Two fire trucks on the ground on either side of a burning building or 1.3 miles apart. they each measure the angle of elevation to the fire which are 58° and 52°. How far is each truck from the fire? Please help ASAP thank you so much!
Answers
The distance of the first truck from the fire is 0.578 mile and the distance of the second truck from fire is 0.722 mile.
Distance of each truck from the fireUsing sine rule, we find the length of AB and BC as shown in the image.
a/sin A = b/sin B = c/sin C
Angle C = 180 - (58 + 52) = 70⁰
1.3/(sin 70) = b/(sin 52)
b = (1.3sin 52) / (sin 70)
b = 1.09 mile
c = (1.3sin 58) / (sin 70)
c = 1.1732 miles
Bisect angle C, and use sine rule again to find the lengths of bisected line AB.
1.09/(sin 90) = x/[sin (90 - 58)]
1.09/(sin 90) = x/(sin 32)
x = (1.09 sin 32)/(sin 90)
x = 0.578 mile
Truck B's position from the fire = 1.3 miles - 0.578 mile = 0.722 mile
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Related Questions
An investor decides to invest some cash in an account paying 13% annual interest, and to put the rest in a stock fund that ends up earning 7% over the course of a year. The investor puts $1300 more in the first account than in the stock fund, and at the end of the year finds the total interest from the two investments was $1270. How much money was invested at each of the two rates? Round to the nearest integer.
Answers
A percentage is a way to describe a part of a whole. The investment that was put in the account is 6805, while the amount that is invested in the stock is 5505.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
Le the amount that is put into the account is x, while the amount that is invested in the stock market is y. Given the investor puts $1300 more in the first account than in the stock fund, therefore, the equation can be written as,
x - y =1300
x = 1300 + y
Also, at the end of the year the total interest from the two investments was $1270. Therefore, we can write,
0.13x + 0.07y = 1270
Substitute the value of x from the above,
0.13(1300 + y) + 0.07y = 1270
169 + 0.13y + 0.07y = 1270
0.20y = 1101
y = 5505
substitute the value of y in the first equation,
x - y = 1300
x = 6805
Hence, the investment that was put in the account is 6805, while the amount that is invested in the stock is 5505.
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Need the answer for number 3 please!!!!
Answers
Answer:
Perimeter = 2(l + b)
= 2(x + 5x³ + 4 - x²)
= 2x + 10x³ + 8 - 2x²
= 10x³ - 2x² + 2x + 8
Hence, ur answer is the first option.
Answer:
A.
Step-by-step explanation:
L = x
W = 5x³ + 4 - x²
P = 2L + 2W
P(x) = 2x + 2(5x³ + 4 - x²) = 2x + 10x³ + 8 - 2x²
P(x) 10x³ - 2x² + 2x + 8
L = x
W = 5x³ + 4 - x²
P= 2L + 2W
P(x) = 2x + 2(5x³ + 4 - x²) = 2x + 10x³ + 8 - 2x²
= P(x) 10x³ - 2x² + 2x + 8
Flying against the wind, an airplane travels 2520 kilometers in 4 hours. Flying with the wind, the same plane travels 9450 kilometers in 9 hours. What is the rate of the plane in still air and what is the rate of the wind?
Answers
Using the relation between velocity, distance and time, it is found that:
The rate of the plane is of 840 km/h.The rate of the wind is of 210 km/h.What is the relation between velocity, distance and time?Velocity is distance divided by time, that is:
[tex]v = \frac{d}[t}[/tex]
Flying against the wind, an airplane travels 2520 kilometers in 4 hours, that is:
[tex]v - v_w = \frac{2520}{4}[/tex]
[tex]v - v_w = 630[/tex]
[tex]v = 630 + v_w[/tex]
Flying with the wind, the same plane travels 9450 kilometers in 9 hours, hence:
[tex]v + v_w = \frac{9450}{9}[/tex]
[tex]v + v_w = 1050[/tex]
[tex]v = 1050 - v_w[/tex]
Hence, solving for the wind's speed:
[tex]630 + v_w = 1050 - v_w[/tex]
[tex]2v_w = 420[/tex]
[tex]v_w = \frac{420}{2}[/tex]
[tex]v_w = 210[/tex]
For the plane, we have that:
v = 1050 - 210 = 840.
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Given that G=ab find the percentage increase in G when both a and b
increase by 10%
Answers
The percentage change in G is 21 %
What is Percentage change ?Percentage change is defined as the increase or decrease in the value as compared to the original value multiplied by 100.
It is given that
G = ab
when a is increased by 10% the new a will be = 1.1 a
When b is increased by 10% the new b will be 1.1 b
So,
G' = 1.1a *1.1 b
G' = 1.21 ab
G' = 1.21
(G' - G)*100/G = (1.21-1)*100/1
The percentage change is 21 %
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Find the inverse of the function.
y=x+8
Answers
Answer:
y^-1= x +8
Step-by-step explanation:
this may be helpful for you
What is the domain of the function y=√√x+6-7?
x>|-7
x>|-6
x>|6
x>|7
Answers
The domain of the function [tex]y=\sqrt{(x+6)}-7[/tex] is given by (B) that is [tex]x \geq-6[/tex]
Domain of a function refers to the values or range of input values of a function for which the function exists in real.
In this problem the given function is
[tex]y=\sqrt{(x+6)}-7[/tex]
Now the above function exists if the expression under square root is greater or equal to 0, since negative number cannot be square rooted in real, that gives imaginary number.
So, for existence of function it is must to
[tex]x+6\geq0[/tex]
[tex]x\geq-6[/tex]
Hence the domain of the given function is given by [tex]x\geq-6[/tex]
Hence the correct option is (B).
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1) Which relation is a function?
es
A) x = y² - 3
B) x = y - 4x²
C) y² = 4x - 6
D) x² = y²-10
Answers
Answer:
B
Step-by-step explanation:
x = y-4x^2 can be rearranged to get y = 4x^2 + x, which is a function
A manufacturer of pacemakers wants the standard deviation of the lifetimes of the batteries to be less than 1.8 months. A sample of 20 batteries had a standard deviation of 1.6 months. Assume the variable is normally distributed. Find the 95% confidence interval of the standard deviation of the batteries. Based on this answer, do you feel that 1.8 months is a reasonable estimate?
Answers
Answer:
Look down my answer↓:
Step-by-step explanation:
MAT 171
1. The polynomial of degree 5, P(x) has leading coefficient 1, has roots of multiplicity 2 at x=1 and x=0, and a root of multiplicity 1 at x=-4
Find a possible formula for P(x)
2. The polynomial of degree 4, P(x) has a root of multiplicity 2 at x=4 and roots of multiplicity 1 at x=0 and x=-4. It goes through the point (5, 36).
Find a formula for P(x).
3. The polynomial of degree 3. P(x), has a root of multiplicity 2 at x=3 and a root of multiplicity 1 at x=-2. The y-intercept is y=-1.8.
Find a formula for P(x).
Answers
Using the Factor Theorem, the polynomials are given as follows:
1. [tex]P(x) = x^5 + 2x^4 - 7x^3 + x^2[/tex]
2. [tex]P(x) = 0.8(x^4 - 4x^3 - 16x^2 + 64x)[/tex]
3. P(x) = -0.1(x³ - 4x² - 3x + 18)
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.
Item a:
The parameters are:
[tex]a = 1, x_1 = x_2 = 1, x_3 = x_4 = 0, x_5 = -4[/tex]
Hence the equation is:
P(x) = (x - 1)²x²(x + 4)
P(x) = (x² - 2x + 1)(x + 4)x²
P(x) = (x³ + 2x² - 7x + 1)x²
[tex]P(x) = x^5 + 2x^4 - 7x^3 + x^2[/tex]
Item b:
The roots are:
[tex]x_1 = x_2 = 4, x_3 = 0, x_4 = -4[/tex]
Hence:
P(x) = a(x - 4)²x(x + 4)
P(x) = a(x² - 16)x(x - 4)
P(x) = a(x³ - 16x)(x - 4)
[tex]P(x) = a(x^4 - 4x^3 - 16x^2 + 64x)[/tex]
It passes through the point x = 5, P(x) = 36, hence:
45a = 36.
a = 4/5
a = 0.8
Hence:
[tex]P(x) = 0.8(x^4 - 4x^3 - 16x^2 + 64x)[/tex]
Item 3:
The roots are:
[tex]x_1 = x_2 = 3, x_3 = -2[/tex]
Hence:
P(x) = a(x - 3)²(x + 2)
P(x) = a(x² - 6x + 9)(x + 2)
P(x) = a(x³ - 4x² - 3x + 18)
For the y-intercept, x = 0, y = -1.8, hence:
18a = -1.8 -> a = -0.1
Thus the function is:
P(x) = -0.1(x³ - 4x² - 3x + 18)
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Need help with this geometry question
Answers
Answer: 59
Step-by-step explanation:
The measure of an arc is equal to the measure of the central angle intercepted by it.
If : f(x)=x^2, g(x)=x-1. Find (f×g)(x).
Answers
Answer:
[tex] \boxed{ f\cdot{g}(x) = x {}^{3} - x {}^{2}}[/tex]Step by step explanation:
Given that,
[tex]f(x) = {x}^{2} [/tex]
[tex]g(x) = x - 1[/tex]
Solution:
Solving for (f•g)(x):
[tex] = f(x) \cdot g(x)[/tex]
Now substitute the given values.
[tex] = x {}^{2} \cdot(x - 1)[/tex]
[tex] = x {}^{2} (x - 1)[/tex]
Apply distributive property:
[tex] = (x ^{2} \cdot x) - x {}^{2} \cdot 1[/tex]
[tex] \boxed{ f\cdot{g}(x) = x {}^{3} - x {}^{2}}[/tex]Hence,f•g(x) will be [tex] x {}^{3} - x {}^{2}[/tex].
Giving the brainliest to those who answer!
Answers
I need help pronto!!
Answers
Answer:
There were 42 fewer students who chose Football than Hockey.
Step-by-step explanation:
Fraction of students who chose Hockey
= 1 - [tex]\frac{1}{6}[/tex] - [tex]\frac{1}{3}[/tex]
= [tex]\frac{1}{2}[/tex]
[tex]\frac{1}{2}[/tex] units = 21
1 unit = 42
No. of students who chose Football
= 2 units ([tex]\frac{2}{6}[/tex])
= 84 students
No. of students who chose Hockey
= 3 units ([tex]\frac{3}{6}[/tex])
= 126 students
Difference between no. of students who chose Football and Hockey
= 126 - 84
= 42 students
∴There were 42 fewer students who chose Football than Hockey.
The rectangular prism has a vertex at (5, 6, 2). Which
ordered triples represent other vertices of the prism?
Check all that apply.
(0, 0, 2)
(0, 5,6)
(2,0, 5)
(5, 0, 2)
(5, 6, 0)
(6,2,0)
Answers
Answer:
A, D, E
Explanation:
It's right on edge lol
RQ=5x+1 and QT =3x+15. Find QT.
Answers
The length QT is 36 units
How to determine the length QT?The attached image represents the missing information in the question
From the image, we have:
RQ =QT
Substitute known values
5x + 1 = 3x + 15
Evaluate the like terms
2x = 14
Divide by 2
x = 7
Substitute x = 7 in QT = 3x + 15
QT = 3 * 7 + 15
Evaluate
QT = 36
Hence, the length QT is 36 units
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4 Pencils and 2 rulers cost $8. 2 pencils and 4 rulers cost $10. Find the cost of 3 rulers and 3 pencils
Answers
Answer:
$9
Step-by-step explanation:
Let, the price of pencils is x, and the price of rulers is y.
4x+2y=8.....(i)
2x+4y=10......(ii)
From eq(i),
2(2x+y)=8
2x+y=4
y=4-2x eq(iii) .....put in eq(ii)
2x+4(4-2x)=10
2x+16-8x=10
-6x=10-16
x=-6/-6
x=1 put in eq (iii)
y=4-2(1)
y=2
Now, the price of 3 rulers and 3 pencils = 3x+3y=3(1)+3(2)
=9
Please give me brainlist.
Let assume the price of pencil is x and the price of rulers is y. While doing the operations we can remove the units which is $ (for price).
So now we can rewrite the first statement as 4x + 2y = 8.
As everything is dividant of 2, I'm simplifying the eqution by dividing everything by 2.
So, 2x + y = 4 ----(1)
Similarly the second statement is, 2x+4y = 10.
So, 2x + 4y = 10 ----(2).
To solve this we need to make any of the variable (either x or y) zero. We can do that in multiple ways, Here I am trying to make the x =0 by substrating equation 1 from equation 2.
2x + 4y = 10 -
2x + y = 4
___________
-0 + 3y = 6
3y = 6
So y= 6/3=2
Now we have the value of y, to find x apply it in any eqution that has x
I'm applying it in eqution 2
2x + 2 = 4
2x = 2
x=1
Now we want to value the cost of 3 rulers and 3 pencils
3x + 3y = 3(1) + 3(2) = 3 + 6 = 9
So
Solve the system of equations by graphing.
y = x − 6
3x − 3y = 18
Answers
X = 6
Y = (-6)
If k(x) = 5x-6, which expression is equivalent to (k+ k)(4)?
Answers
Example:
[tex](f+g)(x)=f(x)+g(x)[/tex]
To add this, we can substitute in the functions and combine like terms.
Solving the QuestionWe're given:
[tex]k(x)=5x-6[/tex][tex](k+k)(4)=?[/tex]Add k to k:
[tex](k+k)(x) = k(x)+k(x)\\(k+k)(x) = 5x-6+5x-6\\(k+k)(x) = 10x-12[/tex]
Input x as 4:
[tex](k+k)(4) = 10x-12\\(k+k)(4) = 10(4)-12\\(k+k)(4) = 40-12\\(k+k)(4) = 28[/tex]
Answer[tex](k+k)(4)=28[/tex]
(k+k)(4) is equivalent to 28.
What is function ?If we have two non-empty sets X & Y, then each element of X is relative to at least one element of Y. This relation between elements of two sets is called function.
Addition of two functions : If f(x) & g(x) be two functions, then
(f+g)(x) = f(x)+g(x)
What is the required result ?Given, k(x) = 5x-6
Now, Adding function k with k we get,
(k+k)(x) = k(x)+k(x)
= (5x-6)+(5x-6)
= 5x-6+5x-6
= 10x-12
We have to find, (k+k)(4)
∴ (k+k)(4) = (10×4)-12
= 40-12
= 28
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What is true of an equilateral triangle? Two of its side lengths are equal. All its side lengths are equal. None of its side lengths are equal. None of its interior angles are equal. What is true of an equilateral triangle ? Two of its side lengths are equal . All its side lengths are equal . None of its side lengths are equal . None of its interior angles are equal .
Answers
Answer:
All its side lengths are equal
(and all the agle of 60°)
Step-by-step explanation:
What is true of an equilateral triangle? Two of its side lengths are equal. All its side lengths are equal. None of its side lengths are equal. None of its interior angles are equal. What is true of an equilateral triangle ? Two of its side lengths are equal . All its side lengths are equal . None of its side lengths are equal . None of its interior angles are equal .
Identify the category to which the following statement belongs: Brandon has two weeks to decide on the topic of his research paper.
O Not important - Not Urgent
O Not Important - Urgent
O Important - Not Urgent
O Important-Urgent
Answers
Answer:
Important- not urgent
Step-by-step explanation:
The research paper is important but since Brandon has two weeks to decide it is not urgent.
Solve the following systems using the elimination method. -3x+4y=-8 and 3x+ y=-17
Answers
Answer:
(-4, -5)
Step-by-step explanation:
-3x + 4y = -8
+
3x + y = -17
= 5y = -25 = y = -5
-3x + 4(-5) = -8
-3x - 20 = -8
-3x = 12
x = -4
Which statement about –2h2 – 15h – 7 is true?
One of the factors is (h + 2).
One of the factors is (3h – 2).
One of the factors is (2h + 1).
One of the factors is (h – 7).
Answers
Answer:One of the factors of the given expression is (2h + 1).
Step-by-step explanation:
ed
Answer:
C on edge 23
Step-by-step explanation:
because i said so
The table below shows the amount of money spent on skin diving and scuba equipment in some recent years.
Skin Diving and Scuba Equipment
Year
Sales ($millions)
1993
315
1994
322
1995
328
1996
340
1998
345
1999
363
Let x represent the year and y represent the amount of sales, in millions of dollars, in the regression equation.
y = 7.36 x minus 14,354.33,
Use the regression equation to predict the sales of skin diving and scuba equipment in the year 2008.
a.
44,000,000
b.
440,000,000
c.
42,455,000
d.
424,550,000
Please select the best answer from the choices provided
A
B
C
D
Mark this and return
Answers
The sales of skin diving and scuba equipment in the year 2008 is (d) 424,550,000
How to predict the sales in 2008?The regression equation is given as;
y = 7.36x - 14,354.33
In 2008, the value of x is
x = 2008
So, we have:
y = 7.36 * 2008 - 14,354.33
Evaluate
y = 424.55
Hence, the sales of skin diving and scuba equipment in the year 2008 is (d) 424,550,000
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The sales of skin diving and scuba equipment in the year 2008 is (d) 424,550,000.
We have given that,
The table below shows the amount of money spent on skin diving and scuba equipment in some recent years.
How to predict the sales in 2008?The regression equation is given as
y = 7.36x - 14,354.33
In 2008, the value of x is
x = 2008
So, we have y = 7.36 * 2008 - 14,354.33
Evaluate y = 424.55
Hence, the sales of skin diving and scuba equipment in the year 2008 is (d) 424,550,000
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Two trains going in opposite directions leave at the same time. Train B travels 5 mph faster than train A. In 3 hours the trains are 315 miles apart. Find the speed of each train
Answers
Answer:
Step-by-step explanation:
GUYS HELP NOW PLS WHAT IS THE PROBABILITY NOTATION FOR THE PROBABILITY OF CHOOSING A GREEN MARBLE HELPPPP PLS
Answers
The probability notation for the probability of choosing a green marble is P(G)
What is probability?This is simply defined as the extent to which something is likely to occur.
The probability that an event will occur is given as the ratio of the number of favorable outcomes to the total number of outcomes.
How to determine the probability notationProbability notation is a symbol used in indicating the probability of an occurring event. Since our focus is on the probability of obtaining a green marble, then the probability notation will be P(G). This is illustrated below:
Event of green marble = nGTotal event = nTProbability of green marble = P(G)P(G) = nG / nT
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If f(x) = 3x-2 and g(x) = x+²,
find f(g(x)).
f(g(x)) = [?]
Simplify your answer as much as possible.
Answers
Answer:
x
Step-by-step explanation:
[tex]f(g(x)) = 3(\frac{x+2}{3} )-2\\= x + 2 - 2\\= x[/tex]
10 problems for 50 points
Answers
Answer:
1. F
2. F
3. T
4. F
5. F
6. T
7. T
8. F
9. F
10. T
Step-by-step explanation:
1. For the rays to be opposite, they need to have the same starting point and go in different directions. Rays AP and BP use Point A and Point B, respectively, for their starting points.
2. They do not lie on the same line.
3. Points A, B, C, D all lie in the same plane therefore making them coplanar.
4. Points X, Y do not lie in the same plane as A, B.
5. Point X does not lie in the same plane as C, D, B
6. A, P, B are all points on the same line therefore any two of them could be used to represent the same line.
7. PX and PY start at the same point and go in the opposite directions, defining them as opposite rays.
8. Plane AXY cannot be defined as point X and Y are not in a plane.
9. Lines AB and CD cannot both be in a different plane.
10. Both rays sum up to equal Line XY.
How many square decimeters are in 687.1 cm²?
Answers
Answer:
6.871 decimeters
Step-by-step explanation:
687.1 square centimeters = 6.871 square decimeters
1 dm² = 100 cm²
Answer:
6.871
Step-by-step explanation:
calculator
Bob has decided to make his move to his new house easier, so he is going to rent a truck to get it all moved in one trip. He is looking at two truck rental companies. U-Haul rents a 32 ft truck for $19.95 plus 49 cents per mile driven. The formula to calculate the cost with U-Haul is C = 19.95 + 0.49x, where x represents the number of miles driven. Penske rents a truck for 69 cents per mile but has no extra fees. The formula to calculate costs for Penske is C = 0.69x, where x represents miles driven. How many miles indicate that the cost of renting a truck from U-Haul is equal to the cost of renting a truck from Penske?
Answers
equation for Penske is C = 0.69x a)
cost of renting is equal equatin is
19.95 + 0.49x = 0.69x
b) solving the equation 19.95 + 0.49x = 0.69x
19.95 = 0.69x - 0.49x x=99.75
x=99.75
c) inequality is
19.95 + 0.49x > 0.69x
d) solving the inequality 19.95 > 0.2xx < 99.75
x<99.75
e)
U haul can be used if the miles driven is less than
99.75 miles
then it will be less expensive
Which pair of statements describes the end behavior of the graph of the function f(x) = x3 + 2x2 − 5x − 6?
Answers
A function assigns the values. The correct option is D.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The complete question is:
Which pair of statements describe the end behavior of the graph of the function f(x) = x³ + 2x² − 5x − 6?
A.) As x approaches negative infinity, f(x) approaches infinity. As x approaches infinity, f(x) approaches infinity.
B.) As x approaches negative infinity, f(x) approaches infinity. As x approaches infinity, f(x) approaches negative infinity.
C.) As x approaches negative infinity, f(x) approaches negative infinity. As x approaches infinity, f(x) approaches negative infinity.
D.) As x approaches negative infinity, f(x) approaches negative infinity. As x approaches infinity, f(x) approaches infinity.
If we draw the graph of the given function f(x) = x³ + 2x² − 5x − 6, then it can be observed that as x approaches -∞, f(x) approaches -∞. As x approaches ∞, f(x) approaches infinity.
Hence, the correct option is D.
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