Answer:
The total duration of the trip is 48 hours.
Step-by-step explanation:
Let suppose that ship travels at constant speed during its travel. Each stage is represented by the following kinematic equation:
[tex]v =\frac{\Delta s}{\Delta t}[/tex]
Where:
[tex]\Delta s[/tex] - Travelled distance, measured in kilometers.
[tex]\Delta t[/tex] - Time, measured in hours.
[tex]v[/tex] - Speed, measured in kilometers per hour.
Now, each stage is represented by the following expressions:
Outbound trip
[tex]v = \frac{700\,km}{\Delta t}[/tex]
Return trip
[tex]v + 10\,\frac{km}{h} = \frac{700\,kh}{\Delta t - 8\,h}[/tex]
By eliminating [tex]v[/tex] and simplifying the resulting expression algebraically:
[tex]\frac{700\,km}{\Delta t} + 10\,\frac{km}{h} = \frac{700\,km}{\Delta t -8\,h}[/tex]
[tex](700\,km)\cdot \left(\frac{1}{\Delta t - 8\,h}-\frac{1}{\Delta t} \right) = 10\,\frac{km}{h}[/tex]
[tex]\frac{1}{\Delta t - 8\,h}-\frac{1}{\Delta t} = \frac{1}{70}\,\frac{1}{h}[/tex]
[tex]\frac{8\,h}{\Delta t \cdot (\Delta t-8\,h)} = \frac{1}{70}\,\frac{1}{h}[/tex]
[tex]560\,h^{2} = \Delta t\cdot (\Delta t - 8\,h)[/tex]
[tex](\Delta t )^{2}-8\cdot \Delta t - 560 = 0[/tex]
This equation can be solved by means of the Quadratic Formula, whose roots are presented below:
[tex]\Delta t_{1} = 28\,h[/tex] and [tex]\Delta t_{2} = -20\,h[/tex]
Only the first roots offers a physically resonable solution. Then, total duration of the trip is:
[tex]t_{T} = 28\,h +20\,h[/tex]
[tex]t_{T} = 48\,h[/tex]
The total duration of the trip is 48 hours.
Simplify the following expression.
Answer:
3x+11y-3
Step-by-step explanation:
Hey! So here is what you do to solve the problem-
Combine like terms:
(x) 5x-2x=3x
(y) 3y+8y=11y
(#) 7-10 =-3
So....
3x+11y-3 is your answer!
Hope this helps!:)
Find the value of x. Round to the nearest tenth.
15.9
12.4
12.8
16.3
Answer:
x = 15.9
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = adj / hyp
cos 28 = 14/x
x cos 28 = 14
x = 14 / cos 28
x=15.85598
Rounding to the nearest tenth
x = 15.9
A ship travels due north for 100 miles from point C to point A. From point A the ship travels to point B at 60° east of north. From point B, the ship returns to point C heading 45° west of south. What approximate distance did the ship travel from point A to point B? How far does it travel in total?
Answer:
AandB=80miles
Total=240miles
Step-by-step explanation:
Draw the figure first indicating the figures then find the distance each degrees then find the total
The distance ship travels from A to B is 273.2 miles and total distance covered by ship is 707.82 miles.
What is laws of sines?The law of sines specifies how many sides there are in a triangle and how their individual sine angles are equal. The sine law, sine rule, and sine formula are additional names for the sine law.
The side or unknown angle of an oblique triangle is found using the law of sine. Any triangle that is not a right triangle is referred to as an oblique triangle. At least two angles and their corresponding side measurements should be used at once for the sine law to function.
Given distance from C to A = 100 miles north
From B to A ship travels 60° east of north,
and From B to C 45° west of south,
the figure for problem is attached,
from figure we can calculate the angles of A, B and C
so ∠A makes supplementary with 60°
∠A + 60° = 180°
∠A = 120°
for ∠B we need to draw an imaginary perpendicular on the line extending from A, we get
∠B + 45° + 30° = 90° (30° is angle of imaginary right triangle)
∠B = 90 - 75 = 15°
and ∠C can be found by,
∠A + ∠B + ∠C = 180°
∠C = 180 - 15 - 120
∠C = 45°
now use sine formula for triangles,
sinA/a = sinB/b = sinC/c
where A, B and C are angles of triangle and a, b and c are length of opposite side of angle A, B and C respectively.
a = BC, b = AC, and c = AB
so
sinA/BC = sinB/AC = sinC/AB
we have AC = 100 miles
substitute the values
sinC/AB = sinB/AC
sin(45)/AB = sin(15)/100
AB = 100/(√2sin(15))
AB = 100/0.3659
AB = 273.298 miles
and sinA/BC = sinB/AC
BC = AC sinA/sinB
BC = 100(sin 120/sin15)
BC = 100(0.866/0.2588)
BC = 100 x 3.3462
BC = 334.62 miles
total distance = AB + BC + AC
total distance = 334.62 + 273.2 + 100
total distance = 707.82 miles
Hence the distance from A to B is 273.2 miles and total distance is 707.82 miles.
Learn more about laws of sines;
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Solve for x. 23x +2=15x+48x+6
Answer:
[tex]x = - \frac{1}{10} [/tex]Step-by-step explanation:
23x +2 = 15x+48x+6
To solve for x group like terms
That's
Send the constants to the right side of the equation and those with variables to the left side
We have
23x - 15x - 48x = 6 - 2
Simplify
- 40x = 4
Divide both sides by -40
[tex] \frac{ - 40x}{ - 40} = \frac{4}{ - 40} [/tex]We have the final answer as
[tex]x = - \frac{1}{10} [/tex]Hope this helps you
Describe how to solve an absolute value equation
*will give brainliest*
Answer:
Step 1: Isolate the absolute value expression.
Step2: Set the quantity inside the absolute value notation equal to + and - the quantity on the other side of the equation.
Step 3: Solve for the unknown in both equations.
Step 4: Check your answer analytically or graphically.
Step-by-step explanation:
Answer:
Rewrite the absolute value equation as two separate equations, one positive and the other negative
Solve each equation separately
After solving, substitute your answers back into original equation to verify that you solutions are valid
Write out the final solution or graph it as needed
Step-by-step explanation:
If P = (3,4), Find: Rx=1 (P)
Answer:
-1, 4
Step-by-step explanation:
Answer:
Step-by-step explanation:
answer is (-1,4)
Calculate JK if LJ = 14, JM = 48, and LM = 50
Answer:
JK = 6.86
Step-by-step explanation:
The parameters given are;
LJ = 14
JM = 48
LM = 50
[tex]tan(\angle JML )= \dfrac{Opposite \ leg \ length}{Adjacent \ leg \ length} = \dfrac{LK}{JM} = \dfrac{14}{48} = \dfrac{7}{24}[/tex]
[tex]tan \left( \dfrac{7}{24} \right)= 16.26 ^{\circ }[/tex]
∠JML = 16.26°
Given that ∠JML is bisected by KM, we apply the angle bisector theorem which states that a ray that bisects an interior angle of a triangle bisects the opposite (bisected angle facing side) in the proportion of the ration of the other two sides of the triangle.
From the angle bisector theorem, we have;
LM/JM = LK/JK
50/48 = LK/JK................(1)
LK + KJ = 14.....................(2)
From equation (1), we have;
LK = 25/24×JK
25/24×KJ + JK = 14
JK×(25/24 + 1) = 14
JK × 49/24 = 14
JK = 14×24/49 = 48/7. = 6.86.
JK = 6.86
Solve for x and draw a number line. 3x−91>−87 AND 17x−16>18
Answer:
I hope this will help!
Step-by-step explanation:
in exponential growth functions, the base of the exponent must be greater than 1. How would the function change if the base exponent were 1? How would the function change if the base of the exponent were between 0 and 1?
Answer:
GREAT QUESTION!!
Step-by-step explanation:
Bases of exponential functions CANNOT be 1.
It the base was between 0 and 1, .25 for example, then it would be exponential decay, because as x would increase y would decrease.
Just search up exponential decay to see what it looks like, or type in y=.25^x in google search bar.
if this helped, Please give brainly, I need it! Thank you!
Answer:
If the base of the exponent were 1, the function would remain constant. The graph would be a horizontal line. If the base of the exponent were less than 1, but greater than 0, the function would be decreasing.
Step-by-step explanation:
If the base were 1, the function would be constant.
If the base were 1, the graph would be a horizontal line.
If the base were between 0 and 1, the function would be decreasing.
john always wears a shirt, pants, socks, and shoes. he owns 12 pairs of socks, 3 pairs of shoes, 5 pairs of pants, and 5 shirts. how many different outfits can john make? PLEASE ANSWER
Answer:
900 outfits
Step-by-step explanation:
You just have to multiply them all together :)
* Graph these numbers on a number line.
-5,3, -2,1
-5
-5,3,-2,1 on a number line
<-|----|----|----|----|----|----|----|----|->
-5 -2 0 1 3
ASAP PLEASE GIVE CORRECT ANSWER
In a rectangular coordinate system, what is the number of units in the distance from the origin to the point $(-15, 8)$? Enter your answer
distance of a point [tex](x,y)[/tex] from origin is $\sqrt{x^2+y^2}$
so distance is $\sqrt{(-15)^2+(8)^2}=\sqrt{225+64}=\sqrt{289}=17$
Answer:
Distance=17 units
Step-by-step explanation:
Coordinates of the origin: (0, 0)
Coordinates of the point in question: (-15, 8)
Distance formula for any two points [tex](x_1,y_1), (x_2,y_2)[/tex] on the plane:
[tex]distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\distance=\sqrt{(-15-0)^2+(8-0)^2}\\distance=\sqrt{(15)^2+(8)^2}\\distance=\sqrt{225+64} \\distance=\sqrt{289} \\distance=17[/tex]
Dena uses 7.4 pints of white paint and blue paint to paint her bedroom walls. 2/5 of this amount is white paint, and the rest is blue paint. How many pints of blue paint did she use yo paint her bedroom walls
Answer:
4.44 pints
Step-by-step explanation:
7.4 times 3/5
A trader buys tea for $1200 and sells it for $1500. Per sack of tea he makes a profit of $50. How many sacks of tea did he have?
Answer:
6 sacks
Step-by-step explanation:
Buying Price = $1200
Selling Price = $1500
Total profit = Selling price - Buying Price
= $1500 - $1200
= $300
Given that the profit on each sack of tea is $50
Number of Sacks of Tea = Total Profit ÷ profit per sack
= $300 ÷ 50
= 6 sacks
The number of sacks of tea he has is 6.
The first step is to determine the total profit earned by the trader. Profit is the selling price less the cost price.
Profit = selling price - cost price
$1500 - $1200 = $300
The second step is to divide the total profit by the profit made per sack of tea.
Number of sacks = $300 / $50 = 6
To learn more about division, please check: https://brainly.com/question/194007
Find the volume of a pyramid with a square base, where the side length of the base is 17 in 17 in and the height of the pyramid is 9 in 9 in. Round your answer to the nearest tenth of a cubic inch.
Answer:
The volume of the pyramid is 867 inch^3
Step-by-step explanation:
Here in this question, we are interested in calculating the volume of a square based pyramid.
Mathematically, we can use the formula below to calculate the volume V of a square based pyramid.
V = a^2h/3
where a represents the length of the side of the square and h is the height of the pyramid
From the question, the length of the side of the square is 17 in while the height is 9 in
Plugging these values, we have ;
V = (17^2 * 9)/3 = 17^2 * 3 = 867 cubic inch
In 2002, the population of a district was 22,800. With a continuous annual growth rate of approximately 5% what will the population be in 2012 according to the exponential growth function?
Answer:
37,139
Step-by-step explanation:
Given the following :
Population in 2002 = Initial population (P0) = 22,800
Growth rate (r) = 5% = 0.05
Growth in 2012 using the exponential growth function?
Time or period (t) = 2012 - 2002 = 10years
Exponential growth function:
P(t) = P0 * (1 + r) ^t
Where P(t) = population in t years
P(10) = 22800 * (1 + 0.05)^10
P(10) = 22800 * (1.05)^10
P(10) = 22800 * 1.62889
P(10) = 37138.797
P(10) = 37,139 ( to the nearest whole number)
Is a 118 supplementary or complementary?pls ASAP!!
Answer:
[tex]\huge\boxed{Supplementary \ Angle}[/tex]
Step-by-step explanation:
118 is a supplementary angle. It is not a complementary angle because complementary angles add up to 90 and 118 is greater than 90 degrees. So, 118 is a supplementary angle and it is an angle adding up to 180 degrees with any other angle measuring 62 degrees.
Answer:Supplementary
Step-by-step explanation:You should remember that complementary refers to any number from 0-90 and supplementary refers to any number from 90 onwards..
Hereby giving the answer as ''Supplementary''
HELP HELP HELP Sally can paint a room in 4 hours. Joe can paint a room in 6 hours. How
long will it take if they paint the room together? I’m not sure if it’s 1.4
Answer:
2 hrs, 24 min
Step-by-step explanation:
Sally: in one hour, she can paint 1/4 of the room.
Joe: in one our, he can paint 1/6 of the room
Hour one: 1/4+1/6=3/12+2/12=5/12
1÷5/12=1*12/5=12/5
12/5= 2 & 2/5 hours, or 2.4 hours, or 2 hrs 24 minutes
Answer: 2.4 hours
Step-by-step explanation:
1/4 1/6
LCM
3/12+2/12=5/12 repricical 12/5 =2.4
What does the law of cosines reduce to when dealing with a right angle
Answer:
It is reduced to the equation of the Theorem of Pythagoras.
Step-by-step explanation:
Any triangle can be modelled by this formula under the Law of Cosine:
[tex]b = \sqrt{a^{2}+c^{2}-2\cdot a\cdot c\cdot \cos B}[/tex]
Where:
[tex]a[/tex], [tex]b[/tex], [tex]c[/tex] - Side lengths, dimensionless.
[tex]B[/tex] - Angle opposed to the side [tex]b[/tex], measured in sexagesimal degrees.
Now, let suppose that angle B is a right angle (90º), so that b is a hypotenuse and a and c are legs. Hence:
[tex]\cos B = 0[/tex]
And the equation is reduced to the form of the Theorem of Pythagoras, that is to say:
[tex]b = \sqrt{a^{2}+c^{2}}[/tex]
Given that ∆MTW ≅ ∆CAD, which angles are corresponding parts of the congruent triangles? ∠W ≅ ∠C ∠W ≅ ∠D ∠W ≅ ∠A
Answer:
The Answer would be ∠W ≅ ∠C
Step-by-step explanation:
Only one that is congruent
The measure of the angle ∠TWM is congruent to the measure of the angle ∠ADC. Therefore, the correct option is B.
What are congruent triangles?Two triangles are said to be congruent if their corresponding sides and angles are equal.
A triangle is a three-sided polygon with three edges and three vertices in geometry.
Given that the triangle ∆MTW is congruent to the triangle ∆CAD.
So, we have
∠MTW ≅ ∠CAD
∠WMT ≅ ∠DCA
∠TWM ≅ ∠ADC
If two triangles are equivalent, the ratio of matching sides will stay constant.
The proportion of the point ∠TWM is harmonious with the proportion of the point ∠ADC.
Therefore, at that point, the right choice is B.
Learn more about congruent triangles here:
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A triangle and the coordinates of its vertices is shown in the coordinate plane below. Enter the area of this triangle in square units, rounded to the nearest tenth. square units
Answer:
22 units²
Step-by-step explanation:
1/2b*h=area
You can either count the units or use the distance formula.
[tex]d = \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } [/tex]
b = 4 units
h = 11 units
area = (1/2*4)*11 = 22 units²
Please answer this question now
Answer:
Approximately 439.6 square millimeters.
Step-by-step explanation:
The formula for the surface area of a cone is the following:
[tex]A=\pi r^2+\pi r l[/tex]
Where, r is the radius and l is the slant height.
The radius is 7 and the slant height is 13. We also use 3.14 for π Thus:
[tex]A=(3.14)(7)^2+(3.14)(7)(13)\\\text{Use a Calculator}\\A\approx 439.6[/tex]
Answer:
292.77
Step-by-step explanation:
πr(r+[tex]\sqrt{h2+r2}[/tex])
13 x 2 = 26
7 x 2 = 14
26 + 14 = 40
[tex]\sqrt{40}[/tex] = 6.32
7 + 6.32 = 13.32
3.14 x 7 = 21.98
21.98 x 13.32 =
292.77
Sandy’s older sister was given $2,400 and was told to keep the balance of the money after sharing with her siblings. Give Sandy exactly $350. Write Sandy’s portion
Sandy got 350 out of 2400.
Her portion is 350/2400 which can be reduced to:
35/240 = 7/48
The portion is 7/48
A man traveled to his country home, a distance of 150 miles and then back. His average rate of speed going was 50 miles an hour and his average return speed was 30 miles per hour. His average rate of speed for the entire trip was Need help will mark brainlist
Answer:
37.5 mi/h
Step-by-step explanation:
time = distance / speed
On the trip 'going', the time was (150 mi)/(50 mi/h) = 3 h.
On the return trip, the time was (150 mi)/(30 mi/h) = 5 h.
__
speed = distance / time
The average speed for the whole trip was ...
speed = (150 mi +150 mi)/(3 h +5 h) = (300 mi)/(8 h) = 37.5 mi/h
His average rate of speed was 37.5 miles per hour.
kinda confused buttttt anyone know this?
Answer:
Hey there!
The overlapping part is the product.
Thus, the product is 1/8.
Hope this helps :)
How to work out the medium in maths
Answer:
To find the median you cross off the first few numbers and the last few until you get to the middle then when you get the middle number that will be your median
Step-by-step explanation:
Answer:
Below.
Step-by-step explanation:
It's the middle value of a list of numbers arranged in order.
For example the median of the list 1 2 3 4 5 is 3.
If there are an even number of values, the median is the mean of the middle two. For example:
1 3 4 5 7 9:
The middle 2 numbers are 4 and 5 so
the median is (4 + 5) / 2 = 4.5
Jonas needs a cell phone. He has a choice between two companies with the following monthly billing policies. Each company’s monthly billing policy has an initial operating fee and charge per text message. Sprint charges $29.95 monthly plus .15 cents per text, AT&T charges $4.95 monthly plus .39 cents per text. Create equations for the two cell phone plans.
Answer:
Since both companies have a different plan, two equations are created to determine which company Jonas should choose with respect to the number of messages sent.
Step-by-step explanation:
- Sprint = $ 29.95 * X (0.15)
- AT & T = $ 4.95 * X (0.39)
One dollar equals 100 cents, so 0.15 cents equals $ 0.0015 dollars.
- Sprint = $ 29.95 * X (0.0015)
- AT & T = $ 4.95 * X (0.0039)
Si Jonas envía 500 mensajes de texto el valor mensual de cada empresa sería de:
- Sprint = $ 29.95 * 500 (0.0015) = 22.46 dollar per month.
- AT & T = $ 4.95 * 500 (0.0039) = 9.65 dollar per month.
The company Jonas should choose is AT&T.
AT&T also charges a little more per number of text messages, but since the phone's value is so low it would take thousands of text messages to compare to Sprint's monthly value.
What are the lower quartile, upper quartile, and median for this box and
whisker plot?
A) LQ = 22 UQ = 10 Median = 18.5
B) LQ = 10 UQ = 22 Median = 18
C) LQ = 10 UQ = 22 Median = 18.5
D) LQ = 10 UQ = 22 Median = 19
Answer:
C
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
The lower quartile range is shown by the bottom of the box which is at 10.
The median is shown in the middle line, which is closer to 18 than 18.5.
The upper quartile range in the end of the box, which is at 22!
(You can also look at the picture attached if that helps.)
If 2x3 – 4x2 + kx + 10 is divided by (x + 2), the remainder is 4. Find the value of k using remainder theorem. Please help :)
The polynomial remainder theorem states that the remainder of the division of a polynomial [tex]P(x)[/tex] by [tex]x-a[/tex] is equal to [tex]P(a)[/tex].
Therefore
[tex]P(-2)=4\\2\cdot(-2)^3 - 4\cdot(-2)^2 + k\cdot(-2) + 10=4\\-16-16-2k=-6\\-2k=26\\k=-13[/tex]
Please help!
Suppose that [tex]\alpha[/tex] is inversely proportional to [tex]\beta[/tex]. If [tex]\alpha=4[/tex] when [tex]\beta=9[/tex], find [tex]\alpha[/tex] when [tex]\beta=-72[/tex]
Answer:
The answer is
[tex] \alpha = - \frac{1}{2} [/tex]Step-by-step explanation:
From the question
[tex]\alpha[/tex] is inversely proportional to [tex]\beta[/tex] is written as
[tex] \alpha = \frac{k}{ \beta } [/tex]where k is the constant of proportionality
When
[tex]\alpha[/tex] = 4[tex]\beta[/tex] = 9Substituting the values into the formula
we have
[tex]4 = \frac{k}{9} [/tex]
cross multiply
k = 4 × 9
k = 36
So the formula for the variation is
[tex] \alpha = \frac{36}{ \beta } [/tex]
when
[tex]\beta[/tex] = - 72
That's
[tex] \alpha = \frac{36}{ - 72} [/tex]
Simplify
We have the final answer as
[tex] \alpha = - \frac{ 1}{2} [/tex]Hope this helps you
