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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Which is further 104km or 70 miles ?
Answer:
104 km is further than 70 miles.
Step-by-step explanation:
Using the conversion table, we can tell that 1 km = 0.62 miles. Now, let's see which is bigger.
=> 104 km ☐ 0.62 miles=> 0.62 x 104 ☐ 0.62 x 70 => 104 ☐ 70 => 104 > 70Conclusion:
We can clearly see that 104 km is further than 70 miles.
Hoped this helped.
[tex]BrainiacUser1357[/tex]
numbers that equal to 39
Answer:
1 , 3 , 13 , and 39
Step-by-step explanation:
1 x 39 =39
3 x 13 = 39
13 x 3 = 39
39 x 1 =39
Answer:
Step-by-step explanation:
The product 3*13 equals 39. This is in addition to the identity 1*39 = 39.
calculate the simple interest and compound interest on ₹5000 for 2 years at 10% per annum. how much more is the compound interest then the simple interest?
Answer:
Simple: 6000
Compound: 6050
Difference: 50
Step-by-step explanation:
Simple interest formula: A = P(1+rt), where A = final amount, P = initial amount, r = rate, and t = time. Plug our values in to get
A = 5000(1+10% * 2)
convert 10% to a decimal by dividing by 100 and plug that in
10% = 0.1
5000(1+0.1*2) = 5000(1.2) = A = 6000
Compound interest formula: A = P(1+r)^t
Plug our values in
5000(1+0.1)^2 = 6050
Difference = 6050 - 6000 = 50
The cost of a jacket increased from $60.00 to $71.40. What is the percentage increase of the cost of the jacket?
Answer:
19%
Step-by-step explanation:
Percentage increase = ( (final value - original value) / original value ) x 100
= ( ($71.40 - $60.00) / $60.00 ) x 100
= 19%
[tex]71.40 - 60 = 11.40[/tex]
to find the increase of percentage, divide the amount of increasing price with intial price and multiply with 100%
[tex] \frac{11.40}{60} \times 100\% = 19\%[/tex]
so the cost of jacket has increased 19%
Simplify using the laws of exponents.
[2⁴/2³]⁵
To know this answer we need to know how to solve it. Many people skip this part which makes their answer wrong.
It is asking us to simplify it using exponents.
Exponents are these little numbers beside a big number Telling it how much you multiply it by.
EXAMPLES
2^3 is just 2x2x2
2^4 is just 2x2x2x2
Notice the pattern? I hope so!
Now 2 to the power of 4 is 16. Our new equation looks like this
{16/2^3}^5.
Now 2 to the power of 3 is 8.
So, our new equation is
{16/8}^5
In which you get 2^5 which is just 2x2x2x2x2
And you get 32 as the final answer
I hope this helped and if you have questions just tell me!!
Jim has 44 nickels and dimes totaling $2.95. How many nickels does he have?
29 Nickels
15 Dimes
Hope this is helpful!
Expand the following expressions and write in standard form. Show your work.
a) (3x + 2)(1 - 4x)
b) (x - 5)^2(2x + 7)
Please help!!!!
3x(1-4x)+2(1-4x)
3x-12x²+2-8x
-5x-12x²+2
The graph below shows the water level in a tank being drained at a
constant rate. What does the Y-intercept of the graph represent? *
Tank Water Level
16
14
12
10
(1, 10)
Height (in.)
(4,4)
01234567
Time (h)
O The initial height of the water before any water drained out.
The number of hours it takes to completely empty the tank of water
O The number of hours needed to drain 1 inch of water from the tank
The number of inches that the tank can hold
Answer:
the initial height of water.
Step-by-step explanation:
when time equals zero, no water has been drained.
the volume of the tank is unknown however the volume in the tank is 12 at time zero
PLEASE HELP ME!!
The pie chart below showshow we annual budget for the passasted Manufacturers Company is divided by department. Use this chant to answer the
(a) Which department accounts for approximately one-third of
the annual budget
Support
Sales
Research
Engineering
Support
Media
Marketing
(b) Appraimately what percentage of the and botinet is
used for Sales and Research combined
Write your answer as a multiple of 10%- that is, 10%, 20%, 30%,
(C) 16% of the annual budget is used for Mariesting,
approximately what percentage is used for Support
2%
09%
18%
300%
Answer:
a) Research
b) 50%
c) 18% (as marked)
Step-by-step explanation:
a)About 1/3 of the chart is covered by the segment marked Research.
__
b)Sales and Research together cover almost half the chart, about 50%.
__
c)The size of the Support sector is about 3 times the size of the Marketing sector. This lets us estimate Support at about 18% of the budget.
Find the slope of the line going through the pair of points: (11, 7), (-9, 8)
20
O-20
0 - 20
O 20
Answer:
1/-20 or -0.05
Step-by-step explanation:
Q6 (i) please i don’t know what i’m doing wrong
Answer:
x = 4
Step-by-step explanation:
Square both sides
x+5 = 25-10sqrt(x)+x
20 = 10sqrt(x)
sqrt(x) = 2
Square both sides again
x=4
Verify sol
x = 4
John is 9 times as heavy as his dog.
Determine which of the statement's below is true.
O John weighs 900% more than his dog.
O John weighs 800% more than his dog.
O John's dog weighs 800% less than John.
sources
O John weight is 800% of his dog's weight.
Answer:
John weighs 900% more than his dog
Step-by-step explanation:
The weight of John is 8x more than his dog.
Given that, John is 9 times as heavy as his dog.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Let weight of John's dog be x, then weight of John will be 9x.
Difference of weight = 9x-x
= 8x
Therefore, the weight of John is 8x more than his dog.
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a
The eighth-grade class has a total of 162 students. The students need to be
divided evenly into homerooms. There needs to be at least 20 students in
each homeroom. List all the possible combinations. Which combination
makes the most sense? Explain.
Answer:
162/20 Would be your answer, however, it wouldn't make sense as you can not switch students into decimals. Therefore, you could make 7 classes of 20, and one of 22, and 6 classes of 20, and two of 21. Therefore, there are two combinations that are possible.
Step-by-step explanation:
Refer to the answer.
Answer:
56
Step-by-step explanation:
Write the name of a polynomial (using the degree) with the sequence of the
outputs: (5,2,-1,-4, ...}*
Type ONE word
Answer:
pentagon
Step-by-step explanation:
5 degree angle
Plz help me with this
i need help on this- It says on the top Which Division equation IS represented by the drawing below-°
Answer:
D im pretty sure
Step-by-step explanation:
If each line is 20 x 3 = 60 12 dots 60 + 12 = 72 divided by 3 circles = 24
What is the equation of the line that passes through the point (-1, -7) and has a
slope of 2?
Answer:
y = 2x - 5
Explanation:
Since the slope is given as 2, we can substitute this into the equation:
y = 2x+b
Now, we can manipulate the point (-1,-7) to be in the form of a y-intercept - (0, y).
Note that a slope of 2 = 2/1, which means the rise = 2(which is added to the y) and run = 1(which is added to the x).
Adding this to our point of (-1,-7), we get:
((-1+1),(-7+2)) = (0, -5)
Therefore -5 is our y-intercept.
Now, substituting -5 into our equation, we get:
y = 2x + -5
Answer:
y=2x-5
Step-by-step explanation:
The slope-intercept form of an equation looks like y=mx+b. Where m is the slope and b is the y-intercept. The slope is already given to us, so m is 2.
To find b use the equation [tex]b=y_1-m*x_1[/tex]. So, to find the y-intercept use b=-7-(2*-1). This equals b=-5.
So, plug in the values to get the final equation y=2x-5.
How many real roots does the quadratic function h (x) = 2x2 – 3x + 6 have?
Iqbal and Sachin have bookshelves of the same size and holding books of the same sizes. Iqbal's shelf is 7/8 full and Sachin's shelf is 12/15 full. If 351 more books of the same size are distributed among them, then they can fill their shelves completely. How many books does Sachin have now?
a)
864
b)
865
c)
800
d)
850
Answer:
540 books
Step-by-step explanation:
It is given that Iqbal's shelf is 7/8 full ..
→ That Means we can say that, iqbal's shelf is (1 - 7/8) = 1/8 is Empty .....
Similarly,
Sachin's shelf is 12/15 full.
→ That Means we can say that, sachin's shelf is (1 - 12/15) = 3/15 is Empty.....
→ Both total Empty = (1/8 + 3/15)
Taking LCM of denominator ,
→ (15+24 /120)
→ 39/120
→ 13/40 part is Empty in both .
Now, it has been said that, when 351 more books are distributed among them , both shelves filled completely .
So, we can say that :----
→ 13/40 part ---------------- 351
→ 1 part ---------------------- 351*40/13 = 1080 = Total Books in Both Selves .
__________________
Now, since bookshelves of the same size and holding books of the same sizes ,,
→ Both have Books in Each = 1080/2 = 540 books .
What is the coefficient of the term x°ys in the
expansion of the binomial expression
(2x - y)8?
Answer:
if it is (2x-y)8
then it is 16x - 8y
[tex]x^0[/tex]y = 1.y = y
so the co efficient of y is -8
Step-by-step explanation:
A moneylender’s income decreased by $60 When the rate of interest dropped from 8% per annum to 7 3/4 % per annum . What was his principal?
Answer:
$24,000
Step-by-step explanation:
The difference for principal amount P is ...
(8% × P) - (7 3/4% × P) = $60
0.0025P = $60
P = $24,000 . . . . . multiply by 400
His principal was $24,000.
Does the point (4, 8) satisfy the equation y = 2x?
Answer:
Yes
Step-by-step explanation:
You can answer this question by putting in the x-value [the 4 in (4, 8)] in for the x variable to see if you get the y-value [the 8 in (4, 8)] as the solution.
y=2(4)
y=8
Since 8 was the answer then yes, (4, 8) satisfies the equation y = 2x.
This is for the real ones- find the missing side x. Giving brainliest.
Answer: The answer is X equals 10 2/3.
Explanation: This is a proportion. We see that the right rectangle when turned to the right is proportional to the left rectangle. On the left rectangle, the smaller side is 6 ft, and the larger side is 16 ft. On the right rectangle, the smaller side is 4 ft. 6 ÷ 1.5 = 4, therefore 16 ÷ 1.5 = 10 2/3.
if Sophia took a bath at 9:36 and finish at 10:30 how much time did she use in taking a bath
Answer:
54 minutes
Step-by-step explanation:
1) There are 60 minutes in an hour. So, you can do 60-36 to find the first value. (24)
2) Add 24 minutes to 30 and get 54 minutes.
2.4x-9.1x+12.5= -39.44
Solve for x
Answer:
x= 2597/335
Step-by-step explanation:
collect like terms
2.4x-9.1x= -6.7x
-39.44-12.5 = -51.94
-6.7x=-51.94
divide both sides by -6.7
x= 2597/335
This is a true or false question. (Question in the photo)
Answer:
Step-by-step explanation: The answer is False.
Answer:
True my mom helped
Step-by-step explanation:
that's all I know
P l e a s e NO LINKS!
Which word has reflectional symmetry across a horizontal line?
A. BOOK
B. LOOK
C. NOOK
D. ROOK
Answer:
A BOOK
Step-by-step explanation:
pretty sure its that
The word BOOK shows a reflection symmetry across a horizontal line.
Hence, option (A) is correct.
What is reflection?Reflection is basically a mirror image of the shape, in which the image of a given figure changes accordingly to a given line or axis.
Solve with the help of options,
(A)
BOOK
To find the reflection across a horizontal line,
When word B reflected over horizontal line, it is symmetrical
Word O is symmetrical.
And K is also symmetrical across a horizontal line.
Therefore, BOOK is a reflection symmetry across a horizontal line.
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x over 2 +2= 15 two step equations
Answer:
[tex]\boxed{\boxed{\sf x=84}}[/tex]
Step-by-step explanation:
[tex]\sf \cfrac{x}{6} +2=16[/tex]
Multiply both sides of the equation by 6:
[tex]\sf x+12=96[/tex]
Subtract 12 from both sides:
[tex]\sf x=96-12[/tex]
Subtract 12 from 96:
[tex]\sf x=84[/tex]
_________________________________
Answer:
[tex] \sf \: \longmapsto\frac{x}{6} + 2 = 16[/tex]
[tex]\sf \: \longmapsto\frac{x}{6} = 16 - 2[/tex]
[tex]\sf \: \longmapsto \frac{x}{6} = 14[/tex]
[tex]\sf \: \longmapsto \: x = 14 \times 6[/tex]
[tex]\sf \: \longmapsto \: x = 84[/tex]
Step-by-step explanation:
[tex]\fbox {\fbox {\fbox {\fbox{ \pink{HeavenMistress}}}}}[/tex]
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