The expression for distance AB is :389 tan 88.60°. The angle D is 88.35°.The value of angle CAD in radians is 0.0532 rad.
Step-by-step explanation:
Given the information, you can sketch triangle ACB with ∠C=88.60° and a perpendicular bisector of segment CD as AB that forms 90° at B where the diatnace from C to B given as 389 ft you can find the length of the perpendicular bisector AB which is the distance between tower A and B.
Apply the tangent of an angle rule, where tangent of angle = opposite side length/adjacent side length
tan 88.60°=O/A
tan 88.60°=AB/389
AB=389 tan 88.60° = 15916.87 ⇒ 15917 (nearest foot)
B.
Given distance BD as 459 ft and the distance between tower A and B as 15917 ft you can calculate the value of angle ∠D by applying the tangent of an angle formula.
tan Ф=O/A where Ф=∠D
tan ∠D =15917/459
tan ∠D =34.6772834701
tan⁻(34.6772834701) =88.35°
C.
Finding angle ∠A in radians will be;
Applying the sum of angles in a triangle theorem
∠A=180°-(88.60°+88.35°) = 180°-176.95°=3.05°
Changing degrees to radians, multiply value of degrees by π/180°
3.05×π/180 =0.05323254 ⇒ 0.0532 rad
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Keywords : horizontal distance,towers, elevation, perpendicular line, distance, equation, expression,hundredth
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Length: 32 in
Width: 9 in
Height: 9 in
Which is the best estimate of the lateral area of a cube with edges that are 2.1 inches long?
Answer:
The lateral Area of a cube [tex]= 17.64in^{2}[/tex]
Step-by-step explanation:
In Mathematics Geometry, the lateral surface of a solid object like cube would be the face of the sold on its side, excluding base. Meaning, any surface, apart from base, would be included to determine the lateral surface of the solid.
A cube has six sides - also called faces.
A cube has a base i.e. the bottom side of the cube, and an ant-bottom base i.e. the top side of the cube.
So, lateral area of a cube would exclude both bottom side base and anti-bottom side base. In other words, it is the area of all the sides of the object, excluding the area of its base and top.
Hence, lateral area of a cube is the square of all the remaining four sides of the object, excluding the area of its base and top.
Hence, the lateral area of a cube can be calculated by the formula:
Lateral Area of a cube [tex]= 4s^{2}[/tex], where s is the length of one edge.
So,
As the given length of edge = s = 2.1
So,
lateral Area of a cube [tex]= 4s^{2}[/tex]
[tex]= 4(2.1)^{2}[/tex]
[tex]= 17.64in^{2}[/tex]
Keywords: cube, lateral area
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George invested a total of $5,000 at the beginning of the year in two different funds. At the end of the year, his investment had grown to $5,531. The money in the first fund earned 9%, while the money in the second fund earned 13.5%. Write a system of equations, then solve it to find out how much of the $5,000 was invested into each fund at the beginning of the year
Answer:
The amount invested at 9% was $3,200 and the amount invested at 13.5% was $1,800
Step-by-step explanation:
Let
x ----> the amount invested at 9% (first fund)
5,000-x ----> the amount invested at 13.5% (second fund)
Remember that
[tex]9\%=9/100=0.09[/tex]
[tex]13.5\%=13.5/100=0.135[/tex]
The total interest earned is equal to
[tex]\$5,531-\$5,000=\$531[/tex]
we know that
The amount earned by the first fund at 9% plus the amount earned by the second fund at 13.5% must be equal to $531
so
the linear equation that represent this situation is equal to
[tex]0.09x+0.135(5,000-x)=531[/tex]
solve for x
[tex]0.09x+675-0.135x=531[/tex]
[tex]0.135x-0.09x=675-531[/tex]
[tex]0.045x=144[/tex]
[tex]x=\$3,200[/tex]
so
[tex]\$5,000-x=\$5,000-\$3,200=\$1,800[/tex]
therefore
The amount invested at 9% was $3,200 and the amount invested at 13.5% was $1,800
will can jump rope at a rate of 8 jumps for every 10 seconds. find the unit rate
Answer:
The unit rate is 1.25 seconds per jump.
Step-by-step explanation:
Given:
Will can jump rope at a rate of 8 jumps for every 10 seconds.
Now, to find the unit rate:
So, by dividing we get the unit rate.
At the rate of 8 jumps Will takes 10 seconds.
Thus, for the rate of 1 jump he will take = [tex]10\div 8=1.25\ seconds.[/tex]
Therefore, the unit rate is 1.25 seconds per jump.
What is 3/4 divided by 1/2
Answer:
3/2
Step-by-step explanation:
(3/4)/(1/2)=(3/4)(2/1)=6/4=3/2
Answer: in decimal form it is 0.375
Step-by-step explanation:
Find ∫sin²x cos3x dx
Answer:
[tex]-\frac{1}{4} sin(x)+\frac{1}{6} sin(3x)-\frac{1}{20} sin(5x)+C[/tex]
Step-by-step explanation:
We begin with the integral [tex]\int{sin^2(x)cos(3x)} \, dx[/tex]
First, we can apply the power reducing formula to [tex]sin^2(x)[/tex]
This formula states: [tex]sin^2(x)=\frac{1}{2} -\frac{1}{2} cos(2x)[/tex]
This gives us
[tex]\int{(\frac{1}{2} -\frac{1}{2} cos(2x))(cos(3x)} \, dx \\\\\int{(\frac{1}{2}cos(3x) -(\frac{1}{2} cos(2x)cos(3x)} \, dx \\\\\frac{1}{2} \int{cos(3x)} \, dx -\frac{1}{2} \int{cos(2x)cos(3x)} \, dx[/tex]
Now, we can use integrate the first integral
[tex]\frac{1}{2} \int{cos(3x)} \, dx\\u=3x\\du=3dx\\\\\frac{1}{6} \int{3cos(u)} \, du\\\\\frac{1}{6} sin(u)+C\\\\\frac{1}{6} sin(3x)+C[/tex]
And now we can begin to integrate the second
[tex]-\frac{1}{2} \int{cos(2x)cos(3x)} \, dx[/tex]
To integrate this, we need to use the Product-to-sum formula, which states
[tex]cos(\alpha )cos(\beta )=\frac{1}{2} [cos(\alpha +\beta )+cos(\alpha -\beta )[/tex] . For this formula, we will use [tex]\alpha =3x\\\beta =2x[/tex]
This gives us
[tex]-\frac{1}{2} \int{\frac{1}{2}[cos(5x)+cos(x)] } \, dx \\\\-\frac{1}{4} \int{[cos(5x)+cos(x)] } \, dx\\\\-\frac{1}{4}\int{cos(5x)} \, dx -\frac{1}{4}\int{cos(x)} \, dx[/tex]
We can then use the same process of u-substitution as the previous to get the answer of [tex]-\frac{1}{20} sin(5x)-\frac{1}{4} sin(x)+C[/tex]
Lastly, we can add the values of the two integrals together to give us the final solution of
[tex]-\frac{1}{4} sin(x)+\frac{1}{6} sin(3x)-\frac{1}{20} sin(5x)+C[/tex]
How do I solve 42÷227
Answer:
42÷227=42/227
Step-by-step explanation:
Answer:
0.185
Step-by-step explanation:
Do the long division.
the zeros of f(x) algebraically
Answer:
The zeros are 4, -6, and 1.
Step-by-step explanation:
Given f(x) = x³ + x² - 26x + 24
(x - 4) is a factor of f(x). That means it is a zero of f(x).
To find the remaining factors algebraically, we take out the factor (x - 4) from f(x).
That is, [tex]$ f(x) = x^3 + x^2 - 26x + 24 $[/tex]
[tex]$ \implies x^3 - 4x^2 + 5x^2 - 20x - 6x + 24 $[/tex]
Taking [tex]$ x^2 $[/tex] out, we have:
[tex]$ = x^2(x^2 - 4) + 5x(x - 4) - 6(x - 4) $[/tex]
Taking (x - 4) common out, we have:
[tex]$ = (x - 4) \{x^2 + 5x - 6\} $[/tex]
[tex]$ = (x - 4)(x^2 + 6x - x - 6) $[/tex]
[tex]$ = (x - 4)\{x(x + 6) -1(x + 6)\} $[/tex]
[tex]$ = (x - 4)(x + 6)(x - 1) $[/tex]
This means the zeros are 4, -6, & 1.
a pancake recipe asks for one and one half times ad much milk as flour. if two and one quarter cups of milk is used what quantity of flour would then be needed
Answer:
x = 4/3
Step-by-step explanation:
x = amount of flour
x = amount of milk / 2.5
x =(3 1/3) / 2.5
change both to improper fractions
x = 10/3 / (5/2)
invert and mutiply
x = 10/3 * 2/5
HELP/ANSWER PLZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
Answer:
Step-by-step explanation:
Given f(x) = x - 7 and g(x) = x2.
Find g(f(4)).
g(f(4)) =
Answer:
Step-by-step explanation:
If we are looking to find the composition of g(f(4)), we start at the innermost part of the problem which is to evaluate f(4).
If f(x) = x - 7, then f(4) = 4 - 7. f(4) = -3.
Now take that -3 and evaluate the g(-3).
If g(x) = x^2, then g(-3) = (-3)^2 which is 9.
Therefore, f(g(4)) = 9
Answer:
9
Step-by-step explanation:
edg 2020
Nadia spent 1/4 of her money on a shirt and 2/5 of her money on new shoes. What fraction of Nadias money was spent?
Answer:
13/20 of her money was spent.
Step-by-step explanation:
To find the answer you have to add these two fractions together, and to do that you must find a common denominator.
For this problem I chose to use 20 for the denominator since it is the smallest number that both 4 and 5 have in common.
Keep in mind that, whatever you do to the denominator, you must also do to the numerator, so if you multiply 5 by 4, you must also multiply 2 by 4.
5/20 + 8/20 = 13/20
An artist is making a mural by reproducing a painting at a different scale. The original painting is 12 1/2 inches long and 5 inches wide. The mural will cover an entire wall that is 52.5 feet long and 20 feet wide. What will be the scale that relates the original painting to the mural?
Answer:
The scale is [tex]\frac{1}{60}[/tex]
Step-by-step explanation:
The correct question is
An artist is making a mural by reproducing a painting at a different scale. the original painting is 10 1/2 inches long and 4 inches wide. the mural will cover an entire wall that is 52.5 feet long and 20 feet wide. what will be the scale that relates to the original painting to the mural?
we know that
To find out the scale divide the measure of the original painting by the measure of the mural
so
Long
[tex]\frac{10.5}{52.5}\ \frac{in}{ft}[/tex]
Remember that
[tex]1\ ft=12\ in[/tex]
Convert feet to inches
[tex]\frac{10.5}{52.5*12}=\frac{10.5}{630}\ \frac{in}{in}=\frac{10.5}{630}[/tex]
simplify
[tex]\frac{1}{60}[/tex]
That means ----> 1 unit in the original painting represent 60 units in the mural
Verify the scale with the wide (both scale must be equals)
wide
[tex]\frac{4}{20}\ \frac{in}{ft}[/tex]
Remember that
[tex]1\ ft=12\ in[/tex]
Convert feet to inches
[tex]\frac{4}{20*12}=\frac{4}{240}\ \frac{in}{in}=\frac{4}{240}[/tex]
simplify
[tex]\frac{1}{60}[/tex]
That means ----> 1 unit in the original painting represent 60 units in the mural
2 cars raced at a track. the faster car traveled 20mph faster than the slower car. in the time that the slower car traveled 165 miles, the faster car traveled 225 miles. if the speeds of the cars remained constant, how fast did the slower car travel during the race.
Answer:
The speed of slower car is 55 miles per hour.
Step-by-step explanation:
Given as :
The speed of slower car = [tex]s_2[/tex] = s mph
The speed of faster car = [tex]s_1[/tex] = ( s + 20 ) mph
The distance cover by slower car = [tex]d_2[/tex] = 165 miles
The distance cover by faster car = [tex]d_1[/tex] = 225 miles
The time taken by both cars for travelling = t hours
The speed of the cars remains constant
Now, According to question
∵ Time = [tex]\dfrac{\textrm Distance}{\textrm Speed}[/tex]
So, For slower car
t = [tex]\dfrac{d_2}{s_2}[/tex]
Or, t = [tex]\dfrac{165}{s}[/tex] ............1
So, For faster car
t = [tex]\dfrac{d_1}{s_1}[/tex]
Or, t = [tex]\dfrac{225}{s+20}[/tex] ............2
Now, equating both the equations
I.e [tex]\dfrac{225}{s+20}[/tex] = [tex]\dfrac{165}{s}[/tex]
By cross multiplying
Or, 225 × s = 165 × (s + 20)
Or, 225 s = 165 s + 3300
Or, 225 s - 165 s = 3300
Or, 60 s = 3300
∴ s = [tex]\dfrac{3300}{60}[/tex]
I.e s = 55 miles per hour
So , The speed of slower car = [tex]s_2[/tex] = s = 55 miles per hour
Hence , The speed of slower car is 55 miles per hour. Answer
86.4 is what percent of 192
Answer:45%
Step-by-step explanation:
I believe it’s 45%
Divide 86.4 by 192 and multiply the result by 100 to get the percentage, hence it is 45%.
A figure or ratio that may be stated as a fraction of 100 is a percentage.
If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the word percent means.
Here we have to find:
86.4 is what percent of 192
Divide 86.4 by 192:
86.4 / 192 = 0.45
Multiply the result by 100 to convert it into a percentage,
Therefore,
0.45 x 100 = 45%
Hence,
86.4 is 45 percent of 192.
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What is the slope, m, and the y-intercept of the line that is graphed below?
NO
-5
4-3-2-1, 1
1
2
3
4
5
x
This looks confusing. Can you try reposting this to make it look clear?
An airplane takes 3 hours to travel a distance of 2250 miles with the wind. The return trip takes 5 hours against the wind. Find the speed of the plane in still air and the speed of the wind.
Answer:
Speed of Plane = 600 miles per hour
Speed of Wind = 150 miles per hour
Step-by-step explanation:
The distance equation is D = RT
Where
D is the distance
R is the rate
T is the time
Let rate of airplane be "x" and rate of wind be "c"
Also, note: rate with wind is airplane's and wind's, so that would be "x + c"
and rate against the wind is airplane's minus the wind's, so that would be "x - c"
Now,
2250 miles with wind takes 3 hours, so we can write:
D = RT
2250 = (x + c)(3)
and
2250 miles against the wind takes 5 hours, we can write:
D = RT
2250 = (x - c)(5)
Simplifying 1st equation:
[tex]2250 = (x + c)(3)\\3x+3c=2250[/tex]
Simplifying 2nd equation:
[tex]2250 = (x - c)(5)\\5x -5c=2250[/tex]
Multiplying the 1st equation by 5, gives us:
[tex]5*[3x+3c]=2250\\15x+15c=11250[/tex]
Multiplying the 2nd equation by 3 gives us:
[tex]3*[5x -5c=2250]\\15x-15c=6750[/tex]
Adding up these 2 equations, we solve for x. Shown below:
[tex]15x+15c=11250\\15x-15c=6750\\---------\\30x=18000\\x=600[/tex]
Now putting this value of x into original 1st equation, we solve for c:
[tex]3x+3c=2250\\3(600)+3c=2250\\1800+3c=2250\\3c=450\\c=150[/tex]
Speed of Plane = 600 miles per hour
Speed of Wind = 150 miles per hour
please help thanks ❗
Answer:
see the explanation
Step-by-step explanation:
we know that
The Side Angle Side postulate (SAS) states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent
Remember that if two triangles are congruent, then its corresponding angles and its corresponding sides are congruent
In this problem
PO≅SO ----> given problem
NO≅TO ----> because O is the midpoint NT
∠PON≅∠SOT -----> by vertical angles
so
two sides and the included angle of triangle PON are congruent to two sides and the included angle of triangle SOT
therefore
Triangles PON and SOT are congruent by SAS
hence
∠N≅∠T ----> by definition of congruence (corresponding angles are congruent)
What is the equation of the line that has a slope of -1/3 and a y intercept of 5/2
Answer:
y=-1/3x+5/2
Step-by-step explanation:
Slope intercept form makes this a breeze. Essentially, just plug these values into the following formula:
y = [SLOPE]x + [Y-INTERCEPT]
Answer:
y=-1/3x+5/2
Hope this helps
10 POINTS!!!!
2.Point p is chosen at random on CF. Find the probability that p is on DE .
Answer:
[tex]\frac{8}{17}[/tex]
Step-by-step explanation:
The total length of CF is 17 units and the length of DE is 8 units, so the probability of p being on DE is [tex]\frac{8}{17}[/tex]
Answer:
8/17 is correct.
Step-by-step explanation:
According to the theorem, which statement, about Parallelogram ABCD is true?
bisect = to cut into two equal halves.
so from that theorem Juan used we can derive that once both diagonals bisect each other, the halves of AO = OC and DO = OB.
if a rectangle is 95 meters long and 65 meters wide what is the diagonal
Answer:
115.1
Step-by-step explanation:
F(x)= x^3-9x
What is the average rate of change of f over the interval [1,6]?
Answer: 34
Step-by-step explanation:
The average rate of change of f(x)= x³-9x in interval [1,6] is 34.
Average rate of changeIf f(x) is a function the [a,b] is interval then the average rate of change is [tex]\frac{f(b)-f(a)}{b-a}[/tex]
How to find the average rate of change of f?Given the function is f(x)= x³-9x and the interval is [1,6].
then first we have to find the value of f(1) and f(6).
So
f(1) = (1)³-9(1)
= 1-9
= -8
and
f(6) = (6)³-9(6)
= 216- 54
= 162
therefore average rate of change of f is
[tex]\frac{f(6)-f(1)}{6-1}= \frac{162+8}{6-1}[/tex]
= 170/5
= 34
Hence the average rate of change of f is 34.
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Can someone solve this quick plz
Answer:
length = x + 5
Step-by-step explanation:
Given
area = x² + 8x + 15 and area = length × width
We require to factorise x² + 8x + 15
Consider the factors of the constant term (+ 15) which sum to give the coefficient of the x- term (+ 8)
The factors are + 5 and + 3, since
5 × 3 = 15 and 5 + 3 = 8, thus
x² + 8x + 15 = (x + 5)(x + 3)
x + 3 is the width, thus x + 5 is the length
2x + 7 = 4 + x solve equation using tables
Answer:
x=-3
Step-by-step explanation:
2x+7=4+x
2x-x+7=4
x+7=4
x=4-7
x=-3
Please help! Thanks in advance!
Answer:
The are certain things that need to be carefully observed when you add or combine the polynomials. Here is the list of certain rules for adding/combining polynomials.
Step-by-step explanation:
The are certain things that need to be carefully observed when you add or combine the polynomials - especially the polynomials with more than one variable.
Here are some of the rules for adding polynomials:
First we must identify like terms in the given polynomials, and then combine them based on the correct integer operations.When there is a plus sign, we add polynomials. It must be noted that, within polynomials, we need to add or subtract like terms. For example, when we combine like terms, such as 4x and 5x, we tend to add their coefficients i.e. 4x + 5x = 9xPlease remember we can not add polynomials if they have different exponents. For example, x²+ x can not be added.Lets add and simplify the following polynomials.
(4x + 7y) + (5x – 3y)
First clear the parenthesis.4x + 7y + 5x – 3y
Then make sue to group the like terms in accordance to their variables - try to keep them in alphabetically order, and ultimately just simplify.4x + 5x + 7y - 3y
9x + 4y
So, 9x + 4y is the answer.
Note: I can not further combine or add 9x + 4y as they are un-like. The reason is simple; un-like polynomials have different variables.
The polynomials can be add vertically too.
Just put each variable in its own columnFirst column can be termed as x-column and second column can be termed as y-columnChoosing the horizontal or vertical method is just a matter of taste.Here is the vertical method of adding (4x + 7y) and (5x – 3y) .
4x +7y
5x -3y
________
9x + 4y
________
Keywords: add, combine, polynomials
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Which ordered pair is a solution of the equation?
y=-3x-4y=
To find the solution to the given equation y = -3x - 4 from the provided pairs, substitute the values and solve, giving the solution as (0,-2).
The given equation is y = -3x - 4.
To find which ordered pair is a solution, substitute the given pairs into the equation and check:
(1,0): y = -3(1) - 4 = -3 - 4 = -7
(0,-2): y = -3(0) - 4 = -4
(13,-3): y = -3(13) - 4 = -39 - 4 = -43
Therefore, the ordered pair that is a solution of the equation is (0,-2).
what does a midpoint of a line segment create? Choose All The Apply.
(in pic below)
Answer: Two lines of equal length
A point equidistant from two end points
Step-by-step explanation:
The mid - point of a line segment is the point on the segment that is equidistant from the endpoints.
It is not equidistant to all point on the segment , it is only equidistant from the endpoints.
With this , the first option is out.
The midpoint of a line divides the line into two equal part , so the second option holds and the third option holds too.
The two-way table represents data from a survey asking teachers whether they teach English, math, or both. A 4-column table with 3 rows. The first column has no label with entries math, not math, total. The second column is labeled English with entries 34, 40, 74. The third column is labeled not English with entries 22, 8, 30. The fourth column is labeled total with entries 56, 48, 104. Which is the joint relative frequency for teachers who teach math and not English? Round the answer to the nearest percent. 8% 21% 33% 38%
Answer:
b 21%
Step-by-step explanation:
good luck and hurry :)
The given 22 teachers from the total of 104 teachers in the survey gives
the teachers who teach math and not English as approximately; 21%
How can the joint relative frequency be obtained?
The relative frequency table is presented as follows;
[tex]\begin{tabular}{|c|c|c|c|}&English&Not english & Total\\Math&34&22&56\\Not math&40&8&48\\Total&74&30&104\end{array}\right][/tex]
Required:
The joint relative frequency for teachers teaching math and not English
Solution:
The joint relative frequency is the ratio of the frequency of a given category to the total number of data points within the category.
The number of teachers that teach math but not English = 22
Total number of teachers in the survey = 104
Therefore;
[tex]The \ joint \ relative \ frequency = \dfrac{22}{104} \times 100\approx \mathbf{21\%}[/tex]
Therefore;
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in six years rose will be two times as old as anne. Four years ago, anne was one third the age of rose. how old are they now
Answer:
Rose is 34.
Anne is 14.
Step-by-step explanation:
Let rose be x years age now and anne be y years old now. Then:
x + 6 = 2 (y + 6)
x - 4 = 3(y - 4)
Subtracting:
6 - -4 = 2y + 12 - (3y - 12)
10 = - y + 24
-y = -14
y = 14
Substituting for y:
x + 6 = 2(14+6)
x = 40 - 6 = 34.
Find the equation of a line that has the same slope ask why equals 10-4x and the same Y intercept is why equals -9x-8
Answer:
[tex]y=-4x-8[/tex]
Step-by-step explanation:
we know that
The equation of the line in slope intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope
b is the y-intercept
so
1) Find the slope of the given line [tex]y=10-4x[/tex]
The slope is [tex]m=-4[/tex]
2) Find the y-intercept of the given line [tex]y=-9x-8[/tex]
The y-intercept is [tex]b=-8[/tex]
therefore
The equation of the line with
[tex]m=-4[/tex]
[tex]b=-8[/tex]
is equal to
[tex]y=-4x-8[/tex]