Shawna wanted to boat across the river, but did not know how wide it was. She walked along the shore for 90 feet and sighted across the water to the point she wanted to go. The angle that the sight line made with the shoreline was 65°. What was the distance across the river?
The distance across the river, given the angle of the line of sight and the
distance along the shoreline is found using trigonometric ratios.
The distance across the river is approximately 193 feet.Reasons:
The distance along the the shore Shawna walked before sighting across the river = 90 feet
The angle made by the line of sight and the shoreline, θ = 65°
Required:
The distance across the river.
Solution:
Taking the initial location of Shawna to be the closest place to point she wanted to go across the river, we have;
The shortest distance across the river = A perpendicular line
Therefore, the following sides, form a right triangle;
The line of sight.The distance along the shoreline Shawna walked, andThe closest distance across the river.Where:
The line of sight = The hypotenuse side
The distance she walked = The adjacent side to angle 65° angle
The closest distance across the river = The opposite side to the 65° angle
By trigonometric ratio, we have;
[tex]\displaystyle tan(\theta) = \frac{Opposite \, side \, to\ angle}{Adjacent\, side \, to\, angle} = \mathbf{\frac{Distance \ across \ the \ river}{Distance \ along \ the \ shoreline}}[/tex]Which gives;
Opposite side to angle = tan(θ) × Adjacent side to angle
Therefore;
Distance across the river = tan(65°) × 90 feet ≈ 193.0 feet
The distance across the river is approximately 193 feetLearn more about trigonometric ratios here:
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Please answer this I am so bad at math
For triangle MNO, the statements that are true are m ∠ MNP < m ∠ ONP and MP< OP.
We are given a triangle MNO.
We are also given that:
m ∠ MNP = 38°
m ∠ ONP = 39°
This clearly means that:
m ∠ MNP < m ∠ ONP
Also, since m ∠ MNP < m ∠ ONP , the sides opposite to the angles will also follow the same relationship.
Side opposite to ∠ MNP is MP
and side opposite to ∠ ONP is OP
so, the relation will become:
MP < OP
Therefore, we get that, for triangle MNO, the statements that are true are m ∠ MNP < m ∠ ONP and MP< OP.
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The statements m MNP m ONP and MP < OP are true for triangle MNO.
A triangle MNO is presented to us.
Additionally, we learn that
m ∠ MNP = 38°
m ∠ ONP = 39°
This demonstrates that:
m, MNP, m, and ONP
The sides that are opposite to the angles will also adhere to the same relationship because m MNP m ONP.
MP is the side that faces MNP.
and OP is the side opposite to ONP.
hence, the relationship will be:
MP < OP
As a result, we understand that for triangle MNO, the assertions m MNP m ONP and MP OP are true.
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What is the solution to the following system 3x+3y+6z=9
Answer:
x=1 y=1 z=1
Step-by-step explanation:
3+3+3=9
and
3x+3y+3z=9
How i can answer this question?
Answer:
A and D
Step-by-step explanation:
[tex]20 r + 60t = 20(r+3t) = 4\cdot 5(r +3t)=4(5r +15t)[/tex]
How i can answer this question
Answer:
Your correct Awnsers are A and D
Max correctly starts solving the linear equation 1/2(x+8) = - 3 by writing x+8= - 6. Which of the following properties justifies what Max wrote?
1) The distributive property
2) The commutative property of addition
3) The addition property of equality
4) The multiplication property of equality
Can someone please take the time out of their day and help me with this question
[tex]\large\huge\green{\sf{Answer:-}}[/tex]
[tex] \red {\mathbb{ \underline { \tt By \: using \: Pythagoras \: theorm}}}[/tex]
[tex]h {}^{2} = p {}^{2} + b {}^{2} \\ x {}^{2} = (7 {}^{2} + 6 {}^{2} )ft {}^{2} \\ x {}^{2} = (49 +3 6)ft {}^{2} \\ x {}^{2} = 85 ft\\ x = \sqrt{85 } ft \\ [/tex]
the length of missing side= √85=9.2 ft
What is the unit of time (t) when calculating interest?
Answer:
t = time in decimal years; e.g., 6 months is calculated as 0.5 years. Divide your partial year number of months by 12 to get the decimal years.
Step-by-step explanation:
There are 81 calories in a 0.75 cup serving of chicken noodle soup. How many calories are in a 2 cup serving?
Answer:
162Step-by-step explanation:
There are 81 calories in a 0.75 cup serving of chicken noodle soup. How many calories are in a 2 cup serving?
0.75*2=2 cups
81*2=162
Answer:
x = 216
Step-by-step explanation:
[tex]\frac{81}{0.75}[/tex] = [tex]\frac{?}{2}[/tex]
I hope this helps!!
The students in Gwen's class got to choose between pizza and burgers for the celebration on
the last day of school. 28 students picked the pizza. If there are 35 students in all in Gwen's class, what percentage of the students picked the pizza?
Write your answer using a percent sign (%).
Answer:
80% of the class picked the pizza
Step-by-step explanation:
In order to find a percentage, you are supposed to divide the amount of how much someone has picked by the total amount (in this case pizza's). Here is how I got 80%,
28/35 = 0.8
0.8*100 = 80
So the answer is 80%
Mario started his homework at 3:30 he finished 25 minutes later what time did he finish his homework
Answer:3.55
Step-by-step explanation:
you add the time dude
A rectangular piece of metal is 25 in longer than it is wide. Squares with sides 5 in long are cut from the four corners and the flaps are folded upward
to form an open box. If the volume of the box is 2730 in3, what were the original dimensions of the piece of metal?
What is the original width? in
Answer:
Here you go
Step-by-step explanation:
24 original width
49 original length
is -54 colder than -127
Answer:
-127 is colder
Step-by-step explanation:
-54 is closer to 0 than -127 so -127 is colder
They are both negatives BUT! -127 is greater than -54 and the 0 is the begginging of frezing point
David makes a pizza with 8 slices of equal size . He covers 5 of the 8 slices with pepperoni. What percentage of the pizza is covered with pepperoni
Answer:
5/8 * 100 = 62.5 %
Brian has DVDs and CDs. The number of CDs he has can be modelled with the formula C = 2D + 11, where C represents the number of CDs and D represents the number DVDs. If he has 41 CDs, how many DVDs does he have?
Answer: 15 DVDs
Step-by-step explanation:
C = 2D + 11
41 = 2D + 11
2D = 30
D = 15 DVDs
The area of a rectangular pool is 5628 m^(2). If the width of the pool is 67m, what is its length?
Answer: 84 m
Step-by-step explanation:
To find area, you multiply the width by the length ( A = L x W). Here, it is asking for the length, giving the area of the pool and the width. With this information, you can inverse operation ( division) to find the length of the pool. So:
5628 / 67 = 84
This tells us that the length of the pool is 87 meters. To check this answer, multiply 67 and 84. If it's equivalent to 5628, the given area, then 84 is indeed the length of the pool.
67 x 84 = 5628.
Thus, the length of the pool is 84 m.
What is the common ratio between successive terms in the sequence?
Answer:
The common ratio of a geometric progression is calculated by dividing two consecutive terms and simplifying it to the simplest form. In the sequence, the ratio 1/3 is the same and is called the common ratio
Step-by-step explanation:
The common ratio of a geometric progression is calculated by dividing two consecutive terms and simplifying it to the simplest form. In the sequence, the ratio 1/3 is the same and is called the common ratio
1. Nathan bought a bicycle for $230 at an auction. He fixed it up and sold it at a 30% markup. How much did
Nathan sell the bike for?
Nathan bought a bicycle for $230 at an auction. Nathan sells the bike for $299 at a 30% markup.
What is the percentage?A percentage is a minimum number or ratio that is measured by a fraction of 100.
Nathan bought a bicycle for $230 at an auction. He fixed it up and sold it at a 30% markup.
So, the markup price, we get
30% of $230
= 30/100 x 230
= 3 x 23
= 69
Total selling price = 230 + 69
= 299
Thus, Nathan sells the bike for $299.
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what is 17/5 - 16/5 as an improper fraction
Answer: 1/5 is a proper fraction, it can not be written as a mixed or improper fraction
Step-by-step explanation:
17/5 - 16/5
1/5
How I can answer this question, NO LINKS, if you answer correctly I will give u brainliest!
[tex]\huge \bf༆ Answer ༄[/tex]
Let's solve this using unitary method ~
[tex] \sf3 \: seconds = 63 \: meters[/tex][tex] \sf1\: second= 63 \div 3 \: meters[/tex][tex] \sf1\: second= 21 \: meters[/tex][tex] \sf5\: seconds= 21 \times 5 \: meters[/tex][tex] \sf5\: seconds= 105 \: meters[/tex]Therefore , the ostrich will run 105 meters in 5 seconds.
3/5 of a number is 30. What’s the number?
Therefore, the number is 50.
Hoped this helped.
[tex]-BrainiacUser1357-[/tex]
SR1-2
Paula is standing on a bridge that is 110 above the water below. She throws a
pebble over the edge of the bridge, and it hits the top of a 24 foot high bridge
guard. The quadratic equation that models the path of the pebble is:
p(t) = –16t2 + 48t + 110
such that t is the time in seconds and p is the height of the pebble.
The time it will take the pebble to reach the maximum height is 1.5secs
Given the quadratic equation that models the path of the pebble expressed as p(t) = –16t^2 + 48t + 110
We can calculate the time taken by the pebble to reach the maximum height.
At maximum height, the velocity of the pebble is zero i.e. p'(t) = 0
p'(t) = -32t + 48
0 = -32t + 48
32t = 48
t = 48/32
t = 1.5secs
Hence the time it will take the pebble to reach the maximum height is 1.5secs
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Evaluate the expression. 5 x (-6 / -1 + -10)
Answer:
-20
Step-by-step explanation:
PEMDAS
Parentheses -> Exponents -> Multiplication -> Division -> Addition -> Subtraction
1.) First, we can rewrite this equation to make it easier to understand
5 x (-6 / -1 + - 10)
5(-6 / -1 - 10)
2.) Begin by dividing inside the parentheses
5(-6 / -1 - 10)
5(6 - 10)
3.) Solve
5(6 - 10)
5(-4)
-20
or
5(6 - 10)
5(6) 5(-10)
30 - 50
-20
Therefore, the expression equals -20.
a locker room contains 21 books. you select 7 books at random. how many different sets of books can you select
Answer:
14
Step-by-step explanation:
3x7=21 you take away 7 books you would have 14 left or 7x2
0.517 converted into a percent
Answer:
51.7%
Step-by-step explanation:
Because percent is out of 100, you multiply 0.517 by 100 and get 51.7, which is your percent.
four water bottles can hold 8 gallons of water how much water can ten big water bottles hold
Answer:
20 gallons of water.
Step-by-step explanation:
4 water bottles = 8 gallons
1 water bottle = 2 gallons
X = Number of Water bottles
N = Gallons Per Water Bottle
X * N
10 * 2
20
RS= 6x-8
UV= 4x+2
write and solve an equation to find the value of x (show work)
What is the length of RS
What is the length of UV
Answer:
The length of RS is 22
The length of UV is 22
Step-by-step explanation:
6x-8. ---------- equation (i)
4x+2 ------------ equation (ii)
Now,
equating equation i and ii, we get
6x-8 = 4x+2
or, 6x-4x = 2+8
or, 2x = 10
or, x = 10/2
.°. x = 5
Then,
length of RS = 6x-8
= 6×5-8
= 30-8
= 22
Again
length of UV = 4x+2
= 4×5+2
= 20+2
= 22
Which statement is true when looking at a black ball?
Answer:
Only the primary color wavelengths are being absorbed by the ball.
Answer:Which statement is true when looking at a black ball?
Group of answer choices
Only the primary color wavelengths are being reflected by the ball.
All color wavelengths are being reflected by the ball.
All color wavelengths are being absorbed by the ball.
Only the primary color wavelengths are being absorbed by the ball.
Step-by-step explanation:
x^2=x+2
Please solve by factoring
But I’ll take anything honestly
Answer:
Step-by-step explanation:
[tex]\sf x^2=x+2[/tex]
Subtract x+2 from both sides of the equation:
[tex]\sf x^2-(x+2)=x+2-(x+2)[/tex]
[tex]\sf x2-x-2=0[/tex]
Now, factor left side of equation:
[tex]\sf (x+1)(x-2)=0[/tex]
Set the factors equal to zero:
[tex]\sf x+1=0[/tex] [tex]\sf x-2=0[/tex]
[tex]\boxed{\sf x=-1}[/tex] [tex]\boxed{\sf x=2}[/tex]
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I have to mach the special of angles