Answer:
1.10
Step-by-step explanation:
that's your answer
The location of the tug boat relative to the port will be 30.83 miles.
What is trigonometry?Trigonometry is the branch of mathematics that set up a relationship between the sides and angles of right-angle triangles.
The distance of ship A from the port is x
X²= 18²+30²
X²= 324+900
X²=1224
X=34.9857 miles
Bearing from port:-
Tanθ= 18/30
θ = tan^-1 3/5
θ= 31°
N 31° E
The distance of ship B from the port is y.
Y²= 27²+10²
Y²= 729+100
Y²= 829
Y=28.7924 miles
Bearing from port:-
Tanθ = 2.2
θ = 69.7°
90-69.7= 20.3
N 20.3°W
The distance between the two ships is z.
Z²=34.9857²+28.7924²-2(24.9857)(28.7924)cos(31+69.7°)
Z²= 2053+267.1
Z²= 2320.1
Z=48.18 miles
One-fifth of 48.18
=9.63 miles
The distance of the boat is D.
D/sin 60 = 34.9857/sin 100.7
D=30.83 miles
Therefore, the location of the tug boat relative to the port will be 30.83 miles.
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Let ABC be a triangle such that AB=13 BC=14 and CA=15. D is a point on BC such that AD Bisects
Answer:
Area of triangle ADC is 54 square unit
Step-by-step explanation:
Here is the complete question:
Let ABC be a triangle such that AB=13, BC=14, and CA=15. D is a point on BC such that AD bisects angle A. Find the area of triangle ADC .
Step-by-step explanation:
Please see the attachment below for an illustrative diagram
Considering the diagram,
BC = BD + DC = 14
Let BD be [tex]x[/tex] ; hence, DC will be [tex]14-x[/tex]
and AD be [tex]y[/tex]
To, find the area of triangle ADC
Area of triangle ADC = [tex]\frac{1}{2} (DC)(AD)[/tex]
= [tex]\frac{1}{2}(14-x)(y)[/tex]
We will have to determine [tex]x[/tex] and [tex]y[/tex]
First we will find the area of triangle ABC
The area of triangle ABC can be determined using the Heron's formula.
Given a triangle with a,b, and c
[tex]Area =\sqrt{s(s-a)(s-b)(s-c)}[/tex]
Where [tex]s = \frac{a+b+c}{2}[/tex]
For the given triangle ABC
Let [tex]a[/tex] = AB, [tex]b[/tex] = BC, and [tex]c[/tex] = CA
Hence, [tex]a = 13, b= 14,[/tex] and [tex]c = 15[/tex]
∴ [tex]s = \frac{13+14+15}{2} \\s= \frac{42}{2}\\s = 21[/tex]
Then,
Area of triangle ABC = [tex]\sqrt{(21)(21-13)(21-14)(21-15)}[/tex]
Area of triangle ABC = [tex]\sqrt{(21)(8)(7)(6)}[/tex] = [tex]\sqrt{7056}[/tex]
Area of triangle ABC = 84 square unit
Now, considering the diagram
Area of triangle ABC = Area of triangle ADB + Area of triangle ADC
Area of triangle ADB = [tex]\frac{1}{2} (BD)(AD)[/tex]
Area of triangle ADB = [tex]\frac{1}{2}(x)(y)[/tex]
Hence,
Area of triangle ABC = [tex]\frac{1}{2}(x)(y)[/tex] + [tex]\frac{1}{2}(14-x)(y)[/tex]
84 = [tex]\frac{1}{2}(x)(y)[/tex] + [tex]\frac{1}{2}(14-x)(y)[/tex]
∴ [tex]84 = \frac{1}{2}(xy) + 7y - \frac{1}{2}(xy)[/tex]
[tex]84 = 7y\\y = \frac{84}{7}[/tex]
∴ [tex]y = 12[/tex]
Hence, [tex]y =[/tex] AD = 12
Now, we can find BD
Considering triangle ADB,
From Pythagorean theorem,
/AB/² = /AD/² + /BD/²
∴13² = 12² + /BD/²
/BD/² = 169 - 144
/BD/ = [tex]\sqrt{25}[/tex]
/BD/ = 5
But, BD + DC = 14
Then, DC = 14 - BD = 14 - 5
BD = 9
Now, we can find the area of triangle ADC
Area of triangle ADC = [tex]\frac{1}{2} (DC)(AD)[/tex]
Area of triangle ADC = [tex]\frac{1}{2} (9)(12)[/tex]
Area of triangle ADC = 9 × 6
Area of triangle ADC = 54 square unit
Hence, Area of triangle ADC is 54 square unit.
help pls!! 15 points!
Answer:
Third option choice
Step-by-step explanation:
Notice that the angle is in the second quadrant, where the cosine is negative, the sine is positive and the tangent negative. In particular given the value of the cosine you are located at the angle 150 degrees, which gives a sine of 1/2 and a tangent given by [tex]-\sqrt{3} /3[/tex]
Therefore the third option is the correct one.
Taxi fare in Tampa costs a base fee of $4 plus an additional $0.85 for each mile traveled. How much would a person pay to take a taxi from work to home if the distance is 17 miles? Question 14 options: A) $18.45 B) $21 C) $14.45 D) $20.40
Answer:
A. $18.45
Step-by-step explanation:
17 miles * .85 = 14.45 + 4.00 = 18.45
HELP!!!!!
k+a=500(1). 3k+10a=3,600(2)
Which equation has at least one of its variables with a 1 as a coefficient?
Answer:
eqn 1. ( k + a = 500 )
Step-by-step explanation:
In eqn. 1 , both 'k' & 'a' have co-efficient as 1. But in eqn. 2 , 'k' has co-efficient as 3 & 'a' has co-efficient as 10.
Sebastian has a bag of 15 blue marbles, 18 red marbles, and 12 yellow marbles. He reaches into the bag three times and pulls out 2 red marbles and a blue marble. What is the probability that he reaches into the bag and pulls out a yellow marble next? A. 1/4 B. 8/21 C. 2/7 D. 5/14
===================================================
Explanation:
Initially there are 15+18+12 = 45 marbles total. He selects 3 marbles (2 reds, 1 blue).
Assuming he doesn't put the three marbles back, this means there are now 45-3 = 42 marbles overall. The yellow count hasn't changed since the first three marbles do not involve yellow. We have 12 yellow out of 42 which leads to the fraction 12/42 to represent the probability of getting yellow.
Reduce 12/42 to get 2/7. You divide both parts by the GCF 6.
-------
Side note: if he did put the marbles back, then the probability of getting yellow would be 12/45 = 4/15
Evaluate the triple integral ∭EzdV where E is the solid bounded by the cylinder y2+z2=81 and the planes x=0,y=9x and z=0 in the first octant.
Answer:
I = 91.125
Step-by-step explanation:
Given that:
[tex]I = \int \int_E \int zdV[/tex] where E is bounded by the cylinder [tex]y^2 + z^2 = 81[/tex] and the planes x = 0 , y = 9x and z = 0 in the first octant.
The initial activity to carry out is to determine the limits of the region
since curve z = 0 and [tex]y^2 + z^2 = 81[/tex]
∴ [tex]z^2 = 81 - y^2[/tex]
[tex]z = \sqrt{81 - y^2}[/tex]
Thus, z lies between 0 to [tex]\sqrt{81 - y^2}[/tex]
GIven curve x = 0 and y = 9x
[tex]x =\dfrac{y}{9}[/tex]
As such,x lies between 0 to [tex]\dfrac{y}{9}[/tex]
Given curve x = 0 , [tex]x =\dfrac{y}{9}[/tex] and z = 0, [tex]y^2 + z^2 = 81[/tex]
y = 0 and
[tex]y^2 = 81 \\ \\ y = \sqrt{81} \\ \\ y = 9[/tex]
∴ y lies between 0 and 9
Then [tex]I = \int^9_{y=0} \int^{\dfrac{y}{9}}_{x=0} \int^{\sqrt{81-y^2}}_{z=0} \ zdzdxdy[/tex]
[tex]I = \int^9_{y=0} \int^{\dfrac{y}{9}}_{x=0} \begin {bmatrix} \dfrac{z^2}{2} \end {bmatrix} ^ {\sqrt {{81-y^2}}}_{0} \ dxdy[/tex]
[tex]I = \int^9_{y=0} \int^{\dfrac{y}{9}}_{x=0} \begin {bmatrix} \dfrac{(\sqrt{81 -y^2})^2 }{2}-0 \end {bmatrix} \ dxdy[/tex]
[tex]I = \int^9_{y=0} \int^{\dfrac{y}{9}}_{x=0} \begin {bmatrix} \dfrac{{81 -y^2} }{2} \end {bmatrix} \ dxdy[/tex]
[tex]I = \int^9_{y=0} \begin {bmatrix} \dfrac{{81x -xy^2} }{2} \end {bmatrix} ^{\dfrac{y}{9}}_{0} \ dy[/tex]
[tex]I = \int^9_{y=0} \begin {bmatrix} \dfrac{{81(\dfrac{y}{9}) -(\dfrac{y}{9})y^2} }{2}-0 \end {bmatrix} \ dy[/tex]
[tex]I = \int^9_{y=0} \begin {bmatrix} \dfrac{{81 \ y -y^3} }{18} \end {bmatrix} \ dy[/tex]
[tex]I = \dfrac{1}{18} \int^9_{y=0} \begin {bmatrix} {81 \ y -y^3} \end {bmatrix} \ dy[/tex]
[tex]I = \dfrac{1}{18} \begin {bmatrix} {81 \ \dfrac{y^2}{2} - \dfrac{y^4}{4}} \end {bmatrix}^9_0[/tex]
[tex]I = \dfrac{1}{18} \begin {bmatrix} {40.5 \ (9^2) - \dfrac{9^4}{4}} \end {bmatrix}[/tex]
[tex]I = \dfrac{1}{18} \begin {bmatrix} 3280.5 - 1640.25 \end {bmatrix}[/tex]
[tex]I = \dfrac{1}{18} \begin {bmatrix} 1640.25 \end {bmatrix}[/tex]
I = 91.125
7 |r/5|=7
solve the equation
Answer:
r=5 or r=−5
Step-by-step explanation:
Answer:
fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffg
Step-by-step explanation:
Evaluate each expression if a = 12, b = 9, and c = 4.
2c(a + b)
answers
312
336
45
168
Answer:
168
Step-by-step explanation:
2c(a+b) = 2 . 4 . (12 + 9) = 2 . 4 . 21 = 8 . 21 = 168
One number is two less than three times another. If their sum is decreased by two, the result is four. Find the numbers.
The smaller of the numbers is ___ and the larger is ___
Answer: The smaller of the numbers is 2 and the larger is 4.
Step-by-step explanation: 2x3-2=4. 2+4-2=4
Answer:
The bigger number is 1 and the smaller number is also 1
Step-by-step explanation:
One number is 2 less than 3 times another
x + 2 = 3y
If their sum is decreased by 2 the result is 4
(x + 2 + 3y) - 2 = 4
x + 3y = 4
x = 4 - 3y
Substituting value of x, 4 - 3y , in x + 2 = 3y
4 - 3y + 2 = 3y
6 - 3y = 3y
6 = 3y + 3y
6 = 6y
Divide both sides by coefficient of y, 6
y = 1
Substituting value of y, 1 in x + 2 = 3y
x + 2 = 3(1)
x + 2 = 3
x = 3 - 2
x = 1
HELP ME WITH THIS (a+5)(b-3)
Answer:
The answer is ab-3a+5b-15
Step-by-step explanation:
apply de disruptive property by multiplying each term a+5by each term b-3
Hope this helps :)
Answer:
here you go ab-3a+5b-15
Find the dimensions of a triangle given the base, height, and area. b=8 inches h=7 inches A=28 square inches
Answer:
Step-by-step explanation:
The formula for the area of a triangle of base b and height h is A = (1/2) (b)(h).
Here A = 28 in^2, so 28 in^2 = (1/2)(8 in)(7 in), or
28 in^2 = 28 in^2
Four new word processing software programs are to be compared by measuring the speed with which various standard tasks can be completed. Before conducting the tests, researchers note that the level of a person’s computer experience is likely to have a large influence on the test results. Discuss how you would design an experiment that fairly compares the word processing programs while simultaneously accounting for possible differences in users’ computer proficiency.
Answer:
The following are the solution to this question:
Step-by-step explanation:
The average frequency of each of the four new word processing applications, that can be determined as well as the computer expertise of the consumer, which can be calculated as low and medium. Its information could then be displayed in a table of 3×3, and we'll use ANOVA 2 ways to demonstrate those two comparisons.
n f(x) = 2x , x=5. What is the value of the function?
The shipping cost for order at an online store is 1/10 the cost of the items you order. What is an expression for the total cost of an order of $79? A. 0.10($79) B. $79 + 0.1($79) C. $(79 + 0.10)
Answer:
B. $79 + 0.1($79)
Step-by-step explanation:
Given that;
the shipping cost for an order = 1/10 multiply by the cost of the items bought;
i.e. [tex]\dfrac{1}{10}\times x[/tex]
where
x = cost of items ordered for.
This implies that:
[tex]\implies[/tex] x + 0.1x
The objective is to determine the expression for the total cost of an order which is $79
x = 79
Then, the total cost of an order is
$79 + 0.1($79)
what is the height of a trapezoid with one base equal to 20m, the other base equal to 7m, and an area of 135m^2
Answer:
The height is 10 mStep-by-step explanation:
Area of a trapezoid is given by
[tex]A = \frac{1}{2} (a + b)h[/tex]where
a and b are the bases
h is the height
From the question
A = 135 m²
a = 20m
b = 7 m
Substitute the values into the above formula and solve for the height
That's
[tex]135 = \frac{1}{2} (20 + 7)h \\ 135 = \frac{1}{2} \times 27h \\ 135 \times 2 = 2 \times \frac{1}{2} \times 27h \\ 270 = 27h[/tex]Divide both sides by 27
That's
[tex] \frac{27h}{27} = \frac{270}{27} [/tex]We have the final answer as
10 mHope this helps you
Please help me on this one!
Answer:
-1/2
Step-by-step explanation:
The slope of a line parallel is to another line is the same.
So the line in the picture has a slope of -1/2, and since the other line is parallel to the first one, its slope is also -1/2
Samuel was riding in the back seat of the station wagon on the way home after a long and tiring day at the
beach. He fell asleep halfway home. He didn't wake up until he still had half as far to go as he had already
gone while asleep. How much of the entire trip home was Samuel asleep?
Help with diagram please
Answer:
Samuel slept for 1/4 of the distance.
Step-by-step explanation:
The information provided are:
Samuel fell asleep halfway home.He didn't wake up until he still had half as far to go as he had already gone while asleep.Consider that the total distance covered was 1.
Then from the first point we know that Samuel fell asleep after covering a distance of 1/2.
It is provided that he woke up only after covering half of the remaining distance.
That is, he slept for 1/4 of the remaining distance.
Thus, Samuel was asleep for 1/4th of the entire trip home.
if PN=29cm and MN=13 , then PM=?
*see attachment for the figure referred to
Answer/Step-by-step explanation:
1. PN = 29
MN = 13
PM = ?
[tex] PN = PM + MN [/tex] (Segment addition postulate)
[tex] PN - MN = PM [/tex] (subtract MN from each side)
[tex] 29 - 13 = PM [/tex] (substitute)
[tex] 16 = PM [/tex]
[tex] PM = 16 cm [/tex]
2. PN = 34, MN = 19, PM = ?
[tex] PN = PM + MN [/tex] (sediment addition postulate)
[tex] PN - MN = PM [/tex] (subtract MN from each side)
[tex] 34 - 19 = PM [/tex] (substitute)
[tex] 15 = PM [/tex]
[tex] PM = 15 cm [/tex]
3. PM = 19, MN = 23, PN = ?
[tex] PN = PM + MN [/tex] (Segment addition postulate)
[tex] PN = 19 + 23 [/tex] (substitute)
[tex] PN = 42 cm [/tex]
4. MN = 82, PN = 105, PM = ?
[tex] PN = PM + MN [/tex] (segment addition postulate)
[tex] PN - MN = PM [/tex] (subtract MN from each side)
[tex] 105 - 82 = PM [/tex] (substitute)
[tex] 23 = PM [/tex]
[tex] PM = 23 cm [/tex]
5. PM = 100, MN = 100, PN = ?
[tex] PN = PM + MN [/tex] (Segment addition postulate)
[tex] PN = 100 + 100 [/tex] (substitute)
[tex] PN = 200 cm [/tex]
Which of the following quadratic functions has a graph that opens downward? A.y= 3/2x^2 -3x+15 B.y= 5/2x-3x^2 C.y= 3x^2-x-1 D.y= -(2x^2-1)
it says if
ax^2+bx+c=0
a<0
answer is D because, there is (-) near of x^2
HELP PLEASE, BRAINLIEST AND 15 POINTS
Answer:
Step-by-step explanation:
MP, same thing
Answer:
MP
Step-by-step explanation:
PM is the same thing as MP just flipped around. So, they are equal to each other.
Hope This Helps :)
Prices of a certain item have a distribution that is skewed to the left with outliers in the left tail. Which of the measures of central tendency is the best to summarize this data set?a. Mode b. Median c. Mean
Answer: b. Median
Step-by-step explanation:
The most common measures of central tendency are :
a. Mode - It is used in nominal data.
b. Median - It is used as central tendency when data is skewed or having outliers in the data.
c. Mean - It is the best measure of central tendency when data does not have outliers because it affect mean badly.
Given, Prices of item have a skewed distribution with outliers in the left tail.
That means , the best measure of central tendency to summarize this data set is median.
So, the correct option is b.
Which ordered pair is generated from the equation shown below? y = 3x -2
Answer:
hope this helps
Step-by-step explanation:
I don't know I have a similar one but I also don't know that one
Step-by-step explanation:
Explain in detail with at least two sentences how to represent the product of A and B geometrically given that A=15 + 56i and B = 7 + 4i. Give the coordinate of A • B in polar form.
Answer:
Basically each part of the first complex number gets multiplied by each part of the second complex number. You are multiplying 2 binomials.
(15 + 56i(7 + 4i)
= 105 + 60i + 392i + 224i^2
= 105 + 452i - 224 ( because i^2 = -1)
= - 119 + 452i
Step-by-step explanation:
let me know if this helps!
What is 64 186 300 in standard form
Answer:
Sixty-four , one eighty six, three hundred
Step-by-step explanation:
That’s it.-,
Answer:
sixty four million, one-hundred eighty-six thousand three hundred
Step-by-step explanation:
which expression is equivalent to the given expression? (1/7x+6)-(4/7x+3)
Answer:
-2/7x+3
Step-by-step explanation:
1/7x+6-4/7x-3
-3/7x+3
What is the place value of the digit 9 in 45.93
The correct answer is
tenths
Answer:
Thousandth
Step-by-step explanation:
Mathematics Free Test 1- 0.75 as a fraction.
Answer: [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
Convert from decimal to fraction.
0.75 = 3/4. That is your answer.
Answer:
3/4 i believe.
Step-by-step explanation:
|14| > 14 true or false
Answer:
false
Step-by-step explanation:
since its the absolute value it will be equal to 14
x + 3 = -3 what is x
x = - 6
Step-by-step explanation:x + 3 = - 3
x = - 3 - 3
x = - 6
Answer:-6
Step-by-step explanation:
X+3=-3
X=-3-3
X= -6
idfwuomg1 5000+25000
Answer:
40,000
Step-by-step explanation:
15000+25000=40000
Answer: 40,000
Step-by-step explanation:
25,000 + 15,000 = 40,000
Hope this helps
Plz mark brainliest