Grayson spots an airplane on radar that is
currently approaching in a straight line,
and that will fly directly overhead. The
plane maintains a constant altitude of
7225 feet. Grayson initially measures an
angle of elevation of 19 to the plane at
point A. At some later time, he measures
an angle of elevation of 39° to the plane at
point B. Find the distance the plane
traveled from point A to point B. Round
your answer to the nearest tenth of a foot
if necessary.
Answers
Using the slope concept, it is found that the distance traveled from point A to point B was of 12060.8 ft.
What is a slope?The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.
At point A, the vertical change is of 7225 feet, with an angle of 19º, hence:
[tex]\tan{19^\circ} = \frac{7225}{x_A}[/tex]
[tex]x_A = \frac{7225}{\tan{19^\circ}}[/tex]
[tex]x_A = 20982.9[/tex]
At point B, the vertical change is of 7225 feet, with an angle of 39º, hence:
[tex]\tan{39^\circ} = \frac{7225}{x_B}[/tex]
[tex]x_B = \frac{7225}{\tan{39^\circ}}[/tex]
[tex]x_B = 8922.1[/tex]
The distance in feet is given by:
[tex]d = x_A - x_B = 20982.9 - 8922.1 = 12060.8[/tex]
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Related Questions
Use the function f(x) = x2 − 2x 8 and the graph of g(x) to determine the difference between the maximum value of g(x) and the minimum value of f(x). a parabola that opens down and passes through 0 comma 3, 3 comma 12, and 5 comma 8 2 5 7 12
Answers
The difference between the maximum value of g(x) and the minimum value of f(x) is 5.
Given function is:
[tex]f(x)=x^{2} -2x+8[/tex]......(1)
What is the general form of a quadratic equation?The general form of a quadratic equation is [tex]ax^{2} +bx+c=0[/tex] with [tex]a\neq 0[/tex].
As we know the minimum value of a quadratic function is [tex]\frac{4ac-b^{2} }{4a}[/tex] when a>0
For f(x) a>0 so minimum value of f(x) = [tex]\frac{4*1*8-(-2)^2}{4*1}[/tex]=7
From the graph, the maximum value of g(x) =12
So, the difference between the maximum value of g(x) and the minimum value of f(x) =12-7 =5
Hence, the difference between the maximum value of g(x) and the minimum value of f(x) is 5.
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The lengths of two sides of a triangle are 4 inches and 7 inches. What is a possible length, in inches, of the third side?
Answers
Answer:
well if im wrong then sorry but i think its 11 !!
Step-by-step explanation:
The possible length of the third side should be greater than 11.
What is triangle?A triangle is a polygon with three sides having three vertices. The angle formed inside the triangle is equal to 180 degrees. It means that the sum of the interior angles of a triangle is equal to 180°.
Given that the lengths of two sides of a triangle are 4 inches and 7 inches.
We need to find the possible length of the third side,
So, according to the triangle inequality theorem,
For any given triangle, the sum of two sides of a triangle is always greater than the third side.
So, the sum of two sides = 4 + 7 = 11
Hence the possible length of the third side should be greater than 11.
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You have a combination lock with 3 secret digits. Find the 3 correct digits using the following clues and enter your answer below. 128 One digit is right and in its place 157 One digit is right, but in the wrong place Two digits are right but both are in the 8 41 wrong place 362 All digits are wrong 62 4 One digit is right, but in the wrong place din
Answers
Answer:
184
Step-by-step explanation:
in the number 128 the number eight is right it should be to the right then in the number157 one is right it should be to the left in 841 8and 1 are in the wrong position 8 - right 1 - left then in the number 624 the number 4 is right but in the wrong position it should be in the middle the answer is digit 1,8,4
The 3 secret digit numbers are 4, 7, and 8. Then the combination lock with 3 secret digits is 478.
What are permutation and combination?A permutation is an act of arranging the objects or elements in order. Combinations are the way of selecting objects or elements from a group of objects or collections, in such a way the order of the objects does not matter.
You have a combination lock with 3 secret digits.
362 All digits are wrong then 3, 6, and 2 should not be there.
624 One digit is right but in the wrong place. Then 4 digit is right.
841 Two digits are right but both are in the wrong place. Then the place of 4 should be first.
128 One digit is right and in its place. Then the first place is occupied by 4 so 1 is incorrect. Then the third digit is 8.
157 One digit is right but in the wrong place. Then in the second place, the wrong digit is there then there is 7 in the second place.
The combination lock with 3 secret digits is 478.
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A rectangular swimming pool is 17 meters long, 14 1/2 meters wide, and 5 1/2 meters deep. What is its
volume?
Answers
Answer:
1355.75 m
Step-by-step explanation:
Volume of a rectangle = length x breadth x height
Volume of recatngular swimming pool = 17 x 14.5 x 5.5
volume of rectangular swimming pool = 1355.75 m
Which expression is equivalent to 4+w+12w
Answers
Answer:
13w+4 or 4+13w
Step-by-step explanation:
w is the same as one then it will be 4+w(1)+12w =12w+w(1)=13w
4 over here does not have friend therefore it renains to be 4 =13w+ 4
PLEASE HELP ASAP!!!
Answers
Answer:
V = 54π or V = 169.56 units³
Step-by-step explanation:
The volume of a cylinder is given by the formula:
V = πr²h
If we use 3.14 as pi we get this:
V = (3.14)×(3)²×(6)
V = 3.14×9×6
V = 3.14×54
V = 169.56
Since it is volume the units will be units³
So our final answer is 169.56 units³
If you wanted an exact in pi form you would do the same steps but not simplify pi:
V = πr²h
V = π×(3)²×6
V = π×9×6
V = 54π
An arithmetic sequence is given by 20, 17, 14, 11, ...
(a) Write down the value of the common difference, d.
(b) Find a100
(c) Find s100
Answers
Answer:
The common difference equals:
[tex]-3[/tex]
The sum of the sequence equals:
[tex]62[/tex]
The explicit formula of this sequence is:
[tex]a_n=20+(n-1)*(-3)[/tex]
The recursive formula of this sequence is:
[tex]a_n=a_((n-1))-3[/tex]
The nth terms:
[tex]20,17,14,11,8,5,2...[/tex]
Step-by-step explanation:
An arithmetic sequence, or arithmetic progression, is a set of numbers in which the difference between consecutive terms (terms that come after one another) is constant. This difference is called the common difference.
1. Find the common difference.Find the common difference by subtracting any term in the sequence from the term that comes after it.
[tex]a_2-a_1=17-20=-3\\a_3-a_2=14-17=-3\\a_4-a_3=11-14=-3[/tex]
The difference of the sequence is constant and equals the difference between two consecutive terms.
[tex]d=-3[/tex]
2. Find the sum.Calculate the sum of the sequence using the sum formula:
Formula
[tex]Sum=\frac{(n(a_1+a_n))}{2}[/tex]
Plug in terms
[tex]Sum=(4*(a_1+a_n))/2[/tex]
[tex]Sum=(4*(20+a_n))/2[/tex]
[tex]Sum=(4*(20+11))/2[/tex]
Simplify the expression
[tex]Sum=(4*(20+11))/2[/tex]
[tex]Sum=(4*31)/2[/tex]
[tex]Sum=124/2[/tex]
[tex]Sum=62[/tex]
The sum of this sequence is [tex]62[/tex].
This series corresponds to the following straight line [tex]y=-3x+20[/tex]
3. Find the explicit form.The formula for expressing arithmetic sequences in their explicit form is:
Formula: [tex]a_n=a_1+(n-1)*d[/tex]
Plug in the terms.
[tex]a_1=20[/tex] (this is the 1st term)
[tex]d=-3[/tex] (this is the common difference)
[tex]a_n[/tex] (this is the nth term)
[tex]n[/tex] (this is the term position)
The explicit form of this arithmetic sequence is:
[tex]a_n=20+(n-1)*(-3)[/tex]
4. Find the recursive form.The formula for expressing arithmetic sequences in their recursive form is:
Formula: [tex]a_n=a_((1-n))+d[/tex]
Plug in the d term.
[tex]d=-3[/tex](this is the common difference)
The recursive form of this arithmetic sequence is:
[tex]a_n=a_((n-1))-3[/tex]
5. Find the nth element.[tex]a_1=a_1+(n-1)*d=20+(1-1)*-3=20[/tex]
[tex]a_2=a_1+(n-1)*d=20+(2-1)*-3=17[/tex]
[tex]a_3=a_1+(n-1)*d=20+(3-1)*-3=14[/tex]
[tex]a_4=a_1+(n-1)*d=20+(4-1)*-3=11[/tex]
[tex]a_5=a_1+(n-1)*d=20+(5-1)*-3=8[/tex]
[tex]a_6=a_1+(n-1)*d=20+(6-1)*-3=5[/tex][tex]a_7=a_1+(n-1)*d=20+(7-1)*-3=2[/tex]
Terms and topics:
Artithmetic SequencesPeter graphed two points given below on a coordinate plane.
(-6, 4), (3, 4)
What is the distance between the points?
Answers
Answer:
9
Step-by-step explanation:
Because the y-coordinates are the same but the x-coordinates are different so -6 to 3 would be 9 because -6 to 0 is 6 and 0 to 3 is 3 and 3 + 6 equals 9
Answer:
distance: 9 units
Explanation:
[tex]\sf distance \ between \ points \ : \ \sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
Here coordinates : (-6, 4), (3, 4)
substitute the following values and put into the equation
[tex]\sf \rightarrow \sqrt{(4-4)^2+(3-(-6))^2}[/tex]
[tex]\sf \rightarrow \sqrt{(3+6)^2}[/tex]
[tex]\sf \rightarrow \sqrt{81}[/tex]
[tex]\sf \rightarrow 9[/tex]
I ONLY GOT 1 MIN!!!! PER QUESTION HELP
Chase wrote this description.
I saw a four sided figure. It had one pair of congruent sides that were not parallel. It also had one pair of parallel lines.
What shape has Chase described?
a parallelogram
a rhombus
a trapezoid
a kite
Answers
Answer:
options c
trapezoid
saw a four sided figure. It had one pair of congruent sides that were not parallel. It also had one pair of parallel lines.
saw a four sided figure. It had one pair of congruent sides that were not parallel. It also had one pair of parallel lines.What shape has Chase described?
trapezoidRomeo has a work that pays 100 pesos per 1 hour. How much would he make in 10 hours?
Answers
Answer: he would get 1000
Step-by-step explanation:
100 x 10 =1000
Answer:
$1,000
Step-by-step explanation:
Since he makes 100 pesos in 1 hour, all you have to do is multiply 100 by 10. When multiplying a number by 10, all you do is move the decimal point back one. In this case, our decimal point is imaginary, so when we move it back one, you just add a zero at the end of the number. That gives you 1000.
Look at the figure.what is another way of naming line M
Answers
Answer:
Another way of saying line M is to say Line X or Y
Help please!!! :')
Given a diameter of a circle at endpoints (8,-7) and (4,5), algebraically find the equation of the circle.
thank you smm <3
Answers
Answer:
(x-6)^2 + (y+1)^2=40
Step-by-step explanation:
see image. Use Midpoint Formula to find the center. Then use Distance Formula to find the diameter. Cut the diameter in half to find the radius. Use the circle formula to insert (h,k) the center and r, the radius to find the equation. See image.
Answer: [tex](x - 6)^2 + (y + 1)^2 = 40[/tex]
=========================================================
Explanation:
The x coordinates of the given endpoints are x = 8 and x = 4. Apply the midpoint to them to get [tex]\frac{x_1+x_2}{2} = \frac{8+4}{2} = \frac{12}{2} = 6[/tex] which is the x coordinate of the midpoint. I added them up and divided by 2.
Similar steps will have the y coordinate of the midpoint be
[tex]\frac{y_1+y_2}{2} = \frac{-7+5}{2} = \frac{-2}{2} = -1[/tex]
Overall, the midpoint of those given points is (6, -1)
This is the center of the circle because the two endpoints are part of a diameter.
-------------------------------------------------
Now turn to the template
[tex](x - h)^2 + (y -k )^2 = r^2[/tex]
We will plug in the center (h,k) = (6, -1) and one of the endpoints for (x,y). Let's say we go for (x,y) = (4,5)
This leads us to the following:
[tex](x - h)^2 + (y -k )^2 = r^2\\\\(4 - 6)^2 + (5 - (-1) )^2 = r^2\\\\(4 - 6)^2 + (5 + 1 )^2 = r^2\\\\(-2)^2 + (6 )^2 = r^2\\\\4 + 36 = r^2\\\\r^2 = 40\\\\[/tex]
We don't need to isolate r itself. If you wanted, you could take the square root of both sides to see that the radius is [tex]r = \sqrt{40} \approx 6.3246[/tex]. However, again we don't need to solve for r entirely when forming the circle's equation.
With that [tex]r^2[/tex] value in mind, and the h & k values as well, we go from this template
[tex](x - h)^2 + (y -k )^2 = r^2[/tex]
to this final answer
[tex](x - 6)^2 + (y + 1)^2 = 40[/tex]
What is the correct answer?
Answers
Answer:
B
Step-by-step explanation:
When multiplying exponents with the same base, you add the powers together.
In B, that is exactly what they are showing when they do:
[tex]2^{\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}}[/tex]
A cuboid has volume of 120cm.
The area of the base of the cuboid is 30cm?
Work out the surface area of the cuboid.
Answers
Answer:
already answered
Step-by-step explanation:
go to this
https://brainly.in/question/16866439
2(3x+2)=6x+4 linear equations
Answers
Answer:
0 or 6x+4=6x+4 (Technically no slope at all!!)
Step-by-step explanation:
You need to do distributive property and then solve for x!!
meaning the 2(3x+2) has to get distributive property process.
6x+4=6x+4
That shall be equal together!!! (You could stop here!!)
If continue:
6x-6x=4-4
0=0
HELPPP WHATS THE PERMITER
Answers
Answer:
48 is the perimeter
Step-by-step explanation:
I gotchu
Nadya bakes 20 cookies every half hour. Vasil sells 38 cookies per hour. How many cookies are left unsold if they work from 6:00 am till noon.
Answers
Answer:
12
Step-by-step explanation:
20*2= 40 cookies per hour,
she is working 6 hours so she sells 240 cookies total
240-(38*6) = 12
Nadya bakes 20 cookies every half hour. Vasil sells 38 cookies per hour. 12 cookies that are left unsold and if they work from 6:00 am till noon.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Nadya bakes 20 cookies every half hour. Vasil sells 38 cookies per hour.
We need to find many cookies that are left unsold and if they work from 6:00 am till noon.
20 x 2= 40 cookies per hour,
she is working 6 hours so she sells 240 cookies
The total
= 240 - (38 x 6)
= 12
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Help I’m literally confused on these
Perpendicular Bisector Theorem
Answers
Answer:
UV = 10
Step-by-step explanation:
VX is a perpendicular bisector of the base UW , then Δ UVW is isosceles with the 2 legs being congruent , that is
UV = VW = 10
Tom is exchanging money for his trip to india. the exchange rate of us dollars to indian rupees is 1:45.897. tom needs 11,550 rupees. the currency exchange service he is using charges a fee of 7.25% after the exchange is made. how many us dollars will it cost tom to get the rupees he wants? round to the nearest dollar. a. $235 b. $252 c. $263 d. $270
Answers
The total US dollars it cost to Tom to get the rupees he wants for the trip of India is $270 round to the nearest dollar.
How to calculate the percentage?Percentage of a number is the part of the number expressed in the in every hundred. Percentage of a number is expressed with the symbol '%'.
To calculate the percentage part of number, multiply it with the original number and divide with 100.
Tom is exchanging money for his trip to india. The exchange rate of us dollars to indian rupees is,
[tex]r=\dfrac{1}{45.897}[/tex]
Tom needs 11,550 rupees. The dollars need for 11550 Indian rupees are,
[tex]n=\dfrac{11550}{45.897}\\n=251.65[/tex]
The currency exchange service he is using charges a fee of 7.25% after the exchange is made. Thus the total dollar requied after the service charge is,
[tex]n=251.65+\dfrac{7.25}{100}\times251.65\\n=251.65+18.245\\n=269.895\\n\approx270[/tex]
Thus, the total US dollars it cost to Tom to get the rupees he wants for the trip of India is $270 round to the nearest dollar.
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Factor the trinomial 6x^{2} + 5x - 25. Which of the following is a factor?
Answers
Answer:
its (3x-5)
Step-by-step explanation:
Answer:
C. (3x - 5)
Step-by-step explanation:
1. Find a solution pair that gives the sum of b (5):
-10 + 15 = 5
2. Break the expression into groups:
(6x² - 10x) + (15x - 25)
3. Factor out the common factor in each group:
2x(3x - 5) + 5(3x - 5)
4. Factor out the common pair (3x - 5) using the distributive property:
(3x - 5)(2x + 5)
hope this helps!
A vase has 4 yellow flowers, 4 red flowers, and 8 blue flowers. Donna took a flower smelled it and put it back ,then took another flower and smelled it. What is the probability that the first flower was red and the second flower was blue?
Answers
Answer:
1/8
Step-by-step explanation:
Since the flower was replaced, these two drawings are independent events and the final probability is the product of the two individual probabilities.
total number of flowers: 16
yellow: 4
red: 4
blue: 8
p(red) = 4/16 = 1/4
p(blue) = 8/16 = 1/2
p(red then blue) = 1/4 × 1/2 = 1/8
Answer: 1/8
Which of the following proves these triangles are congruent
Answers
Answer:
ASA
Step-by-step explanation:
ASA rule states that: If two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle, then the triangles are congruent.
Eleven more than three times a number is at most 62
Answers
Answer:
11-3×62=496
Step-by-step explanation:
by getting 8 by subtracting 11 and 3 yoy can do this
[tex]62[/tex]
[tex] \times 8[/tex]
The number is 17 and less and the inequality is 3x + 11 ≤ 62
Given,
Eleven more than three times a number is at most 62
We need to find the number and the inequality.
What are the inequalities?
< mean less than
> means greater than
≤ means less than or greater than
≥ means greater than or equal to
Find the meaning of the statement.
more than means adding
times means multiply
At most 62 means the maximum is 62 and we use ≤ 62.
Find the expression.
Eleven more than three times a number is at most 62
Let x be the number.
3x + 11 ≤ 62
Find x value.
3x + 11 ≤ 62
3x + 11 62
3x ≤ 62 - 11
3x ≤ 51
x ≤ 51/3
x ≤ 17
Thus the number must be 17 and less and the inequality is 3x + 11 ≤ 62
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A line with a slope of 4 passes through (6,11). Complete the equation of this line in point-slope form.
Answers
11= 4*6+b
Solve for b
11=16+b
B= -5
Answer in slope int form:
Y=4x-5
Answer in point slope form:
y- -1=4(x-1)
Or
Y+1=4(x-1)
Answer:
y – 11 = 4 (x-6)
Step-by-step explanation:
ttm
When three squares are joined at their vertices to form a right triangle, the combined area of the two smaller
squares is equal to the area of the largest square. Which three squares support this statement?
5 cm
3 cm
Answers
Answer:
Top right (one what has 16cm^2 and 9cm^2)
Step-by-step explanation:
The one in the top right and even though I cannot see what the area is of the biggest square, I can tell what it should be the two smaller squares combined
Hope this helps :)
if 0.002 is rewritten as 2 x 10x what is the value of x
Answers
Answer:
0.0001
Step-by-step explanation:
2 x 10 x 0.0001 equals 0.0002. If you want confirmation do on a calculator
Answer:
10,000
Step-by-step explanation:
you move the decimal point 3 places to the right to end up with 2 so add as many zeros as many times you moved the decimal point from the 0.002.
What is the equation of the line that passes through the point (4,-6) and has a slope of -5/2?
Please I’m desperate I already tried and it was wrong I’ll mark Brainlist
Answers
Answer:
y = (-5/2)X + 4
Step-by-step explanation:
we know that the equation of a line is y = mx + b
m = -5/2
so
y = -5/2x + b
to find b:
-6 = -10 + b
b = 4
so
y = (-5/2)X + 4
Answer:
Use the point-slope form of a linear equation:
[tex]y-y_1=m(x-x_1)[/tex]
where:
[tex]m[/tex] = slope[tex](x_1,y_1)[/tex] = point on lineGiven:
[tex]m=-\dfrac52[/tex][tex](x_1,y_1)=(4,-6)[/tex]Substitute given information into the equation:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-(-6)=-\dfrac52(x-4)[/tex]
[tex]\implies y+6=-\dfrac52x+10[/tex]
[tex]\implies y=-\dfrac52x+4[/tex]
Therefore, the equation of the line in different formats is:
[tex]\textsf{slope-intercept form: }y=-\dfrac52x+4[/tex]
[tex]\textsf{standard form: }5x+2y=8[/tex]
Which quadratic function in vertex form has a vertex at (-2, 5) And passes through the point (2, -3)?
Answers
Answer:graph{-19/9(x+3)^2+5 [-10, 2, -20, 10]}
Step-by-step explanation:
y
=
−
19
9
(
x
+
3
)
2
+
5
Explanation:
If an equation representing a parabola is in vertex form such as
y
=
a
(
x
−
k
)
2
+
h
then its vertex will be at
(
k
,
h
)
. Therefore the equation for a parabola with a vertex at (-3, 5), will have the general form
y
=
a
(
x
+
3
)
2
+
5
If this parabola also passes through the point
(
0
,
−
14
)
then we can determine the
a
parameter.
−
14
=
a
(
0
+
3
)
2
+
5
9
a
=
−
19
a
=
−
19
9
So our equation in vertex form is
y
=
−
19
9
(
x
+
3
)
2
+
5
graph{-19/9(x+3)^2+5 [-10, 2, -20, 10]}
Aida bought a flower rug for her bedroom, as shown below.
Note: Figure is not drawn to scale
If a = 12 in, which of the following is closest to the area of the rug?
A.
298.08 in2
B.
257.04 in2
C.
334.08 in2
D.
370.08 in2
Answers
Antonio purchased a bin with the following measurements the diameter is 21 inches and the height is 36 inches. Solve terms of pi.