Answer:
324-6x
Step-by-step explanation:
A boat is heading towards a lighthouse, where Meena is watching from a vertical
distance of 120 feet above the water. Meena measures an angle of depression to the
boat at point A to be 18º. At some later time, Meena takes another measurement and
finds the angle of depression to the boat (now at point B) to be 44º. Find the distance
from point A to point B. Round your answer to the nearest foot if necessary.
Answer:
245 ft
Step-by-step explanation:
The geometry of the problem can be modeled by a right triangle in which Meena's height is the side opposite the angle of depression, and the distance to the boat is the side adjacent to the angle of depression. The mnemonic SOH CAH TOA reminds us of the relation ...
Tan = Oppsite/Adjacent
__
The more useful trig function for this problem is the inverse of the tangent function, the cotangent. Using that function, we have ...
cot(angle) = (distance to boat)/(Meena's height)
Then the distance to the boat is ...
distance to boat = (Meena's height)×cot(angle)
The change in distance from A to B is then ...
A -B = (120 ft)(cot(18°) -cot(44°))
= (120 ft)(3.0777 -1.0355) ≈ 245.06 ft
The distance from point A to point B is about 245 feet.
Find the value of x such that the line containing (1,2) and (5,3) is perpendicular to the line containing (x,4) and (3,0)
The value of x that makes the line containing (1,2) and (5,3) perpendicular to the line containing (x,4) and (3,0) is x = 2.
To determine the value of x such that the line containing (1,2) and (5,3) is perpendicular to the line containing (x,4) and (3,0), we need to find the slope of both lines and apply the concept of perpendicular lines.
The slope of a line can be found using the formula:
slope = (change in y) / (change in x)
For the line containing (1,2) and (5,3), the slope is:
slope1 = (3 - 2) / (5 - 1) = 1 / 4
To find the slope of the line containing (x,4) and (3,0), we use the same formula:
slope2 = (0 - 4) / (3 - x) = -4 / (3 - x)
Perpendicular lines have slopes that are negative reciprocals of each other. In other words, if the slope of one line is m, then the slope of a line perpendicular to it is -1/m.
So, we can set up the equation:
-1 / (1/4) = -4 / (3 - x)
Simplifying this equation:
-4 = -4 / (3 - x)
To remove the fraction, we can multiply both sides by (3 - x):
-4(3 - x) = -4
Expanding and simplifying:
-12 + 4x = -4
Adding 12 to both sides:
4x = 8
Dividing both sides by 4:
x = 2
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Using the information in the Box-and-Whisker plot
below, what is the 3rd Quartile?
100 points btw
The coordinates points of point B are from the given graph is closest to (4, 0).
What is the coordinate point?
The Cartesian coordinates (also called rectangular coordinates) of a point are a pair of numbers (in two dimensions) or a triplet of numbers (in three dimensions) that specified signed distances from the coordinate axis.
We have,
To find:
Which of the following points is closest to (4, 0)?
Also, we have given the graph with points A, B, C, and D.
The coordinate points of each point are from the given graph:
A = (0, -5),
B = (4, 0),
C = (0, 4),
and D = (0, -4).
Therefore, the coordinates points of point B are from the given graph is closest to (4, 0).
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Answer: B
Step-by-step explanation:
yea
What type of angles are labeled and what is the value of m? Show your work.
Answer: I believe
M = 80
Step-by-step explanation:
100 - 20 = 80
11 12 13 14 15
A rectangle has an area of (x2 − 17x + 72) square units. Since the area of a rectangle is determined using the formula, A = lw, what could be the length and width of the rectangle?
length = (x − 8) units and width = (x − 9) units
length = (x + 9) units and width = (x + 8) units
length = (x − 6) units and width = (x − 12) units
length = (x + 12) units and width = (x + 6) units
Answer:
The results are the opposite sign of x1 and x2.
\(lenght \: = (x - 8) \: and \: width \: = (x - 9)\)
Step-by-step explanation:
\( {x}^{2} - 17x + 72 = 0\)
\(Δ = {(17)}^{2} - 4(1 \times 72)\)
\(Δ = 289 - 288 = 1\)
\(x1 \: and \: x2 = \frac{17± \sqrt{1}}{2} \)
\(x1 = \frac{17 + 1}{2} = 9\)
\(x2 = \frac{17 - 1}{2} = 8\)
The graph shows the amount of savings over time in Eliana's account. Lana, meanwhile, puts $50 each week into her savings account. If they both begin with $0, who is saving at the greater rate?
Select the correct choice below and fill in the answer boxes to complete your choice.
A.
Lana saves at a greater rate because her unit rate of $_ per week is greater than Eliana's unit rate of $_ per week.
B.
Eliana saves at a greater rate because her unit rate of $_ per week is greater than Lana's unit rate of $_ per week.
Answer:
A. Lana saves at a greater rate because her unit rate of $50 per week is greater than Eliana's unit rate of $48 per week.
Step-by-step explanation:
Eliana's savings per week = the rate of change of the graph
The rate of change of the graph given = \( \frac{y_2 - y_1}{x_2 -x_1} \)
Using the points (0, 0) and (2, 96),
Rate of change = \( \frac{96 - 0}{2 - 0} = \frac{96}{2} = 48 \)
This rate of change means, Eliana puts $48 dollars per week into her account.
Since Lana's saving rate per week is $50, therefore:
Lana saves at a greater rate because her unit rate of $50 per week is greater than Eliana's unit rate of $48 per week.
What is (are) the x-value(s) that solve the system of equations y = x and y = 2x – 1?
Answer:
y=1 x=1
y = 2x – 1
replace y with x
x=2x-1
x-2x = - 1
-x = -1
x= 1
y=x =1
Help :) Round to the nearest 10ths
Answer:
A=0.6
Step-by-step explanation:
Answer:
0.6 is your answer
Step-by-step explanation:
the tenths place is the 1st number after the decimal which would be 5 and you would want to round that up to 6 because the number after it is iver 5 (closer to 10 than it is 1)
hope this helps:) have a good day:)
Pls help - Let f (x) = 2x + 1. Graph t(x) = f(x - 3). Describe the
transformation from the graph of f(x) to the graph of g(x).
Answer:
The transformation from f(x) to t(x) can be described as a shift to the right 3 units in the positive x direction.
Step-by-step explanation:
I can’t say anything about the graph g(x) because it’s not defined. Perhaps the relation between g(x) and t(x) was described somewhere else? Otherwise it might have been a typo and they indeed wanted the transformation from f(x) to t(x).
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Answer:
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<_>
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()_()
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Step-by-step explanation:
how to change a vector direction by 90 degree
Answer:
multiply the X part of the vector by -1, and then swap X and Y values
Step-by-step explanation:
The sum of two numbers is 12. The difference of the two numbers is 6. What are the two numbers?
Answer:
3 and 9
Step-by-step explanation:
x+y=12
y-x=6
y-x=6
+x. +x
y=6+x
x+(6+x)=12
6+2x=12
-6. -6
2x=6
/2. /2
x=3
3+y=12
-3. -3
y=9
Hopes this helps please mark brainliest
the circumference of circle x in which a = 49pi in squared
Answer:
C = 14 pi inches
Step-by-step explanation:
The area of a circle is given by
A = pi r^2
49 pi = pi r^2
Divide each side by pi
49 pi/pi = pi /pi r^2
49 = r^2
Take the square root of each side
7 = r
The circumference is given by
C = 2 * pi *r
C = 2 * pi *7
C = 14 pi inches
Every 20th person in line at grocery store was asked whether they had used their price plus card today. Out of 50 people, 38 said yes. Is this a valid sampling method? If so, find how many of the 800 people in the store would be expected to be using their price plus card.
Answer:
This is an example of systematic sampling, which is a valid sampling method if the ordering of the individuals in the population does not affect the results. However, it may not be a representative sample if there is any pattern or bias in the order of the individuals.
Using the given information, we can estimate the proportion of people who have used their price plus card as:
38/50 = 0.76
Therefore, we can expect that approximately 0.76 of the 800 people in the store would be using their price plus card:
0.76 x 800 = 608 people.
Answer:
Yes
608 people
Step-by-step explanation:
800 × 38 =30400
30400 ÷ 50 =608
A professor wants to estimate the average time it takes his students to finish a computer project. Based on previous evidence, he believes that the standard deviation is approximately 3.6 hours. He would like to be 96% confident that his estimate is within 5 hours of the true population mean. Use RStudio to determine how large of a sample size is required without rounding any interim calculations.
Answer:
A sample size of 3 is required.
Step-by-step explanation:
We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:
\(\alpha = \frac{1 - 0.96}{2} = 0.02\)
Now, we have to find z in the Z-table as such z has a p-value of \(1 - \alpha\).
That is z with a pvalue of \(1 - 0.02 = 0.98\), so Z = 2.054.
Now, find the margin of error M as such
\(M = z\frac{\sigma}{\sqrt{n}}\)
In which \(\sigma\) is the standard deviation of the population and n is the size of the sample.
Based on previous evidence, he believes that the standard deviation is approximately 3.6 hours.
This means that \(\sigma = 3.6\)
He would like to be 96% confident that his estimate is within 5 hours of the true population mean. Use RStudio to determine how large of a sample size is required without rounding any interim calculations.
The sample size needed is of n, and n is found when M = 5. So
\(M = z\frac{\sigma}{\sqrt{n}}\)
\(5 = 2.054\frac{3.6}{\sqrt{n}}\)
\(5\sqrt{n} = 2.054*3.6\)
\(\sqrt{n} = \frac{2.054*3.6}{5}\)
\((\sqrt{n})^2 = (\frac{2.054*3.6}{5})^2\)
\(n = 2.19\)
Rounding up:
A sample size of 3 is required.
Write to the nearest 1/2kg 1kg 620g
The value of 1kg 620g to kg is 1.62 kg
Conversion of kilograms to gramsGiven the expression 1kg 620g
Since 1000g = 1kg, hence;
620g = 0.62kg
Substitute
1kg 620g = 1 + 0.62
1kg 620g = 1.62kg
Hence the value of 1kg 620g to kg is 1.62 kg
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Finn has a round tablecloth with a radius of 1 yard. What is the tablecloth's area? Use 3.14 for pi
Answer:
The answer I got was 3.14.
Step-by-step explanation:
PLZ HELP!!! BRAINLYEST WILL BE GIVEN TO BEST ANSWER!!!! IF YOU PUT A LINK I WILL REPORT YOU!!!!! DONT TRY ME!!!!!! YALL BEEN WASTING MY POINTS LATELY I HATE IT SO NO SNEAKY LINK OR NON ANSWER OR U WILL BE REPORTED.
I tried to count it but with 8 annoying siblings messing with u all the time, it is impossible
2(2x - 4) = 3(x + 4)
Answer:
24
Step-by-step explanation:
i dont know if its correct
What is the area of a circle with a diameter of 37 inches?
in²
(Use 3.14 for Pi.)
Answer:
1073.45 in²
Step-by-step explanation:
What is the area?The area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.
What is the diameter?Diameter is the length across the entire circle, the line splitting the circle into two identical semicircles.
The equation to solve for the area of a circle is:
π × \(r^{2}\) = Area of a circleBut wait, we don't have a radius to fix in the equation! Well to solve for the radius when given diameter, we can use the expression:
diameter ÷ 2 = radiusNow that we know this, we can insert 37 in for the diameter:
37 ÷ 2 = 18.5So, the radius of the circle is 18.5 inches.
Inserting 18.5 into the expression for the radius:
π × \(18.5^{2}\) =Using 3.14 for pi:
3.14 × \(18.5^{2}\) = 1073.45 in²Therefore, the area of a circle with a diameter of 37 inches is 1073.45 in².
What is an example of "A one-to-one function of P onto Q is an isomorphism of P and Q "?
An example of a one-to-one function that is an isomorphism between sets P and Q is the function f: P -> Q defined as f(x) = 2x, where P and Q are the sets of integers.
How to Identify a One-to-One Function?An example of a one-to-one function that is an isomorphism between sets P and Q is the function f: P -> Q defined as f(x) = 2x, where P and Q are the sets of integers.
This function is one-to-one because for every element x in P, there is a unique element 2x in Q. It is onto because every element y in Q has a preimage x in P such that f(x) = y (e.g., y/2 = x).
Furthermore, this function preserves the group structure between P and Q, as it satisfies the properties of an isomorphism. In this case, the group structure is addition, and the function f preserves addition: f(x + y) = 2(x + y) = 2x + 2y = f(x) + f(y) for all x, y in P.
Therefore, the function f: P -> Q defined as f(x) = 2x is an example of a one-to-one function that is an isomorphism between sets P and Q.
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Please help me as sooon as possible
Answer:
2km north and 5km east
Step-by-step explanation:
count boxes north and boxes east between the points
Answer: Sam is 3 km north and 6 km east of the theater.
Hope this helped! Have a blessed day! :D
how do you find answer to 9/35 - 1/5?
Answer:
2/35
Step-by-step explanation:
\(\frac{9}{35}-\frac{1}{5}=\frac{9}{35}-\frac{7}{35}=\frac{2}{35}\)
What is.. 4x-2=(x+3)+2
Answer:
x = 7/3
Step-by-step explanation:
4x - 2 = x + 3 + 2
4x - 2 = x + 5
Rearranging the terms, we get,
4x - x = 5 + 2
3x = 7
x = 7/3
Hence, x = 7/3.
Determine the points of discontinuity for the following rational function. y= x+6/x^2 +11x+30
The function has a vertical asymptote at x = -6 and a hole at x = -5.
To find the points of discontinuity, we need to look for values of x that make the denominator of the fraction equal to zero. We can factor the denominator of the rational function as follows:
x² + 11x + 30 = (x + 6)(x + 5)
So the function is undefined for x = -6 and x = -5, since these values make the denominator equal to zero.
These are the points of discontinuity for the rational function.
At x = -6, the function has a vertical asymptote. To see this, we can examine the behavior of the function as x approaches -6 from the left and right:
As x approaches -6 from the left (i.e., x < -6), the denominator becomes a large negative number, while the numerator is a small negative number. So the fraction becomes a large negative number. As x approaches -6 from the right (i.e., x > -6), the denominator becomes a large positive number, while the numerator is a small positive number. So the fraction becomes a large positive number. Therefore, the function has a vertical asymptote at x = -6.
At x = -5, the function has a hole.
To see this, we can factor out the common factor (x + 6) from the numerator and denominator of the fraction:
y = (x + 6)/(x + 6)(x + 5) = 1/(x + 5)
So the function is undefined at x = -5, but we can see that the numerator and denominator have a common factor of (x + 5), which cancels out. Therefore, the function has a hole at x = -5, and can be defined at this point by the limit as x approaches -5:
lim (x -> -5) y = lim (x -> -5) 1/(x + 5) = -∞
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Select all the points that are on the graph of the line 2x+8y= 16,
a.
(0,2)
b. (0,4)
C. (1,2)
d. (1,4)
e. (4,1)
f. (8,0)
Answer:
Step-by-step explanation:
a, e, f
Dividing fractions word problems, please help I need it........
Answer:
25
Step-by-step explanation:
l x w = h
25 x 7.2 = 180
How do you write 582% as a fraction or mixed number?
Answer:
5.82
Step-by-step explanation:
582 / 100 = 5.82
you divide the number by 100 to get your decimal.
Which of the following will isolate the variable in the expression 6q+12?
Answer
A. Subtract 12, then divide by 6
B. Multiply by 6, then add 12
C. Divide by 6, then subtract 12
D. add 12 then multiply by 6
z varies directly as √√x and inversely as y. If: = 179 when x=25 and y= 7, find zifx = 64 and y = 4. (Round off your answer to the nearest hundredth.)
z=
We know that z varies directly as √√x and inversely as y, which can be written as:
z = k(√√x)/y
where k is the constant of proportionality.
To find the value of k, we can use the values given when x = 25 and y = 7:
179 = k(√√25)/7
179 = k(5/7)
k = (179*7)/5
k = 250.6
Now we can use this value of k to find z when x = 64 and y = 4:
z = 250.6(√√64)/4
z = 250.6(2)/4
z = 125.3
Therefore, z ≈ 125.3 when x = 64 and y = 4.