The tower is 260 feet away from the fire.
How to apply trigonometric function?The height of the tower is the opposite side while the distance from the tower to the fire is the adjacent side.
Given:
Angle of depression = 30°.
Opposite side = 150 feet.
Now,
tan [tex]\thtea\\[/tex][tex]\theta[/tex]= P/B
tan 30 [tex]\thtea\\[/tex]= 150/B
1/√3= 150/B
B= 150*√3
B= 150*1.732
B= 259.8
B= 260 feet.
Hence, the tower is 260 feet away from the fire.
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For what values of a can you solve the linear system az + 3y = 2 and 4x + 5y = 6 by elimination without
multiplying first?
The values
and
Answer:
4, -4
Step-by-step explanation:
I think the first equation is ax + 3y = 2, not az + 3y = 2.
ax + 3y = 2
4x + 5y = 6
To use elimination, you need the coefficients of a to either add to zero, or to have a difference of zero if you subtract them.
a + 4 = 0
a = -4
a - 4 = 0
a = 4
Answer: a must be 4 or -4.
Answer:
-4 and 4
Step-by-step explanation:
Given linear system:
[tex]ax+3y=2[/tex]
[tex]4x+5y=6[/tex]
In order to solve the given linear system by elimination without multiplying first, [tex]a[/tex] must be either -4 or 4. That way, when you add or subtract the equations, the variable [tex]x[/tex] will be eliminated.
when [tex]a = -4[/tex]:
[tex]\large\begin{array}{ l r c c l r}& -4x & + & 3y & = & 2\\+ & 4x & + & 5y & = & 6\\\cline{1-6}& & & 8y & = & 8\\\cline{1-6}\end{array}[/tex]
when [tex]a = 4[/tex]:
[tex]\large\begin{array}{ l r c c l r}& 4x & + & 3y & = & 2\\- & 4x & + & 5y & = & 6\\\cline{1-6}& & & -2y & = & -4\\\cline{1-6}\end{array}[/tex]
What is the volume of a cube with sides measuring 1.5 inches
Answer:
A cube with a side length of 3 inches has a volume of 27 cubic inches.
Step-by-step explanation:
yes
Which expression is equivalent to 18x+8y?
Answer
2 (9 x + 4 y)
Hope this helps :)
16) Graph g(x) = x + 3 + 2
only answer if you know!! no spams
Answer:
The answers would be D and C.
Hope this helps!
Write an equation for the translation of y =5/x
that has the asymptotes x= -7 and y= 7
The equation for the translation of y = 5/x is y = 5/(x+7) + 7 if that has the asymptotes x= -7 and y= 7
What is hyperbola?
It is a curve in two-dimensional geometry having two parts, they both are symmetric. In other words, It can be defined as the number of points in the two-dimensional geometry that have a constant difference from that point to two fixed points in the plane.
We have:
[tex]\rm y = \dfrac{5}{x}[/tex]
Vertical asymptotes x= -7 and
Horizontal asymptotes y= 7
After translation:
[tex]\rm y = \dfrac{5}{x+7}+7[/tex]
Thus, the equation for the translation of y = 5/x is y = 5/(x+7) + 7 if that has the asymptotes x= -7 and y= 7
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Find the area of a sector of the circle below. Express in terms of pie and as a decimal.
[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=18\\ \theta =40 \end{cases}\implies \begin{array}{llll} A=\cfrac{(40)\pi (18)^2}{360}\implies A=36\pi \\\\\\ A\approx 113.097 ~m^2 \end{array}[/tex]
Answer:
36π (m²) or ≈ 113.14 m²
Step-by-step explanation:
[tex]A_{circle}[/tex] = [tex]\pi r^{2}[/tex]
[tex]A_{sector}[/tex] = x
[tex]\frac{360^o}{40^o}[/tex] = [tex]\frac{18^2 \pi }{x}[/tex]
9 = [tex]\frac{18^2 \pi }{x}[/tex]
x = 36π
or
x ≈ 36 × [tex]\frac{22}{7}[/tex] ≈ 113.14 m ²
What is the value of the expression (3/4)³
81/256
27/64
9/12
27/4
Answer:
9/12
Step-by-step explanation:
Answer:
The answer is
9 over 12
9/12
A survey of high schools offering honors classes to ninth graders reveals that 38% of the high schools offer no honors classes, 12% offer one honors class, 25% offer two honors classes, 20% offer three honors classes, and 5% offer four honors classes.
A high school is selected at random. What is the probability that it offers an even number of honors classes?
0.62
0.30
0.68
0.32
Using the discrete distribution, it is found that the probability that it offers an even number of honors classes is of 0.68.
What is the discrete probability distribution?The distribution for the number of honors classes the school offers is given by:
P(X = 0) = 0.38P(X = 1) = 0.12.P(X = 2) = 0.25.P(X = 3) = 0.2.P(X = 4) = 0.05.Hence the probability of an even number is given by:
P(even) = P(X = 0) + P(X = 2) + P(X = 4) = 0.38 + 0.25 + 0.05 = 0.68.
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I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answer:
294 inches squred
Step-by-step explanation:
3 x 10 = 30
3 x 9 = 27
10 x 9 = 90
2(30) + 2(27) + 2(90) = 294
A small motorboat travels 8mph in still water. It takes 3 hours longer to travel 44 miles going upstream than it does going downstream. Find the rate of the current. (Hint: 8+x= rate going downstream and 8−x= rate going upstream.)(Round your answer to the nearest tenth.)
The rate of the current is 2.03 mph if the small motorboat travels 8mph in still water. It takes 3 hours longer to travel 44 miles going upstream than it does going downstream.
What is a quadratic equation?Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] Where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
Let's suppose the rate of the current = r
The time it takes to go downstream + 4 hours = time to go upstream
As we know the:
[tex]\rm Time = \dfrac{Distance}{ Rate }[/tex]
Now,
[tex]\rm \dfrac{44}{ (8 + r)} + 3 = \dfrac{44}{ (8 - r)}[/tex]
After solving:
[tex]\rm \dfrac{44}{ (8 - r)}-\dfrac{44}{ (8 + r)} =3[/tex]
After cross multiplication
44(8+r) - 44(8-r) = 3(8+r)(8-r)
88r = 3(64 - r²)
3r² + 88r - 192 = 0
After solving the above quadratic equation, we get:
r = 2.03 or
r=−31.37 (reject as it is negative)
So, the r =2.03 mph
Thus, the rate of the current is 2.03 mph if the small motorboat travels 8mph in still water. It takes 3 hours longer to travel 44 miles going upstream than it does going downstream.
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Order the numbers from greatest to least?
2/9, 21%, 5/20, 8%
Answer:
5/20, 2/9, 21%, 8%
Step-by-step explanation:
2/9 = 0.22
21% = 0.21
5/20 = 0.25
8% = 0.08
0.25>0.22>0.21>0.08
mark brainliest please!
Use the quadratic formula to solve x^2- 5x + 3 = 0.
Answer: Heyaa! ~
Your Answer is... x = 5 ± √ 13/ 2
Step-by-step explanation:
Solve the equation for x by finding a, b, and c of the quadratic then applying the quadratic formula.
Hopefully this helps you!
-Matthew ^^
Which mixed number is equivalent to
19/3
Answer:
6 1/3
Step-by-step explanation:
You just have to see how many times it goes into it
Evaluate the expression:
-a^2 + c(a-c) - n^2 a= -3 c= -2 n= 3
Answer: -a^2+c\left(a-c\right)-n^2a=3\quad :\quad c=-\frac{-a+\sqrt{-3a^2-4an^2-12}}{2},\:c=-\frac{-a-\sqrt{-3a^2-4an^2-12}}{2}
Step-by-step explanation: YW! plese mark branlest!
how to find 2 square root of 3
Answer:
sqrt12
Step-by-step explanation:
being given any problem like this, let's use the form y√x, y representint 2, and x is 3, but it's generalized
in order to find the unsimplified √ we would do 2(yx). Which in this case is 12
Five marbles labeled 1 through 5 are placed in a bag. A marble is randomly pulled and the number is recorded before the marble is
placed back in the bag. The results of the simulation of 20 marble pulls are shown in a dot plot.
Which dot plot models an unfair data-generating process?
Using the dot plot concept, it is found that the left plot on the bottom row shows an unfair data-generating process.
What does a dot plot show?The dot plot shows the number of times each measure appears in the data-set.
In this problem, each trial has 5 possible outcomes and there are 20 trials, hence each number should appear 20/5 = 4 times.
On the left plot of the bottom row, outcomes 1 and 5 appear 7 times, while outcomes 2, 3 and 4 appear 2 times, which are the furthest values from 5, hence it is an unfair data-generating process.
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Answer:
Step-by-step explanation:
PLEASE HELP ME, I GIVE 69 POINTS FOR CORRECT ANSWER
A square pyramid has a base with an area of 20 square meters, and its lateral faces have a slant height of x meters. Sydney is constructing a second square pyramid with the same size base, but the lateral faces of her pyramid have a slant height twice as long, 2x. Which statement best describes how the surface area of Sydney’s pyramid compares to the surface area of the original pyramid?
A: Sydney’s pyramid will have the same surface area because the One-half in the expression for the area of the triangular faces will make up for the slant height being doubled.
B: Sydney’s pyramid will have the same surface area because the slant height is not used when finding surface area.
C: Sydney’s pyramid will have a surface area that is exactly double the original pyramid’s because the slant height is used when finding the area of every lateral face.
D: Sydney’s pyramid will have a surface area that is greater than the original pyramid’s but not double the area because the slant height is not used when finding the area of the base.
(PS: If you choose C, you're wrong.)
Answer:
D
Step-by-step explanation:
I hope this helps! If it does, please mark me Brainliest! Thanks in advance!
Sand and gravel are mixed in the ratio 5:3 to form ballast.
How much sand is mixed with 750kg of gravel ?
Work Shown:
sand/gravel = 5/3
x/750 = 5/3
3x = 750*5
3x = 3750
x = 3750/3
x = 1250
This question is worth 20 points if someone answers it!
The maximum number of tourists in the third week will be maximum in the numberville city.The solution of f(x)=h(x) will be x(5,2).
What are equations?The equation is actually a relationship between the numbers and the variables.
To calculate the number of the tourists in the third week we will put the value 3 in every function:
[tex]f(x)=x^2+5x+10=(3)^2+(3\times 3)+10=29\\\\\\g(x)=3^x=3^3=27\\\\\\h(x)=10x=10\times 3=30[/tex]
So we can see that the function third h(x) numberville city is having a maximum number of tourists.
The solution of f(x)=h(x) will be calculated as:
[tex]x^2-3x+10=10x\\\\\\x^2-7x+10=0\\\\\\x^2-5x-2x+10=0\\\\\\x(x-5)-2(x-5)=0\\\\\\x=5,2[/tex]
Hence the solution of f(x)=h(x) will be x(5,2).
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Which sport is required to have both male and female competitors?
A. Water polo
B. Swimming
C. Hockey
D. Mixed doubles tennis
please help thank you
Jack and Marcy are at an amusement park. Jack is standing 75 meters from a hot air balloon ride. He is recording Marcy with his cell phone as she gets into the basket of the balloon and the hot air balloon begins to rise.
Tan65°=h/75m
2.1445 × 75 = h
h = 160.83
Step-by-step explanation:
This is very very simple
Many counties in Florida missed many school days in the fall of 2004 due to hurricanes that year. To make up those days, they added time to each school day for a portion of the year. It was decided that in order to make up a 6 hour school day, 10 minutes would be added to each day. How many extended days would be needed to make up 3 school days?
Answer:
if 10 minutes was added each day 30 minutes is how long it would extend in 3 days
Please help I need it quick!!!! Please
Answer:
Question 1
Cost per 10,000 Popsicle sticks = $725.20
⇒ Single Popsicle stick = 725.20 ÷ 10000 = $0.07 (nearest cent)
Question 2
Cost per 1,000 motherboards = $8,730
⇒ Cost of Single motherboard = 8730 ÷ 1000 = $8.73
Cost per 10 motherboards = $100
⇒ Cost of Single motherboard = 100 ÷ 10 = $10
Difference = 10 - 8.73 = $1.27
Question 3
Create a table with the cost per 1 unit:
[tex]\begin{array}{| c | c | c | c |}\cline{1-4} \sf PART & \sf COST\:PER\:1\:of\:10 & \sf COST\:PER\:1\:of\:1000 & \sf COST\:PER\:1\:of\:10000\\\cline{1-4} \sf Motherboard & \$10.00 & \$8.73 & \$7.04 \\\cline{1-4} \sf Processor & \$5.00 & \$1.25 & \$0.63 \\\cline{1-4} \sf Popsicle & \$0.10 & \$0.09 & \$0.07 \\\cline{1-4} \sf Motor & \$4.50 & \$0.18 & \$0.04 \\\cline{1-4} \sf Sensor & \$6.30 & \$4.54 & \$3.18 \\\cline{1-4} \sf Small\:gear & \$1.00 & \$0.80 & \$0.70 \\\cline{1-4} \end{array}[/tex]
From inspection of the table, the Motor saves the most money per unit when 10,000 is bought, since the difference between the cost of 1 unit is the greatest for this part.
Question 4
Cost of 1100 motherboards
= cost of 1000 + cost of 10 x 10
= 8730 + 100 x 10
= 8730 + 1000
= $9,730
Question 5
Cost of 12050 sensors
= cost of 10000 + cost of 1000 x 2 + cost of 10 x 5
= 31752 + 4536 x 2 + 63 x 5
= 31752 + 9072 + 315
= $41,139
The owner of a local movie theater keeps track of the number of tickets sold in each purchase. The owner determines the probabilities based on these records. Let X represent the number of tickets bought in one purchase. The distribution for X is given in the table. A 2-column table with 5 rows. Column 1 is labeled number of tickets with entries 1, 2, 3, 4, 5. Column 2 is labeled Probability with entries 0.17, 0.55, 0.20, 0.06, 0.02. What is the probability that a randomly selected purchase has less than two tickets? 0.17 0.55 0.72 0.83
Answer:
0.17
Step-by-step explanation:
The probability for purchasing 2 tickets at a time can be given as 0.17. The correct option is (A).
What is probability?Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.
The probability of any event always lie in the close interval of 0 and 1 [0,1].
Suppose X be the event to represent the number of tickets in purchase.
Then, as per the question distribution table can be formed as follows,
The number of tickets (X) P(X) Probability
1 0.17
2 0.55
3 0.20
4 0.06
5 0.02
Thus, the probability of selecting less than two tickets can be obtained as,
P(X < 2) = P(X = 1)
⇒ 0.17
Hence, the probability for a purchase to have less than two tickets is given as 0.17.
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Evaluate: 2 • [(6 + 1)2 + 1]
Answer:
20
Step-by-step explanation:
2•[(6+1)2+1]
2•[(7)3]
2•10
• means times
2×10
20 answer
Answer:
p
Step-by-step explanation:
2 • [(6 + 1)2 + 1]
First The Brackets :
[(6 + 1)
->>> 6 + 1
= 7
But there's a bracket around 6 + 1 so now we multiply
-->>> [(7)2 + 1]
->>> 7 x 2
= 14
So now we add :
-->>> 14 + 1
= 15
And now we multiply:
->>> 15 • 2
--->>> 30
Hope it helps :))))
How can I get 9th grade to add up to 500? You can only change summer and fall. Thank you
Answer:
8th fall- 203 9th fall-95
Step-by-step explanation:
the 9th total is 500
8th fall is 203
9th fall is 95
13. What is the distance between the y-intercept of the function f(x) = 2(3)* and the y-intercept of the function g(x) represented by the table below?
Answer:
the answer is letter C.
I hope this can help you!
3x+5y= -9
Y= 2x-7
Use substitution to solve the system
Answer:
x = 2
Step-by-step explanation:
3x + 5y = -9 ___(1)
y = 2x - 7
Substituting y's value in (1) ..
3x + 5( 2x - 7) = -9
3x + 10x -35 = -9
13x = -9 + 35
13x = 26
x = 26/13
x = 2
Tell whether the system has one solution, infinitely many solutions, or no solution.
Answer:
Has infinite solutions
Explanation:
-x + 5y = -3..... eq1
2x - 10y = 6 .... eq2
===============
make x the subject in equation 1
-x + 5y = -3
-x = -3 - 5y
x = 5y + 3
========= insert this in equation 2
2(5y + 3) - 10y = 6
10y + 6 -10y = 6
6 = 6
So, Has infinite solutions as L.H.S = R.H.S