The area of a triangle with legs that are 15 mm, 10 mm, and 20 mm is [tex]72.618 mm^{2}[/tex]
Further Explanation;Area Area is a measure of how much space is occupied by a given shape. Area of a substance is determined by the type of shape in question.For example;
Area of a rectangle is given by; Length multiplied by width Area of a circle = πr². where r is the radius of a circle, Area of a square = S², Where s is the side of the square.etc.Area of a triangle The area of a triangle is given based on the type of the triangle in question.Right triangle.The area of a right triangle is given by;= 1/2 x base x height
Scalene triangleIt is a triangle that with sides and angles that are not equal.Area of a scalene triangle depends on the features of the triangle given.For example;
Sine FormulaArea of a triangle = 1/2 ab sin θ, when given two sides of the triangle and the angle between themHeron's formulaArea of a triangle = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex] when given all the sides of the triangle. where [tex]s =\frac{(a+b+c)}{2}[/tex]In this case we are given, a = 15 mm, b = 10 mm, c = 20 mm
Therefore, we use the Heron's formula;
Area= [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]
[tex]s =\frac{(a+b+c)}{2}[/tex]
[tex]s= \frac{(15+10+20)}{2} \\s= 22.5[/tex]
Therefore;
Area = [tex]s\sqrt{s(s-a)(s-b)(s-c)}[/tex]
= [tex]22.5\sqrt{22.5(22.5-15)(22.5-10)(22.5-20)}[/tex]
=[tex]\sqrt{22.5(7.5)(12.5)(2.5)} \\\sqrt{5273.4375}[/tex]
[tex]= 72.618 mm^{2}[/tex]
Keywords: Area, Area of a triangle, Heron's formula, Sine formula, Scalene triangle.
Learn more about: Perimeter: https://brainly.com/question/12905000 Area: https://brainly.com/question/12905000 Area of a triangle: https://brainly.com/question/4125306Heron's Formula: https://brainly.com/question/10713495Level: Middle school
Subject; Mathematics
Topic: Area
Sub-topic: Area of a triangle
Manuel rented a truck for one day. There was a base fee of $14.95, and there was an additional charge of 87 cents for each mile driven. Manuel had to pay $248.98 when he returned the truck. For how many miles did he drive the truck?
Final answer:
After calculations, it is determined that Manuel drove approximately 269 miles.
Explanation:
Manuel rented a truck which had a base fee of $14.95 and an additional charge of 87 cents per mile. To find the number of miles driven, we need to subtract the base fee from the total amount paid and then divide by the cost per mile.
First, subtract the base fee from the total cost:
Total amount paid = $248.98
Base fee = $14.95
Amount paid for miles = $248.98 - $14.95 = $234.03
Next, divide the amount paid for miles by the cost per mile:
Cost per mile = 87 cents = $0.87
Number of miles driven = $234.03 / $0.87 = 269 miles (approximately)
Therefore, Manuel drove approximately 269 miles with the rented truck.
A triangle is cut out of a square whose side length is 8 feet. What will be the approximate area, in square feet, of the remaining board?
Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine if the events are unusual. If convenient, use the appropriate probability table or technology to find the probabilities.
A newspaper finds that the mean number of typographical errors per page is six. Find the probability that (a) exactly four typographical errors are found on a page, (b) at most four typographical errors are found on a page, and (c) more than four typographical errors are found on a page.
In this case, the Poisson distribution is the best one to use. The formula for Poisson distribution is given as:
P[x] = e^-m * m^x / x!
Where,
m = mean number of typographical errors = 6
x = sample value
A. The probability of exactly 4 errors are found on a page is:
P[4] = e^(-6) * 6^4/4!
P[4] = 0.1339
B. The probability that at most 4 errors will be the summation of x = 0 to 4:
P[0] = e^(-6) * 6^0/0! = 2.479 E -3
P[1] = e^(-6) * 6^1/1! = 0.01487
P[2] = e^(-6) * 6^2/2! = 0.04462
P[3] = e^(-6) * 6^3/3! = 0.08924
Therefore summing up all including the P[4] in A gives:
P[at most 4] = 0.2851
C. The probability that more than 4 would be the complement of answer in B.
P[more than 4] = 1 - P[at most 4]
P[more than 4] = 1 - 0.2851
P[more than 4] = 0.7149
6300 and 530
The value of 3 in ___is____times the value of 3 in ___.
Which expression is equivalent to the following complex fraction? (2/x)-(4/y)/(-5/y)+(3/x)
To find the equivalent expression, multiply the first fraction by y and the second fraction by x. Simplify the expression by combining like terms.
Explanation:To find the expression equivalent to the given complex fraction, we can simplify it step by step. First, multiply the numerator and denominator of the first fraction (2/x) by y, and multiply the numerator and denominator of the second fraction (-5/y) by x. This gives us (2y)/(xy) - (4x)/(-5x). Next, simplify the expression by combining like terms. The final equivalent expression is (2y - 4x)/(xy + 5x).
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A total of 804 tickets were sold for the school play. They were either adult tickets or student tickets. There were 54 more student tickets sold than adult tickets. How many adult tickets were sold?
Choose the polynomial written in standard form. (5 points)
xy2 + 4x4y + 10x2
x4y2 + 4x3y + 10x
x4y2 + 4x3y5 + 10x2
x6y2 + 4x3y8 + 10x
The polynomial in standard form from the given options is [tex]x^4y^2 + 4x^3y + 10x[/tex], as it orders the terms by degree in descending order, first by the degree of x and then y.
The term standard form in mathematics, especially in relation to polynomials, refers to a way of writing the polynomial so that the terms are ordered by their degree in descending order. More specifically, for a polynomial in two variables, x and y, the standard form would have the terms arranged first by the degree of x, then y, from highest to lowest.
Looking at the options provided in the question, the polynomial that is written in standard form would have the highest degree term first, and so on. The polynomial [tex]x^4y^2 + 4x^3y + 10x[/tex] follows this convention, with the terms ordered by decreasing powers of x first and y second. Therefore, this is the polynomial written in standard form.
Note that while the other options are all polynomials, they do not follow the standard form convention as closely as the correct option provided.
what is 46 2/3 of 28
a projectile is launched straight up from ground level with an initial velocity of 320 ft/sec when will it's height above ground be
1538 feet
To calculate when the height of the projectile will be 1538 feet, use the kinematic equation and solve the quadratic equation for time.
Explanation:To calculate when the height of the projectile will be 1538 feet, we can use the kinematic equation for free-falling objects. The equation is: h = [tex]h0 + v0*t - 16*t^2,[/tex] where h is the height above ground, h0 is the initial height (0 in this case), v0 is the initial velocity (320 ft/sec in this case), and t is the time.
Substituting the given values into the equation, we have: 1538 = 0 + 320*t - 16*t^2. Rearranging this equation, we get: [tex]16*t^2[/tex]- 320*t + 1538 = 0.
Now we can solve this quadratic equation for t by using the quadratic formula: t = (-b ± sqrt([tex]b^2[/tex] - 4ac)) / (2a), where a = 16, b = -320, and c = 1538. Plugging in these values, we can calculate the values of t.
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The Henderson family and the Tran family each used their sprinklers last summer. The Henderson family's sprinkler was used for 15 hours. The Tran family's sprinkler was used for 40 hours. There was a combined total output of 1800L of water. What was the water output rate for each sprinkler if the sum of the two rates was 70L per hour?
Henderson family’s sprinkler: __ L per hour
Tran family’s sprinkler: __ L per hour
water weighs about 8.34 lb per gallon about how many ounces per gallon is the weight of the water
Water weighing 8.34 lb per gallon is equivalent to about 133.44 ounces per gallon.
The question at hand is how to convert the weight of water from pounds per gallon to ounces per gallon. Given that we know water weighs about 8.34 lb per gallon, we can use the conversion factor of 16 ounces in a pound to perform this calculation. Here's how you can do it:
Find the unit equivalence which is that 1 pound is equal to 16 ounces.Then, multiply the weight of the water in pounds by the number of ounces in a pound.Perform the multiplication: 8.34 lb * 16 oz/lb = 133.44 ozTherefore, water weighs approximately 133.44 ounces per gallon.
which is greater 2 or -13?
y=-x y=2x+3 graph the equation to solve the system
solve the equation 14x+7y=24 for x
You inherit one hundred thousand dollars. You invest it all in three accounts for one year. The first account pays 4% compounded annually, the second account pays 3% compounded annually, and the third account pays 2% compounded annually. After one year, you earn $3,650 in interest. If you invest five times the money in the account that pays 4% compared to 3%, how much did you invest in the 4% account?
Translate to an algebraic expression. 5 INCREASED BY y
Perform the indicated operation. (5 - 2i 2) 2
On two investments totaling $10,500, Brian lost 6% on one and earned 8% on the other. If his net annual receipts were $497, how much was each investment?
if p is a polynomial show that lim x→ap(x)=p(a
Let p(x) be a polynomial, and suppose that a is any real number. Prove that
lim x→a p(x) = p(a) .
Solution. Notice that
2(−1)4 − 3(−1)3 − 4(−1)2 − (−1) − 1 = 1 .
So x − (−1) must divide 2x^4 − 3x^3 − 4x^2 − x − 2. Do polynomial long division to get 2x^4 − 3x^3 − 4x^2 – x – 2 / (x − (−1)) = 2x^3 − 5x^2 + x – 2.
Let ε > 0. Set δ = min{ ε/40 , 1}. Let x be a real number such that 0 < |x−(−1)| < δ. Then |x + 1| < ε/40 . Also, |x + 1| < 1, so −2 < x < 0. In particular |x| < 2. So
|2x^3 − 5x^2 + x − 2| ≤ |2x^3 | + | − 5x^2 | + |x| + | − 2|
= 2|x|^3 + 5|x|^2 + |x| + 2
< 2(2)^3 + 5(2)^2 + (2) + 2
= 40
Thus, |2x^4 − 3x^3 − 4x^2 − x − 2| = |x + 1| · |2x^3 − 5x^2 + x − 2| < ε/40 · 40 = ε.
Find the value of x, rounded to the nearest tenth. Please help me!!
The value of x for the circle is 25.8. The correct option from the following is (D).
Simple closed shapes include circles. It is the collection of all points in a plane that are a certain distance from the center. A segment is a section of a straight line that has every point on the line that lies in its middle and is enclosed by two clearly defined endpoints.
The products of two secant lines that cross one another outside of a circle are equal.
The value of x is:
5(x+5) = 7(15+7)
5x + 25 = 7 × 22
5x + 25 = 154
5x = 154 - 25
5x = 129
x = 129/5
x = 25.8
Hence, the value of x is 25.8.
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The Sugar Sweet Company is going to transport its sugar to market. It will cost $6500 to rent trucks, and it will cost an additional $250 for each ton of sugar transported. Let C represent the total cost (in dollars), and let S represent the amount of sugar (in tons) transported. Write an equation relating C to S . Then use this equation to find the total cost to transport 19 tons of sugar.
Answer: Equation relating C to S : [tex]C=6500+250S[/tex]
The total cost to transport 19 tons of sugar is $11, 250.
Step-by-step explanation:
Given : It will cost $6500 to rent trucks, and it will cost an additional $250 for each ton of sugar transported.
Total cost = $6500 + $250 x (amount of sugar transported ( in tons))
Let C represent the total cost (in dollars), and let S represent the amount of sugar (in tons) transported.
Then, the equation relating C to S would be : [tex]C=6500+250S[/tex]
When S= 19 , we get
[tex]C=6500+250(19)=6500+4750= 11250[/tex]
Hence, the total cost to transport 19 tons of sugar would be $11, 250.
An equation that relates Cost to the amount of sugar S
C = 6500 + 250S
The total cost is $1120
The total cost of transporting 19 tons of sugar at 250 eachC = total cost
C = 6500 + 250(19)
Total cost = 6500 + 4750
= 11250
Therefore the total cost of transporting the 19 tons of sugar is $11250
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there were 137 tickets purchased for a major league baseball game the lower box tickets cost $12.50 and the upper box tickets cost $10 the total amount of money spent was $1,502.50 how much of each kind of ticket
lower box = x
upper box = y
x+y=137
x=137-y
12.50x + 10y=1502.50
12.50(137-y) + 10y=1502.50
1712.5-12.50y+10y=1502.50
1712.5-2.50y=1502.50
-2.5y=-210
y=-210/-2.50 = 84
y = 84
x=137-84=53
53 lower box tickets
84 upper box tickets
if f(x) = 3x - 2 then f (8) - f(-5)=
Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a recent year. suppose a sample of 100 major league players was taken. find the approximate probability that the mean salary of the 100 players exceeded $4.0 million.
Final answer:
The probability is approximately 0.267.
Explanation:
To find the approximate probability that the mean salary of the 100 players exceeded $4.0 million, we can use the Central Limit Theorem and the Z-score formula. The Z-score formula is:
Z = (x - μ) / (σ / sqrt(n))
where x is the value we want to find the probability for (in this case $4.0 million), μ is the mean of the population ($3.26 million), σ is the standard deviation of the population ($1.2 million), and n is the sample size (100).
We calculate the Z-score as follows:
Z = (4.0 - 3.26) / (1.2 / sqrt(100)) = 0.617
We then use a Z-table or a calculator to find the probability corresponding to a Z-score of 0.617. The probability is approximately 0.267.
A line passes through the point (6−6) and has a slope of 3/2 . Write an equation in point-slope form for this line.
A collection of quarters and nickels is worth $3.75. There are 27 coins in all. Find how many of each there are.
Q +N =27
Q=27-N
0.25Q + 0.05N =3.75
0.25(27-N) + 0.05 =3.75
6.75-0.25N+0.05N=3.75
6.75-0.2N=3.75
-0.2N=-3
N=-3/-0.2 = 15
15 nickels
27-15 = 12
12 quarters
15x0.05 = 0.75
12 x 0.25 = 3.00
3.00 + 0.75 = 3.75
12 quarters & 15 nickels
Help me find solutions to this equation and write the answers in radians in terms of pi . Thanks!
Cosine law part 2 in need of help (ignore question 67)
FInd the approximations to at least two decimal places for the coordinates of Point Z in the figure below. The angle theta or Q is -80 degrees and the radius is 11.
Z = ?
Also if you can explain to me, that would be great.
Point Z's polar coordinates can be found by using the formulas x = r*cos(θ) and y = r*sin(θ), converting the angle from degrees to radians first. Use r = 11 and θ = -80 degrees.
Explanation:This question deals with the concept of polar coordinates, coordinates given by a distance from the origin (radius) and an angle from the positive x-axis (-80 degrees in this case). Point Z's coordinates can be found using the formulas: x = r*cos(θ) and y = r*sin(θ). Here r (the radius) is 11 and θ is -80 degrees, but remember we need to convert this angle to radians because the trigonometric functions in most calculators use radians. That can be done using the formula: Radians = Degrees * (π / 180). Hence calculate x and y to find Point Z.
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A fish is 5 feet below the surface of a lake. If its position can be recorded as −5 feet, what would the position of 0 represent?