Hi there! Hopefully this helps!
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1 / 2 / 3 = 0.16666666666.
0.16666666666 in fraction form: 1/6.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Firstly we need to divide 1 into halves (halves is "2", 1 / 2 = 0.5.)
Now that we have 0.5, we need to divide 0.5 by 3.
0.5 / 3 = 0.16666666666
Answer:
1/6
Step-by-step explanation:
Hey there!
Well let's start with,
1 ÷ 2 = .5
.5 ÷ 3 = .1666666 repeating
As a fraction it would be 1/6
Hope this helps :)
y = f(x) = 2x
Find f(x) when x = 2.
Enter the correct answer.
Answer:
f(x) = 4Step-by-step explanation:
f(x) = 2x
When x = 2
Substitute the value of x into f(x)
That's
f(2) = 2(2)
= 4
Hope this helps you
Answer:
f(2)= 4
Step-by-step explanation:
To find f(2) we will use y=2x since f(x)=y
●y=2*2= 4 wich is f(2)
evaluate 1/2^-2x^-3y^5 for x=2 and y=-4
Answer:
[tex] - \frac{1}{32} [/tex]Step-by-step explanation:
Given,
x = 2
y = - 4
Now, let's solve:
[tex] \frac{1}{ {2}^{ - 2} \: {x}^{ - 3} \: {y}^{5} } [/tex]
plug the values
[tex] \frac{1}{ {2}^{ - 2} \: {(2)}^{ - 3} \: {( - 4)}^{5} } [/tex]
A negative base raised to an odd power equals a negative
[tex] \frac{1}{ {2}^{ - 2} \times {2}^{ - 3} \times {( - 4}^{5}) } [/tex]
Determine the sign of the fraction
[tex] - \frac{1}{ {2}^{ - 2} \times {2}^{ - 3} \times {4}^{5} } [/tex]
Write the expression in exponential form with a base of 2
[tex] - \frac{1}{ {2}^{ - 2} \times {2}^{ - 3} \times {2}^{10} } [/tex]
Calculate the product
[tex] - \frac{1}{ {2}^{5} } [/tex]
Evaluate the power
[tex] - \frac{1}{32} [/tex]
Hope this helps...
Best regards!!
I would like to say that people need to work harder on writing good answers.
Answer:
Yes, it can.
Step-by-step explanation:
Looking at this table, we can see that each type of hat is ALWAYS next to the same type of flower.
Berets are ALWAYS next to Daffodils.
Panamas are ALWAYS next to Sunflowers.
Cloches are ALWAYS next to Violets.
Bowlers are ALWAYS next to Irises.
Fedoras are ALWAYS next to Narcissuses.
If we assume that every type of FLOWER is a number and every type of HAT is also a number, these will all match up.
So, they are consistent.
This means that the type of flower can be represented as a function of the type of hat.
Hope this helped!
Answer:
No
Step-by-step explanation:
There is not a known causation or correlation between the two variables.
Which data distribution would most likely have a mean and median that are not close in value? Bar graph. The horizontal axis is unnumbered. The vertical axis is numbered 0 to 50. The first bar is 8. The second bar is 30. The third bar is 42. The fourth bar is 29. The fifth bar is 9. Bar graph. The horizontal axis is unnumbered. The vertical axis is numbered 0 to 50. The first bar is 21. The second bar is 44. The third bar is 35. The fourth bar is 45. The fifth bar is 20. A bar graph. The horizontal axis is unnumbered. The vertical axis is numbered 0 to 50. The first bar is 38. The second bar is 43. The third bar is 21. The fourth bar is 5. The fifth bar is 1.
Answer:
The third one.
Step-by-step explanation:
The last bar graph is skewed to the right, since the values of its fourth and fifth bars are way smaller than the values of its first, second, and third graphs. The drastically smaller values pull down the mean of the last bar graph, making it be more different from the median.
Comparatively, bar graphs one and two have approximately symmetrical distributions of numbers on both sides of the central bar. This means that their mean is balanced out on both sides and that neither of them is significantly skewed left or right.
A bar graph. The horizontal axis is unnumbered. The vertical axis is numbered 0 to 50. The first bar is 38. The second bar is 43. The third bar is 21. The fourth bar is 5. The fifth bar is 1 is data distribution would most likely have a mean and median that are not close in value.
We have to determine, which data distribution would most likely have a mean and median that are not close in value.
According to the question,
The mean and the median both reflect the skewing, but the mean reflects it more.
The last bar graph is skewed to the right since the values of its fourth and fifth bars are way smaller than the values of its first, second, and third graphs.
The drastically smaller values pull down the mean of the last bar graph, making it be more different from the median.
The mean and the median are the same. This example has one mode (unimodal), and the mode is the same as the mean and median.
Bar graphs one and two have approximately symmetrical distributions on both sides of the central bar.
This means that their mean is balanced out on both sides and that neither of them is significantly skewed left or right.
Hence, The horizontal axis is unnumbered. The vertical axis is numbered 0 to 50. The first bar is 38. The second bar is 43. The third bar is 21. The fourth bar is 5. The fifth bar is 1.
To know more about Probability click the link given below.
https://brainly.com/question/23044118
Marta Fuentes had a balance of $1,200.50 in her checking account. The bank issued her a credit of
$505 and charged her $12 for new checks. Thee will be no outstanding checks or deposits. What
should her checkbook balance be?
Answer:
$683.50Step-by-step explanation:
Initial balance of Marta Fuentes = $1200.50
Charge made by her bank;
Credit of $505 and Charge on new checks is $12.
Total charge incurred = $505+$12
Total charge incurred = $517
Since there will be no outstanding checks or deposit, her checkbook balance will be the difference between the initial balance and amount charged by the bank.
Checkbook balance = $1200.50 - $517
Checkbook balance = $683.50
Hence her checkbook balance should be $683.50
Hey statue is mounted on top of a 25 foot hill from the base of the hill to where you are standing is 53 feet in the statue subtends an angle of 12.4 to where you are standing find the height of the statue
Answer:
The height of the statue is 217 m
Step-by-step explanation:
The hill is 25 ft above the ground,
you are standing 53 ft from the base of the hill,
angle of depression from the top of the angle to where you stand is 12.4°
Let us designate the total height from the base of the hill to the top of the statue as y.
This problem will then form a right angle triangle problem, with the base as the opposite side to the angle, and the total height of the statue and the hill as the adjacent side.
given the opposite as 53 ft,
and the adjacent as y,
and angle ∅ = 12.4°
we use tan ∅ = opp/adj
tan 12.4 = 53/y
0.219 = 53/y
y = 53/0.219 = 242 m
But this height y from base of the hill to the top of the statue is equal to the height of the hill from the base which is 25 ft, and the height of the statue from the top of the hill. This means
y = 242 = 25 + n
where n is the height of the statue.
242 = 25 + n
n = 242 - 25 = 217 m
Select the sequences that are geometric.
18, 36, 54, 72, …
4.1, 8.2, 16.4, 32.8, …
–7, 14, –28, 56, …
980, 784, 627.2, 501.76, …
5, 2, –1, –4, …
Answer:
BCD
Step-by-step explanation:
Answer: B,C & D
Step-by-step explanation:
Subtract -134 from the sum of 38 and -87.
Answer:
[tex]\boxed{85}[/tex]
Step-by-step explanation:
Sum of 38 and -87:
=> 38 + (-87)
=> 38 - 87
=> -49
Subtraction of -134 from -49:
=> -49 - (-134)
=> -49 + 134
=> 85
If a test has 40 questions and you get 200 points for the whole test, how many points are each question worth?
Answer:
5
Step-by-step explanation:
To find the points for each question, you must divide the number of points (200) by the number of questions (40) to get the number of points for each question
[tex]\frac{200}{40}[/tex]
Divide 200 by 40 to get
[tex]\frac{5}{1}[/tex] or [tex]5[/tex]
Hope this helps. If you have any follow-up questions, feel free to ask.
Have a great day!
Answer:
5 points
Step-by-step explanation:
200points / 40 questions = 5points/1question
then:
1 questión worths 5 points
Please answer it now in two minutes
Answer:
Area of the triangle WXY = 365.3 mm²
Step-by-step explanation:
By applying Sine rule in the given triangle XYW,
[tex]\frac{\text{SinY}}{\text{WX}}=\frac{\text{SinX}}{\text{YW}}[/tex]
[tex]\frac{\text{Sin70}}{\text{WX}}=\frac{\text{Sin43}}{\text{24}}[/tex]
WX = [tex]\frac{24.\text{Sin70}}{\text{Sin43}}[/tex]
= 33.068 mm
= 33.07 mm
Area of a triangle = [tex]\frac{1}{2}a.b.\text{Sin}\theta[/tex]
where a and b are the sides of the triangle and θ is the angle between the sides a and b.
Area = [tex]\frac{1}{2}(33.07)(24)\text{SinW}[/tex]
Since, m∠X + m∠Y + m∠W = 180°
m∠W = 180 - (43 + 70)
= 67°
Area of the triangle WXY = [tex]12\times (33.07)\text{Sin67}[/tex]
= 365.29 mm²
≈ 365.3mm²
HELP
Kevin has $25 in his checking
account. If Kevin has $2.20
less than 4 times the amount
that Molly has in her
account, what is the
amount of money in
Molly's account?
Answer:
$6.8
Step-by-step explanation:
Let x be the amount of money in Molly's amount
according to question,
4x-25=2.20
4x=2.20+25
4x=27.20
x=27.20/4
x=6.8
So,the amount of money in Molly's amont is $6.8
Answer: $6.80
Step-by-step explanation:
We will represent the amount of money that Molly has with a m. So it tells us the relationship between Kevin's amount and Molly's amount. It is says Kevin has 2.20 less that 4 times Molly's amount so we could represent it by the equation.
25 = 4m -2.20 solve for m.
+2.20 +2.20
27.20 = 4m
m= 6.8
4(6.8) = 27.20 - 25 = 2.20
URGENT! PLEASE help me! Full solutions please, and no nonsense answers.
Answer:
[tex]\frac{1}{3x+52}[/tex]
Step-by-step explanation:
Given
[tex]\frac{\frac{1}{x^2+51x+50} }{\frac{2}{x+50}+\frac{1}{x+1} }[/tex]
= [tex]\frac{\frac{1}{(x+50)(x+1)} }{\frac{2(x+1)+x+50}{(x+50)(x+1)} }[/tex]
= [tex]\frac{1}{(x+50)(x+1)}[/tex] × [tex]\frac{(x+50)(x+1)}{2x+2+x+50}[/tex] ← cancel (x + 50)(x + 1) on numerator/denominator
= [tex]\frac{1}{3x+52}[/tex]
Answer:
[tex]\Large\boxed{\sf \bf \ \ \dfrac{1}{3x+52} \ \ }[/tex]
Step-by-step explanation:
Hello, please consider the following.
We need to do something with that, right !?
[tex]\dfrac{\left(\dfrac{1}{x^2+51x+50\right)}}{\left(\dfrac{2}{x+50}+\dfrac{1}{x+1}\right)}[/tex]
What can we say from [tex]x^2+51x+50[/tex] ?
The sum of the zeroes is -51=(-1)+(-50) and the product is 50 = (-1) x (-50), so we can factorise. Let's do it !
[tex]x^2+51x+50=x^2+50x+x+50=x(x+1)+50(x+1)=(x+1)(x+50)[/tex]
That's a pretty cool first result !
Now, let's play with the denominator.
[tex]\dfrac{2}{x+50}+\dfrac{1}{x+1}\\\\\text{*** We put on the same denominator which is (x+1)(x+50) ***}\\\\=\dfrac{2(x+1)}{(x+50)(x+1)}+\dfrac{x+50}{(x+1)(x+50)}\\\\=\dfrac{2(x+1)+x+50}{(x+50)(x+1)}\\\\=\dfrac{2x+2+x+50}{(x+50)(x+1)}\\\\=\dfrac{3x+52}{(x+50)(x+1)}\\[/tex]
We are almost there.
Let's combine all these results together !
[tex]\dfrac{\left(\dfrac{1}{x^2+51x+50\right)}}{\left(\dfrac{2}{x+50}+\dfrac{1}{x+1}\right)}\\\\\\=\dfrac{\left(\dfrac{1}{(x+1)(x+50)\right)}}{\left(\dfrac{3x+52}{(x+50)(x+1)}\right)}}\\\\\\=\large\boxed{\dfrac{1}{3x+52}}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Find the vertex form
Hi,
[tex]y=5x^{2} +12x-2\\y=x(5x+12)-\frac{46}{5} \\y=5(x+\frac{6}{5} )^{2}-\frac{46}{5} \\[/tex]
Have a good day.
NEED HELP ON THIS ASAP WEE WOO WEE WOO
Answer:
50
Step-by-step explanation:
what is the slope of a line parallel to the line whose equation is 3x-3y=-45
Answer:
The slope is 1Step-by-step explanation:
To find the slope first write the equation in the form
y = mx + c
where m is the slope
c is the y intercept
3x - 3y = -45
3y = 3x + 45
Divide both sides by 3
y = 3/3x + 45/3
y = x + 15
From the equation the slope = 1
Parallel lines have equal slope
So
The line parallel to the above line is also
1
Hope this helps you
Use the elimination method to solve the system of equations.
3x + 4y = 8
x-y=12
O A. (8,4)
O B. (-4,8)
C. (0,2)
O D. (8,-4)
Answer:
Option D. (8, – 4)
Step-by-step explanation:
3x + 4y = 8 ..... (1)
x – y = 12.... (2)
To solve the above equation by elimination method, do the following:
Step 1:
Multiply equation 1 by the coefficient of x in equation 2 i.e 1.
Multiply equation 2 by the coefficient of x in equation 1 i.e 3. This is illustrated below:
1 × Equation 1
1 × (3x + 4y = 8)
3x + 4y = 8 ...... (3)
3 × Equation 2
3 × ( x – y = 12)
3x – 3y = 36......(4)
Step 2:
Subtract equation 3 from equation 4. This is illustrated below:
. 3x – 3y = 36
– (3x + 4y = 8)
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
– 7y = 28
Divide both side by the coefficient of y i.e –7
y = 28/–7
y = – 4
Step 3:
Substitute the value of y into any of the equation to obtain the value of x. In this case, we shall substitute the value of y into equation 2 as shown below:
x – y = 12
y = –4
x – (–4) = 12
x + 4 = 12
x = 12 – 4
x = 8
Therefore, the solution to the equation above is (8, – 4)
Answer:
(8, – 4)
Step-by-step explanation:
my math teacher told me
Question 20 of 32
If f(x) = 4x2 - 6 and g(x) = x2 - 4x - 8, find (f - g)(x).
O A. (f- g)(x) = 5x2 - 4x - 14
O B. (f - g)(x) = 3x2 - 4x - 2
O c. (f- g)(x) = – x2 - 14
O D. (f- g)(x) = 3x2 + 4x + 2
SUBMIT
(f - g)(x) = f(x) - g(x)
(f - g)(x) = ( f(x) ) - ( g(x) )
(f - g)(x) = (4x^2 - 6) - ( x^2 - 4x - 8)
(f - g)(x) = 4x^2 - 6 - x^2 + 4x + 8
(f - g)(x) = (4x^2-x^2) + 4x + (-6+8)
(f - g)(x) = 3x^2 + 4x + 2
Answer: Choice DKala's final exam has true/false questions, worth 3 points each, and multiple choice questions, worth 4 points each. Let x be the number of true/false questions she gets correct, and let y be the number of multiple choice questions she gets correct. She needs at least 82 points on the exam to get an A in the class. Using the values and variables given, write an inequality describing this.
Answer:
3x + 4y ≥ 82
Step-by-step explanation:
3x + 4y ≥ 82
we can read as: 3 time of right answers of true/false plus 4 times of right answers of multiple choice must be bigger or at least 82
Write the following phrase as an expression. "7 more than n"
Answer:
7+n
Step-by-step explanation:
More indicates that we are adding an amount to n.
So since it is 7 more, we need to add 7 to n.
Note that an expression does not include an equal sign, so we are done.
Other commonly seen phrases are:
less than -> indicates subtraction
product of -> indicates multiplication
divided by -> division
which equation represents the line that is perpendicular yo y=3/2x+1 and passes through (-12,6)
Answer:
y = -2/3x - 2
Step-by-step explanation:
Step 1: Find slope m of perpendicular line
Simply take the negative reciprocal of the given line
m = -2/3
y = -2/3x + b
Step 2: Find b
6 = -2/3(-12) + b
6 = 8 + b
b = -2
Step 3: Rewrite perpendicular equation
y = -2/3x - 2
piece of wire 8 m long is cut into two pieces. One piece is bent into a square and the other is bent into a circle. (a) How much wire should be used for the square in order to maximize the total area
Answer:
piece of wire 8 m long
one piece is bent into square:
the square has four equal sides , so at least 4 m has to be cut from the wire to form a square with side=1 m.
the perimeter of the square =2L+2W=2(1)+2(1)=4 m
that is the max. amount can be cut from the wire, since the other part is bent into a circle.
( note if you cut more, the square will take the whole wire)
Perimeter=2L+2W=2(2)=2(2)=8 m and the area=2*2=4 m²)
Area and perimeter are two crucial characteristics of 2D shapes in mathematics.
The perimeter of the square exists 8 m and the area exists 4 m².
What is the perimeter and area of a square?Area and perimeter are two crucial characteristics of 2D shapes in mathematics. The area and perimeter both specify the shape's boundaries and the space they occupy, respectively. Area and perimeter are significant mathematical concepts that are used to daily life. All sizes and shapes, regular or unusual, are covered by this. Each shape's area and perimeter calculations are unique.
Piece of wire is 8 m long and one piece is bent into square:
The square has four equal sides , so at least 4 m has to be cut from the wire to form a square with side = 1 m.
The perimeter of the square = 2L + 2W = 2(1) + 2(1) = 4 m
Which exists the maximum amount that can be cut from the wire, since the other part is bent into a circle.
Perimeter = 2L + 2W =2(2) = 2(2) = 8 m and the area = 2 × 2= 4 m²
To learn more about perimeter and area, refer to:
brainly.com/question/19819849
#SPJ2
Xavier buys a two-quart bottle of juice for $5.12. What is the unit rate of the cost of the juice per fluid ounce?
Answer:
The cost is $.08 per ounce or 8 cents per ounce
Step-by-step explanation:
1 quart = 32 ounces
2 quarts = 64 pints
2 quarts costs 5.12
Take the cost and divide by the number of ounces
5.12 / 64
.08 per ounce
The cost is $.08 per ounce or 8 cents per ounce
=================================================
Explanation:
1 quart = 32 fluid ounces
2 quarts = 64 fluid ounces (multiply both sides by 2)
He paid 5.12 dollars for 64 fluid ounces, so the unit rate is 5.12/64 = 0.08 dollars per fluid ounce, or 8 cents per fluid ounce.
---------
We can think of it this way in terms of an equation
5.12 dollars = 64 fluid ounces
5.12/64 dollars = 64/64 fluid ounces ... divide both sides by 64
0.08 dollars = 1 fluid ounce
We divided both sides by 64 to turn "64 fluid ounces" into "1 fluid ounce", due to how the term "unit rate" is set up. The term "unit" means "one". Basically we're finding the cost per 1 unit, or per 1 fluid ounce.
Help please I need the answer ASAP
Answer:
please mark my answer brainliest
Step-by-step explanation:
ok
These figures are similar. The area of one is give. Find the area of the other.
Answer:
64 in²
Step-by-step explanation:
Given that the two figures are similar, therefore, the ratio of the area areas of both figures is proportional to the ratio of the square of the corresponding side lengths of both figures. This means:
[tex] \frac{100}{x} = \frac{10^2}{8^2} [/tex]
Where x is the area of the other figure.
Solve for x
[tex] \frac{100}{x} = \frac{100}{64} [/tex]
Cross multiply
[tex] 100*64 = 100*x [/tex]
Divide both sides by 100
[tex] \frac{100*64}{100} = \frac{100*x}{100} [/tex]
[tex] 64 = x [/tex]
Area of the other figure = 64 in²
Please answer ASAP. A baseball is hit upward from a platform that is m high at an initial speed of 29m/s. The approximate height of the baseball, h meters, after x seconds is given by the equation: h - 1= -5x^2 + 29x a) determine the time period for which the baseball is higher than 18m. Give the answer to the nearest tenth of a second. Explain your strategy. b) What are the restrictions on the domain and range of the related function?
Answer:
a) about 0.7 seconds to 5.1 seconds.
b) Listed below.
Step-by-step explanation:
h - 1 = -5x^2 + 29x
h = -5x^2 + 29x + 1
a) We will find the amount of time it takes to get to 18 meters.
18 = -5x^2 + 29x + 1
-5x^2 + 29x + 1 = 18
-5x^2 + 29x - 17 = 0
We will then use the quadratic formula to find the answer.
[please ignore the A-hat; that is a bug]
[tex]\frac{-29±\sqrt{29^2 - 4 * -5 * -17} }{2 * -5}[/tex]
= [tex]\frac{-29±\sqrt{841 - 340} }{-10}[/tex]
= [tex]\frac{-29±\sqrt{501} }{-10}[/tex]
= [tex]\frac{-29 ± 22.38302929}{-10}[/tex]
= [tex]\frac{-6.616970714}{-10}[/tex] and [tex]\frac{-51.38302929}{-10}[/tex]
= 0.6616970714 and 5.138302929
So, the time period for which the baseball is higher than 18 metres ranges from about 0.7 seconds to 5.1 seconds.
b) Restrictions on the domain and range of the function are that the domain and range can never be negative, since time cannot be negative, and height cannot be negative. The height cannot exceed the vertex of the parabola, since that is the highest the ball will ever go. It cannot exceed that height since gravity will cause the ball to fall down.
Hope this helps!
Linear system please help 41 points * please please please help will give brainlist small chart
Answer:
Length 1 - Width = 19, Area = 19
Length 2 - Width = 18, Area = 36
Length 3 - Width = 17, Area = 51
Length 4 - Width = 16, Area = 64
Length 5 - Width = 15, Area = 75
Step-by-step explanation:
Area Formula: A = lw
Since we only have a combined total of 20 m to use, we have to subtract the number of length in order to find length:
Length 1 = 20 - 1 = Width 19 m
Length 2 = 20 - 2 = Width 18 m
Length 3 = 20 - 3 = Width 17 m
Length 4 = 20 - 4 = Width 16 m
Length 5 = 20 - 5 = Width 15 m
Then we simply plug in our l values and w values into the area formula:
A = 1(19) = 19 m²
A = 2(18) = 36 m²
A = 3(17) = 51 m²
A = 4(16) = 64 m²
A = 5(15) = 75 m²
width from 1-5 =
when lem
length=1, width=19
length=2,width=18
length=3,width=17
length=4,width=16
length=5,width=15
length =1,Area=19
length=2,Area=36
length=3,area=51
length=4,area=64
length=5,area=75.
Step-by-step explanation:
to get our width, we minus each length from the given value which is 20m.
e.g.
when length =1 our width becomes 20-1=19.
and you do same for the rest.
the formula for the area was given to us in the question so we use that to find the area.
A=Length×Width.
e.g when length=1, width =19
so the area becomes 1×19=
[tex] {19m}^{2} [/tex]
please note that your area should be in
[tex] {m}^{2} [/tex]
The rectangular classroom is 36ft in length and 32 feet in with. The scale drawing of the floor has a length of 9 inches. What is the area, in square inches, of the floor in the scale drawing? Explain your answer.
Answer:
72 inch²
Step-by-step explanation:
Rectangular classroom
Length=36ft
Width=32ft
scale drawing length = 9 inches
Scale drawing width=x
Ratio of the length to the scale drawing length = 36/9
Ratio of the width to the scale drawing width=32/x
To find x
36/9=32/x
Cross product
36x=32*9
x=288/36
=8
x=8
Area of a rectangle= length × width
Length=9 inches
Width=8 inches
Area of the rectangular classroom= 9 inches × 8 inches
=72 inch²
9. A solid rectangular block of copper 5 cm by 4 cm by 2 cm
is drawn out to make a cylindrical wire of diameter 2 mm.
Calculate the length of the wire.
Answer:
length = 1273.2 cm or 12.73 m
Step-by-step explanation:
Assume no loss.
diameter of wire, d = 2 mm
radius of wire, r = 1 mm = 0.1 cm
Volume of block, V = 5*4*2 = 40 cm^3
cross sectional area of wire, A = pi (r^2) = pi 0.1^2 = 0.01pi cm^2
Length of wire
= V/A
= 40 cm^3 / 0.01pi cm^2
= 4000/pi cm
= 1273.2 cm
= 12.73 m
The hypotnuse of a right triangle is three times the length of its first leg. Theblength of the other leg is four feet. Find the lengths of the first leg and the hypotnduse and enter them in the below squares in this order. For non-integer answer(s), round your answer(s) to the nearest tenth.
Answer:
Length of first leg = 1.4feet
Hypotenuse = 4.2feet
Explanation:
Since we are dealing with a right angled triangle, we will apply the Pythagoras theorem to solve the question. According to Pythagoras theorem, the square of the hypotenuse is equal to the sum if the square of the other two legs.
Mathematically, a² = b²+c² where a is the hypotenuse and b, c are the other two legs.
From the question, since hypotenuse of a right triangle is three times the length of its first leg, then a = 3b.
Also the other leg is four feet i.e c= 4
Substituting this values into the Pythagoras formula;
a²=b²+c²
(3b)² = b²+4²
9b² = b²+16
9b²-b² = 16
8b² = 16
b² = 16/8
b² = 2
b = √2
b = 1.4
Since a = 3b
a = 3(1.4)
a = 4.2
Hence, the length of the first leg is 1.4feet and that of the hypotenuse is 4.2feet both to the nearest tenth.
If angles θ and α are complementary and sin θ = 3/4, what is cos α?
Answer:
3/4
Step-by-step explanation:
Since, angles θ and α are complementary.
Therefore,
θ + α = 90°
θ = 90° - α
Taking sin both sides.
sin θ = sin (90° - α)
sin θ = cos α (sin (90° - θ) = cos θ)
Since, sin θ = 3/4.....(given)
Hence, cos α = 3/4