The perimeter of a triangle is 510 ft and the sides are in the ratio of 11:16:24. Find the area of the triangle. Need help, is there a specific formula for this?
Answers
The side lengths are in the ratio 11:16:24, so let them be
11k, 16k, and 24k for some number k.
11k+16k+24k=510
k(11+16+24)=510
51k=510
k=10
so the actual sides are 110, 160 and 240 feet.
2.
There is a famous formula, called Heron's formula, which calculates the area of a triangle, given its sides a, b and c.
we first calculate the half perimeter, which we usually denote by u:
[tex]u= \frac{a+b+c}{2} [/tex]
then the theorem states that the area A is as follows:
[tex]A= \sqrt{u(u-a)(u-b)(u-c)} [/tex]
3.
In our case:
[tex]u= \frac{a+b+c}{2} =\frac{110+160+240}{2} = \frac{510}{2} [/tex]
[tex]u-a= \frac{510}{2} -110= \frac{510-220}{2} = \frac{290}{2} [/tex]
[tex]u-b= \frac{510}{2} -160= \frac{510-320}{2} = \frac{190}{2} [/tex]
[tex]u-a= \frac{510}{2} -240= \frac{510-480}{2} = \frac{30}{2} [/tex]
[tex]A= \sqrt{\frac{510}{2}*\frac{290}{2}* \frac{190}{2} * \frac{30}{2}} =7,258.745[/tex] feet squared
Answer:D 7,258.745 ft squared
Final answer:
To find the area of a triangle with sides in a given ratio, first find the value of x by setting up and solving an equation using the perimeter. Then, multiply each side by x to find the base and height of the triangle. Finally, substitute the base and height into the formula for the area of a triangle.
Explanation:
To find the area of a triangle, we can use the formula: Area = 1/2 × base × height. In this case, we don't know the base and height directly, but we do know that the sides of the triangle are in the ratio of 11:16:24. Let's assume the sides are 11x, 16x, and 24x. The perimeter of the triangle is 510 ft, which means 11x + 16x + 24x = 510. Simplifying this equation, we get 51x = 510. Therefore, x = 10. Now we can find the base and height of the triangle by multiplying the corresponding sides by 10. The base is 11x * 10 = 110 ft and the height is 16x * 10 = 160 ft.
Now we can substitute these values into the formula to calculate the area of the triangle. Area = 1/2 × base × height = 1/2 × 110 ft × 160 ft = 8800 square feet.
Related Questions
!!! HELP What values for (picture of equation) satisfy the equation?
Answers
(a) a pizza parlor has a choice of 11 toppings for its pizzas. from these 11 toppings, how many different 7 -topping pizzas are possible?
Answers
To solve for the number of different possible pizzas with 7 toppings out of 11 and the arrangement of these toppings is not important, therefore we use the combination formula.
The formula for combination is:
n C r = n! / r! (n – r)!
where,
n = is the total number of toppings = 11
r = the number of toppings in a pizza = 7
Substituting the values into the equation:
11 C 7 = 11! / 7! (11 – 7)!
11 C 7 = 11! / 7! * 4!
11 C 7 = 330
Therefore there are a total different 330 pizzas with 7 different combinations toppings.
Final answer:
330 different combinations.
Explanation:
The student's question is about combinations in Mathematics, specifically how many 7-topping pizzas can be made from a choice of 11 toppings. This is a combinatorics problem, and the solution involves the use of the combination formula, which is given as:
C(n, k) = n! / (k!(n-k)!)
where n is the total number of items to choose from, k is the number of items to choose, n! denotes the factorial of n, and C(n, k) represents the number of combinations.
In this case, n is 11 (the total number of toppings) and k is 7 (the number of toppings on the pizza).
Therefore, the number of different 7-topping pizzas possible is:
C(11, 7) = 11! / (7!(11-7)!) = 11! / (7!4!) = (11x10x9x8)/(4x3x2x1) = 330
Hence, 330 different 7-topping pizzas are possible.
What is the area of the obtuse triangle given below?
Answers
A = 1/2 * 11 * 7 = 38.5
your answer is D
hope that helps :)
Answer:
Option (d) is correct.
The area of triangle is 38.5 square units
Step-by-step explanation:
Given: An obtuse triangle.
We have to find the area of this obtuse angle.
Consider the given obtuse triangle
Area of triangle = [tex]\frac{1}{2}\cdot b \cdot h[/tex]
where b = Base
h = height
Given : base = 11 units
and height = 7 units
Thus, Area of triangle = [tex]\frac{1}{2}\cdot 11 \cdot 7[/tex]
Simplify, we have,
Area of triangle = 38.5
Thus, The area of triangle is 38.5 square units
The depth of the water at the end of a pier changes periodically along with the movement of tides. On a particular day, low tides occur at 12:00 am and 12:30 pm, with a depth of 2.5 m, while high tides occur at 6:15 am and 6:45 pm, with a depth of 5.5 m. Let t = 0 be 12:00 am. Which periodic function, sine or cosine, would be a simpler model for the situation? Explain.
Answers
Answer: A cosine function would be a simpler model for the situation.
The minimum depth (low tide) occurs at
t = 0. A reflection of the cosine curve also has a minimum at t = 0.
A sine model would require a phase shift, while a cosine model does not.
Step-by-step explanation:
Using a cosine function is simpler to model the tide changes because it starts at the maximum value, aligning with the high tide occurrence.
The depth of the water at the end of a pier changes periodically due to tides. Given that low tides occur at 12:00 am and 12:30 pm with a depth of 2.5 m, and high tides occur at 6:15 am and 6:45 pm with a depth of 5.5 m, we need to model this situation with a periodic function.
Let's align this with a cosine function for simplicity. In general, the cosine function can be modeled as y = A cos(B(t - C)) + D, where:
A is the amplitude (half of the difference between high tide and low tide depth, (5.5 m - 2.5 m)/2 = 1.5 m)B determines the period (a full tide cycle is roughly 12 hours and 25 minutes or 747.5 minutes; B = 2π/747.5)C is the horizontal shift (shift corresponding to the time of the first high tide, 6.25 hours or 375 minutes, so C = 375)D is the midline of the function (average depth, (5.5 m + 2.5 m)/2 = 4 m)Therefore, the function becomes: y(t) = 1.5 cos((2π/747.5)(t - 375)) + 4. Using a cosine function is simpler because it starts at the maximum value, which corresponds to the high tide.
Is the relation {(3, 5), (–4, 5), (–5, 0), (1, 1), (4, 0)} a function? Explain. Type your answer below
Answers
If you had something like {(1,2),(4,5),(1,7)} then it wouldn't be a function since x = 1 repeats itself. In this example, x = 1 leads to more than one output.
{(3, 5), (–4, 5), (–5, 0), (1, 1), (4, 0)}
As long as there are the same x-value does not have multiple y-value results, it will be a function. This data array doesn't contain any recurring x-values. Therefore, this is a function (in simple terms of speaking).
At the movie theatre, child admission is $6.20 and adult admission is $9.80 . On Monday, twice as many adult tickets as child tickets were sold, for a total sales of $593.40 . How many child tickets were sold that day?
Answers
x= child
2x = adult
6.20x +9.80(2x) =593.40
6.20x +19.6x=593.40
25.80x =593.40
x=593.40/25.80 = 23
23 childrens tickets were sold
identify the maximum and minimum values of the function y = 3 cos x in the interval [-2π, 2π]. Use your understanding of transformations, not your graphing calculator.
Answers
The x interval of [-2π, 2π] ensures that all y values are enclosed; the cosine makes two full sweeps.
The maximum value of the function y = 3 cos x will be 3.
The minimum value of the function y = 3 cos x will be - 3.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The function is,
⇒ y = 3 cos x
In the interval [-2π, 2π].
Now,
Since, The function is,
⇒ y = 3 cos x
Hence, We get;
The maximum value of the function y = 3 cos x is,
⇒ y = 3 cos2π
⇒ y = 3 × 1
⇒ y = 3
And, The minimum value of the function y = 3 cos x is,
⇒ y = 3 cos(-2π)
⇒ y = 3 × - 1
⇒ y = - 3
Thus, The maximum value of the function = 3.
The minimum value of the function = - 3.
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Please Help. Thank you
Answers
Five members of the soccer team and five members of the track team ran the 100-meter dash. Their times are listed in the table below: Soccer Track 12.3 12.3 13.2 11.2 12.5 11.7 11.3 12.2 14.4 13.7 What is the difference of the means for the two groups? 0.52 12.22 12.74 24.96
Answers
track : (12.3 + 11.2 + 11.7 + 12.2 + 13.7) / 5 = 61.1 / 5 = 12.22
difference is : 12.74 - 12.22 = 0.52 <=
Answer:
Hence, the difference in Mean of two teams is:
0.52
Step-by-step explanation:
Five members of the soccer team and five members of the track team ran the 100-meter dash.
Their time is listed as:
Soccer Track
12.3 12.3
13.2 11.2
12.5 11.7
11.3 12.2
14.4 13.7
The mean of the soccer team is given by:
[tex]Mean_1=\dfrac{12.3+13.2+12.5+11.3+14.4}{5}\\\\Mean_1=12.74[/tex]
The mean of track team is given by:
[tex]Mean_2=\dfrac{12.3+11.2+11.7+12.2+13.7}{5}\\\\Mean_2=\dfrac{61.1}{5}\\\\Mean_2=12.22[/tex]
Hence, the Difference in Mean is:
[tex]Mean_1-Mean_2\\\\=12.74-12.22\\\\=0.52[/tex]
Hence, the difference in Mean of two teams is:
0.52
Write a variable expression for 9 more than a number s.
Answers
More than suggests addition.
A bicycle store costs $2400 per month to operate. The store pays an average of $60 per bike. The average selling price of each bicycle is $120. How many bicycles must the store sell each month to break even? Write a system of equations to represent the situation, then solve.
Answers
Using linear functions, it is found that the store must sell 40 bicycles each month to break even.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.A bicycle store costs $2400 per month to operate, and pays an average of $60 per bike, hence the cost function is given by:
C(x) = 2400 + 60x
The average selling price of each bicycle is $120, hence the revenue function is given by:
R(x) = 120x
It breaks even when cost equals revenue, hence:
R(x) = C(x)
120x = 2400 + 60x
60x = 2400
x = 240/6
x = 40.
The store must sell 40 bicycles each month to break even.
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To determine the number of bicycles the store must sell each month to break even, we can set up a system of equations. The store must sell 40 bicycles each month to break even.
Explanation:To determine the number of bicycles the store must sell each month to break even, we can set up a system of equations.
Let's say the number of bicycles sold per month is x.
The monthly operating cost of the store is $2400.
The cost of producing each bike is $60, so the total cost to produce x bikes would be $60x.
The average selling price of each bike is $120, so the total revenue from selling x bikes would be $120x.
To break even, the total revenue should equal the total cost, so we can set up the equation:
$120x = $60x + $2400
Simplifying the equation, we get:
$60x = $2400
Dividing both sides by $60, we find:
x = 40
Therefore, the store must sell 40 bicycles each month to break even.
Which of the following is an arithmetic sequence?
a -7/11,6/11, -5/11, 4/11
b -3/4, -3/5, -3/6, -3/7
c 1/2,2,7/2,5
d 3/4,-3/2, 3, -6
Answers
and then - 3/2 x - 2 = 3
3 x - 2 = - 6
Hope that helps <3
The sequence 3/4,-3/2, 3, -6 is the arithmetic sequence.
Common differenceThe difference between two successive terms of an arithmetic progression is known as a common difference.
How to check the common difference?(a)
We will find the common difference between each term of the given sequences by subtracting a term and its previous term.
[tex](\frac{6}{11}- \frac{-7}{11}) \neq (\frac{-5}{11} -\frac{6}{11} )\neq (\frac{4}{11} -\frac{-5}{11})[/tex]
[tex]\frac{13}{11}\neq \frac{-11}{11}\neq \frac{9}{11}[/tex]
So, option (a) is incorrect.
(b)
We will take the common difference between the terms.
[tex](\frac{-3}{5} -\frac{-3}{4} )\neq (\frac{-3}{6} -\frac{-3}{5} )\neq (\frac{-3}{7} -\frac{-3}{6} )\\[/tex]
[tex]\frac{3}{20} \neq \frac{3}{30}\neq \frac{3}{42}[/tex]
So, option (b) is also incorrect.
(c)
We will take the common difference between the terms.
[tex](2-\frac{1}{2} )= ( \frac{7}{2}-2 )= (5 - \frac{7}{2} )[/tex]
[tex]\frac{3}{2}= \frac{3}{2} = \frac{3}{2}[/tex]
Since the difference between the terms is common.
Thus, option (c) is correct.
(d)
We will take the common difference between the terms.
[tex](\frac{-3}{2}- \frac{3}{4})\neq (3-\frac{3}{2})\neq (-6-3)[/tex]
[tex]\frac{-18}{2}\neq \frac{9}{2}\neq (-9)[/tex]
So, option (d) is incorrect.
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Which of the following is an extraneous solution of sqrt(-3x-2)=x+2 a.-6 b.-1 c.1 d.6
Answers
for example a, x - 6 is not extraneous because
left side = sqrt (-3*-6 - 2) == sqrt16 = 4 or -4
right side = -6 + 2 = -4
so x = -6 is not extraneous
Answer:
- 6 is the extraneous solution.
Step-by-step explanation:
Given : [tex]\sqrt{-3x -2} = x + 2[/tex].
To find : Which of the following is an extraneous solution .
Solution : We have given that [tex]\sqrt{-3x -2} = x + 2[/tex].
Taking square both sides
-3x - 2 = [tex](x+2)^{2}[/tex].
On applying identity [tex](a+b)^{2}[/tex] = a² + b² + 2ab
Then ,
-3x -2 = x² + 2² + 2 * 2 *x
-3x -2 = x² + 4 + 4x.
On adding both sides by 3x
-2 = x² + 4 + 4x + 3x
-2 = x² + 4 + 7x
On adding both sides by 2
0 = x² + 4 + 7x + 2
On switching sides
x² +7x + 6 = 0
On Factoring
x² +6x + x + 6 = 0
x ( x+ 6 ) +1 (x +6 ) = 0
On grouping
( x +1) ( x +6) = 0
x = -1, -6.
Let check for x = -6
[tex]\sqrt{-3 (-6) -2} = -6 + 2[/tex].
4 = -4
An extraneous solution is a root of a transformed equation that is not a root of the original equation.
Therefore, -6 is the extraneous solution.
What number should be added to both sides of the equation to complete the square? x^2 â 10x = 7?
Answers
Basically, the p value should be half of b and the square root of c.
The bulldog soccer team wants to increase the size of its
Practice field by a scale factor of 1.5. The field is a rectangle that currently measures 30 ft by 80 ft. The measurements of the new practice field should be 45 ft by ft.
Answers
multiply 80 by 1.5
80*1.5 = 120 feet
Best explained and correct answer gets brainliest.
Answers
total = 2372* (1+0.045)^20=
2372*1.045^20=
2372 * 2.411714025= 5720.585
she will have 5720.59 in 20 years
Find the value tan 39 degrees. Round to the nearest ten-thousandth
A ) 0.8098
B ) 0.6293
C ) 0.7771
D ) 3.6146
Answers
mine gives tan 39 = 0.8097840332
which is 0.8098 to nearest ten thousandth.
xy is displayed by a scale factor of 1.3 with the origin as the center of dialation to create the image xy. if the slope and length of xy are m what is the slope of xy
Answers
Answer:
he XY is dilated by a scale factor of 1.3 with the origin as the center of dilation to create the X'Y'. So the length of X'Y' is 1.3 times of origin but the slope is the same. The slope is m
Step-by-step explanation:
What is the distance between the points (22, 27) and (2, -10)? if necessary, round your answer to two decimal places.a. 57 units?
Answers
(22,27)....x1 = 22 and y1 = 27
(2,-10)....x2 = 2 and y2 = -10
now we sub
d = sqrt (2 - 22)^2 + (-10 -27)^2)
d = sqrt (-20^2) + (-37^2)
d = sqrt (400 + 1369)
d = sqrt 1769
d = 42.06 <==
Answer:
42.06
Step-by-step explanation:
Two points (22,27) and (2,-10)
using distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
So, distance between (22,27) and (2,-10) is D
[tex]D=\sqrt{(22-2)^2+(27-(-10))^2}[/tex]
[tex]D=\sqrt{(20)^2+(37)^2}[/tex]
[tex]D=\sqrt{400+1369}[/tex]
[tex]D=\sqrt{1769}[/tex]
[tex]D=42.059[/tex]
Round off two decimal place.
[tex]D=42.06[/tex]
Hence, The distance between the points is 42.06
Which ordered pair is a solution to the system of inequalities? y <3 and y >-x+5 ?
A. (6,1)
B. (2,1)
C. (3,0)
D. (-2,4)
PS. for the equation y>-x+5, the sign should be greater than or equal to. I just can't find the key on my phone (>)
Answers
find an ordered pair that is a solution to the equation x-4y=4
Answers
Ordered pairs that are solutions to the equation x-4y=4 is (4, 0) and (0, -1).
The given equation is x-4y=4.
We need to find an ordered pair that is a solution to the equation.
How to find the solution to an equation?The solutions of linear equations are the points at which the lines or planes representing the linear equations intersect or meet each other. A solution set of a system of linear equations is the set of values to the variables of all possible solutions.
From the graph, we can observe that (4, 0) and (0, -1) are solutions.
Verification of the solution (4, 0):
4-4y=4
⇒-4y=0
⇒y=0
Verification of the solution (0, -1):
0-4y=4
⇒-4y=4
⇒y=-1
Therefore, ordered pairs that are solutions to the equation x-4y=4 is (4, 0) and (0, -1).
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find the x intercepts of the parabola with vertex (2,13) and y-intercept (0,5) write your answer in this form: (x1,y1),(x2,y2) if necessary, round to the nearest hundredth
Answers
(x-h)^2 = +/- 4a (y-k) or (y-k)^2 = +/- 4a(x-h)
where
(h,k) is the coordinates of the vertex
a is the length of the focus from the vertes
+4a if the parabola opens upwards or to the right
-4a if the parabola opens downwards or to the left
The vertex (2,13) is situated in the 1st quadrant of the Cartesian plane. It only has y-intercept. This means that it only passes the y-axis once. Therefore, the parabola must open downwards and it passes the x-axis twice. The intersections at the x-axis are the x-intercepts. If the parabola has 2 x-intercepts, then the equation would be (x-h)^2 = -4a(y-k).
Let's use the y-intercept (0,5) to determine 4a:
(0-2)^2=-4a(5-13)
4a = 0.5
Therefore, the equation of the parabola is (x-2)^2 = -1/2(y-13). To find the x-intercepts, let y=0.
(x-2)^2 = -1/2(0-13) = 6.5
x-2 = +/- √6.5 = +/- 2.55
x = 4.55 and and -0.55
The x-intercepts are (-0.55,0) and (4.55,0).
Answer:
(-0.55,0),(4.55,0)
Solve x 2 + 9x + 8 = 0 by completing the square. What are the solutions?
Answers
x^2+9x+8=0
(x+1)(x+8)=0
x+1=0
x=-1
x+8 = 0
x=-8
solutions are -1 and -8
Find H to the nearest degree.
Answers
sin(H) = GF/HF
sin(H) = 5/13
arcsin(sin(H)) = arcsin(5/13)
H = 22.61986 ... which is approximate
H = 23 degrees ... round to the nearest whole number
Answer is choice A
A bakery sold apple pies for $11 and blueberry pies for $13. One Saturday they sold a total of 38 pies and collected a total of $460. How many apple pies did they sell and how many blueberry pies did they sell?
Answers
A= apple pie
B = blueberry pie
a+b=38
a=38-b
11a + 13b =460
11(38-b) + 13b = 460
418-11b +13b = 460
2b=42
b=42/2 =21
they sold 21 blueberry pies and 17 apple pies
If the factors of a polynomial are x-2 and x-5, what values of x make that polynomial 0?
A. 1 and 2
B. -2 and -5
C. 2 and 5
D. Cannot be determined
Answers
Dominique is thinking about buying a house. The table below shows the projected value of two different houses for three years.
House 1 (value in dollars) year 1: 286,000 year 2: 294,580 year 3: 303,417.40 House 2 (value in dollars) year 1: 286,000 year 2: 295,000 year 3: 304,000
Part A: What type of function, linear or exponential, can be used to describe the value of each of the houses after a fixed number of years? Explain your answer.
Part B: Write one function for each house to describe the value of the house f(x), in dollars, after x years.
Part C: Dominique wants to purchase a house that would have the greatest value in 25 years. Will there be any significant difference in the value of either house after 25 years? Explain your answer, and show the value of each house after 25 years.
Answers
The functions for House 1 and House 2 are [tex]\(f_1(x) = 5079.6x + 248900.4\)[/tex] and [tex]\(f_2(x) = 4666.\overline{66}x + 256000\)[/tex] respectively.
After 45 years, House 1 will be valued at $477,555, and House 2 will be valued at $465,000.
Here's the step-by-step solution with complete calculations for the given problem:
Part A: Identifying the Function Type
- House 1:
- Year 1 to Year 2: [tex]\(259,059.60 - 253,980 = 5,079.60\)[/tex]
- Year 2 to Year 3: [tex]\(264,240.79 - 259,059.60 = 5,181.19\)[/tex]
- House 2:
- Year 1 to Year 2: [tex]\(263,000 - 256,000 = 7,000\)[/tex]
- Year 2 to Year 3: [tex]\(270,000 - 263,000 = 7,000\)[/tex]
The functions are linear because the changes are constant for House 2 and almost constant for House 1.
Part B: Formulating the Equations
- House 1 Equation:
- Slope (m): [tex]\(5079.6\)[/tex]
- Y-intercept (c): [tex]\(248900.4\)[/tex]
- Equation: [tex]\(f_1(x) = 5079.6x + 248900.4\)[/tex]
- House 2 Equation:
- Slope (m): [tex]\(4666.\overline{66}\)[/tex]
- Y-intercept (c): [tex]\(256000\)[/tex]
- Equation: [tex]\(f_2(x) = 4666.\overline{66}x + 256000\)[/tex]
Part C: Calculating Future Values
- House 1 Value at Year 45:
[tex]- \(f_1(45) = 5079.6 \times 45 + 248900.4 = 477555\)[/tex]
- House 2 Value at Year 45:
[tex]- \(f_2(45) = 4666.\overline{66} \times 45 + 256000 = 465000\)[/tex]
These equations predict the values of the houses after 45 years based on the given data. House 1 will be valued at $477,555, and House 2 will be valued at $465,000.
Simplify fraction 23076923076923/10000000000000
Answers
The number of hours walked varies inversely with the speed of the walker. if it takes sam 12 hours to complete his walking goal at 5 miles per hour, how long would it take him at 3 miles per hour?
Answers
h = k/s
Substituting the known values,
12 = k/5
k = 60
For the second scenario,
h = k/s
Substituting the calculated value for k and the given value for speed,
h = (60)(3 miles/hour)
h = 20 hours
h = 20 hours
Therefore, it will take 20 hours to walk with a speed of 3 miles per hour.
The path of a ping pong ball that is hit from one end of the table can be modeled by the equation (y= -1/4 x^2 5x) where x is measured in inches and represents the horizontal distance from the edge of the table, and y represents the height of the ping pong ball in inches above the table. What is the maximum height of the ping pong ball?
A.
The ball reaches a maximum height of 30 inches above the table.
B.
The ball reaches a maximum height of 20 inches above the table.
C.
The ball reaches a maximum height of 25 inches above the table.
D.
The ball reaches a maximum height of 27 inches above the table.
Answers
To find the maximum height, you must solve this equation through differential calculus. To find the maxima or minima, you differentiate the equation y in terms of x and equate it to zero.
y' = 2(-1/4)x + 5 = -1/2*x + 5 = 0
By doing this, you would solve the value of x or the horizontal distance.
-1/2*x = -5
x =-5*-2
x = 10 inches
Finally, we substitute this x to the original equation to determine the maximum height y.
y = -1/4*10 + 5(10)
y = 25 inches
The answer is C.