Two lighthouses are located 40 miles from each other. A boat is spotted at an angle of 37 degrees northeast of the western lighthouse. At this point, the boat is 28 miles from the eastern lighthouse. How far is the boat from the western lighthouse?
A. 46.27 miles
B. 17.43 miles
C. Either 46.27 miles or 17.43 miles
D. There is no possible solution.
Answer:
C. Either 46.27 miles or 17.43 miles
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PLS HELP ME!!!!! ONEHUNDRED POINTS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
ruth was hauling a wide load out of portland. at 7:00 am she headed north from exit 102 at an average speed of 35 pmh. michael headed north from the same exit at 9:00 am in his pontiac. by 3:00 pm the same day michael was 20 miles ahead of ruth. what was michael's average speed
Answer:
Ruth was out of Portland at 35mph at 7:00 am
so at 9 am, she was 70 miles ahead of Michael
but Michael was 20 miles ahead by 3 pm.
so in 6 hours, he went past Ruth by 90 miles which is 90/6 = 15mph
Michael speed = ruth speed + 15. = 35 + 15 = 50mph
Write an expression for the total Surface Area (SA) of a rectangular prism whose base is a square with side of length x and height of y.
The table below shows the relative frequencies of the color of cars bought last month by males and females. Which percentage represents the car bought most often?
Options:
20%
31%
43% is wrong
57%
(I already did my other questions, this is the only one I needed help with)
Suppose the diameter of a circle is \color{green}{10}10 start color green, 10, end color green. what is its radius
The measure of an angle is 27°. what is the measure of a complementary angle?
The measure of a complementary angle to a 27 degree angle is 63 degrees because two angles are complementary if their measures add up to 90 degrees. This is calculated by subtracting the given angle from 90.
Explanation:The measure of an angle is given as 27°, and you are asked to find the measure of a complementary angle. In mathematics, two angles are considered complementary if their measures add up to 90 degrees. Therefore, to find the measure of a complementary angle, you subtract the given angle from 90 degrees.
So, to solve this problem, you would simply subtract 27 from 90.
The calculation would look like this:
90-27 = 63. Therefore, the measure of the complementary angle is 63°.
In Miami the number of accidents increased by 20% over a four year period.how many accidents were there in 2013 if there were 5120 in 2009
A footbridge is in the shape of an arc of a circle. the bridge is 10 ft tall and 27 ft long, horizontally. what is the radius of the circle that contains the bridge? round your answer to the nearest tenth.
The radius of the circle that includes the footbridge, given the bridge's arc length and height, is 14.1 ft.
Explanation:The problem relates to the geometry of a circle, specifically the concept of the arc length and radius. Given the arc length (L) and the height of the arc (h), we can use these to find the radius (r) of the circle using the formula r = L²/(8h) + h/2.
Here, the arc length is the horizontal length of the footbridge, which is 27 ft and the height h is the height of the bridge, 10 ft.
Substituting these values into the formula we get:
r = (27² ft)/(8*10 ft) + 10 ft/2 = 729/80 + 5 = 14.1 ft
So, to the nearest tenth of a foot, the radius of the circle that includes the footbridge is 14.1 ft.
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Which polar coordinates represent the point plotted on the graph? Select all that apply. (2 answers)
a. (-4, 90 degrees)
b. (4, 90 degrees)
c. (4, -90 degrees)
d. (-4, 270 degrees)
e. (-4, -270 degrees)
Answer: The correct options are (b) and (d).
Explanation:
It the polar form [tex]r^2=x^2+y^2[/tex], where
[tex]x=r\cos \theta,y=r\sin \theta[/tex]
The polar coordinate are in the form of [tex](r,\theta)[/tex].
From the given figure it is noticed that the value of r is 4 and [tex]\theta=\frac{\pi}{2}[/tex] or [tex]90^{\circ}[/tex] .
So the point is defined as [tex](4,90^{\circ})[/tex] and option b is correct.
The value,
[tex](r\cos \theta, r\sin \theta)=(0,4)[/tex]
Check the each option if we get the same value then that option is correct.
For option a.
[tex](r\cos \theta, r\sin \theta)=(-4\cos 90^{\circ} , -4\sin 90^{\circ})=(0,-4)[/tex]
Therefore option (a) is incorrect.
For option c.
[tex](r\cos \theta, r\sin \theta)=(4\cos (-90)^{\circ} , 4\sin (-90)^{\circ})=(0,-4)[/tex]
Therefore option (c) is incorrect.
For option d.
[tex](r\cos \theta, r\sin \theta)=(-4\cos (270)^{\circ} , -4\sin (270)^{\circ})\\(-4\cos (360-90)^{\circ} , -4\sin (360-90)^{\circ})=(0,4)[/tex]
Therefore option (d) is correct.
For option (e).
[tex](r\cos \theta, r\sin \theta)=(-4\cos (-270)^{\circ} , -4\sin (-270)^{\circ})\\(-4\cos (270)^{\circ} , 4\sin (270)^{\circ})=(0,-4)[/tex]
Therefore option (e) is incorrect.
Answer:
1. A
2. B, D
3. A, D, E
4. C
5. A
Step-by-step explanation:
If a person uses $700 in credit with an interest of 14%,what is that person going to owe after three billing cycles with simple interest
what is the value of x, if the volume of the cone is 12piem^3
Write the equation in standard form using integers y=4x+5
A cruise ship can cover 17 nautical miles in 374 minutes. How many nautical miles will it travel in 330 minutes?
The ship's speed in deep water is 0.045 nautical miles per minute. In shallow water, the ship's maximum speed typically decreases due to increased drag and turbulence.
To find the speed of the ship in very deep water:
Calculate speed = Distance / Time = 17 nmi / 374 min = 0.045 nautical miles per minute.For the ship's speed in shallow water:It depends on the water resistance; usually, in shallow water, the ship's maximum speed decreases due to increased drag and turbulence.Which is least expensive per oz rounded to the nearest cent: 20 oz for $1.79 or 2 lb 2 oz for $2.59?
A.) 20 oz
B.) 2 lb 2 oz
C.) Neither
Answer:
B.) 2 lb 2 oz
Step-by-step explanation:
$1.79 for 20 ounces gives us
1.79/20 = $0.0895 ≈ $0.09 per ounce.
1 lb = 16 oz.; this means that 2 lb = 2(16) = 32 oz.
$2.59 for 2 lb 2 oz then gives us
2.59/34 = $0.07617647059 ≈ $0.08 per ounce.
The second choice is cheaper by 1 cent.
If f(x) = 1000(3)x and g(x) = 8x. Which statement is true? A) None are true. B) as x → ∞, f(x) < g(x). C) as x → ∞, f(x) = g(x). D) as x → ∞, f(x) > g(x).
Answer: f(x) > g(x).
If f(x) = 1000(3)x and g(x)=8x
fx=3000x
f=3000x/x
f=3000
g(x)=8x
g=8x/x
g=8
For whatever amount of X (positive), the statement f(x) > g(x) is true.
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Simplify (2√5 + 3√7)² Show ALL your work.
4+3x-ax=9-7x+bx
PLEASE HELP
Answer:
[tex]x=\frac{5}{(10-a-b)}[/tex]
Step-by-step explanation:
4+3x-ax=9-7x+bx
take all variable terms at one side and all constant terms at one side,
3x+7x-bx-ax=9-4
10x-ax-bx=5
x(10-a-b)=5
[tex]x=\frac{5}{(10-a-b)}[/tex]
Find one pair of real numbers, $(x,y),$ such that $x + y = 6$ and $x^3 + y^3 = 144.$
[tex]\[\{(3 + \sqrt{5}, 3 - \sqrt{5})}\][/tex] is the one pair of real numbers [tex]\((x, y)\)[/tex] that satisfies the given equations.
Given the system of equations:
[tex]\[x + y = 6\][/tex]
[tex]\[x^3 + y^3 = 144\][/tex]
We can use the identity for the sum of cubes:
[tex]\[x^3 + y^3 = (x + y)(x^2 - xy + y^2)\][/tex]
Substitute [tex]\(x + y = 6\):[/tex]
[tex]\[x^3 + y^3 = 6(x^2 - xy + y^2)\][/tex]
Given [tex]\(x^3 + y^3 = 144\)[/tex], we substitute this into the equation:
[tex]\[144 = 6(x^2 - xy + y^2)\][/tex]
Divide both sides by 6:
[tex]\[24 = x^2 - xy + y^2\][/tex]
Next, we use the square of the sum:
[tex]\[(x + y)^2 = x^2 + 2xy + y^2\][/tex]
Substitute [tex]\(x + y = 6\):[/tex]
[tex]\[6^2 = x^2 + 2xy + y^2\][/tex]
[tex]\[36 = x^2 + 2xy + y^2\][/tex]
We already have [tex]\(x^2 - xy + y^2 = 24\)[/tex]. Let’s denote the first and second equations:
1. [tex]\(x^2 - xy + y^2 = 24\)[/tex]
2. [tex]\(x^2 + 2xy + y^2 = 36\)[/tex]
Subtract the first equation from the second equation:
[tex]\[(x^2 + 2xy + y^2) - (x^2 - xy + y^2) = 36 - 24\][/tex]
[tex]\[3xy = 12\][/tex]
[tex]\[xy = 4\][/tex]
Now, we have two equations:
1. [tex]\(x + y = 6\)[/tex]
2. [tex]\(xy = 4\)[/tex]
We solve these equations using the quadratic formula. Consider the quadratic equation:
[tex]\[t^2 - (x+y)t + xy = 0\][/tex]
[tex]\[t^2 - 6t + 4 = 0\][/tex]
Solve for [tex]\(t\)[/tex] using the quadratic formula [tex]\(t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\):[/tex]
[tex]\[t = \frac{6 \pm \sqrt{36 - 16}}{2}\][/tex]
[tex]\[t = \frac{6 \pm \sqrt{20}}{2}\][/tex]
[tex]\[t = \frac{6 \pm 2\sqrt{5}}{2}\][/tex]
[tex]\[t = 3 \pm \sqrt{5}\][/tex]
Thus, the solutions for [tex]\(x\)[/tex] and [tex]\(y\)[/tex] are:
[tex]\[x = 3 + \sqrt{5}, \quad y = 3 - \sqrt{5}\][/tex]
or
[tex]\[x = 3 - \sqrt{5}, \quad y = 3 + \sqrt{5}\][/tex]
A number x, rounded to 1 decimal place is 12.3 write down the error interval for x
The error interval for a number x rounded to 12.3 is 12.25 ≤ x < 12.35, indicating the range that x could be before rounding to one decimal place.
Explanation:If a number x, rounded to 1 decimal place, is 12.3, the error interval for x defines the range of values that x could be in order to round to 12.3. Since the value is rounded to one decimal place, we consider half of a tenth (0.05) on either side of 12.3 to find the error interval. Hence, the lower bound of the error interval would be just below 12.3 (12.25), and the upper bound would be just before it would round up to the next tenth (12.35).
The error interval for x can be written as: 12.25 ≤ x < 12.35.
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Error interval for [tex]\( x \)[/tex] rounded to 1 decimal place as 12.3 is from 12.25 to 12.35.
To find the error interval for the number [tex]\( x[/tex], rounded to 1 decimal place as 12.3, we need to consider the possible range of values that [tex]\( x \)[/tex] could have been before rounding.
1. Lower Bound: To find the lower bound, we need to consider the smallest value [tex]\( x \)[/tex] could have been that would round to 12.3 when rounded to 1 decimal place. The smallest value that would round up to 12.3 is 12.25.
2. Upper Bound: Similarly, to find the upper bound, we need to consider the largest value [tex]\( x \)[/tex] could have been that would round to 12.3 when rounded to 1 decimal place. The largest value that would round down to 12.3 is 12.35.
So, the error interval for [tex]\( x \)[/tex] is from 12.25 to 12.35.
Find the surface area of a sphere with radius, r = 11 in.
Surface Area = ________ in^2
(Type an exact answer in terms of pi.)
PLZ help
which inequality does the graph represent
The inequality the graph represent is y > x - 2.
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions. An inequality is a mathematical statement that compares two values or expressions using a relational operator, such as less than (<), greater than (>), less than or equal to (≤), greater than or equal to (≥), or not equal to (≠). Inequalities are used to describe relationships between quantities or to express constraints or conditions.
We are given that;
The number line
Now,
The slope of the line is 1 and the y-intercept is -2,
so we can write y = x - 2 for the equation of the line.
The line is dashed, so we know that y is not equal to x - 2.
The region above the line is shaded, so we know that y is greater than x - 2.
Therefore, by the inequality the answer will be y > x - 2.
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I really need help with these questions:
Use basic identities to find the simplified expression-
1. (cos^2 x + sin^2 x) / (cot^2 x - csc^2 x)
2. cosine θ^2 / sine θ^2 + csc θ sin θ
Explanations would be greatly appreciated
If the pattern below follows the rule "Starting with four, every consecutive line has a number one more than the previous line," how many marbles must be in the seventh line?
The number of balls in 7th line would be 10.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is a pattern as shown in the image.
An arithmetic sequence is of the form -a, a + d, a + 2d, a + 3d, ......,
{d} is common difference and {a} is first term.We can write the pattern as -
4, 5, 6, 7, .....
This is a arithmetic progression. We can write the nth term as -
a{n} = a + (n - 1)d
a{7} = 4 + (7 - 1) x 1
a{7} = 4 + 6
a{7} = 10
Therefore, the number of balls in 7th line would be 10.
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On two examinations, you have grades of 83 and 89. there is an optional final examination, which counts as one grade. you decide to take the final in order to get a course grade of a, meaning a final average of at least 90
Find the surface area of a rectangular prism with a height of 6 inches, a width of 7 inches, and a length of 13 inches. A) 338 in2 B) 422 in2 C) 520 in2 D) 1364 in2
If you can, please explain. Thank you vv much! :D
Answer:
422 in.2
Step-by-step explanation:
Substitute the measurements of the rectangular prism into the formula SA = 2(lw) + 2 (lw) + 2(lh): 2(13)(7) + 2(6)(7) + 2(13)(6) = 422 in2.
An airplane left Miami, FL. At the same time another plane left Santiago, Chile. The two planes flew toward each other at rates of 625 mph and 575 mph. If Miami and Santiago are 4200 miles apart, how long will it take until the planes pass each other?
Simplify the expression -2x^2(4x − 3).
-8x3 − 6x2
-8x3 + 6x2
8x3 − 6x2
8x3 + 6x2
Two mechanics worked on a car. the first mechanic worked for 10 hours, and the second worked for 15 hours. together they charged a total of 1800. what was the rate charged per hour by each mechanic if the sum of the two rates was $155 per hour ?
The rates charged per hour by the first and second mechanics will be $105 and $50.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that two mechanics worked on a car, the first mechanic worked for 10 hours, and the second worked for 15 hours. together they charged a total of 1800.
Suppose x is the hourly rate for the first mechanic and y is the hourly rate of the second.
If the total money earned is 1800.
10x + 15 y = 1800 ---- (1)
If both have their individual rates the sum of the hourly rate is,
x+ y = 15 -------- (2)
Rearrange the equation,
x = 155- y
Substitute the value of x in equation 1 we get,
10x + 15 y = 1800
10(155-y) + 15y = 1800
1150 - 10y + 15y = 1800
5y = 250
y = 50
Substitute the value of y in equation 2 we get,
x = 155- y
x= 155 - 50
x = 105
Thus, the rates charged per hour by the first and second mechanics will be $105 and $50.
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True or false ???????????????please help
PLS ANSWER! THE WORLD HATES ME!!
0.29999999999 As a fraction
Here is your answer:
All you need to do is keep the 29 and then add a hundred because of how many 9's there are.
Also, you could see that:
[tex] .29999999999 \neq \frac{29999999999}{100000000000} [/tex]
Which would also mean that:
[tex] \frac{29999999999}{100000000000} \neq \frac{29}{100} [/tex]
Therefore the answer is "29/100."
Hope this helps!
Answer:
13/46
Step-by-step explanation: