Answer:
hi
Step-by-step explanation:
1. Circle the two boats you picked for your trip.
the yacht and the tall ship (aka the pirate ship)
2. Make sense of the problem.
what do you know?
The tall ship makes the trip in 10 hours. The yacht makes the trip in 2.5 hours. The tall ship is 30 knots slower than the yacht.
what do you want to find out?
How fast is each boat traveling in knots (nautical miles per hour)?
what kind of answer do you expect?
probably just some numbers like 10 miles per hour or 40 miles per hour
Writing some expressions
3. Write an expression for the distance going to the island. Let x be the speed of the boat you are taking to the island. Distance is equal to speed times time. (2 points)
the expression would be D = 10(x-30), d is the distance. it could also be simplified to 10x - 300
4. Write an expression for the speed of the boat coming back from the island in terms of the other boat's speed. Let x be the speed of the boat you are taking to the island. (2 points)
so the yacht's speed would be S = x knots, s is for speed.
5. Write an expression for the distance returning from the island. Use the expression for speed you found in question 4. Remember that distance is equal to speed times time. (2 points)
the distance returning from the island would be D = 2.5x.
6. Each ship travels the same distance. Set the distances equal to each other to get the equation for the speed of the ship you are taking to the island. (1 point)
10x - 300 = 2.5x
7. Solve the equation from question 6 for x. What does this tell you? (5 points: 1 point for showing your work, 3 points for solving for x, 1 point for explaining the answer)
10x - 300 = 2.5x
10x - 300 + 300 = 2.5x + 300
10x -2.5x = 300
7.5x = 300
x = 40
x is the speed of the yacht. (40 nautical miles per hour)
8. How fast does the second boat travel? Show your work. (2 points: 1 point for showing your work, 1 point for the answer)
the yacht travels at 40 nautical miles per hour and the tall ship travels at 100 (10x - 300) nautical miles per hour.
9. When you get to the island, you decide to take a kayak tour to a nearby reef. A kayak is a small boat you row with a paddle.
Find the speed for the kayak. Use one of these facts to help.
The steamboat's speed is 4 less than 8 times the speed of the kayak.
The tall ship's speed is 1 more than 3 times the speed of the kayak.
The yacht's speed is 5 less than 15 times the speed of the kayak.
Write and solve an equation for the speed of the kayak. Show your work. (5 points: 2 points for writing a correct equation, 3 points for the solution)
the equation for the speed of the kayak is 40 = 15x - 5, which in this case, x is the speed of the kayak
40 = 15x - 5
40 + 5 = 15x -5 + 5
45 = 15x
x = 3
therefore, the speed of the kayak is 3 nautical miles per hour.
10. The length of your trip to the island is 40 nautical miles less than 20 times the distance to the reef.
It's 2:00 p.m. now, and your boat leaves the island at 7:30 p.m. Will you be able to kayak to the reef and back by then?
If so, how long will you have to spend at the reef?
If not, how late will you be for the return trip?
Explain how you plan to solve this problem. Then solve the problem, showing all work. (5 points: 2 points for the explanation of the plan, 1 point for deciding if you will make it back to the island on time, and 2 points for determining either how long you can spend at the reef or how late you'll be)
the distance to the island is 100 nautical miles, so the expression would be 100 = 20x -40, with x being the distance to the reef.
we can solve for x by doing:
100 = 20x -40
100 + 40 = 20x - 40 + 40
140 = 20x
140 / 20 = x
x = 7
so the distance from my starting point to the reef will be 7 nautical miles, and the distance from the island to the reef would be 93 nautical miles.in that case, I would be like a day and a half late, but if you are trying to say that the ship is waiting for me at the starting point of my "adventure", then I would not be late if I kayak from my starting point to the reef, in fact, I could stay at the reef for like 50 min, because:
7 / 3 = 2 1/3 hours.
2 1/3 x 2 = 4 2/3 hours or 280 min. (to the reef and back)
7:30 p.m. - 2:00 p.m. = 5 1/2 hours or 330 min. (how much time I have till the ship leaves)
330 - 280 = 50 min. (how many min I can spend at the reef)
This is for the people that want to find out how to find the distance to the island.
jamescodwell answered all the questions correctly btw.
Step-by-step explanation:
Distance travelled divided by trip time = speed
trip time multiplied by speed = distance travelled
So the steamboat makes the trip in 5 hours travelling at a speed of 20 knots.
5 * 20 = 100 The trip to the island is 100 nautical miles.
A forensic accountant usually takes additional coursework in which field?
Answer:
law enforcement
Step-by-step explanation:
can yall please start answering more questions about the subject
The point (3,65) lies on the graph representing a proportional relationship. Which of the following points also lie on the same graph?
Answer:
Step-by-step explanation:
ohhh
Answer:
A B and E all fall on the line expressed.
Step-by-step explanation:
the floor of a house is shaped like a parallelogram the height of the parallelogram is 8 feet less than the base. the base is 48 feet. the length of the other side of the parallelogram is 45 ft what is the area of the floor?
Answer:
1920 ft^2
Step-by-step explanation:
base = 48 ft
height = 48 ft - 8 ft = 40 ft
area = base * height
area = 48 ft * 40 ft
area = 1920 ft^2
Solve |2x - 1| + 3 = 6.
Answer:
x =2 x = -1
Step-by-step explanation:
|2x - 1| + 3 = 6.
Subtract 3 from each side
|2x - 1| + 3-3 = 6-3
|2x - 1|= 3
An absolute value has two solutions, one positive and one negative
2x-1 =3 2x -1 = -3
Add 1 to all sides
2x-1+1 =3+1 2x-1+1 = -3+1
2x = 4 2x =-2
Divide by 2
2x/2 = 4/2 2x/2 = -2/2
x =2 x = -1
Steps to solve:
|2x - 1| + 3 = 6
~Subtract 3 to both sides
|2x - 1| = 3
~Since we are working with an absolute value, one answer will be positive and one will be negative.
2x - 1 = 3
~Add 1 to both sides
2x = 4
~Divide 2 to both sides
x = 2
2x - 1 = -3
~Add 1 to both sides
2x = -2
~Divide 2 to both sides
x = -1
Best of Luck!
Factor 8x3 − 343.
A) (2x − 7)(4x2 + 14x + 49)
B) (2x − 7)(4x2 + 28x + 49)
C) (2x − 7)(4x2 −14x + 49)
D) (2x − 7)(4x2 − 28x + 49)
Which expression is equivalent to 27x3 + 125?
A) (3x – 5)(9x2 – 15x + 25)
B) (3x – 5)(9x2 + 15x – 25)
C) (3x + 5)(9x2 – 15x + 25)
D) (3x + 5)(9x2 + 15x – 25)
please explain if you could, thank you
Answer:
A) (2x − 7) (4x² + 14x + 49)
C) (3x + 5) (9x² − 15x + 25)
Step-by-step explanation:
Sums and differences of cubes factor as:
a³ + b³ = (a + b) (a² − ab + b²)
a³ − b³ = (a − b) (a² + ab + b²)
8x³ − 343 is a difference of cubes.
(2x)³ − 7³
(2x − 7) (4x² + 14x + 49)
27x³ + 125 is a sum of cubes.
(3x)³ + 5³
(3x + 5) (9x² − 15x + 25)
The function g(x) is graphed below. Find g(2).* N 22 need help solving please
Answer:
x =2, The function g(x) = g(2) = 1
Cuantos paquetes de 10 vasos ocupo para empacar 1367 vasos
Queremos encontrar y resolver una expresion algebraica para ver cuantos paquetes necesitamos para empacar los vasos.
La solución es 137 paquetes.
Veamos como obtener la solución.
Cada paquete puede sostener 10 vasos, y tenemos un total de 1367 vasos.
Entonces lo que debemos ver es cuantos grupos de vasos tenemos en 1367, esto será simplemente el cociente entre 1367 y 10.
1367/10 = 136.7
El problema ahora es que no podemos sar un 0.7 de un paquete, así que debemos redondear esto al proximo número entero, que es 137.
Así, podemos concluir que se necesitaran 137 paquetes para empacar los 1367 vasos.
Si quieres aprender más, puedes leer.
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what is
(-1/3)+1/4+(-1/5)
Answer:
-17/60
Step-by-step explanation:
(-1/3)+1/4+(-1/5)
What type of number is negative 15 over 3
Answer:
Rational number
Step-by-step explanation:
Rational numbers are defined as the quotient (division result) of two integers
What is
10x + 300 = 800
Pls
Answer:
x = 50
Step-by-step explanation:
10x + 300 = 800
subtract 300 from both sides
10x = 500
divide each side by 10
x = 50
Step-by-step explanation:
First group like terms
10x
[tex]10x + 300 = 800 \\ [/tex]
300 moves and joins 800 on the other side making it negative
[tex]10x = 800 - 300 = 500[/tex]
[tex]10x = 500[/tex]
10 then divides 500
Making the answer x=50
1/5 X B = 40 what is b
Answer:B = 200
Step-by-step explanation:multiply both sides by 5
5*1/5 = 5*40
B = 200
How do i find the domain and range on a graph
Answer:
domain = x
range = y
ASAP!!! Please help! Due in 15 mins!!!! Help me plsss!!!!
Which equation represents the function described by this table?
A) f (x) = x + 7
B) f(x) = -7x
C) f (x) = x - 7
D) f (x) =7x
The triangle will be enlarged by a scale factor of 10. A triangle with base 10 centimeters and height 7 centimeters. What will be the area of the new triangle?
Answer:
3500cm^2
Step-by-step explanation:
Area of a triangle= bxh/2
10x10=100
7x10=70
100x70=7000
7000/2=3500
Answer:
3500 cm²
Step-by-step explanation:
The given triangle has an area of ...
A = (1/2)bh = (1/2)(10 cm)(7 cm) = 35 cm²
The area of the enlarged triangle will be 10² = 100 times that, or 3500 cm².
__
You can see this if you use the enlarged dimensions in the area formula:
A = (1/2)bh = (1/2)(10·10 cm)(10·7 cm) = 100·35 cm² = 3500 cm
can you help me with this queistion
Answer:
B
Step-by-step explanation:
Choose the appropriate descriptor for the term gram. mass volume length area
Answer:
Mass is the appropriate term.
Step-by-step explanation:
Evaluate 3|−5| − 2|−2|
Answer:118
Step-by-step explanation:
3!-5!-2!-2! =? IF ! MEANS FACTORIAL, 3! MEANS 3X2X1=6,
-5! MEANS -5X4X3X2X1=-120
-2!= -2X1=-2
-2!=-2X1=-2
PROBLEM BECOMES 6--120-2-2=118
Find the general expression for the slope of a line tangent to the curve of y=2x^2+4x at the point P(x,y) . Then find the slopes for x=-3 and x=0.5. Sketch the curve and the tangent lines. What is the general expression for the slope of a line tangent to the curve of the function y=2x^2+4 at the point P(x,y) ?
Never mind I got it. mtan=6x+4. Sub in x values, for x=-2, take 6(-2)+4 = -8, and for x=1.5. 6(1.5)+4=13.
Complete Question
Find the general expression for the slope of a line tangent to the curve of y=2x^2+4x at the point P(x,y) . Then find the slopes for [tex] x = 3[/tex] and x=0.5. Sketch the curve and the tangent lines. What is the general expression for the slope of a line tangent to the curve of the function y=2x^2+4 at the point P(x,y) ?
Answer:
The generally expression for the slope of [tex]y = 2x^2 + 4x[/tex] is [tex]y' = 4x +4[/tex]
The graph is shown on the first uploaded image
The generally expression for the slope of [tex]y=2x^2+4[/tex] is [tex]y' = 4x[/tex]
Step-by-step explanation:
From the question we are told that
The equation of the curve is [tex]y = 2x^2 + 4x[/tex]
First we differentiate the equation
So
[tex]y' = 4x +4[/tex]
Therefore the generally expression for the slope tangent to the curve [tex]y=2x^2+4x[/tex] is [tex]y' = 4x +4[/tex]
The next step is to substitute for x = 3 and x = 0.5
So for [tex]x_1 = 3 [/tex]
[tex]y' = 4(3) +4[/tex]
[tex]y' =m_1= 16[/tex]
And for [tex]x_2 = 0.5[/tex]
[tex]y' = 4(0.5) +4[/tex]
[tex]y' =m_2= 6[/tex]
Here m_1 and m_2 are slops of the curve
Next we obtain the coordinates of the tangent lines
So at [tex]x_1 = 3 [/tex]
[tex]y_1 = 2(3)^2 + 4(3)[/tex]
[tex]y_1 = 21[/tex]
So the coordinate for the first tangent line is
[tex](x_1 , y_1 ) = (3 , 21)[/tex]
At [tex]x_2 = 0.5 [/tex]
[tex]y_2 = 2(0.5)^2 + 4(0.5)[/tex]
=> [tex]y_2 = 2.5[/tex]
So the coordinate for the second tangent line is
[tex](x_2 , y_2 ) = (0.5 , 2.5)[/tex]
Next we obtain the equation for the tangent lines
So generally the slope is mathematically represented as
[tex]m = \frac{y - y_1 }{x-x_1}[/tex]
For [tex](x_1 , y_1 ) = (-3 , 21)[/tex] and [tex]y' =m_1= 16[/tex]
[tex] 16 = \frac{y -21 }{x-3)}[/tex]
=> [tex]y = 16x - 27[/tex]
For [tex](x_2 , y_2 ) = (0.5 , 2.5)[/tex] and [tex]y' =m_2= 6[/tex]
[tex] 6 = \frac{y -2.5 }{x-0.5}[/tex]
[tex]y = 6x -0.5[/tex]
Generally the general expression for the slope of a line tangent to the curve of the function y=2x^2+4 at the point P(x,y) is mathematically evaluated by differentiating y=2x^2+4 as follows
[tex]y' = 4x[/tex]
PLEASE HELP!!!!!!!!!!!!!!!!! | For what values of y does the following equation have no solutions for x? | xy + 5y + 4x + 20=1
Answer:
y = -4
Step-by-step explanation:
We can solve for x to see.
x(y+4) +5y +20 = 1
x(y +4) = -19 -5y . . . . . subtract 5y+20
x = (-19 -5y)/(y +4)
x is undefined (no solution) for y = -4.
Answer:
y = -4
Step-by-step explanation:
If we look at xy + 5y, we see that both terms share a factor of y. This gives us
y(x + 5) + 4x + 20 = 1
Similarly, 4x and 20 share a factor of 4, giving us
y(x + 5) + 4(x + 5) = 1
Now we see that these two terms share a factor of x + 5, so factoring gives us
(y + 4)(x + 5) = 1
Dividing both sides by y+4 gives us
x + 5 = 1/(y + 4)
Finally, we subtract both sides by 5 to get
x = 1/(y + 4) - 5
Thus, since we can not have a 0 in the denominator, we see that if y = -4 then x will have no solution. For any other value of y, we can find the solution for x using this equation.
16.56 divided by 0.08=
Answer:207
Step-by-step explanation:
A truck can be rented from Company for 50 dollars a day plus 0.50 per mile. Company B charges 30 dollars a day plus 0.90 per mile to rent the same truck. Find the number of miles in a day at which the rental costs for company A and company B are the same.
Answer:
no company a gets 3 miles company b gets 5 miles
Step-by-step explanation:
Solve the equation . Check your solution
Answer:
x=48/8=6
Step-by-step explanation:
simple form
8x-48=0
fractionized
8(x-6)=0
For the right triangles below, find the exact values of the side lengths b and d.
If necessary, write your responses in simplified radical form.
60°
30°
5
b
=b
45°
45°
d
7
=d
Answer:
Step-by-step explanation:
The question lacks the required diagram. Find the diagram attached below;
According to the first triangle, taking 30° as the reference angle, the opposite side of the triangle will be 5 and the adjacent will be the unknown side "b"
According to SOH, CAH, TOA;
tanθ = opposite/adjacent (using TOA)
Given;
θ = 30°, opposite = 5 and adjacent = b
tan30° = 5/b
b = 5/tan30°
b = 5/(1/√3)
b = 5*√3/1
b = 5√3
According to the 45° triangle, the opposite side of the triangle will be d and the hypotenuse will be 7
Using SOH;
sinθ = opposite/hypotenuse
Given;
θ = 45°, opposite = d and adjacent = 7
sin45° = d/7
d = 7sin45°
d = 7(1/√2)
d = 7/√2
Rationalize 7/√2
= 7/√2*√2/√2
=7√2/2
Hence the value of d is 7√2/2
if I spend 6/11 of my money on books what fraction of it will remain
Prasha has five blocks of wood The total weight of all five blocks of wood is 3 kilograms. 4 of the blocks of wood each have a weight of 650 grams. Work out the weight, in grams, of the other block of wood. Step by step please :).
The weight of the other block of wood is 400 grams.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, Prasha has five blocks of wood the total weight of all five blocks of wood is 3 kilograms.
4 of the blocks of wood each have a weight of 650 grams.
∴ (4×650) = 2600 grams is the total weight.
So, the weight of the other block of wood is (3000 - 2600) grams.
= 400 grams.
learn more about the unitary method here :
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The manufacturer of pencils spends $0.05 to make each pencil and sells them for 0.25. The manufacturer also has fixed
costs each month of $2000. Find the number of pencils x that the manufacturer needs to sell in order to break even
Answer:
x=10000
Step-by-step explanation:
The break even point occurs when costs equal revenue. Write the break-even formula and solve to find
C(x)0.05x−20000.2xx=R(x)=0.25x=2000=10000.
if t(x)=-x+3, then what is f(x)=(t*t)(x)
Answer:
[tex]f(x) = {x}^{2} - 6x + 9[/tex]
Step-by-step explanation:
If f(x) = (tt)(x), that's essentially squaring t(x) so
[tex]f(x) = {t(x)}^2 \\ f(x) = (-x +3)^2 \\ f(x) = (-x +3)(-x +3) \\ f(x) = -x(-x +3) +3(-x +3)\\ f(x) = x^2 -3x -3x +9 \\ f(x) = x^2 -6x +9[/tex]
Please help! Will give brainliest.
Your cost for each light saber is $2.45 plus you have to pay a fixed weekly fee of $250 for the booth. You plan to sell each light saber for $4.15.
Write an expression that represents the profit for selling (n) light sabers in a given week.
How many light sabers must you sell in order to make a positive profit? (Profit>=0)
In order to make a positive profit, you would have to sell at least (blank) light sabers.
$4.15n - ($250 + $2.45n)
Now that we have our expression, let's set it greater than or equal to 0
$4.15n - ($250 + $2.45n) >= 0
Let's simplify the left side.
$4.15n - $250 - $2.45n >= 0.
Combine like terms.
$1.7n - $250 >= 0
Add $250 to both sides.
$1.7n >= $250
Divide both sides by $1.7
n >= 148
You would need to make 148 light sabers to make a positive profit.
HELP PLEASE THANK YOU SO SO SO MUCH <3
2. Graph the system of inequalities. Make sure your solution area is clear in your graph.
Then name a Solution Point____________ & a Non-Solution Point_____________
y ≥ 2x - 1
y ≥ -4
y < -x + 2
Fun fact:
The longest word in any of the major English language dictionaries is pneumonoultramicroscopicsilicovolcanoconiosis, a word that refers to a lung disease contracted from the inhalation of very fine silica particles, specifically from a volcano; medically, it is the same as silicosis.
Cool right? Here are more fun facts.
1 “I am” is the shortest complete sentence in the English language.
2 Supercalifragilisticexpialidocious (*breath*) is NOT the longest word in English.
Like that?
Banging your head against a wall for one hour burns 150 calories.
In Switzerland it is illegal to own just one guinea pig.