Tia climbed to the top of an observation tower overlooking a bird sanctuary and used the telescope at the top to observe two nests. The first nest was 400 meters away from the observation tower. Tia turned the telescope 135 degrees to observe the second nest, which was 300 meters away. How far apart are the two nests?
Answers
Answer:
648 m
Step-by-step explanation:
Given observations of two nests, one at 400 m, and the other at 300 m in a direction 135° from the first, you want to know the distance between the nests.
Law of CosinesThe law of cosines can be used to find the third side of a triangle, given two sides and the angle between them. It tells us ...
c² = a² +b² -2ab·cos(C)
In this scenario, we have a=400, b=300, and C=135°. The distance c is then ...
c² = 400² +300² -2·400·300·cos(135°) ≈ 419,705.63
c ≈ √419,705.63 ≈ 647.8
The two nests are about 648 meters apart.
Related Questions
b)
73cm
92cm
56 cm
What is the
the
area and perimeter
Answers
Answer:
Area=2044..... perimeter=221
Step-by-step explanation:
Step1:- Area =1/2×breath×height
1/2×73×56
1/2×4088
= 2044
Area =2044cm^2
Step2:- Perimeter= a+b+c
=73+56+92
=221
Perimeter=221cm
Shawn has 2 3/4 cups of berries. He uses 5/8 cups of berries to make a smoothie. He then uses 1/2 cup for a fruit salad.
Part A: How many cups of berries did he use?
Answers
what is 0.25x 2.6 pls help me this is hw
Answers
Answer:
0.65
Step-by-step explanation:
Frame three equations with solution x=-5
Answers
The three equations with solution x=-5 Are as follows:
25 + x = 15 ............... equation 1.
7x = -35 .......................equation 2.
15 + x = 10 ..................equation 3
In mathematics, what is linear equation?There is not more then one or two variables in a linear equation. In a linear equation, no variable is raised to a power larger than one or utilized as the denominator of a fraction. When you locate two values that satisfy a linear equation and display them on a coordinate grid, every one of the points falls on the same line.
What is a linear equation with one variable?A linear equation in one variable seems to be an equation that has just one solution and is stated in the form ax+b = 0, where a but instead b are two integers and x is a variable. 2x+3=8, for example, is a mathematical expression with a single variable.
According to the given information:x=-5 Given
This also can be written as :
25 + x = 15 ............... equation 1.
7x = -35 .......................equation 2.
15 + x = 10 ..................equation 3
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Can somebody help me if you know what this is
Answers
Answer:-2,2.5,-7/3
Step-by-step explanation:
Which equation represents a line which is parallel to the line
y = −3/5x − 7?
-
3x + 5y = 15
5x + 3y = 12
3y - 5x = 6
3x - 5y = -30
Submit Answer
Answers
Answer:
3x+5y=15
Step-by-step explanation:
3x+5y=15
5y=-3x-15
y=-3/5x-3
Because it has the same slope and a different y-intercept, it is parallel because the lines won't ever touch.
The sum of two numbers is 14. Using x to represent the smaller of the two numbers , translate "the sum of twice the smaller number and two more than the larger number" into a variable expression. Then simplify
Answers
The smaller number is 4 and the larger number is 10.
Given that, the sum of the two numbers is 14.
What is an equation?In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, x represents the smaller of the two numbers.
Then the larger number is
The sum of twice the smaller number and two more than the larger number = 2x+2
Now, x+2x+2=14
⇒3x+2=14
⇒3x=12
⇒x=4
So, 2x+2=10
Therefore, the smaller number is 4 and the larger number is 10.
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Hi
The following set of four ordered pairs below defines the vertices, in counterclockwise order, of a quadrilateral (four-sided figure).
((-4, 1), (1, 2), (-1,6).(-6,5)}
Step 1 of 3: Find the slopes of the indicated sides of the quadrilateral. Simplify your answer.
Side connecting (-4,1) and (-6,5)
Side connecting (1, 2) and (-1,6)
G
7
a
Suba
Answers
The slope of the side connecting (-4,1) and (-6,5) = -2
The slope of the side connecting (1,2) and (-1,6) = -2
The slope of the segment joining two points (x₁, y₁) and (x₂, y₂) = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
We have to find the slope of the side joining the points (x₁, y₁) = (-4,1) and (x₂, y₂) = (-6,5)
Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{5-1}{-6--4}[/tex]
= 4/ -2
= -2
We have to find the slope of the side joining the points (x₁, y₁) = (1, 2) and (x₂, y₂) = (-1,6)
Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{6-2}{-1-1}[/tex]
= 4/-2
= -2
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if LK=MK, LK=7x-10, KN=x+3, MN=9x-11, and KJ=28, find LJ
Answers
Congruent segments are LK=MK, LK=7x-10, KN=x+3, MN=9x-11, and KJ=28, the LJ will be-
LJ = 18 + 28 = 46
LJ = 18 + 28 = 46
These are Congruent segments
Let J, K, L, M, N are points on the same line.
MK = MN + (-KN) = MN - KN = 9x - 11 - x - 3 = 8x - 14
As LK = MK and LK = 7x - 10, then
7x - 10 = 8x - 14
8x - 7x = -10 + 14
x = 4
LJ = MK + KJ
MK = LK = 7x - 10 = 7(4) - 10 = 28 - 10 = 18
LJ = 18 + 28 = 46
Congruent segments are segments which have the equal length. ≅ points that lie at the equal line are called collinear.
A theorem is a mathematical assertion that can be proved. The midpoint of a phase is a point that divides the phase into two congruent segments
If three or more points lie on a single straight line, they are said to be collinear. An axis is a term used to describe a line on which points are located, particularly if that line is connected to a triangle or other geometric shape. Since two points determine a line, two points are trivially collinear.
Two line segments are congruent if they have the same length. They do not need to have the same position or orientation
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Thomas bought 12 glass and plastic cups from
the store. Glass cups cost $3.25 and plastic
cups cost $2.75. Thomas spent a total of
$36.00. How many glass cups (g) and how
many plastic cups (p) did he buy?
g+p=12
3.25g +2.75p = 36
[?] glass cups [] plastic cups
Answers
Thomas bought 6 glass cups and 6 plastic cups
How to calculate the number of glass and plastic cups ?
Thomas bought 12 glass and plastic cups from the store
Glass cups costs $3.25
Plastic cups cost $2.75
He spent a total of $36
Let g represent the number of glass cups and p represent the number of plastic cups
g + p= 12.........equation 1
3.25g + 2.75p= 36..........equation 2
From equation 1
g+p= 12
g= 12-p2
Substitute 12-p for g in equation 2
3.25(12-p)+2.75p = 36
39-3.25p+2.75p= 36
39-0.5p= 36
-0.5p= 36-39
-0.5p= -3
p= -3/-0.5
p= 6
Substitute 6 for p in equation 1
g + 6= 12
g= 12-6
g= 6
Hence there are 6 glass cups and 6 plastic cups
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Ethan got his first job and is making $8.50 an hour. He really wants to buy a couple of video games, so he is trying to estimate how much his paycheck will be. The first week Ethan works, he gets 18 hours. The second week Ethan works, he gets 25 hours. If Ethan pays 10% federal income tax and 2% state income tax, what can he expect to bring home in his first paycheck?
Answers
If Ethan got his first job and is making $8.50 an hour. He really wants to buy a couple of video games, so he is trying to estimate how much his paycheck will be. The amount he can expect to bring home in his first paycheck is: $321.64.
PaycheckTotal hours=18 hours+25 hours
Total hours=43 hours
Income tax=Federal income tax+ State income tax
Income tax=10%+2%
Income tax=12%
Hence,
First paycheck:
First paycheck=$8.50×43 hours×(1-12%)
First paycheck=$8.50×43 hours×0.88
First paycheck=$321.64
Therefore if Ethan got his first job and is making $8.50 an hour. He really wants to buy a couple of video games, so he is trying to estimate how much his paycheck will be. The amount he can expect to bring home in his first paycheck is: $321.64.
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1. Consider the following propositions
• P: 2+5=3
. Q: Warsaw is the capital of Poland.
. R: The US has the largest population in the world.
Answers
R= is incorrect
the answer is china :)
Lena has to make 20 gallons of punch for a potluck. The punch is made of soda and fruit drink. The cost of the soda is $1.90 per gallon and the cost of the fruit drink is $2.10 per gallon. Lena’s budget requires that the punch cost $2 per gallon. How many gallons of soda and how many gallons of fruit drink does she need?
Answers
Answer:
10 for each
Step-by-step explanation:
1.90 x 10 = 19
2.10 x 10 = 21
so 19 + 21 = 30
Select the correct answer.
Function bis nonlinear, and b(9) = 4. Which equation could represent function b?
Answers
The nonlinear- function which represents b(9)=4 is given by b(x)=72/x - 4 .
In mathematics and physics, a nonlinear system is one in which the change in the output is not proportional to the change in the input. Engineers, biologists, physicists, mathematicians, and many other scientists are interested in nonlinear problems since the majority of systems are inherently nonlinear.
Nonlinear function graphs don't resemble lines at all. It contains the formula f(x) = ax + b. Its equation can take any form, with the exception of f(x) = ax + b. The slope of the curve is the same between any two points. The point pairs on the graph do not all have equal slopes.
Of all the given options: the only equations which imply that b(9)=4 are :
i) b(x)=72/x - 4 and (iv) b(x)=4
Of this two options only the first option is non-linear.
Hence the required option is b(x)=72/x - 4 .
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Disclaimer:
The missing options are:
i) b(x) = 72/x - 4
ii) b(x) = √x + 7
iii)b(x) = 2x+1
iv) b(x) = 4
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In Smithville, there were 234 teachers in 1990 and 318 teachers in 2000. Find the percent of increase in the number of teachers in Smithville during this time period.
Answers
Answer:
35.90%
Step-by-step explanation:
First, subtract the new no with that of 1990
318-234= 84
percentage of increase will be given by;
84/234×100= 35.8974%
One lap around a track is 1/4 mile. It takes Parker 1/20 hour to sprint
one lap. What is Parker's unit rate, in miles, around the track
Answers
Answer:
Parker's unit rate is 5 miles per hour or 5mph.
Step-by-step explanation:
1 hour = 60 minutes
60/20 = 3 minutes
3 minutes for 1 lap
1 lap = 1/4 mile
1/4 mile (1 lap) x 4 laps = 1 mile
4 laps = 12 minutes
12 minutes per mile
60/12 = 5
5 miles per hour
There are 5 people from Arizona (A), 7 people from California (C), and 3 people from Nevada (N)
equally qualified for a job. There are three job openings for three different people. What is the probability that not all three people are from Arizona
Answers
Answer
.9780
Step-by-step explanation:
Probability, not all 3 people are from Arizona
Arizona Equals 1- 2/91 = 89/91 = .9780
Probability is .9780
Find the distance between the points A and B given below. (That is, find the length of the segment connecting A and B.) Round your answer to the nearest hundredth. 1 unit B
Answers
Answer:
theres no picture
Pentagon FGHJK is similar to pentagon MPQST. K What is the value of x? A 16 cm B Not here C) 12.5 cm 18 cm G S 12 cm M P
Answers
Answer:
I think it's a (16cm) ....
Which of the following correctly explains how the Product of Powers and Quotient of Powers Properties helps you to multiply and divide numbers
in scientific notation?
OA) Each number has a factor that is a power of 10. Because the bases are the same, these properties can be applied to multiply or di-
vide the powers of 10.
OB) Because numbers written in scientific notation have exponents, you can use the Laws of Exponents to multiply or divide the
numbers.
OC) The Product of Powers Property and the Quotient of Powers Property can be used to multiply and divide any numbers.
OD) Each number has a factor that is a power of 10. Because the bases are different, these properties can be applied to multiply or di-
vide the powers of 10.
Answers
The correct option regarding the operations with scientific notation is given as follows:
B) Because numbers written in scientific notation have exponents, you can use the Laws of Exponents to multiply or divide the numbers.
What is scientific notation?A number in scientific notation is given by:
[tex]a \times 10^b[/tex]
With the base being [tex]a \in [1, 10)[/tex].
An example of a multiplication in scientific notation is:
[tex]2 \times 10^3 \times 3 \times 10^5 = 6 \times 10^{3 + 5} = 6 \times 10^8[/tex]
That is, we multiply the factors, and for the bases of 10, we keep the bases and add the exponents. In a division, we would divide the factors, and for the base of 10, we keep the base and subtract the exponents.
That is, since the numbers have exponents, rules of exponents are used for both multiplication and division, and option b is correct.
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Calculate the perimeter of the rectangle in centimeters.
Lenght= 14cm
Width= 8cm
Answers
P=2(l+w)=2·(14+8)=44cm
A Web music store offers two versions of a popular song. The size of the standard version is 2.9 megabytes (MB). The size of the high-quality version is 4.1 MB. Yesterday, there were 1360 downloads of the song, for a total download size of 4532 MB. How many downloads of the high-quality version were there?
Answers
The number of standard version download and high-quality download is 870 and 490 respectively.
Number of downloads of the high-quality versionlet
Number of high-quality download = yNumber of standard version = xx + y = 1360
2.9x + 4.1y = 4532
From (1)
x = 1360 - y
Substitute x = 1360 - y into (2)
2.9x + 4.1y = 4532
2.9(1360 - y) + 4.1y = 4532
3944 - 2.9y + 4.1y = 4532
- 2.9y + 4.1y = 4532 - 3944
1.2y = 588
y = 588/1.2
y = 490
Substitute y = 490 into (1)
x + y = 1360
x + 490 = 1360
x = 1360 - 490
x = 870
So therefore, number of standard version download and high-quality download is 870 and 490 respectively.
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-3y+7y+4y^3-2y^2+6y^3-7y^3-5y
Answers
Community Gym charges a $60 membership fee and a $65 monthly fee. Workout Gym charges a $190 membership fee and a $55 monthly fee. After how many months will the total amount of money paid to both gyms be the same? What will the amount
Answers
Answer:
13 months$905Step-by-step explanation:
You want the cost and the number of months of membership such that the cost of both gyms is the same.
Total costThe total cost of x months of membership at each gym will be the sum of its initial fee and the product of the monthly fee and the number of months.
SetupThe cost at Community Gym is ...
c = 60 + 65x
The cost at Workout Gym is ...
w = 190 +55x
These costs will be the same when ...
c = w
60 +65x = 190 +55x
SolutionSubtracting 60+55x from both sides of the equation leaves ...
10x = 130
x = 13 . . . . . . divide by 10
The cost will be the same after 13 months.
That cost will be ...
60 +65(13) = 60 +845 = 905
The amount paid at each gym after 13 months will be $905.
What is the length of a rectangular holding pond with an area of 5 1/10 square miles and a width of 1/6 mile?
Answers
Simplify negative 3 and 4 over 5 minus 5 and 2 over 3.
Answers
Answer:
-9 7/15
Step-by-step explanation:
I took the test lol. Also if your in advanced you should know this!
Find the y-intercept, x- intercept and slope of the line with equation 8x +12y = 16.
(PLEASE EXPLAIN IN STEPS)
Answers
Answer juvhfVO"zohgvjozi nandish pro nbhvmno
Does 8÷10+7÷100 equal to 0.87
Answers
Answer:
Yes
Step-by-step explanation:
8÷10+7÷100=
8/10 + 7/100=
80/100 + 7/100= ==> make the denominators equal to each other
(80+7)/100=
87/100=0.87 √
Answer:
yes it does
Step-by-step explanation:
8÷10=0.8
7÷100=0.07
0.8+0.07=0.87
or the easy way ig
8÷10+7÷100=0.87
Charmaine invested her savings in two investment funds. The amount she invested in Fund A was 3 times as much as the amount she invested in Fund B. Fund A returned a 6% profit and Fund B returned a 15% profit. How much did she invest in Fund B, if the total profit from the two funds together was 1380?
Answers
Using a system of equations, it is found that she invested 318.71 into Fund B.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
For this problem, the variables are given as follows:
Variable x: Amount invested in Fund A.Variable y: Amount invested in Fund B.The amount she invested in Fund A was 3 times as much as the amount she invested in Fund B, hence:
x = 3y.
Fund A returned a 6% profit and Fund B returned a 15% profit, and the total profit was of 1380, hence:
1.06x + 1.15y = 1380.
We have that x = 3y, hence:
1.06(3y) + 1.15y = 1380.
4.33y = 1380
y = 1380/4.33
y = 318.71.
She invested 318.71 into Fund B.
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if AC=38 3/4,AB=6x, BC=8x+1/4
what’s the value of x?
Answers
Applying the segment addition postulate:
x = 2.75
AB = 6x = 6(2.75) = 16.5 units
BC = 8x + 1/4 = 8(2.75) + 1/4 = 22.25 units.
What is the Segment Addition Postulate?Based on the segment addition postulate, since B lies between points A and C on a line segment, then:
AB + BC = AC
AC = 38 3/4
AB = 6x
BC = 8x + 1/4
Substitute
6x + 8x + 1/4 = 38 3/4 [segment addition postulate]
14x + 1/4 = 155/4
14x = 155/4 - 1/4
14x = (155 - 1)/4
14x = 154/4
14x × 4 = 154
56x = 154
x = 154/56
x = 2.75
AB = 6x = 6(2.75) = 16.5 units
BC = 8x + 1/4 = 8(2.75) + 1/4 = 22.25 units.
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