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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Astronomers often measure large distances using astronomical units (AU) where 1 AU is the average distance from Earth to the Sun. In the image, drepresents the distance from a star to the Sun. Using a technique called "stellar parallax," astronomers determined 0 is 0.00001389 degrees.
write an expression to calculate d for any star
By calculating the distance of a star to the Sun, astronomers can calculate the distance from Earth to the star.
[tex]\displaystyle \mathrm{The \ \mathbf{expression} \ to \ calculate \ \mathit{d} \ for \ any \ \mathbf{star} \ is; \ \underline{d \ is \ \frac{1 \, AU}{tan(\theta)}}}[/tex]Reasons
The given parameters are;
The distance from the star to the Sun = d
The angle formed by the ray to the Sun and the ray to Earth from the star, θ = 0.00001389 degrees
The average distance from Earth to the Sun = 1 AU
By trigonometric ratios, we have;
[tex]\displaystyle tan(\theta) = \mathbf{\frac{Opposite}{Adjacent}}[/tex]
Therefore;
[tex]\displaystyle tan(\theta) = \frac{1}{d}[/tex]
The expression to calculate for d for any star is therefore;
[tex]\displaystyle \underline{ d \ is \ \frac{1 \, AU}{tan(\theta) }}[/tex]The angle given for θ for the referenced star is θ = 0.00001389
Therefore;
[tex]\displaystyle d = \frac{1 \, AU}{tan(0.00001389^{\circ}) } \approx 4,124,966.13 \, AU[/tex]
Learn more about trigonometric ratio here:
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Which expression represents the expanded version of the expression below?
4x(3x+7)
Answer:
X is just a variable.
Step-by-step explanation:
Sarah is 2 inches taller than the quotient of billy’s height and 5. Let b represent Billy’s height. write an expression that represents Sarah’s height
So, this has many steps to it.
This part is to let us know what symbols we should use (VERY IMPORTANT)
1. Since you know that Sarah is two inches taller, we would use a + sigh in our expression
2.Then you look for the key word which is quotient and that means to divide
All of our symbols are in now. Time for the next step
This part us know what we are dividing and adding.
Now 2+ b/5
Answer:
[tex]2 + \frac{b}{5} [/tex]
Hope you could get an idea from here.
Doubt clarification - use comment section.
Can someone please help !!
Can someone help me with this one I would appreciate it very much!!
Answer:
12.5 pounds
Step-by-step explanation:
16 ounces = 1 pound
200 ounces = 1 × 200/16 = 12.5 pounds
Please show any steps you used to solve the equation!
Solve the equation [tex]sec(theta)=2 \\0\leq theta\ \textless \ 2\pi[/tex]
I'll mark brainliest if correct!
sec(θ) = 2
By definition of secant,
cos(θ) = 1/2
Solve for θ :
θ = arccos(1/2) + 2nπ or θ = -arccos(1/2) + 2nπ
(where n is any integer)
θ = π/3 + 2nπ or θ = -π/3 + 2nπ
We get two solutions in the interval 0 ≤ θ < 2π :
θ = π/3 or θ = 5π/3
i need help with this problem, but i don't want someone to just give me the answer. i need it to be taught step-by-step to me because for some reason i can't understand how everyone tells me to do it. i need to learn this as I've been on this one test for the past 2 weeks. I've been trying to find a tutor or something that will actually help me the way i need to be helped. so please, just give me a simple answer that will help me with the 3 other questions after it.
the lesson name is called solving real world systems of equations via elimination.
here is the question:
jared bought 7 cans of paint. a can of red paint costs 3.75. a can of black paint costs 2.75. jared spent 22.25 in all. how many cans of black (b) and how many cans of red (r) did he buy?
r+b=7
3.75 + 2.75 = 22.25
this is a lesson in 8th grade math.
Answer:
Hallo, I will help you with the problem T^T
Step-by-step explanation:
3.75r + 2.75b = 22.25
3.75r = The amount a red can costs, MULTIPLIED BY the amount of red cans they bought!
2.75b = The amount a black can costs, MULTIPLIED BY the amount of black cans they bought!
So this means that they bought:
3 cans of red paint.
And 4 cans of black paint.
Now you may be thinking, how do you know?
If you multiply the COST 3.75, by 3 cans of red paint, you get 11.25
And then if you multiply the COST of the black paint (The cost for a can of black paint is 2.75) multiply that by 4, you get 11 :0
So add 11 + 11.25 and you get 22.25 :]
Comment if you have any questions, no matter how insignificant you think they may be, I will help you :]
move the numbers to the blanks to order them from least to greatest value.
0.1 -9/8 4 |-5/6| -0.78
Answer:
-9/8, -5/6 -0.78, 0.1, 4
Step-by-step explanation:
since they're negative, it makes them look bigger than others but they're not. I think I got it right. hope I could help!
All 150 eighth grade students at a local middle school were asked how many hours they studied during the week. Each row of the table represents one sample from the population. Find the mean Of each sample
Which row has the greatest mean?
1
2
3
4
The answer is 2...
It's row 2
Answer:
Row 2 (B)
Step-by-step explanation:
We can find out the answer just simply by adding up each of the rows seperately and finding out which one has the highest value, since all of the rows have the same amount of spaces that you need to divide by. Row 2 has the highest value with 23.
Which number sentence is not true?
101 < 100
101 = 0
|-100[< 101
1-100] > [0]
The first one & the second one
Answer:
Both first and second one are not true.
Step-by-step explanation:
The first one translates to "101 is less than 100". This statement is false.
Second one translates to " 101 is equal to 0". Obviously, this isn't true.
Hope this helps! Brainliest would be appreciated!!
Victoria made some chocolate pudding. For every 2 cups of chocolate, she added 5 cups of milk. The ratio of chocolate to milk in Victoria's chocolate pudding is ____.??
A. 2
B. 2 over 5
C. 5 over 2
Answer:
B. 2 Over 5
Step-by-step explanation:
The answer would be B because 2 cups of chocolate to 5 cups of milk the ratio would be 2:5 and you can't put 5:2 because it's asking the ratio of chocolate milk to chocolate pudding not chocolate pudding to chocolate milk.
pleaseee help mee tysm
Answer:
the answer is c
Step-by-step explanation:
Guys this is the last question for the day please help me out.
Answer:
So it's 350 - D - B.
And 350 - A - D.
Hope that helped?
Enter the value of x + 27.
х
1
o
1x + 27)
67°
1) Commutative Property of addition and multiplication: (Commutative, x; Commutative, +) ... 24) -6 + 10 = 4 25) - 8 - 12 = 20 26) -8 +6= -2 27) -7 - 5= -12.
What is the value of the digit in the hundred thousands place?
61,889,248
A. 60,000,000
B. 800,000
c. 100,000
D. 80,000
Answer:
C
Step-by-step explanation:
12>-2(y-4) solve the inequality
[tex]12>-2(y-4)\\\\\implies -\dfrac{12}2 <y-4~~~;[\text{Dividing by a negative number, so reverse the inequality.}]\\\\\implies -6<y-4\\\\\implies -6+4<y\\\\\implies -2<y\\\\\implies y>-2\\\\\text{Interval,}~ (-2,\infty)[/tex]
someone who is good a math please answer this today asap will give brainliest
The length of a rectangle is 4 more than its width. The perimeter is 40 feet.
What are the length and width of the rectangle?
Hint: The perimeter of a rectangle is given by the formula P = 2l + 2w.
The width is 8 ft and the length is 12 ft.
The width is 13 ft and the length is 7 ft.
The width is 7 ft and the length is 13 ft.
The width is 12 ft and the length is 8 ft.
Answer:
the Answer is C
Step-by-step explanation:
We are given –
The perimeter is 40 feet and the length of a rectangle is 4 more than its width. Let the length be " l " and the width be " w ".As we know that –
Rectangle is a four sided polygonal figure, i.e, a quadrilateral, in which the opposite sides are of equal length and are parallel. Also its diagonals bisects each other.[tex].\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \huge \boxed{ \bf{ \: \: \: \: \: \: }} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tiny\sf{A \: rectangle} [/tex]
Perimeter = 2 (l + w) unitsArea = lb sq.unitsAccording to the question –
Width = w feet Length = w+4 feet[tex]\qquad[/tex][tex] \pink{\bf \longrightarrow Perimeter _{(Rectangular) } = 2( Length + Breadth) }[/tex]
[tex]\qquad[/tex][tex] \bf \longrightarrow Perimeter _{(Rectangular) } = 2 (l + w)[/tex]
[tex]\qquad[/tex][tex] \sf \longrightarrow 40 = 2( w+ 4 +w)[/tex]
[tex]\qquad[/tex][tex] \sf \longrightarrow 40 = 2 ( 2w +4)[/tex]
[tex]\qquad[/tex][tex] \sf \longrightarrow 40 = 4w +8[/tex]
[tex]\qquad[/tex][tex] \sf \longrightarrow 4w = 40-8[/tex]
[tex]\qquad[/tex][tex] \sf \longrightarrow 4w = 32[/tex]
[tex]\qquad[/tex][tex]\sf \longrightarrow w = \cancel{\dfrac{32}{4}}[/tex]
[tex]\qquad[/tex][tex] \pink{\bf\longrightarrow w = 8 \:feet}[/tex]
Width of perimeter is = 8 feetSubstituting the value of w–
[tex]\qquad[/tex][tex]\purple{\bf \longrightarrow Length\: of \: rectangle = (w+4)\: feet }[/tex]
[tex]\qquad[/tex][tex]\bf \longrightarrow Length\: of \: rectangle = 8+ 4 \:feet [/tex]
[tex]\qquad[/tex][tex]\purple{\bf \longrightarrow Length\: of \: rectangle = 12\: feet}[/tex]
Henceforth, The width is 8 ft and the length is 12 ft.__________________________________________
Solve the inequality.
D
— < -4
-5
A vegetable cart sells potatoes for $0.24 and tomatoes for $0.76. Fred bought 12 vegetables in total. He only bought potatoes and tomatoes. If Fred paid $6.52 total, how many potatoes did he buy?
Let potatoes be a and tomatoes be b
[tex]\\ \sf\longmapsto a+b=12---(1)[/tex]
[tex]\\ \sf\longmapsto 0.24a+0.76b=6.52[/tex]
Simplify 2nd one
[tex]\\ \sf\longmapsto 0.06a+0.19b=1.63[/tex]--(2)
Solving both equations
b=7a=12-7=5will give brainliest
Answer: x > − 4
Step-by-step explanation: Divide each term in − 4 x < 16 by − 4 and simplify.
(Try to solve b. and c. with only these resources and if you still need help, let me know.)
The measure of angle b = 80° and the measure of angle c = 40°. the measure of angle a equals....?
angle a = 180°-80°-40°=60°
plsss help mee i donot now the answer
Activity 1: Identifying Hypothesis and Conclusion Directions: Identify the hypothesis and the conclusion for each of the following statements.
1. If you live in Manila, then you live in the Philippines.
2. If a triangle is a right triangle, then one of its interior angle is a 90-degree angle.
3. A square is not a triangle.
4. An even number is divisible by 2.
5. The measure of an acute angle is less than 90.
Answer:
1. If you live in Manila(hypothesis) then you live in the Philippines ( conclusion)
2. If a triangle is a right triangle (hypothesis), then one of its interior angle is a 90-degree angle ( conclusion)
3. A square is not a triangle (conclusion)
4. An even number is divisible by 2. (conclusion)
5. The measure of an acute angle is less than 90. (conclusion)
Solve for a
1/12 a +21 = 25
Hope This Helped!
Step-by-step explanation:
First off we need to take the whole equation and multiply it so that we can get rid of the fractioned exponent. The number we would use is 12, giving us the new equation: a + 252 = 300. We then can subtract 252 from both sides of the equation, to get the exponent by itself and intentionally create an answer. This would be: a + 252 = 300,-252=48 or a = 48
We are left with A being equal to 48.
[tex]\dfrac 1{12} \cdot a +21 = 25\\\\\\\implies \dfrac a{12} = 25-21\\\\\\\implies \dfrac a{12} =4 \\\\\\\implies a = (12)(4) = 48[/tex]
I cannot figure this out. Any help would be appreciated.
-4x -2 + 3x - 10 How many terms are there? SIMPLIFY. What is the coefficient of x?
Answer:
Number of coefficients of x: 2 coefficients (-4 and 3)
Number of terms: They're 4 terms. (-4x, -2, + 3x, and -10)
Simplified: - x - 12
Step-by-step explanation:
1) Subtract the numbers.
-4x - 12 + 3x
2) Combine like terms.
- x - 12
please help and show work
Answer:
x = 8
Step-by-step explanation:
∆D = ∆F
40°+2∆D = 180°
2∆D = 140
∆D = 70°
11x-18 = 70
11x = 88
x = 88/11
x = 8
What is the pre-image of vertex A' if the image shown on the graph was created by a reflection across the y-axis?
(–8, –6)
(–6, 8)
(8, 6)
(6, –8)
Answer:
The answer is B. (-6,8) !
Step-by-step explanation:
help me with this pls
Answer:
Yes they both = 125
Step-by-step explanation:
How can I Graph
-7x= -105
Answer:
see explanation
Step-by-step explanation:
- 7x = - 105 ( divide both sides by - 7 )
x = 15
A line with equation x = c is a vertical line parallel to the y- axis passing through all points with an x- coordinate of c
Thus x = 15 is a vertical line passing through all points with an x- coordinate of 15
Plot (15, 0 ) , (15, 3 ) and (15, - 3) and join a straight line through them for graph
The shortest route from London to Swansea is 180 miles. A lorry is expected to take 4.5 hours to travel this route. The lorry actually travels by a different route which increases the distance by 15%, but it still arrives in 4.5 hours. By how many more mph than the expected speed does the lorry travel?
Answer:
6mph
Step-by-step explanation:
180/4.5=40
180 × (1+15%)=207
207/4.5=46
46-40=6