.

b. It has rotational symmetry with an angle of rotation of 30 deg.

If you draw a line between each pair of opposite peaks, that line is an axis of reflectional symmetry. Since there are 12 peaks, there are 6 such lines.

d. It has reflectional symmetry with 6 lines of symmetry.

Answer:

It has rotational symmetry with an angle of rotation of 30°.

Step-by-step explanation:

A shape is said to possess rotational symmetry, when it still looks the same after some rotation.

We can see, that the given shape looks the same from every angle and every side.

So, the correct answer is: It has rotational symmetry with an angle of rotation of 30°.

30 degrees because it has 12 angles and [tex]360/12=30[/tex] degrees.

Answer:

Distributive Property.

Step-by-step explanation:

Cos(A-B)= Cos A- Cos B

The variables in the parenthesis gets multiplied into the Cos

Cos A - Cos B

Answer: 5

Step-by-step explanation: The distance between two numbers can be found by finding the absolute value of the difference of the numbers. Put more simply, subtract -3 - 2 to get -5, which has an absolute value of 5. Or, you can do 2 - -3 to get 5, which has the same absolute value of 5.

The distance between -3 and 2 on the number line is 5 units.

It is the measurement done between two points on a surface.

Distance=speed*time

If we plot -3 and 2 on the number we find that -3 will be on the left side of 0 and 2 will be on the right side of 0. To reach 2 from -3 we have to first go to-2 then -1, then 0 and then 0 to 1 and 1 to 2.

Hence we have to go to 5 units. That's why the distance between -3 and 2 is 5 units.

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Step-by-step explanation:

6 (x+5 )^2 +5(x+5)-4=0

let x+5= y

6y^2 + 5y - 4=0

6y^2 + 8y - 3y-4 =0

2y (3y+4) - 1 (3y+4)=0

(2y-1)(3y+4)=0

2y-1=0 or 3y+4=0

y=1/3 or -4/3

Recall that x+5=y

When y=1/3

x+5=1/3

x= -14/3

when y= -4/3

x+5=-4/3

x = -11/3

Answer:

u=(x+5)

Step-by-step explanation:

Answer:

($4.00/x)+($4.50/y)

Step-by-step explanation:

we know that

Apples cost 80 cents for x apples

so

One apple cost $0.80/x

Oranges cost 75 cents for y oranges

so

One orange cost $0.75/y

Find the cost of 5 apples and 6 oranges

Multiply the number of apples by the cost of one apple and multiply the number of oranges by the cost of one orange

so

5($0.80/x)+6($0.75/y)=($4.00/x)+($4.50/y)

Final answer:

The cost of 5 apples at 80 cents each is $4.00 and the cost of 6 oranges at 75 cents each is $4.50. The total cost for 5 apples and 6 oranges is therefore $8.50.

Explanation:

To calculate the cost, in dollars, of 5 apples and 6 oranges at a fruit stand where apples cost 80 cents for x apples and oranges cost 75 cents for y oranges, you can follow these steps:

Determine the cost per apple by dividing 80 cents by x. Since we do not have the value of x, assume x equals 1 for this explanation, making the cost 80 cents per apple.

Multiply the cost per apple by 5 to find the total cost for 5 apples.

Determine the cost per orange by dividing 75 cents by y. Assuming y equals 1 for this explanation, the cost is 75 cents per orange.

Multiply the cost per orange by 6 to find the total cost for 6 oranges.

Add the total cost for apples and oranges to find the combined cost, converting cents to dollars as necessary.

Therefore, the cost for 5 apples is 5 × 0.80 = $4.00, and the cost for 6 oranges is 6 × 0.75 = $4.50. Adding these together, the total cost for 5 apples and 6 oranges is $4.00 + $4.50 = $8.50.

Answer:

A

Step-by-step explanation:

The equation of a circle is:

(x - h)² + (y - k)² = r²

where (h, k) is the center and r is the radius.

Here, the center is (2, 1) and the radius is 1.

(x - 2)² + (y - 1)² = 1²

The equation of the given circle is Option(A)  [tex](x-2)^{2} + (y - 1)^{2} = 1[/tex] .

The standard equation of any circle is given as -

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

where (h,k) is the coordinate of the center of the given circle and r is the length of radius of the circle.  

In the diagram given aside, we can see that the circle has its center at (2,1) and also the radius of the circle measures 1 units.

Thus, we have h = 2 , k = 1 and r = 1 in the standard representation.

The equation of the circle is -

⇒ [tex](x-2)^{2} + (y - 1)^{2} = 1^{2}[/tex]

∴  [tex](x-2)^{2} + (y - 1)^{2} = 1[/tex]

Therefore, the equation of the given circle is Option (A) [tex](x-2)^{2} + (y - 1)^{2} = 1[/tex] .

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Final answer:

The domain of the pancake mix function N(p) is 0 <= p <= 4 and the range is 0 <= N(p) <= 480, assuming the school has 4 packages and each package feeds 120 people.

Explanation:

The high school pancake breakfast fundraiser question deals with writing the domain and range for a given function. Our function is N(p) = 120p, where N(p) represents the number of people fed by p packages of pancake mix, and each package feeds 120 people. Since the school has 4 packages of pancake mix, the domain, which is the set of all possible values of p (packages), would be 0 <= p <= 4, as they cannot use negative packages and have only 4 packages available. The corresponding range would be the number of people that can be fed, which is from 0 to 4 times 120, so 0 <= N(p) <= 480.

Final answer:

The total number of roots in the function H(x) = x³ - 7x² - x + 7 is 3, with 2 real roots and 1 complex root.

Explanation:

The function H(x) = x³ - 7x² - x + 7 is a cubic function, meaning it is a polynomial of degree 3. The total number of roots for a cubic function is always 3. This is because the highest power of x in the function is 3.

To determine the number of real roots, we can use the rule of signs. We count the number of sign changes in the coefficients of the function. In this case, we have two sign changes from positive to negative. Therefore, there are either 2 or 0 real roots.

To find the number of complex roots, we subtract the number of real roots from the total number of roots. So, in this case, there must be 3 - 2 = 1 complex root.

The number of roots that the function H(x) has is: a total of 3 roots

What is the number of roots of the Polynomial?

The function H(x) = x³ - 7x² - x + 7 is a polynomial of degree 3.

According to the fundamental theorem of algebra, a polynomial of degree n has exactly n roots, counting multiplicities.

In this case, the function has 3 roots, which may be real or complex, taking into account their multiplicities. The number of roots is determined by the degree of the polynomial, and the roots are the values of x for which the polynomial is equal to zero. Therefore, the function H(x) has a total of 3 roots

Answer:

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

Step-by-step explanation:

Given equation of line is:

2x-3y=13

We will convert the equation of line in point-slope form to find the slope of the line

Let  

m_1  be the slope of the line

So,

2x-3y=13

-3y= -2x+13

Dividing both sides by -3

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

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

The co-efficient of x is the slope of the line.

So,

m_1=2/3

Let

m_2  be the slope of second line

As we know that product of slopes of two perpendicular line is -1

m_1 m_2= -1

2/3*m_2= -1  

m_2= -1*3/2

m_2= -3/2

So m2 is the slope of the line perpendicular to given line.

The standard equation of a line is  

y=mx+b

To find the equation of line through (-6,5), put the point and slope in the given form and solve for b

5= -3/2 (-6)+b

5=18/2+b

5=9+b

b=5-9

b= -4  

Putting the values of slope and b, we get

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

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

Step-by-step explanation:

The equation of the line in Slope-intercept form is:

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

Where "m" is the slope and "b" is the y-intercept.

To express the given equation of the line in this form, we need to solve for "y":

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

We can identify that the slope of this line is:

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

Since the slopes of perpendicular lines are negative reciprocals, then the slope of the other line is:

[tex]m=-\frac{3}{2}[/tex]

Now, we need to substitute the given point  and the slope into  [tex]y=mx+b[/tex] and solve for "b":

[tex]5=-\frac{3}{2}(-6)+b\\\\5=9+b\\\\5-9=b\\\\b=-4[/tex]

Substituting values, we get that the equation of this line is:

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

Answer: We need a picture or a description of how we need to find the value ok k.

Step-by-step explanation:

recall your d = rt, distance = rate * time.

s = Samantha's speed rate

one thing to bear in mind is that, when Samantha is going upstream, she's not really going "s" mph fast, because she's going against the current, and the current's rate is 4 mph and subtracting speed from her, then she's really going "s - 4" fast.

Likewise, when she's going downstream because she's going with the current, the current is adding speed to her, so she's going "s + 4" fast.

Now, let's say the distance she covered both ways was the same "d" miles.

Let's recall that since there are 60 minutes in 1 hour, 12 minutes is 12/60 = 1/5 of an hour.

[tex]\bf \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ Upstream&d&s-4&1\\ Downstream&d&s+4&\frac{1}{5} \end{array}\qquad \implies \begin{cases} d=(s-4)(1)\\ d=(s+4)\left( \frac{1}{5} \right) \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \stackrel{\textit{from 1st equation}}{\boxed{d}=s-4}\qquad \qquad \stackrel{\textit{substituting on the 2nd equation}~\hfill }{\boxed{s-4}=\cfrac{s+4}{5}\implies 5s-20=s+4} \\\\\\ 4s-20=4\implies 4s=24\implies s=\cfrac{24}{4}\implies s=6[/tex]

Answer:

6 mph

Step-by-step explanation:

Let the the total distance is D and the speed of Samantha's speed in still water is x ( in mph ),

Here, speed of stream = 4 mph,

Thus, the speed in upstream = (x - 4) mph,

Speed in downstream = (x + 4) mph,

We know that,

[tex]Speed =\frac{Distance}{Time}\implies Time =\frac{Distance}{Speed}[/tex]

∴ Time taken in upstream = [tex]\frac{D}{x-4}[/tex]

And, time taken in downstream = [tex]\frac{D}{x+4}[/tex]

According to the question,

[tex]\frac{D}{x-4}=1\implies D = x-4-----(1)[/tex]

[tex]\frac{D}{x+4}=\frac{12}{60}\implies \frac{D}{x+4}=\frac{1}{5}\implies 5D=x+4----(2)[/tex]

Equation (1) - 5 equation (2),

0 = x + 4 - 5x + 20

0 = -4x + 24

4x = 24

⇒ x = 6 mph.

Hence, Samantha swims with the speed 6 mph.