Answer:
3 meters
Step-by-step explanation:
Assuming the window is rectangular
A = l*h
18 = 6*h
Divide each side by 6
18/6 = 6h/6
3 = h
A ship moves through the water at 30 miles/hour at an angle of 30° south of east. The water is moving 5 miles/hour at an angle of 20° east of north. Identify the ship's vector, the water current's vector, and the vector representing the ship's actual motion.
Answer:
a. 25.98i - 15j mi/h
b. 1.71i + 4.7j mi/h
c. 27.69i -10.3j mi/h
Step-by-step explanation:
a. Identify the ship's vector
Since the ship moves through water at 30 miles per hour at an angle of 30° south of east, which is in the fourth quadrant. So, the x-component of the ship's velocity is v₁ = 30cos30° = 25.98 mi/h and the y-component of the ship's velocity is v₂ = -30sin30° = -15 mi/h
Thus the ship's velocity vector as ship moves through the water v = v₁i + v₂j = 25.98i + (-15)j = 25.98i - 15j mi/h
b. Identify the water current's vector
Also, since the water is moving at 5 miles per hour at an angle of 20° south of east, this implies that it is moving at an angle 90° - 20° = 70° east of north, which is in the first quadrant. So, the x-component of the water's velocity is v₃ = 5cos70° = 1.71 mi/h and the y-component of the water's velocity is v₄ = 5sin70° = 4.7 mi/h
Thus the ship's velocity vector v' = v₃i + v₄j = 1.71i + 4.7j mi/h
c. Identify the vector representing the ship's actual motion.
The velocity vector representing the ship's actual motion is V = velocity vector of ship as ship moves through water + velocity vector of water current.
V = v + v'
= 25.98i - 15j mi/h + 1.71i + 4.7j mi/h
= (25.98i + 1.71i + 4.7j - 15j )mi/h
= 27.68i -10.3j mi/h
Which equation represents the general form a circle with a center at (–2, –3) and a diameter of 8 units?
x2 + y2 + 4x + 6y – 51 = 0
x² + y² – 4x – 6y – 51 = 0
x2 + y2 + 4x + 6y – 3 = 0
x2 + y2 – 4x – 6y – 3 = 0
The equation for the given circle is:
[tex]x^2 + y^2 + 4x + 6y - 3 = 0[/tex]
How to get the equation of the circle?
Remember that for a circle whose center is (a, b) and has a radius r, the equation is:
[tex](x - a)^2 + (y - b)^2 = r^2[/tex]
In this case, the center is (-2, -3) and the diameter is 8 units, so the radius is r = 4.
Then the equation is:
[tex](x + 2)^2 + (y + 3)^2 = 4^2[/tex]
Expanding the squares we get:
[tex](x^2 + 2*2*x + 4) + (y^2 + 2*3*y + 3^2) = 16\\\\x^2 + y^2 + 4x + 6y + 4 + 9 - 16 = 0\\\\x^2 + y^2 + 4x + 6y - 3 = 0[/tex]
So the correct option is the third one.
If you want to learn more about circles:
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In a right triangle, Sin (4x + 10) º = Cos (6x) º. What is the value of x?
Answer:
x = 8
Step-by-step explanation:
According to trigonometry identity
sin x = Cos (90-x)
Hence if we have;
Sin (4x + 10) º = Cos (6x)
Sin (4x + 10) º = Sin(90- 6x)
4x + 10 = 90 - 6x
4x+6x = 90 - 10
10x = 80
x = 80/10
x = 8
Hence the value of x is 8
Leticia places a 10 foot ladder against a wall at a 70° with the
ground. Determine how far the base of the ladder is from the
wall.
O 3.42 feet
0 27.47 feet
O 9.4 feet
29.24 feet
none of these
Answer:
To solve this problem you must apply the procedure shown below:
1. You have that ladder measures 10 foot and forms and angle of 70 degrees with the ground.
2. Therefore, you have:
Sinα=opposite/hypotenuse
α=70°
opposite=x
hypotenuse=10
3. When you substitute the values, you obtain:
Sin(70°)=x/10
4. Now, solve for x, as following:
x=(10)(Sin(70°)
x=9.39 feet
Therefore, the answer is: 9.39 feet.
Step-by-step explanation:
mr.harrington drive 164 miles. his car used 8 gallons of gas. how many miles per gallon of gas does the car average
Answer:
20.5 mpg
Step-by-step explanation:
Here we're looking to calculate the car's fuel economy, expressed in miles per gallon, or mpg:
164 miles
------------------ = 20.5 mpg
8 gallons
To simplify 8.3 − 4
1
5
( 6.1 +
1
2
) , which operation must be performed first?
Answer:
the question in the parenthesis
Step-by-step explanation:
because thats how the order of operations work
What is the area and perimeter of square
Answer:
The answer is A
Step-by-step explanation:
This I because the area of a square is =
(length of on side)² = l²
The options there are not perfect squarss except A
which is 64 in²
And we know that 8² will give you 64
so then it means one side is 8 in
So the area =
8² = 8 in × 8 in = 64 in²
for a family with 6 children what is the probability that they have exactly one boy and 5 girls
Answer:
Ok so the probability would be 16%(can be round to)
Step-by-step explanation:
Can someone help me with this please I have to have it done ??
Given:
The scale factor of the actual sports utility vehicle to the toy model is 50:1.
Actual length = 7 feet
Actual width = 5 feet
To find:
The length and width of the toy model.
Solution:
a. Let l be the length of the toy model, then
[tex]\dfrac{\text{Actual length}}{\text{Length of the toy model}}=\dfrac{50}{1}[/tex]
[tex]\dfrac{7}{l}=\dfrac{50}{1}[/tex]
[tex]7=50l[/tex]
[tex]\dfrac{7}{50}=l[/tex]
[tex]0.14=l[/tex]
Therefore, the length of the toy model is 0.14 feet.
b. Let w be the width of the toy model, then
[tex]\dfrac{\text{Actual width}}{\text{Width of the toy model}}=\dfrac{50}{1}[/tex]
[tex]\dfrac{5}{w}=\dfrac{50}{1}[/tex]
[tex]5=50w[/tex]
[tex]\dfrac{5}{50}=w[/tex]
[tex]0.10=w[/tex]
Therefore, the width of the toy model is 0.10 feet.
plzz helpp all of this is due today :(
Answer: square root property
Step-by-step explanation:trust me
What is the length of AC?
A.72
B.96
C.136
D.132
Answer:
The answer is 136 .
HELP ASAP 50 POINTS What is the equation of a circle with a diameter with endpoints (5,2) and (3,-4)
Answer: I believe it's (x-1) 2+(y-1) 2=13
(-9x + 32) - (15x + 41)
Answer:
Step-by-step explanation:
Distribute the Negative Sign:
=−9x+32+−1(15x+41)
=−9x+32+−1(15x)+(−1)(41)
=−9x+32+−15x+−41
Combine Like Terms:
=−9x+32+−15x+−41
=(−9x+−15x)+(32+−41)
=−24x+−9
Answer:
-24x - 9
Step-by-step explanation:
Combine like terms.
Two students are reading a book. Keith reads 6 pages a day. Tameka reads 5 pages a day, but she starts sooner and has already read 15 pages.
Part A
Write a system of equations to represent the situation, using d for days and p for pages.
Part B
Graph the system of equations. (Click to draw on the graph.)
Question 3
Part C
Will Keith and Tameka ever be on the same page on the same day? Explain.
Answer: keith
Step-by-step explanation:
The system of equations to represent the number of pages read per day by Keith and Tameka, using d for days and p for pages are,
p = 6d
p = 5d + 15
Since we know that,
A system of equations is the set of equations in which the finite set of equations is present for which the common solution is sought.
Two students are reading a book. Keith reads 6 pages a day.
The equation for Keith, where d for days and p for pages can be given as,
p = 6xd
p = 6d
Tameka reads 5 pages a day, but he starts sooner and has already read 15 pages. The equation for Tameka, where d for days and p for pages, can be given as,
p = 5xd + 15
p = 5d + 15
Hence, the system of equations to represent the number of pages read per day by Keith and Tameka, using d for days and p for pages are,
p = 6d
p = 5d + 15
Learn more about the system of equations here;
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please help explain it step by step
Answer:
452 m
Step-by-step explanation:
During a game, a spinner landed on several different colors,
yellow
6
red
3
purple
2
green
12
-blue
3
Considering this data, how many of the next 13 spins should you expect to land on purple?
spins
2/26 that is the answer ok now peace
Part A
Find the formula for the corresponding inverse function g(x).
Part B
Select all of the points that would appear on the graph of y = g(x).
1. A
2. B
3. C
4. D
5. E
6. F
There is a geometrical relation that arc of circle is equal to the central angle.
And there is another relation that arc of a circle is equal to (radius *arc)
Aren't these two relation conflicting?
Help ASAP please how can I solve this please due at 12:30 need helps
Answer:
a) C = 75n +60
b) see graph
c) 210
Step-by-step explanation:
75 n -C + 60 = 0
Add C to each side
75 n -C + 60 + C = 0+C
75 n + 60 = C
Rewritng
C = 75n +60
This is in slope intercept form where y = mx+b
75 = m and 60 =b
See the graph
The slope is 75 and the y intercept is (0,60)
The scale is 1 on the n axis ( time) and 100 on the C axis (cost)
Let n be two hours
Cost = 75(2) +60
=150 +60
=210
can someone help me match these too?
ANSWER:
A is number 3
B is number 2
Step-by-step explanation:
The left side is A and B (order)
the right side is 1,2,3,4 (order)
explanation: A is number 3 because as said in A the tram already has 5 people which is what we start with a1 = 5 and we add 11 at each stop as shown in the equation.
B is number 2 for the same reason as it started with 2 but added 4 inches of rain each time.
1.) Write the probability as a fraction in simplest form. P (D) *
B.
A
С
F
D
E
1/6
4/5
about 50%
6
Answer:
Hello! answer: 1/6
Step-by-step explanation:
The probability of landing on D is 1/6 because there are 6 spots on the spinner you can land on A, B, C, D, E, and F and there is only 1 section labelled "D" therefore the probability of landing on D is 1/6 hope that helps!
6) What is the mean (average) of this set of
data:
3 4 6 7 10 15 19 21
Answer:
59
Step-by-step explanation:
Answer:
The mean of this data set is 10.6
Step-by-step explanation:
To find the Mean of a data set, you add up all the values and then divide by the number of values.
3 + 4 + 6 + 7 + 10 + 15 + 19 + 21 = 85
This data set has 8 values.
85 ÷ 8 = 10.6
Which expression has an equivalent value to x2 + 9x + 8 for all values of x?
(x + 1)(x + 8)
(x + 2)(x + 6)
(x + 4)(x + 4)
(x + 5)(x + 4)
Which equation represents a line that passes through (5,1) and has a slope of 1/2?
Answer:
y = 1/2x - 3/2
Step-by-step explanation:
y = 1/2x + b
1 = 1/2(5) + b
1 = 5/2 + b
-3/2 = b
Answer:
y=1/2x-3/2
Step-by-step explanation:
y-y1=m(x-x1)
y-1=1/2(x-5)
y-1=1/2x-5/2
y=1/2x-5/2+1
y=1/2x-5/2+2/2
y=1/2x-3/2
Someone pls answer #3 and 4
Will reward brainliest to the first most accurate answer ASAP.
Answer:
hiii my pic lol (✿^‿^)(✿^‿^)(✿^‿^)(✿^‿^)
Kendra can see the top of her apartment building reflected in a small fish pond in a park across the street. She is standing 2 m from the pond, and the distance from the pond to the apartment building is 40 m. If Kendra's eyes are 150 cm above the ground, how tall is the apartment building?
Answer:
Step-by-step explanation:
According to problem description, we have two triangles
The first one: the fish pond and feet and eyes of Kendra
The second one the fish pond and the side wall of the apartment
These two triangles have angle α as common angle and its tan
tan α = 1.5/ 2 = x/ 40 then note : 150 cm = 1.5 m
1.5/ 2 = x/ 40
x = 40 * 1.5 / 2
x = 30 m
John starts on the ground floor of a building. He runs up five flights of stairs, then runs
up 6 flights of stairs, then runs down 8 flights of stairs, then runs up four flights of stairs,
and then stops. Each story of the building is 11 feet high. How many feet above the
ground is John when he stops? PLS HELP
Answer:
77 feet above the ground.
Step-by-step explanation:
After going up 11 flights, (5 +6), he goes down 8, which brings you to 3 and then back up to 7 (3 +4). Since each story is 11 feet high, you multiply 7 and 11, to get a total of 77.
The function f(x)=2.14/55x + 0.31 can be used to determine the cost, in dollars, of a gallon of gas x years since 1960.
Part A - According to the function, what was the cost, in cents, of a gallon of gas in 1960?
Part B - According to the function, how much did the cost increase each year, rounded to the nearest whole cent?
Answer:
The answer is below
Step-by-step explanation:
The equation for a linear function is given as:
y = mx + b
where m is the slope of the function (that is the rate of change), b is the initial value of y when x is 0.
Given that the function where x represent the number of years since 1960 and y is the cost in dollar as:
[tex]f(x)=\frac{2.14}{55}x+0.31[/tex]
a) In the year 1960, that is x = 0, the cost of a gallon of gas is given as:
[tex]f(0)=\frac{2.14}{55}(0)+0.31\\\\f(0)=\$0.31[/tex]
b) From the function [tex]f(x)=\frac{2.14}{55}x+0.31[/tex], we can see that the rate of change is 2.14/55. Therefore, the cost increase each year by 4 cents per year.
Evaluate expression-What is the value of the expression when x=11 and y=7
A.4
B.128
C.49
D.14
Answer:
C. 49
Step-by-step explanation:
Start by filling in your values.
[tex]7^{2} + 99 / 11 - 9[/tex]
Solve using PEMDAS.
49 + 99 / 11 - 9
49 + 9 - 9
58 - 9
49
Answer:
[tex]c .\: \: 49[/tex]
Step-by-step explanation:
[tex] {y}^{2} + 99 \div x - 9[/tex]
[tex] {7}^{2} + 99 \div 11 - 9[/tex]
[tex] 49 +99÷11-9[/tex]
[tex]49+9-9[/tex]
[tex]58-9[/tex]
[tex]49[/tex]
Hope it is helpful...IT ISNT THE 1st OR 2nd HELP LOOK AT IMAGE PLEASE
Answer:
Last option
Step-by-step explanation:
First method :
Red Line:
Take 2 coordinates through which the line passes. Let it be (0, 7) and (14, 0).
[tex]slope, m=\frac{ 0-7}{14-0} = -\frac{7}{14} = -\frac{1}{2}[/tex]
[tex]Equation : (y - 7) = -\frac{1}{2}(x)[/tex]
[tex]2y - 14 = -x\\2y + x = 14\\4y + 2x = 28[/tex] [tex][ multiply \ by \ 2 \ on \ both \ sides][/tex]
Blue Line:
Take coordinates through which the line passes.
Let it be (-4, -12) and (-10, -9).
[tex]slope, m = \frac{-9 + 14}{-10} = \frac{5}{-10} = -\frac{1}{2}[/tex]
[tex]equation : (y + 12) = -\frac{1}{2} (x+4)\\[/tex]
[tex]y = -\frac{1}{2}x - 2 - 12\\\\y = -\frac{1}{2}x -14\\\\2y = -x - 28\\\\-2y = x +28[/tex]
Second Method:
From the graph it is clear the lines are parallel. The slopes of line parallel to each other are equal. So convert each equation into standard line equation form :y = mx + b
And check for set of equation whose slope are same.
First set :
[tex]y = 10x - 15 \\\\=> slope = 10\\\\-9x + 2y = 10\\2y = 9x + 10\\\\y = \frac{9}{2}x + 5 => slope = \frac{9}{2}[/tex]
Slopes are not equal.
Second set :
[tex]2y = 2x + 5\\y = x + \frac{5}{2}\\slope = 1\\\\\\3x -4y = -5\\4y = 3x + 5\\\\\y = \frac{3}{4}x + \frac{5}{4}\\\\slope = \frac{3}{4}[/tex]
Slopes are not equal.
Third set :
[tex]y = 3x +10 \\slope = 3\\\\\\2x - 3y = -6\\3y = 2x +6\\\\y = \frac{2}{3}x + 2\\\\slope = \frac{2}{3}[/tex]
Slopes are not equal.
Fourth set :
[tex]2x + 4y = 28\\4y = -2x +28\\\\y = -\frac{1}{2}x + 7\\\\slope = -\frac{1}{2}\\\\\\-2y = x + 28\\\\y = -\frac{1}{2}x - 14\\\\slope = -\frac{1}{2}[/tex]
Slopes are same.