Answer:
[tex]y-5=\frac{-1}{2}(x+2)[/tex] point-slope form
[tex]y=\frac{-1}{2}x+4[/tex] slope-intercept form
Step-by-step explanation:
The slope-intercept form of a line is y=mx+b where m is the slope and b is the y-intercept.
The slopes of perpendicular lines are opposite reciprocals.
The slope of y=2x-5 is 2.
So we are looking for a line perpendicular to y=2x-5 which means we first to the take the opposite reciprocal of it's slope giving us:
opposite reciprocal of (2) is opposite (1/2)=-1/2.
So the slope of the line we are looking for is -1/2.
This means are equation for our line is in this form:
[tex]y=\frac{-1}{2}x+b[/tex]
To find b we will use a point (x,y) that is on our line.
We are given a point (x,y)=(-2,5).
Plug this into our equation:
[tex]5=\frac{-1}{2}(-2)+b[/tex]
[tex]5=1+b[/tex]
Subtract 1 on both sides:
[tex]4=b[/tex]
So the equation for our line that we are looking for is:
[tex]y=\frac{-1}{2}x+4[/tex] (slope-intercept form).
You could also go for point-slope form [tex]y-y_1=m(x-x_1)[/tex] where m is the slope and [tex](x_1,y_1)[/tex] is a point on the line.
We have m=-1/2 and (x1,y1)=(-2,5) so our equation in point slope-form is:
[tex]y-5=\frac{-1}{2}(x-(-2))[/tex]
Simplifying just a hair:
[tex]y-5=\frac{-1}{2}(x+2)[/tex].
If f(x) = 3x? - 4 and g(x) = x+2, find (f - g)(x).
O
O
O
O
A. 3x2 - *-6
B. 3x2 - x-2
C. 3x -8
D. *- 3x - 2
Answer:
The answer is A, (3x2-x-6)
Step-by-step explanation:
f(x)=3x2 -4
g(x)=x+2
f(x)-g(x)= 3x2-4 -x-2= 3x2-x-6
Final answer:
The expression (f - g)(x) is found by subtracting g(x) from f(x) and simplifying, which results in 3x² - x - 6, corresponding to option A.
Explanation:
To find (f - g)(x) when f(x) = 3x² - 4 and g(x) = x + 2, we need to subtract the function g(x) from f(x). The operation looks like this:
(f - g)(x) = f(x) - g(x) = (3x² - 4) - (x + 2)
Let's perform the subtraction step by step:
Distribute the negative sign to both terms in g(x):
(3x²- 4) - x - 2
Combine like terms:
3x² - x - 4 - 2
Final simplification:
3x² - x - 6
Therefore, the correct answer is 3x² - x - 6, which matches option A from the provided choices.
the radius of Earth is 6400 km. the distance of the moon from the Earth's surface is 380000 km. find the radius of the moon which subtends an angle of 20'at the centre of the earth
Answer:
1100 km
Step-by-step explanation:
The problem doesn't clearly state whether the 380,000 km is from the Earth's surface to the moon's center, or to the moon's surface. Since we'll be rounding to 2 significant figures, it's not enough to make a difference, so I'll assume it's to the moon's center.
Draw circle representing the moon and earth. Draw tangent lines from the earth's center to the edge of the moon. The angle between these lines is the subtended angle. Now draw a line representing the moon's radius from the center of the moon to the point where the tangent line intersects. Notice this forms a right angle.
(See attached diagram)
Using trigonometry:
sin(θ/2) = r / (R + h)
r = (R + h) sin(θ/2)
Given that R = 6400 km, h = 380,000 km, and θ = 20' = 1/3 degrees:
r = (6400 + 380000) sin(1/6 °)
r = 1100
The moon's radius is 1100 km.
Determine the slant asymptote for the function f(x)=3x^2-4x + 5/ x-3
Answer:
y=3x+5
Step-by-step explanation:
To determine the slant asymptote you must perform polynomial division and also the degree of the numerator must be one greater than degree of the denominator for it to even exist. (We do have that here by the way since degree of the top is 2 and the degree of the bottom is 1).
Let's begin the division process:
I'm using synthetic. You can also use long.
3 goes on the outside because we are dividing by x-3
3 | 3 -4 5
| 9 15
----------------------
3 5 20
So [tex]\frac{3x^2-4x+5}{x-3}=3x+5+\frac{20}{x-3}[/tex]
So the slant aymptote is y=3x-5 since 20/(x-3) approaches 0 as x approaches infinity.
To find the slant asymptote of the given function, perform long division to divide the numerator by the denominator. As x approaches infinity, the slant asymptote is 3x + 5.
Explanation:To find the slant asymptote of the function f(x) = (3x^2 - 4x + 5) / (x - 3), we need to determine what happens as x approaches positive or negative infinity. We can do this by dividing the numerator polynomial by the denominator polynomial using long division.
Performing long division, we get:
3x^2 - 4x + 5 / (x - 3) = 3x + 5 + (8 / (x - 3))
As x approaches infinity, the 8 / (x - 3) term becomes negligible and we are left with the slant asymptote:
f(x) = 3x + 5
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Can someone please do 41 and 45???? Thanks!!!
Answer:
Part 41) The solution of the compound inequality is equal to the interval [-1.5,-0.5)
Part 45) The solution of the compound inequality is equal to the interval
(-∞, -0.5] ∪ [1,∞)
Step-by-step explanation:
Part 41) we have
[tex]-4\leq 2+4x < 0[/tex]
Divide the compound inequality into two inequalities
[tex]-4\leq 2+4x [/tex] -----> inequality A
Solve for x
Subtract 2 both sides
[tex]-4-2\leq 4x [/tex]
[tex]-6\leq 4x [/tex]
Divide by 4 both sides
[tex]-1.5\leq x [/tex]
Rewrite
[tex]x\geq -1.5[/tex]
The solution of the inequality A is the interval -----> [-1.5,∞)
[tex] 2+4x < 0[/tex] -----> inequality B
Solve for x
Subtract 2 both sides
[tex]4x < -2[/tex]
Divide by 4 both sides
[tex]x < -0.5[/tex]
The solution of the inequality B is the interval ------> (-∞, -0.5)
The solution of the inequality A and the Inequality B is equal to
[-1.5,∞)∩ (-∞, -0.5)------> [-1.5,-0.5)
see the attached figure N 1
Part 45) we have
[tex]2x-3\leq -4[/tex] or [tex]3x+1\geq 4[/tex]
Solve the inequality A
[tex]2x-3\leq -4[/tex]
Adds 3 both sides
[tex]2x\leq -4+3[/tex]
[tex]2x\leq -1[/tex]
Divide by 2 both sides
[tex]x\leq -0.5[/tex]
The solution of the inequality A is the interval ------> (-∞, -0.5]
Solve the inequality B
[tex]3x+1\geq 4[/tex]
Subtract 1 both sides
[tex]3x\geq 4-1[/tex]
[tex]3x\geq 3[/tex]
Divide by 3 both sides
[tex]x\geq 1[/tex]
The solution of the inequality B is the interval -----> [1,∞)
The solution of the compound inequality is equal to
(-∞, -0.5] ∪ [1,∞)
see the attached figure N 2
HELP FAST WILL MARK BRAINLIEST
How much money would you have to invest in order to get $20,000 after 25 years in a 11% annual interest account that is compounded weekly?
Answer:
[tex]\$1,282.28[/tex]
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=25\ years\\ A=\$20,000\\ r=0.11\\n=52[/tex]
substitute in the formula above
[tex]20,000=P(1+\frac{0.11}{52})^{52*25}[/tex]
[tex]20,000=P(1.0021)^{1,300}[/tex]
[tex]P=20,000/(1.0021)^{1,300}[/tex]
[tex]P=\$1,282.28[/tex]
Which equations and/or functions represent the graphed
line? Select four options.
Answer with explanation:
The equation of line having X intercept (-4,0) and Y intercept (0,2) is given by the formula
[tex]\rightarrow \frac{x}{a}+\frac{y}{b}=1\\\\ \rightarrow \frac{x}{-4}+\frac{y}{2}=1\\\\ \rightarrow x -2 y= -4\\\\ x -2 y+4=0[/tex]
6x-5y=5
3x+5y=4
The x-coordinate of the solution to this system of equation is
Answer:
x=1
Step-by-step explanation:
1) 6x-5y=5
2) 3x+5y=4
ets perform the following operation
1) +2), This leads to the following equation:
6x+3x-5y+5y=5+4
From where we obtain the solution for x
9x=9
x=1
please help this is mainly on fuctions
Answer:
B and C
Step-by-step explanation:
We are going to look at each choice:
Let's look at choice A.
f(5)=1
f(5) means look at function f and then see which piece contains x=5.
5>1 so we are looking at [tex]x^2[/tex] for x=5 which gives you [tex]5^2=25[/tex], this is not 1.
The answer is not A.
Let's look at choice B.
f(2)=4
f(2) means look at function f and then see which piece contains x=2.
2>1 so we are looking at [tex]x^2[/tex] for x=2 which gives you [tex]2^2=4[/tex], so this is true that f(2)=4.
Let's look at choice C.
f(1)=5
f(1) means look at function f and then see which piece contains x=1.
1=1 which means we are using [tex]5[/tex] for x=1, so f(1)=5 which is what choice C says so choice C is true.
Let's look at choice D.
f(-2)=4
f(-2) means look at function f and then see which piece contains x=-2
-2<1 so we use [tex]2x[/tex] for x=-2, so we get 2(-2)=-4 which is not 4 so f(-2)=4 is not true.
Rewrite the polynomial 4x^2-7x^3-x^6+3x^4-1 in descending order, using coefficients of 0 for any missing
terms.
Which term is first second third, etc., when the polynomial is written in this way?
Match the term number to the appropriate term.
Term 7
Select an option
Term 6
Select an option
Term 5
Select an option
Term 4
Select an option
Term 3
Select an option
Term 2
Select an option
Term 1
Select an optio
Answer:
The polyester in standard form with zero placeholders is
-x^6+0x^5+3x^4+-7x^3+4x^2+0x+-1
7th term -1
6th term 0x
5th term 4x^2
4th term -7x^3
3rd term 3x^4
2nd term 0x^5
1st term -x^6
Step-by-step explanation:
We want to write 4x^2-7x^3-x^6+3x^4-1 in descending order means want the exponents to being counting down.
6 is the highest exponent so lets rearrange this so that tern comes first:
-x^6+.....
5 is the highest but we are missing so now we have:
-x^6+0x^5+....
4 is the next highest and I see +3x^4 in our polynomial so that comes next:
-x^6+0x^5+3x^4+...
3 is the next highest and I see -7x^3 so that term comes next:
-x^6+0x^5+3x^4+-7x^3+....
2 is the next highest and I see +4x^2 so that term comes next:
-x^6+0x^5+3x^4+-7x^3+4x^2+...
1 is the next highest and we are missing an x term so the next term is +0x.....
-x^6+0x^5+3x^4+-7x^3+4x^2+0x+....
0 is the next highest and will be the last term we write. This is the constant tern, the term without the variable and that is -1.
-x^6+0x^5+3x^4+-7x^3+4x^2+0x+-1
Now I guess you are reading this from left to right when numbering the terms as first, second, and so on...
1st term -x^6
2nd term 0x^5
3rd term 3x^4
4th tern -7x^3
5th term 4x^2
6th term 0x
7th term -1
Factor this trinomial completely.
-6x2 + 26x+ 20
Answer:
−2(3x+2)(x−5)
Step-by-step explanation:
−6x2+26x+20=
=−2(3x+2)(x−5)
Help with this question thanks
Answer:
37.7 = h
Step-by-step explanation:
Area of a rectangle is base * height
A =bh
Substitute what you know
1059.37 = 28.1 * h
Divide each side by 28.1
1059.37/28.1 = 28.1 * h/28.1
37.7 = h
The midsegment of ABC IS IM. What is the length of MC if BC is 18 inches
long?
A. 36 inches
B. 18 inches
C.27 inches
D. 9 inches
Answer:
D. 9 inches
Step-by-step explanation:
By using proportionality theorem,
Triangle BLM ~ Triangle BAC
[tex] \frac{bm}{bc} = \frac{bl}{ba} [/tex]
as ba = bl + la and as bl = la
Therefore, bl + la = 2bl
[tex] \frac{bm}{bc} = \frac{bl}{2bl} [/tex]
Now, we get,
[tex] \frac{bm}{18} = \frac{1}{2} [/tex]
as bc = 18
Hence,
[tex]bm = 9 \: inches[/tex]
Answer: D. 9 inches
Step-by-step explanation:
Given : The midsegment of Δ ABC is line segment IM.
Such that for side BC , BM=MC [ Show in the picture ] (1)
and BC= BM+MC (2)
The length of BC = 18 inches (3)
From (1) and (2), we have
[tex]BC=MC+MC\\\\\Rightarrow\ BC=2MC[/tex]
Using (3), we have
[tex]2MC=18\text{ inches}\\\\\Rightarrow\ MC=\dfrac{18}{2}=9\text{ inches}[/tex]
Therefore, the length of MC = 9 inches.
Hence, D is the correct option.
Which will result in a difference of squares?
(-7x+4)(-7x+4)
(-7x+4)(4-7%)
0 (-7x+4)(-78-4)
(-7x+4)(7x-4)
Answer:
The expression which will result in difference of two squares is:
(–7x + 4)·(–7x – 4)
Step-by-step explanation:
We know that the formula of the type:
(a-b)(a+b)=a²-b²
i.e. it is a difference of two square quantities. (a^2 and b^2)
since,
a= -7x , b=4
(-7x+4)(-7x-4)= (-7x)² - (4)²
=(7x)² - 4²
So the expression is a difference of two square quantities:
(7x)² and (4)²
Hence the answer is (–7x + 4)·(–7x – 4)....
which of the following is an equation of a line parallel to the equation [tex]y=\frac{1}{2} x+1[/tex]
Answer:
Any equation of a line having a slope of 1/2.
Step-by-step explanation:
It appears that the question gives answer choices and this problem could have many solutions, but parallel lines have equal slopes. The slope of this line is 1/2 since it is in y=mx+b form where m is the slope. So a few examples of equations of lines parallel to the given equation would be y = 1/2x - 5 or y = 1/2x + 10 etc.
If x is in west of y and y is in north of z, towards which direction of x is z?
Answer: southeast
Step-by-step explanation:
Draw a picture showing x to the left of y and z below y:
x y
z
This results in z being south and east from x
If x is in west of y and y is in north of z, direction of x with respect to z is South-east .
What is direction of x with respect to z ?Given that x is in west of y and y is in north of z.
To obtain the direction of a respective person with respect to a given person, we draw the given image as mentioned in the question.
Drawing the required direction as per given in question -
x y
z
Thus, we can clearly see that z is South-east direction of x.
Therefore, if x is in west of y and y is in north of z, direction of x with respect to z is South-east .
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What are the coordinates of the image of vertex F after a
reflection across the line y=-X?
(-1,-3)
(3,-1)
(1,3)
(-3,1)
G(-2. -3)
F(1.-3)
E -1, -5
H(2-5)
This takes too long to do. I will provide the steps.
For each point given, plug into the equation y = - x.
Point 1:
(-1, -3)
y = -x
y = -(-1)
y = 1
The first point reflected across the line y = - x is (-1, 1).
Do the same with the remaining points.
(Free points)
Factorise x³ + 216y³ + 8z³ - 36xyz
Answer:
[x+6y+2z][x²+(6y)²+(2z)²-6xy-12yz-2xz]
Step-by-step explanation:
x³+216y³+8z³-36xyz
x³+(6y)³+(2z)³-3×6×2×xyz
As we know
a³+b³+c³-3abc=(a+b+c)(a²+b²+c²-ab-bc-ca)
Let a=x
b=6y
c=2z
Now.
[x+6y+2z][(x²+(6y)²+(2z)²-x×6y-6y×2z-x×2z]
[x+6y+2z][x²+(6y)²+(2z)²-6xy-12yz-2xz]
Answer:
have a good day
Step-by-step explanation:
you deserve it
Write an expression for "7 less than y."
Answer:
(y - 7)
Step-by-step explanation:
"7 less than y" means just that.... that you have 7 fewer units then the value of y.
Expression for [tex]7[/tex] less than [tex]y[/tex] is equal to [tex]y-7[/tex].
What is an expression?" An expression is defined as the representation of the relation between variables and numbers using mathematical operation."
According to the question,
Given statement,
[tex]7[/tex] less than [tex]y[/tex]
Expression for the given statement is,
[tex]y - 7[/tex]
Hence, the expression for [tex]7[/tex] less than [tex]y[/tex] is equal to [tex]y-7[/tex].
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Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Answer:
1. mode
2. median
3. mean
3.
Determine the angle PMA of the lampshade.
15 cm-
25 cm
-25 cm.-
M
Answer:
∠PMA=55°
Step-by-step explanation:
see the attached figure with the letter X to better understand the problem
we know that
In the right triangle PXM
PX=LA=25 cm
XM=AM-15/2=25-7.5=17.5 cm
∠PMA=∠PMX
tan(∠PMA)=(PX)/(XM)
tan(∠PMA)=(25)/(17.5)
∠PMA=arctan((25)/(17.5))=55°
The figures are similar. Find the area. The area of △ △ A B C is 15 square cm. The height of △ △ A B C is 5 cm and the height of △ △ D E F is 13 cm. Find the area of △ △ D E F . Round to the nearest square cm if necessary.
Answer:
The area of triangle DEF is [tex]282\ cm^{2}[/tex]
Step-by-step explanation:
step 1
Find the scale factor
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor
To find the scale factor, divide the height of triangle DEF by the height of triangle ABC
Let
z ------> the scale factor
[tex]z=\frac{13}{5}[/tex]
step 2
Find the area of triangle DEF
we know that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
Let
z -----> the scale factor
x ----> the area of triangle DEF
y -----> the area of triangle ABC
[tex]z^{2}=\frac{x}{y}[/tex]
we have
[tex]z=\frac{13}{5}[/tex]
[tex]y=15\ cm^{2}[/tex]
substitute and solve for x
[tex](\frac{13}{5})^{2}=\frac{x}{15}[/tex]
[tex]x=(\frac{169}{25})(15)[/tex]
[tex]x=282\ cm^{2}[/tex]
Koalas absorb only 25% of the fiber they eat. A koala absorbed 10.5 ounces of fiber in one day. How many ounces of fiber did he eat that day?
[tex]\huge{\boxed{\text{42 ounces}}}[/tex]
25% is equal to [tex]\frac{1}{4}[/tex], so multiplying it by 4 gets 100%. This means we can multiply 10.5 by 4 to get 100% of the fiber the koala ate that day.
[tex]10.5*4=\boxed{42}[/tex]
Answer:
42 ounces
Step-by-step explanation:
So a koala absorbs 25% of fiber they eat.
A koala absorbed 10.5 ounces in a day.
Let x be the amount of ounces of fiber the source(s) actually contained that day.
So we have 25% of x is 10.5
As an equation that is .25x=10.5 or 1/4 *x=10.5.
.25x=10.5
To solve this equation you can divide both sides by .25 giving you
x=10.5/.25=42.
If you chose the other equation which is an equivalent equation you would multiply both sides by 4.
1/4 *x=10.5
x=4(10.5)
x=42
Multiplying monomials and binomials
Answer:
The product of 28w(w-17) is 28w^2 - 476w
Step-by-step explanation:
Given
28w(w-17)
We have to find the product of the monomial and binomial polynomials
The term 28w will be distributed to w-17
So,
= (28w)(w) - (28w)(17)
= 28w^2 - 476w
Therefore, the product of 28w(w-17) is 28w^2 - 476w ..
Final answer:
When multiplying monomials and binomials, you can follow certain rules. Multiply the numerical coefficients, add the exponents of the variables, and then combine like terms if possible.
Explanation:
When multiplying monomials and binomials, you can follow a few rules. For monomials, you simply multiply the numerical coefficients and add the exponents of the variables. For binomials, you can use the distributive property to multiply each term of one binomial by each term of the other binomial. Then, combine like terms if possible.
For example, let's say we have (2x^2)(3x^3). We would multiply the coefficients (2 * 3 = 6) and add the exponents of the variable x (2 + 3 = 5). So the resulting expression is 6x^5.
what is the inverse operation of F(x)=2x+3
Answer:
[tex]f^{-1}[/tex](x) = [tex]\frac{x-3}{2}[/tex]
Step-by-step explanation:
Let y = f(x) and rearrange making x the subject
y = 2x + 3 ( subtract 3 from both sides )
y - 3 = 2x ( divide both sides by 2 )
[tex]\frac{y-3}{2}[/tex] = x
Change y back into terms of x, hence
[tex]f^{-1}[/tex](x ) = [tex]\frac{x-3}{2}[/tex]
Keep in mind that f(x) means the same thing as y so...
y = 2x + 3
To find the inverse operation you switch the places of x and y like so...
x = 2y + 3
Now you must solve for y. To start off you must subtract 3 to both sides.
x - 3 = 2y + 3 - 3
x - 3 = 2y
Now divide 2 to both sides to completely isolate y
(x - 3) / 2 = 2y / 2
[tex]\frac{1}{2} x - \frac{3}{2}[/tex] = y
OR
[tex]\frac{x}{2} -\frac{3}{2}[/tex] = y
Hope this helped!
~Just a girl in love with Shawn Mendes
Write the equation of the line that passes though (-3,5) and (2,10) in slope intercept form
Answer:
see explanation
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 3, 5) and (x₂, y₂ ) = (2, 10)
m = [tex]\frac{10-5}{2+3}[/tex] = [tex]\frac{5}{7}[/tex], hence
y = [tex]\frac{5}{7}[/tex] x + c ← is the partial equation of the line
To find c substitute either of the 2 points into the partial equation
Using (2, 10), then
10 = [tex]\frac{10}{7}[/tex] + c ⇒ c = 10 - [tex]\frac{10}{7}[/tex] = [tex]\frac{60}{7}[/tex]
y = [tex]\frac{5}{7}[/tex] x + [tex]\frac{60}{7}[/tex] ← in slope- intercept form
A baker has 2,000 grams of flour he uses 425 grams of it what is the mass of the flour left
Answer:
1575 grams
Step-by-step explanation:
If a baker has 2,000 grams of flour and uses 425 grams of it, the mass will become 1575 grams.
2000 - 425 = 1575
Answer:
1575 grams of flour
Step-by-step explanation:
If he had 2000 grams of flour and used 425 grams of it, you have to subtract 2,000 by 425, which would equal 1,575 grams of flour left.
Please help me with this question
Answer:
-2 degrees
Step-by-step explanation:
If you work backwards you will eventually get -2
For example: -3 + 3 = 0, then 0 - 2 = -2, so on...........
The quotient of 6 cubed and 4 squared
ANSWER
13.5
EXPLANATION
We write 6 cubed as 6³
We write 4 squared as 4²
The quotient of 6 cubed and 4 squared is written as
[tex] \frac{ {6}^{3} }{ {4}^{2} } [/tex]
We expand to obtain:
[tex] \frac{6 \times 6 \times 6}{4 \times 4} [/tex]
Cancel out the common factors to get,
[tex] \frac{3 \times 3 \times 3}{2} [/tex]
This simplifies to
[tex] \frac{27}{2} = 13.5[/tex]
The ratio of the number of boys in a school play to the number of students in the play is 7/10. What is the ratio of the number of girls in the play to the number of boys in a play
Answer:
3/7
Step-by-step explanation:
The total number of students in the play is 10.
The number of boys in the play is 7.
The remaining students in the play must be girls, so 10-7=3.
There are 3 girls in the play.
The ratio of girls in the play to boys in the play would be:
girls/boys= 3/7.
Answer:
Step-by-step explanation:
The no of girls is 3/10
Girls : boys
3/10 : 7/10
3 : 7
Darrin can skateboard 2 miles against a 4 mph wind in the same amount of time he skateboards 6 miles with a 4 mph wind. Find the speed Darrin skateboards with no wind.
Answer:
Speed = 8mph
Step-by-step explanation:
Speed of wind = 4mph
Let speed of Darrin with no wind be "x" mph
then resultant speed of Darrin, travelling in direction of wind = (x + 4) mph
Using a result, Time = Distance travelled / Net speed
Time taken by Darrin to travel 6miles in direction of wind = 6 / (x + 4)
When Darrin travel in opposite direction of wind, then its net speed = (x - 4)mph
Darrin travel 2 miles against the wind in 6/(x + 4) hr
then Distance = speed × time
2 = ( x- 4 ) × ( 6/x + 4)
2x + 8 = 6x - 24
4x = 32
x = 8 mph
Therefore speed of Darrin skateboard with no wind = 8mph
Answer:
Speed without wind will be 8 mph
Step-by-step explanation:
Now by revising basic formula here
Velocity = Distance/Time. . . . (A)
Assume speed without wind is 'x'
When Darrin is moving against wind to cover 2 miles;
net speed will be x-4
When Darrin is moving along with the wind to cover 6 miles;
net speed will be x+4
Please note that the time for covering distance of 2 miles and 6 miles is same,
So, from equation (A)
Time = Distance/Velocity,
Time for 2 miles will be
Time = 2/(x-4)
Time for 6 miles will be
Time = 6/(x+4)
Since, the time for both distances is same, here we can equate,
2/(x-4) = 6/(x+4)
by cross multiply
2(x+4) = 6(x-4)
2x+8 = 6x-24
4x = 32
x = 8
So, 8 miles per hour is the speed of Darrin if there is no wind.