a right triangle has one angle that measures 23 degress.The adjacent leg measures 27.6 cm and the hypotenuse measures 30 cm.What is the approximate area of the triangle?Round to the nearest tenth.Area of a triangle =1/2bh
Answers
Answer:
Area of the triangle will be 162.3 cm²
Step-by-step explanation:
From the figure attached,
In the triangle ABC angle ACB = 23°, side BC = 27.6 cm and hypotenuse AC = 30 cm
Now we have to calculate the area of the given right angle triangle.
Since area of a right angle triangle is represented by
Area = [tex]\frac{1}{2}\times b\times h[/tex]
Where b = adjacent side
h = opposite side
To calculate the opposite side of the triangle we will apply Pythagoras theorem in the ΔABC.
AC² = AB² + BC²
AB² = AC² - BC²
AB² = (30)² - (27.6)²
= 900 - 761.76
= 138.24
AB = √138.24
= 11.76
Area of the triangle = [tex]\frac{1}{2}(AB)(BC)[/tex]
= [tex]\frac{1}{2}(11.76)(27.6)[/tex]
= 162.28 cm² ≈ 162.3 cm²
Related Questions
The knife shown below is 14 inches long. write an algebraic expression that represents the length of the blade (in inches).
Answers
14-h=b hope this helped
The required algebraic expression for the length of the blade is x = 14 - h.
Given that,
The knife shown below is 14 inches long.
To write an algebraic expression that represents the length of the blade (in inches).
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Here let the length of the blade of the knife be x,
length of the knife handle be h
Here the total length of the knife is 14 inches
So,
The total length of the knife = length of the blade + length of the handle
14 = x + h
x = 14 - h
Thus, the required algebraic expression for the length of the blade is x = 14 - h.
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What is the inverse of the function f(x) = 2x – 10?
Answers
Answer:
f⁻¹(x) = (1/2)x +5
Step-by-step explanation:
In y = f(x), swap the variables, then solve for y. The expression you get is f⁻¹(x).
... y = 2x -10
... x = 2y -10 . . . . . . swapped variables
... x +10 = 2y . . . . . add 10
... (1/2)x + 5 = y . . . . divide by 2
... f⁻¹(x) = (1/2)x + 5 . . . . . . rewrite using function notation
____ as 9 hundreds is 9 thousands
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Ten as 9 hundreds is 9 thousands.
What is place value?
Place value is the value of each digit in a number.
For example 5 in 350 is 5 tens or 50.
The given digit is 9 thousand which can be written as 9,000
It can be written as,
9,000 = 9 x 1000
or,9,000 = 9 x 10 x 100
So, for require 9 hundreds multiplying 9 by 100 in the above expression
9,000 = 10 x 900
which can be described as Ten as 9 hundreds is 9 thousand.
Hence, ten as 9 hundreds is 9 thousands
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10 as 9 hundreds is 9 thousands.
How to Obtain place values from a given number ?Suppose a number 12345 is given this can be written as
10000 + 2000 + 300 + 40 + 5 if we sum up all these we will get back our given number.
Now if we are asked what is the place value of 2 & 4
So, the place value of 2 in the given number is 2000 & the place value of 4 is 40.
Place value is defined as the value based on the position of that number whether it's in thousand's place or ten's or in 1's place.
In the given question
___ as 9 hundreds is 9 thousand
⇒ ____ as 900 is 9000
if we divide 9000/900 = 10 we will get our answer.
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In a right triangle, he measure of one acute angle is 3 times the sum of the other acute angle and 8, Find the measure of angle 1 and 2
Answers
The sum of the interior angles of a triangle is always 180 degrees. Therefore, 90 + y + 3(y+8) = 180, and so y + 3y + 24 = 90 => 4y= 66, and y = 66/4 = 16.5 degrees.
Let's check: If we're right, then y + 3(y+8) = 90
16.5 + 3(16.5 + 8) = 90 ?
Yes. (check it yourself)
Thus, the 3 angles of this right triangle are 90, 16.5 and 73.5; they add up to 180 degrees.
The measure of angles 1 and 2 are 16.5 and 73.5 respectively.
The sum of the two acute angles is complementary.
Let the complementary acute angles be x and y
Since they form a right angle triangle, hence;
x + y = 90 ............................. 1
If the measure of one acute angle is 3 times the sum of the other acute angle and 8, this is expressed as x = 3(y + 8)
Substitute the value of x into the equation 1 as shown:
3(y+8) + y = 90
3y + 24 + y = 90
4y + 24 = 90
4y = 90 - 24
4y = 66
y = 66/4
y = 16.5
Get the other acute angle:
x = 90 - y
x = 90 - 16.5
x = 73.5 degrees
Hence the measure of angles 1 and 2 are 16.5 and 73.5 respectively.
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The volume of 10000 drops of liquid is 10 fluid ounces what iscthe volume of 10 drops
Answers
-volume of 10,000 drops is 10 fluid ounces
Step 1: Divide 10,000 by 10 (to find how much we need to divide 10 by to get our answer)
10,000/10=1,000
Step 2: Divide 10 by 1,000 (to find our answer)
10/1,000=0.01
Our answer is 0.01. The volume of 10 drops of liquid is 0.01 fluid ounces.
The volume of 10 drops of liquid is approximately 0.0001 fluid ounces.
To find the volume of 10 drops of liquid, we can use the given information that the volume of 10000 drops is 10 fluid ounces. Let's set up a proportion to solve for the volume of 10 drops.
Let V be the volume of 10 drops in fluid ounces.
We know that the volume of 10000 drops is 10 fluid ounces, so we can write:
10,000 drops / V = 10 fluid ounces / 10 drops
Now, cross-multiply and solve for V:
10,000 drops * 10 drops = 10 fluid ounces * V
100,000 drops² = 10 fluid ounces * V
Now, divide both sides by 100,000 drops^2 to solve for V:
V = 10 fluid ounces / 100,000 drops^2
V ≈ 0.0001 fluid ounces
Therefore, the volume of 10 drops of liquid is approximately 0.0001 fluid ounces.
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If the CPI (consumer price index) of 141 increased 8.3 % this year. What was the end of year CPI?
Answers
If the CPI increased by 8.3%, therefore this means that there was a fractional increase of 0.083. So amount increased is:
CPI increase = 141 * 0.083 = 11.703
Therefore the end of year CPI is the sum of the original and the increase:
end of year CPI = 141 + 11.703 = 152.703
Answer:
152.703
What is the product
3/8 * (-3/6)
Enter your answer as a fraction, in simplified form, please
Answers
The points at x equals=_______ and xequals=_______ are the inflection points on the normal curve
Answers
Taking the first derivative, we get f'(x) = –(x–µ)/(σ³/√2π) exp[–(x–µ)²/(2σ²)] = –(x–µ) f(x)/σ².
The second derivative would be f"(x) = [ –(x–µ) f(x)/σ]' = –f(x)/σ² – (x–µ) f'(x)/σ² = –f(x)/σ² + (x-µ)² f(x)/σ⁴.
Setting this expression equal to zero, we get
–f(x)/σ² + (x-µ)² f(x)/σ⁴ = 0
Multiply both sides by σ⁴/f(x):
–σ² + (x-µ)² = 0
(x-µ)² = σ²
x-µ= + – σ
x = µ +– σ
So the answers are x = µ – σ and x = µ + σ.
A biker traveled 20 miles in 4 hours. A unit rate to describe this would be 5 miles per hour. What is another unit rate in this situation?
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Raphael graphed the functions g(x) = x + 2 and f(x) = x – 1. How many units below the y-intercept of g(x) is the y-intercept of f(x)? The y-intercept of f(x) is units below the y-intercept of g(x).Raphael graphed the functions g(x) = x + 2 and f(x) = x – 1. How many units below the y-intercept of g(x) is the y-intercept of f(x)? The y-intercept of f(x) is units below the y-intercept of g(
Answers
Answer:
The y-intercept of f(x) is 3 units below the y-intercept of g(x).
Step-by-step explanation:
We are given,
The functions [tex]f(x)=x-1[/tex] and [tex]g(x)=x+2[/tex].
Now, y-intercept is the point where the graph of the function crosses y-axis.
So, y-intercept is obtained when x= 0.Substituting x= 0 in the functions, we get,
[tex]f(0)=0-1\\f(0)=-1[/tex] and [tex]g(0)=0+2\\g(0)=2[/tex].
Thus, we get that,
The y-intercept of the the function f(x) is -1.
The y-intercept of the function g(x) is at 2.
Thus, the y-intercept of f(x) is 2-(-1)= 3 units below the y-intercept of g(x) as seen below.
Given the following triangle, if c = 17 and a = 15, find the measure of A. 28° 41° 62°
Answers
Using trig, a is the side opposite A, and c is the hypotenuse.
Therefore using SOH-CAH-TOA, sin < = O/H = opposite/hypotenuse:
So sin A = 15/17 = 0.882
[tex]So \: arcsin \: ( {sin}^{ - 1} ) \: of \: 0.882 \: = a[/tex]
A = 61.92° = 62°
Which of the following sets shows all the numbers from the set {2, 3, 4, 5} that are part of the solution to the inequality 4n + 6 > 22?
Answers
4(5)+6= 26
26>22
Well, in this type of question, we just simply need to find the value of n
4n + 6 > 22
4n > 22 - 6
4n > 16
n > 4
From the set, the only number that bigger than 4 is 5.
For proof:
- first, try to replace n with 4
4 (4) + 6 > 22
22 > 22 ..................................Wrong
- then we can try to replace n with a number that is bigger than 4
4(5) + 6 >22
26 > 22 ..................................Correct
in six years, clem kadiddlehopper will be 5 times as old as he was 26 years ago how old is he now?
Answers
in 6 years, he will be x+6 years old
that is 5 times as old as 26 years ago or when he was x-26 years old
so
x+6=5(x-26)
distribute the 5
x+6=5x-130
minus x both sides
6=4x-130
add 130 from boths ides
136=4x
divide both sides by 4
34=x
x=34
he is 34 now
The question involves setting up an equation to determine Clem Kadiddlehopper's current age based on his age in six years and 26 years ago. By solving the equation x + 6 = 5(x - 26), we find that Clem is currently 34 years old.
Explanation:Explanation:
The question asks us to determine Clem Kadiddlehopper's current age based on information about his age in future and past years. Let's define Clem's current age as x years old.
In six years, he will be x + 6 years old. It is stated that in six years, Clem will be five times as old as he was 26 years ago. Since 26 years ago he was x - 26 years old, we can write the equation: x + 6 = 5(x - 26).
To find Clem's age, we will solve the equation:
x + 6 = 5(x - 26)x + 6 = 5x - 1304x = 136x = 34Therefore, Clem Kadiddlehopper is currently 34 years old.
A building casts a 250 meter long shadow at the same time a nearby post 6 meters high casts a shadow 30 meters long what is the height of the building
Answers
Jay went to an amusement park. The park charges an entrance fee of $10.50 and $4.50 for every ride. Jay spent $46.50 on entrance fees and rides. Which fuction can be used to find the number of rides he went on?
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The function to find the number of rides Jay went on is [tex]\( 10.50 + 4.50x = 46.50 \)[/tex]
Let x be the number of rides Jay went on.
The cost of the entrance fee is $10.50, and the cost per ride is $4.50. The total amount Jay spent is $46.50. The equation representing this scenario is:
[tex]\[10.50 + 4.50x = 46.50\][/tex]
To find the number of rides, you can solve for x:
1. Subtract the entrance fee from the total amount:
[tex]\[ 46.50 - 10.50 = 36.00 \][/tex]
2. Divide by the cost per ride:
[tex]\[ \frac{36.00}{4.50} = 8 \][/tex]
So, Jay went on 8 rides.
The function to find the number of rides x is:
[tex]\[f(x) = 10.50 + 4.50x\][/tex]
Setting this equal to the total expenditure ($46.50), the function to find x is:
[tex]\[10.50 + 4.50x = 46.50\][/tex]
How Much Water Can Be Held By A Cylindrical Tank With A Radius Of 12 Feet And A Height Of 30 Feet
Answers
The answer is 13,571.68 feet ^3 of water
V= (3.14)(12^2)(30)
12 squared or 12x12 is 144.
V=(3.14)(144)(30)
Multiply the 3 numbers.
13,564.8 is the product.
So the volume of the Cylindrical tank is 13,564.8.
If you are still don't understand I can help more:)
The school janitor is going to purchase a vacuum cleaner to use in the classrooms. The regular price of a vacuum cleaner is $70. The janitor can buy a used one for $28. How much money will he save if he buys the used vacuum cleaner?
Answers
What is the solution of the proportion 5/x+4=3/x-2
Answers
How many pounds-mass per cubic foot is 40 grams per cubic centimeter?
Question 1 options:
500 lbm/ft^3
3,200 lbm/ft^3.
2,500 lbm/ft^3
1,200 lbm/ft^3
Answers
To convert grams per cubic centimeter to pounds-mass per cubic foot, you can use the conversion factors. By applying the conversion factors of 1 lb = 454 g and 1 ft³ = (30.5 cm)³, you can calculate that 40 grams per cubic centimeter is equal to 500 pounds-mass per cubic foot.
Explanation:To convert grams per cubic centimeter to pounds-mass per cubic foot, we need to use conversion factors. Firstly, we need to convert grams to pounds by using the conversion factor 1 lb = 454 g. Then, we convert cubic centimeters to cubic feet by using the conversion factor 1 ft³ = (30.5 cm)³. Finally, we combine the two conversion factors to find the desired unit: pounds-mass per cubic foot.
Given:
40 grams per cubic centimeterConversion factor:
1 lb = 454 g1 ft³ = (30.5 cm)³Calculation:
40 g/cm³ * (1 lb/454 g) * [(30.5 cm)³/1 ft³] = 40 * 1/(454 * (30.5)³) lb/ft³Simplifying the calculation gives:
40/(454 * (30.5)³) lb/ft³ = 500 lbm/ft³Therefore, 40 grams per cubic centimeter is equal to 500 pounds-mass per cubic foot.
Is the relationship between the temperature scales proportional
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The formula for temperature Fahrenheit involves an offset (y-intercept); this is one reason I claim that the relationship in question is NOT proportional.
2.1, -2.1, 2 and 2 1/11, -2 from least to greatest show work
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so we have -2.1, -2
then, the positives. you have 2.1, 2, and 2 1/11 first we know 2 is the least of them. so now we just need to figure out if 2.1 is greater than or less than 2 1/11. we can convert the decimal to a fraction. so 2.1 is 2 1/10 and 1/10 is greater than 1/11. so it goes 2, 2 1/11, 2.1
then putting it all together: -2.1, -2, 2, 2 1/11, 2.1
Q: Write the slope intercept form of the equation of the line through the given point with the given slope.
Both problems; provide an explanation, please! Thank you!
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[tex]\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ 2}}\quad ,&{{ -1}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies 0 \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-(-1)=0(x-2) \\\\\\ y+1=0\implies \boxed{y=-1}[/tex]
8)
[tex]\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ 5}}\quad ,&{{ 1}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies 3 \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-1=3(x-5) \\\\\\ y-1=3x-15\implies y=3x-15+1\implies \boxed{y=3x-14}[/tex]
The ray GJ is the angle bisector of angle FGH and Measurement FGH =50 degrease what is the measurement of angle FGJ
Answers
if FGH is 50°, then its angle bisector will cut it into two equal halves.
∠FGJ=25°
Let x have a poisson distribution with a variance of 3. find p(x = 2).
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[tex]\mathbb P(X=2)=\dfrac{e^{-\sqrt3}(\sqrt3)^2}{2!}=\dfrac3{2e^{\sqrt3}}\approx0.2654[/tex]
The probability that a Poisson random variable X equals 2, given that its variance is 3, is approximately 0.2240.
Explanation:The student asks about finding the probability that a Poisson random variable X takes on a value exactly equal to 2, given that the variance of X is 3. We know for a Poisson distribution, the variance is equal to its mean, which is denoted by λ (lambda). Therefore, λ = 3.
Using the formula for the Poisson probability mass function (PMF), P(X = k) = (e^(-λ) * λ^k) / k!, we can calculate P(X = 2). Substituting λ = 3 and k = 2, we have:
P(X = 2) = (e^(-3) * 3^2) / 2! = (0.0497871 * 9) / 2 = 0.224041.
We can round this probability to four decimal places:
P(X = 2) ≈ 0.2240.
Fifty eight thousand kilograms of solid waste is equivalent to how many metric tons
Answers
Answer:58 metric ton
Step-by-step explanation:
Given
Fifty eight thousand kilogram of solid waste
We need to convert it into metric tons
and we know 1 metric ton is equivalent to one thousand kilogram i.e. 1000 kg
so 58,000 kg is equivalent to 58 metric ton
STVU is an isosceles trapezoid. If SV = 6x - 5 and TU = 2x + 7, find the value of x.
x=3
Answers
so SV = TU
6x - 5 = 2x + 7
6x - 2x = 7 + 5
4x = 12
x = 3
answer
x = 3
what is 50 divided by 2.5 divided by 0.04
Answers
20 divided by .04 = 500
The value of the 50 divided by 2.5 divided by 0.04 is equal to 500.
To calculate 50 divided by 2.5 divided by 0.04, should follow the order of operations,
which is parentheses, exponents, multiplication and division (from left to right), and finally addition and subtraction (from left to right).
However, there are no parentheses or exponents in this expression, so we can proceed directly to multiplication and division:
50 ÷ 2.5 ÷ 0.04
First, divide 50 by 2.5:
50 ÷ 2.5 = 20
Next, divide the result (20) by 0.04:
20 ÷ 0.04 = 500
Therefore, 50 divided by 2.5 divided by 0.04 equals 500.
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Write and solve an equation for the situation. Eight and one-half years ago, Steven was 7 years old. How old is he now? Make sure you explain and know your answer. I am confused and frustrated, also, I have been working of this for a while and I do not fully understand. Thanks, :). Answer Fast. This means a lot.
Answers
n-8.5=7
n=7+8.5, or 15.5
☺☺☺☺
Eight and one-half years ago the age of Steven was 7 years, then the present age of Steven is 15.5 years.
What is an equation?Mathematical equations with two algebraic symbols on either side of the equal (=) sign are called equation. This connection is illustrated by the left and right expression being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.
Assume the current age of Steven is x years.
From the given information in the question,
8.5 years ago from now,
x - 8.5 = 7 years
x = 15.5 years.
So, the current age is 15.5 years.
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120t-0.4t^4+1000=0
How can i solve this?
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Find three consecutive odd integers whose sum is 87
Answers
3x + 6 = 87
3x = 81
x = 27
The numbers are 27, 29, and 31
Step-by-step explanation: Three consecutive odd integers are represents as follows.
X ⇒ first integer
X + 2 ⇒ second integer
X + 4 ⇒ third integer
Since the sum of these is 87, our equation reads X + X + 2 + X + 4 = 87.
Simplifying on the left, we get 3x + 6 = 87.
Subtracting 6 from both sides, 3x = 81.
Now divide both sides by 3 and x = 27.
Since x, our first odd integer is 27, our next consecutive odd integer will be X + 2 or 27 + 2 which is 29 and X + 4 would be 31.