To find the length ab of a small lake, a surrounding veyor measured angle acb to 96, ac to be 91 yards, and bc to be 71 yards. what is the approximate length of the lake?
Answers
c² = a² + b² − 2ab cos(C)
Applying this in our problem, we get:
AB²= 71²+91²- 2x91x71 cos96
AB²=14627.7 yard²
AB=121 yard
Related Questions
What is the length of an arc cut off by an angle of 3 radians on a circle of radius 8 inches?
Answers
s = 8 × 3 = 24 inches
They traveled 200 kilometers in total, and they biked 40 kilometers more than they were bussed. how many kilometers did they travele by bike
Answers
So...
x + (x+40) = 200
2 x = 160
1 x = 80
200 - 80 = 120km by bike.
What value of c makes the trinomial below a perfect square x2 + 7x + c?
Answers
x² + 7x + c
Group terms that contain the same variable
(x² + 7x )+ c
Complete the square. Remember to balance the equation
(x² + 7x+3.5² )+ c-3.5²
Rewrite as perfect squares
(x+3.5)²+ c-3.5²so
c-3.5² must be zero
c-3.5²=0------- c=3.5²------> c=12.25
the answer is
the value of c must be 12.25
Answer:49/4
Step-by-step explanation:
For which angle is secant undefined?
30°
45°
180°
270°
Answers
The secant is undefined at angle values that represent 1/4 and 3/4 of a full circle. At these angles, the triangle geometrically vanishes into a simple line segment on the Y axis. The value of the triangle's adjacent side is zero and division by zero is undefined.
Answer:
the answer is 180 degrees
Step-by-step explanation:
i used my head and my google maths
PLLLLLLZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Find the value of n.
Answers
How does the volume of an oblique cylinder change if the radius is reduced to 2/9 of its original size and the height is quadrupled?
A. V=2/81pir^2h
B. V=16/81pir^2h
C. V=4/9pir^2h
D. V=16/9pir^2h
Answers
New volume=(old volume)×(4×2/9×2/9)
simplifying the above we get:
New volume=(old volume)×16/81
Thus the new volume is 16/81 times the old volume
old volume=πr²h
Hence:
Answer:16/81πr²h
Haley sings for $1,000 an hour. Her rate increases by 50% after midnight. If she sings one
night from 8:30 pm until 1:00 am, how much should she be paid?
a) $4500 b) $5000 c) $5500 d) $6000
Answers
WILL VOTE BRAINIEST IF CORRECT(must be next few minutes): The formula for the area of circle A is Area=πr2 . Sector CAB is a fraction of circle A. In degrees, the fraction is θ/360∘ . In radians, the fraction is _____. Inserting this fraction into the formula for the area of a circle, and then simplifying, results in the formula _____.
(image attached)
choices: 2pi0, 0pi, 0/2pi, area=0r^2, area= 2pi0r^2, area= 0/2r^2
Answers
The fraction of the sector of a circle in radians is (θπ/180). Substituting this fraction into the formula for the area of a circle, and simplifying, results in the formula for the area of the sector being A = (θπ/360) * r^2.
Explanation:In a circle, the angle in degrees is often converted to radians for calculations. A full circle is equivalent to 360 degrees or 2π radians. Therefore, if the sector angle is θ degrees, then in radians, the equivalent is (θ/360) * 2π = θπ/180.
Inserting this into the formula for the area of a circle, which is A = πr2, the area A of the sector becomes a fraction of the full circle's area, which is calculated as follows: (θ/360) * A = (θ/360) * πr2 = (θπ/180) * r2. Simplifying this results in the formula A = (θπ/360) * r2.
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For a sector in a circle, the fraction is θ/2π in radians. After substituting this into the formula for circle's area, we get the area of sector as Area = (θr²)/2.
Explanation:The fraction in radians for a sector in a circle is θ/2π, because there are 2π radians in a whole circle. As the formula for the area of circle A is Area=πr², when we insert this fraction, which represents the proportion of the circle that Sector CAB occupies, we get the formula for the area of a sector: Area= (θ/2π) * πr². This simplifies to Area= (θr²)/2, as the π's cancel out. This formula says that the area of a sector is proportionate to its central angle and the square of the radius of the circle.
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Divide 2y2 + 8 by 2y + 4. Which expression represents the quotient and remainder?
Answers
Final answer:
To divide 2y² + 8 by 2y + 4, use long division to find the quotient and remainder.
Explanation:
To divide 2y² + 8 by 2y + 4, we can use long division. Here are the steps:
Divide the first term of the dividend by the first term of the divisor, which gives us y.
Multiply the entire divisor by y to get 2y² + 4y.
Subtract 2y² + 4y from the dividend 2y² + 8 to get 4.
Next, divide 4 by 2y + 4, which gives us 2.
Finally, we have a remainder of 0.
Therefore, the quotient is y + 2 and the remainder is 0.
Given that f(x) = x2 − 4x − 3 and g(x) = the quantity of x plus three, over four, solve for f(g(x)) when x = 9.
−6
3
6
9
Answers
[tex] f(x)=x^{2} -4x-3[/tex]
[tex]g(x)=\frac{x+3}{4}[/tex]
So we find
[tex]f(g(x))=f(g(9))=(\frac{9+3}{4})^2 - 4(\frac{9+3}{4})-3[/tex]
[tex] =3^2 - 4(3)-3 [/tex]
[tex]= 9-12-3=-6[/tex]
Now we want to find the solution when x is 9 so we plug in a 9 whenever we see an x
Final answer:
The solution to f(g(x)) when x = 9 is -6.
Explanation:
In mathematics, a function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the codomain), where each input is related to exactly one output.
Given:
f(x) = x2 - 4x - 3, g(x) = (x + 3) / 4
To find f(g(x)) when x = 9:
Calculate g(9): Substitute x = 9 into g(x) to get (9 + 3) / 4 = 12 / 4 = 3Substitute g(9) into f(x): Substitute g(9) = 3 into f(x) to get f(3) = 32 - 4(3) - 3 = 9 - 12 - 3 = -6Therefore, f(g(x)) when x = 9 is -6.
Rewrite the expression log(3x) as an equivalent logarithmic expression using only addition.
Answers
Sharon wants to know the difference between the average amount she stacked and the average amount Diane stacked. Which operation would she use to find the difference?
Answers
Hope this helped :D
Multiply. 0.35 × 0.003 =
Answers
Answer:
0.00105
Step-by-step explanation:
Which is the correct form of the quadratic formula? A) x = b ± b2 - 4ac a B) x = b ± b2 - 4ac 2a C) x = - b ± b2 - 4ac a D) x = - b ± b2 - 4ac 2a
Answers
The quadratic formula is
[tex]x = \frac{-b +- \sqrt{ b^{2}-4ac } }{2a} [/tex]
So the answer is D
Hope this helps!
The correct form of the quadratic formula is x = (-b±√(b² - 4ac)) / (2a).
Hence, option D) is the correct answer.
What is a Quadratic Equation?Quadratic equation is simply an algebraic expression of the second degree in x. Quadratic equation in its standard form is;
ax² + bx + c = 0
Where x is the unknown
To solve for x using the quadratic formula;
x = (-b±√(b² - 4ac)) / (2a)
The correct form of the quadratic formula is x = (-b±√(b² - 4ac)) / (2a).
Hence, option D) is the correct answer.
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What is true about side AB and side AD?
Answers
A line has a slope of -5 and passes through (1,-1). Which is the equation of the line in point-slope form?
Answers
How can you prove a triangle is a right triangle? select one:a. use the distance formula to see if at least two sides are congruent.b. use the slope formula to see if any sides are perpendicular.c. use the distance formula to see if all three sides are congruent.d. use the slope formula to see if any sides are parallel?
Answers
__________________
katy buys ‘x’ cakes.
Gugu buys 3 times as many cakes as katy.
Deanna buys 2 more cakes than Katy.
Each cake costs 85p
The total of the cakes is £52.70
How many cakes did each girl buy?
Answers
Katy bought 12 cakes
Gugu bought 36 cakes
Deanna bought 14 cakes
Explanation:
We are given that:
Katy bought x cakes
Gugu bought 3 times as many as Katy. This means that Gugu bought 3x cakes
Deanna bought 2 cakes more than Katy. This means that Deanna bought x+2 cakes
Total number of cakes bought = x + 3x + x + 2 = 5x + 2 cakes
We know that the price of each cake is 85 p = £0.85 and that the total amount paid is £52.7
This means that:
(5x+2)(0.85) = 52.7
4.25x + 1.7 = 52.7
4.25x = 52.7 - 1.7
4.25x = 51
x = 51 / 4.25
x = 12
Now, we will get the number of cakes that each bought as follows:
Katy bought x cakes = 12 cakes
Gugu bought 3x cakes = 3(12) = 36 cakes
Deanna bought x+2 cakes = 12 + 2 = 14 cakes
Hope this helps :)
Answer:
Katy bought 12 cakes
Gugu bought 36 cakes
Deanna bought 14 cakes
Step-by-step explanation:
3(−4x) + 3(5) = 12
−12x + 15 = 12
−12x + 15 − 15 = 12 − 15
−12x = −3
x =
Answers
Answer: 1/4
don't forget to rate and thank plz.
5/8 ≠ (3/4 + 1/16) because 5/8 < 3/4 EXPLAIN THIS PROBLEM AND WHAT IT MEANS
Answers
- 5/8 = 0.625
- 3/4+1/16 = 0.8125
0.625 = 0.8125, it is not equal but less than
What is the 12th term of the sequence? 3, −9, 27, −81, 243, ...
531441
−531441
177147
−177147
Answers
There are 2 ways you can find this.
A. You can find this by starting with 3, and multiply -3 then multiply -3 to each product after that 11 times. Or...
B. Simply find 3 to the 12th power. Then add a negative since each even term (term 2, 4, 6, etc) are negative.
I hope this helps!
How many times larger is 4 x 1016 than 5 x 108?
Answers
5 × 108 = 540
4,064 ÷ 540 = 7.5
Answer = 7.5
~Aamira~
Hope this helped☺☺
The point (-1.3, -1.7) is located in which quadrant?
Answers
This point would be located in the third quadrant.
Why?
First Quadrant: (2, 2)
Second Quadrant: (-2, 2)
Third Quadrant: (-2, -2)
Fourth Quadrant: (2, -2)
I WILL GIVE BRAINLIEST The area of the surface of the trampoline (square) is equal to twice its perimeter. Find the dimensions. length= 4x ft., width= (x+6) ft.
FACTORING POLYNOMIALS/SOLVE THE EQUATION BY FACTORING HOMEWORK
Answers
length=4x ft, width=(x+6) ft
the perimeter will be:
P=2(L+W)
P=2(4x+(x+6))
P=2(4x+x+6)
P=2(5x+6)
P=(10x+12)
Area of the rectangle is:
A=4x(x+6)
A=4x²+24x
but:
2P=A
thus
2(10x+12)=4x²+24x
20x+24=4x²+24x
thus
4x²+4x-24=0
x²+x-6=0
x²-2x+3x-6=0
x(x-2)+3(x-2)=0
(x-2)(x+3)=0
thus the answer is:
x=-3 or x=2
thus
length=4x=4*2=8 ft
width=(x+6)=(2+6)=8 ft
Algebra question ( Matrices and Determinants ) 20 points
Answers
A. -30
The determinant of B = -18*1 -3*4 = -18-12 = -30
Choose an example of a fixed expense and an example of a variable expense, and explain why they are classified that way.
Answers
Variable costs are those that depend on the level of production of the company. For example, the cost of raw material. In a company that produces juices, the bottles will be part of the cost of raw material, and the amount of bottles to use depends on the amount of juice to produce, if this amount increases the cost of raw material will also increase. On the other hand, the rental cost of the place where the juices are produced will be the same regardless of the amount of juices that are produced, for this reason it is considered a fixed cost.
Fixed costs, such as rent, remain constant regardless of production levels, while variable costs, like raw material expenses, will fluctuate based on the level of production.
Explanation:Firms classify their costs into two categories: fixed costs and variable costs. Fixed costs are expenses that do not change regardless of the level of production. For instance, a lease on a retail space would be considered a fixed cost as it remains the same whether you sell a lot or a little. On the other hand, variable costs are directly tied to the level of production. For example, the cost of buying materials to produce a product tends to rise as the level of production increases. It's variable because the more you produce, the more materials you would need, and therefore the cost varies with the level of output.
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How much of a 14% iodine solution should be added to 89 ounces of a 47% iodine solution to get a 29% solution
Answers
x = ounces of 14% iodine.
y = ounces of 29% iodine.
we know that in a 14% iodine solution, 14% is iodine and the rest is something else, we also know that "x" ounces of the solution have 14% of iodine, how much is that? (14/100) * x, or 0.14x.
likewise, in the 89 ounces of 47% solution there is (47/100) * 89 of iodine.
and likewise as well, in "y" ounces of 29% iodine there is (29/100) * y, or 0.29y of iodine.
bearing in mind that, whatever "x" and "y" may be, x + 89 = y, and that the sum of the iodine amounts also will equate 0.29y.
[tex]\bf \begin{array}{lccclll} &\stackrel{ounces}{amount}&\stackrel{\%~of~iodine}{quantity}&\stackrel{iodine~oz}{amount}\\ &------&------&------\\ \textit{14\% solution}&x&0.14&0.14x\\ \textit{47\% solution}&89&0.47&41.83\\ ------&------&------&------\\ mixture&y&0.29&0.29y \end{array} \\\\\\ \begin{cases} x+89=\boxed{y}\\ 0.14x+41.83=0.29y\\ --------------\\ 0.14x+41.83=0.29\left( \boxed{x+89} \right) \end{cases} \\\\\\ 0.14x+41.83=0.29x+25.81\implies 16.02=0.15x \\\\\\ \cfrac{16.02}{0.15}=x\implies 106.8=x[/tex]
Make a box and whisker plot of the data.
24, 18, 29, 21, 16, 23, 13, 11
Answers
11, 13, 16, 18, 21, 23, 24, 29
Then find the median:
19.5
Then split the data into two sections by the median:
11, 13, 16, 18 and 21, 23, 24, 29
Now find the medians of those sets
14.5 and 23.5
With this information we can conclude Option C is the correct plot
Hope this helps!
minimum-11
lower quartile-17
median-23.5
upper quartile-26.5
maximum-29
PLS HELP ME ASAP WITH 1!
BRAINLIEST WILL BE GIVEN HOPEFULLY
Do question 2 if u can, if u can’t it’s fine
(Random answers gets moderated)
Answers
(a + b)² = a² + 2ab + b²
You would do well to memorize this "formula." Of course, it also helps to be able to double (or halve) a number, and to know the squares of small integers.
1.
x² +2x +1
x² -6x +9
x² +12x +36
x² -0.4x +0.04
4x² +28x +49
9x² +30x +25
2.
(x + 4)²
(x + 3)²
(x - 9)²
(x - 5)²
3. (12/2)² = 36
4. ±2√49 = ±14
A company spent 32% of its annual budget developing a new machine. What fraction of the company's budget was spent developing the new machine?
Answers
We have been given that the company spent 32% of its annual budget developing a new machine.
Let us convert the percentage to fraction.
[tex]32 \%=\frac{32}{100} \\ \\ 32 \%=\frac{4\times 8}{4\times 25}\\ \\ \text{Cancel 4 from numerator and denominator}\\ \\ 32 \%=\frac{8}{25}[/tex]
Thus, when we convert 32% to fraction that will be equal to 8/25.
Hence, [tex]\frac{8}{25}[/tex] company's budget was spent developing the new machine.