A 279-foot rope is cut into three pieces. The second piece is twice as long as the first. The third piece is as long as the second. How long is each piece of rope?
Answers
Step-by-step explanation:
Let's say x is the length of the first piece.
The second piece is 2x.
The third piece is 2x.
So the total length is:
x + 2x + 2x = 279
5x = 279
x = 55.8
That means 2x = 111.6.
So the first piece is 55.8 feet, the second piece is 111.6 feet, and the third piece is also 111.6 feet.
Answer:
Piece 1 : 55.8 ft
Piece 2: 111.6 ft
piece 3: 111.6 ft
Step-by-step explanation:
From the question we can see that the total length of the rope is 279 ft and as mentioned it is cut into three pieces. Since the first piece has no length we can give it a variable of x . Piece two is twice as long as piece one, so we can give it a value of 2x . Lastly, piece three is the same as piece two, so it would also be 2x.
So we can now say the following:
[tex]x + 2x + 2x = 279ft[/tex] .... now we can solve for x.
[tex]5x = 279[/tex]
[tex]x = 55.8 ft[/tex]
So we can see that piece one is 55.8 ft long . Now we can use this value to find pieces two and three.
[tex]2x = P2[/tex]
[tex]2(55.8) = P2[/tex]
[tex]111.6 = P2[/tex]
So pieces two and three are 111.6 ft long
I hope this answered your question. If you have any more questions feel free to ask away at Brainly.
Related Questions
There are 2200 students in a school. 52.5% of them are male. How many are female?
Answers
Answer:
1045 females
Step-by-step explanation:
First, lets calculate how many males there are.
52.5% of 2200 = 1155
Then, calculate the difference between the males and the total.
2200-1155=1045
Have a wonderful day!
There are 1045 female students in the school
How to determine the number of female students?The proportion of male students is given as:
Male proportion = 52.5%
This means that the female proportion is:
Female = 100% - 52.5%
Female = 47.5%
The number of female students is then calculated as:
Female = 47.5% * 2200
Evaluate
Female = 1045
Hence, there are 1045 female students in the school
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The function below represents the annual interest Victoria earns on a savings account. Identify the term that represents the amount of money originally deposited in the account.
f(x) = 300(1 + 0.03)x
300
1
0.03
x
Answers
Answer:
[tex]\$300[/tex]
Step-by-step explanation:
In this problem we have a exponential function of the form
[tex]f(x)=a(b)^{x}[/tex]
where
a is the initial value ( value of the function when the value of x is equal to zero)
b is the base
r is the rate
b=1+r
we have
[tex]f(x)=300(1+0.03)^{x}[/tex]
therefore
The term that represents the amount of money originally deposited in the account is the initial value
For x=0
substitute
[tex]f(0)=300(1+0.03)^{0}[/tex]
[tex]f(0)=\$300[/tex]
Answer:
The correct option is 1.
Step-by-step explanation:
The function is
[tex]f(x)=300(1+0.03)^x[/tex]
We need to find the term that represents the amount of money originally deposited in the account. It means we need to find the initial amount.
Substitute x=0 in the given function, to find the initial value of the function.
[tex]f(0)=300(1+0.03)^(0)[/tex]
[tex]f(0)=300(1)[/tex]
[tex]f(0)=300[/tex]
The term 300 represents the amount of money originally deposited in the account. Therefore the correct option is 1.
In geometry, you can use deductive rules to.
O
A. make conjectures
O
B. prove conjectures
O
C. define terms
O
D. find patterns
Answers
In geometry, you can use deductive rules to prove conjectures
What is Coordinate Geometry?A coordinate geometry is a branch of geometry where the position of the points on the plane is defined with the help of an ordered pair of numbers also known as coordinates.
Deductive reasoning is used in geometry to start with a set of given premises or axioms, and then use logical reasoning and previously established theorems to draw conclusions or prove conjectures.
The main use of deductive rules in geometry is to prove conjectures.
A conjecture is considered proven only when it has been shown that it is logically impossible for it to be false.
Hence, in geometry, you can use deductive rules to Prove conjectures
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A certain triangle has a 30 angle and a 60 angle.
Answers
Answer:
Step-by-step explanation:
It is B, The longest side is sqrt 3 times as long as the shortest side.
Attached is a image showing the side length rules for 30-60-90 triangles.
Hope this helps :)
30-60-90 triangle is twice the length of the shortest side. That’s why the sine of 30 is 1/2, because it’s half the length of the hypotenuse
a keycode must contain 4 letters followed by 3 numbers. The letters may be any letters of the alphabet. The numbers should be any number from 0 to 5. How many different keycode combinations are there?
Answers
Answer:
98,706,816 combinations
Step-by-step explanation:
Let's make a little graphic of it:
Letters (4): ___ ___ ___ ___
Numbers (3): ___ ___ ___
In the 4 lines/placeholders of the letters, it can be ANY letter of the alphabet, it can be any 26 of them.
In the 3 lines of the numbers, it can be any number from 0 - 5, which is 6 numbers.
Thus we can say:
Letters = 26 * 26 * 26 * 26 = 456,976
Numbers = 6 * 6 * 6 = 216
Their PRODUCT is the number of combinations possible.
456,976 * 216 = 98,706,816 combinations
Write an equation: 1/5 of a shipment of books weights 25 pounds
Answers
To find the total weight of the shipment where [tex]\frac{1}{5}[/tex] weighs 25 pounds, we use the equation [tex]\frac{1}{5}[/tex]W = 25 and solve for W, leading to a total weight of 125 pounds.
The question is asking us to write an equation that represents the situation where [tex]\frac{1}{5}[/tex] of a shipment of books weighs 25 pounds.
To find the total weight of the shipment, we should set this up as an equation where the total weight of the shipment is represented by W. Since [tex]\frac{1}{5}[/tex] of the shipment weighs 25 pounds, we can write the equation as [tex]\frac{1}{5}[/tex] W = 25.
To find the weight of the whole shipment, we need to multiply both sides of the equation by 5, which will give us
W = 125 pounds.
When converting units such as pounds to ounces, we use the unit equivalence 1 pound = 16 ounces.
If the weight of the books needed to be in ounces, we could convert 125 pounds by multiplying
125 x 16 = 2000 ounces
Rational numbers do NOT include:
infinite decimals
repeating decimals
terminating decimals
Answers
Answer:
Infinite decimals that do not repeat.
Step-by-step explanation:
Repeating decimals can be as fractions where the top and bottom are integers.
Examples: .3333333333333333333333333333333.... can be written as 1/3.
or .19191919191919191919..... can be written as 19/99.
Terminating decimals can also be written as fractions where the top and bottom are integers.
Examples: .11=11/100 or .161=161/1000
Any number that can be written as a fraction where the top and bottom are integers (bottom integer not 0)
is a rational number.
Repeating decimals are infinite. So what I think they mean by infinite here is numbers like [tex]\pi[/tex] or [tex]\sqrt{2}[/tex]. There are not rational. They cannot be written as a fraction where the top and bottom are integers.
Answer:
Rational numbers do NOT include:
infinite decimals
Step-by-step explanation:
A, B, C, and D have the coordinates (-8,1), (-2,4), (-3, -1), and (-6,5) respectively. which sentence about the points is true?
A. A, B,C, AND D LIE ON THE SAME LINE
B. LINE AB AND LINE CD ARE PERPENDICULAR
C. LINE AB AND LINE CD ARE PARALLEL LINES
D. LINE AB AND LINE CD ARE INTERSECTING LINES BUT ARE NOT PERPENDICULAR
E. LINE AC AND LINE BD ARE PARALLEL LINES
Answers
Answer:
Option B is correct.
Step-by-step explanation:
To check if the lines are parallel or perpendicular, we need to find the slope of lines AB and CD
A=(-8,1), B= (-2,4), C= (-3, -1), and D= (-6,5)
Slope of AB = y₂-y₁/x₂-x₁
Slope of AB = 4-1/-2-(-8)
Slope of AB = 3/-2+8
Slope of AB = 3/6
Slope of AB = 1/2
Slope of CD = y₂-y₁/x₂-x₁
Slope of CD = 5+1/-6-(-3)
Slope of CD = 6/-6+3
Slope of CD = 6/-3
Slope of CD = -2
Lines are parallel if Slope of AB = Slope of CD
Lines are perpendicular if Slope of Ab = -1/Slope of CD
So, Slope of AB = 1/2
Slope of CD = -2
So, LINE AB AND LINE CD ARE PERPENDICULAR
Option B is correct.
There are 32 more apple than oranges in a box. 3/5 of the oranges and 1/3 of the apples are overripe. If the number of overripe apples and the number of oranges is the same, how many pieces of overripe fruit are there?
Answers
The answer is:
There is a total of 48 overripe fruit.
Why?To calculate the number of pieces of overripe fruit we have, we need to write two equations to create a relationship between the number of apples and oranges.
Let be "x" the number of oranges, so:
[tex]Oranges=x\\Apples=x+32[/tex]
Now, we know that 3/5 of the oranges and 1/3 of the apples are overripe, so:
[tex]OverripeApples=\frac{1}{3}(x+32)\\\\OverripeOranges=\frac{3}{5}(x)[/tex]
Then, we have a condition that states that the number of overripe apples and overripe oranges is the same, so:
[tex]\frac{1}{3}(x+32)=\frac{3}{5}(x)[/tex]
[tex]\frac{1}{3}(x)+\frac{1}{3}(32)=\frac{3}{5}(x)[/tex]
[tex]\frac{1}{3}(32)=\frac{3}{5}(x)-\frac{1}{3}(x)[/tex]
[tex]\frac{1}{3}(32)=\frac{3x*3-1*x}{15}=\frac{9x-5*x}{15}=\frac{4x}{15}[/tex]
[tex]\frac{32}{3}=\frac{4x}{15}[/tex]
[tex]\frac{32*15}{3}=4x[/tex]
[tex]\frac{480}{3}=4x[/tex]
[tex]160=4x[/tex]
[tex]\frac{160}{4}=x[/tex]
[tex]40=x[/tex]
Therefore, we have that there are 40 oranges and 72 apples (40+32).
Now, calculating the number of overripe oranges and apples, we have:
[tex]OverripeApples=\frac{1}{3}(72)=24\\\\OverripeOranges=\frac{3}{5}(40)=24[/tex]
Hence, we have that there are 24 pieces of overripe oranges and 24 pieces of overripe apples. It means that there is a total of 48 overripe fruit.
Have a nice day!
what is the inverse of the function f(x)=2x+1
Answers
Answer:The inverse of the linear function f(x)=2x+1 is f^(-1) (x) = (1/2)x-1/2
Step-by-step explanation:
The work is shown below
The boat speed in still water is 30 miles per hour. A boat travels for 3 hours downstream and returns the same distance in 5 hours.find the speed of the stream
Answers
Answer:
7.5 mph.
Step-by-step explanation:
Speed downstream = d / 3 = 30 + x where d = the distance , x =speed of the stream.
Speed upstream = d / 5 = 30 - x.
30 + x = d/3
30 - x = d/5
Adding the 2 equations
60 = d/3 + d/5
8/15 d = 60
d = 60 * 15 / 8 = 112.5 miles.
Now calculate x , the speed of the stream:
112.5 / 3 = 30 + x
x = 112.5 / 3 - 30
= 7.5 mph.
If f(x) =1/9 x-2, what is f-1(x)?
Answers
Answer:
f^-1(x) = 9(x+2)
Step-by-step explanation:
To find the inverse function, exchange x and y and then solve for y
y = 1/9 x -2
Exchange x and y
x = 1/9 y-2
Solve for y
Add 2 to each side
x+2 = 1/9 y-2+2
x+2 = 1/9y
Multiply each side by 9
9(x+2) = 9*1/9y
9(x+2) = y
The inverse function
f^-1(x) = 9(x+2)
Answer:
9x+18
Step-by-step explanation:
[tex]f^{-1}[/tex] means they want you to find the inverse function of y=1/9 x-2.
The inverse is just a swapping of x and y.
People tend to remake the y part the subject again because they want to write it as a function.
Let's start:
[tex]y=\frac{1}{9}x-2[/tex]
Swap x and y:
[tex]x=\frac{1}{9}y-2[/tex]
Now it's time to solve for y:
Add 2 on both sides:
[tex]x+2=\frac{1}{9}y[/tex]
Multiply both sides by 9:
[tex]9(x+2)=y[/tex]
Distribute:
[tex]9x+18=y[/tex]
So The inverse function is:
[tex]f^{-1}(x)=9x+18[/tex]
40 pts!! please help T^T
A football quarterback enjoys practicing his long passes over 40 yards. He misses the first pass 40% of the time. When he misses on the first pass, he misses the second pass 20% of the time. What is the probability of missing two passes in a row?
Answers
A football quarterback enjoys practicing his long passes over 40 yards. He misses the first pass 40% of the time. When he misses on the first pass, he misses the second pass 20% of the time. What is the probability of missing two passes in a row?
30%
Probability of missing two passes in a row is 0.08.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Given
Event E = A football player misses twice in a row.
P(E) = ?
Event X = Football player misses the first pass
P(X) = 0.4
Event Y = Football player misses just after he first miss
P(Y) = 0.2
Both the events are exclusive so the probability of occurring of these two events can be calculated by the formula:
P(E) = P(X).P(Y)
P(E) = 0.4*0.2
P(E) = 0.08
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What is the solution set of - x = -8?
Answers
[tex]-x=-8\\x=8[/tex]
Answer:
x = 8
Step-by-step explanation:
The solution set of - x = -8 is x=8.
- x = -8 = x = 8
Write the equation that contains the point (3, -9), and in which the graph of the line has a slope of 4 in slope-intercept form.
Answers
[tex]\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{-9})~\hspace{10em} slope = m\implies 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-9)=4(x-3) \\\\\\ y+9=4x-12\implies y=4x-21[/tex]
Solve for x -2x + 5 <7
Answers
Answer:
[tex]\large\boxed{x>-1}[/tex]
Step-by-step explanation:
In this question, we're trying to solve for x.
In other words, we're going to need to get x by itself in order to get our answer for the inequality.
Solve:
[tex]-2x + 5 <7\\\\\text{Subtract 5 on both sides to get -2x by itself}\\\\-2x<2\\\\\text{Divide both sides by -2}\\\\\text{Since you're dividing by a negative, the} < \text{will flip to} >\\\\x>-1[/tex]
When you're done solving, you should get x > -1
This means that when you solve for x, you should get x > -1
I hope this helped you out.Good luck on your academics.Have a fantastic day!Find the area of the rhombus. (4)
Answers
Answer:
24 cm2 is the answer or option d
Step-by-step explanation:
What is true about triangle ABC. Select three options
Answers
Answer: The answer is sin A = cos C
Step-by-step explanation: sin A = cos C
Answer:
It should be A, B, C
Step-by-step explanation:
Factor completely 4h2 + g.
Answers
The expression 4h² + g has no common factors or recognizable factoring patterns, and is thus already in its simplest form; it cannot be factored further.
To factor completely the expression 4h² + g, we would look for common factors or recognizable patterns like the difference of squares, perfect square trinomials, or other factoring techniques. However, since 4h² and g have no common factor and the expression is not a difference or sum of cubes, or any other known factoring pattern, it cannot be factored further (assuming g is a constant). In other factoring scenarios, one might look for techniques like grouping, but that's not applicable here either. Therefore, the expression 4h² + g is already in its simplest, factored form as there are no common factors between the terms.
What is the equation of the line (in point-slope form) that passes through the point (2,3) and is parallel to the line y−9=2/3(x+7)?
Answers
Answer:
[tex]\large\boxed{y-3=\dfrac{2}{3}(x-2)}[/tex]
Step-by-step explanation:
[tex]\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\===============================[/tex]
[tex]\text{The point-slope form of an equation of a line:}\\\\y-y_1=m(x-x_1)\\\\m-slope\\\\(x_1,\ y_1)-point\ on\ a\ line\\\\===============================[/tex]
[tex]\text{We have the equation of a line:}\ y-9=\dfrac{2}{3}(x+7)\to m_1=\dfrac{2}{3}.\\\\\text{A slope of parallel line:}\ m_2=m_1=\dfrac{2}{3}.\\\\\text{Put the value of the slope and the coordinates of the point (2, 3)}\\\text{to the equation of a line in point-slope form:}\\\\y-3=\dfrac{2}{3}(x-2)[/tex]
Answer:
The answer is y = -3/2x + 6
Step-by-step explanation:
A ship at sea, the Gladstone, spots two other ships, the Norman and the Voyager, and measures the angle between them to be 44°. The distance between the Gladstone and the Norman is 4510 yards. The Norman measures an angle of 36° between the Gladstone and the Voyager. To the nearest yard, what is the distance between the Norman and the Voyager?
Answers
Answer:
3181 yards.
Step-by-step explanation:
All the given information can be used to draw a simple diagram. The diagram shows a triangle which is formed by the ships. There are two angles given and one side is given. Therefore, the sine rule must be used to solve the question. The sine rule can be written as:
sin V / v = sin G / g.
It can be observed that the angle V is unknown, however, it can be calculated very easily. Simply use the law of triangle in which all the 3 angles sum up to 180 degrees. So V = 180 degrees - 44 degrees - 36 degrees = 100 degrees. So plugging in v = 4510 yards, V = 100 degrees, G = 44 degrees, and g = x yards into the sine rule gives:
sin 100 / 4510 = sin 44 / x.
Cross multiplying gives:
x*sin 100 = 4510*sin 44
Making x the subject gives:
x = (4510*sin 44)/sin 100.
x = 3181 yards (to the nearest yard).
Therefore, Norman and Voyager are 3181 yards apart from each other!!!
Find the equation for the linear function that passes through the points ( see photo )
Answers
Answer:
[tex]f(x)=\frac{3}{2}x-2[/tex]
Step-by-step explanation:
step 1
Find the slope m
we have
(-2,-5) and (4,4)
The slope is equal to
[tex]m=\frac{4+5}{4+2}[/tex]
[tex]m=\frac{9}{6}[/tex]
simplify
[tex]m=\frac{3}{2}[/tex]
step 2
Find the equation of the line into slope point form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=\frac{3}{2}[/tex]
[tex](4,4)[/tex]
substitute
[tex]y-4=\frac{3}{2}(x-4)[/tex]
step 3
Convert to slope intercept form
[tex]y-4=\frac{3}{2}(x-4)[/tex]
[tex]y=\frac{3}{2}x-6+4[/tex]
[tex]y=\frac{3}{2}x-2[/tex]
Convert to function notation
[tex]f(x)=\frac{3}{2}x-2[/tex]
Write 0.00021 correct to 1 significant figure
Answers
Answer:
0.0002
Step-by-step explanation:
0.00021 is a 2 significant figure .after the decimal point the zero can be counted as a significant figure or not ,it depends
Answer:
0.0002.
Step-by-step explanation:
The first significant figure is 2 and since 1 is the second significant figure ( 1 is < 5) the 2 is retained.
3 integers less than 25 range of 10 mean of 13
Answers
Answer:
8, 13, 18
Step-by-step explanation:
If we want the mean to be 13, and there are 3 integers, that means the sum of all 3 integers must be 39. I started at 13 and counted 5 up and 5 down, which already makes sure of the range and the mean is 13 (since it's balanced with 13 being the middle), therefore, 13+5 is 18, 13-5=8.
anyone willing to help out really quick?^^
Answers
Answer:
15.86 inches
Step-by-step explanation:
Area of rectangle = length times width
l = ∛81 inches
w = 3 2/3 inches
= l x w
= ∛81 x 3 2/3
= 15.86 inches
help please Compute the volume of a sphere with a radius of 6 inches. a. 864π in3 b.72π in3 c. 216π in3 d. 288π in3
Answers
Answer:
d. 288π in3
Step-by-step explanation:
The volume of a sphere is given by
V = 4/3 pi r^3
The radius is 6
V = 4/3 pi 6^3
V = 288 pi in^3
The domain of r:(3,-2)(1,2)(-1,-4)(-1,2)
Answers
Answer:
domain {-1,1.3}
Step-by-step explanation:
The domain is the input values, or in this case the first or x values
domain {3,1,-1,-1}
We do not put the same value twice
domain {3,1,-1}
We like to put them in numerical order
domain {-1,1.3}
A bag contains 4 blue balls, 7 yellow balls and 4 white balls. Event A is defined as drawing a blue ball on the first draw and event B is defined as
drawing a white ball on the second draw. If two balls are drawn from the bag, one after the other and not replaced,
what is P(B|A) expressed in simplest form?
Answers
Final answer:
The conditional probability of drawing a white ball on the second draw after a blue ball has been drawn on the first draw from a bag of balls without replacement is 2/7.
Explanation:
The question asks for the probability of drawing a white ball on the second draw, given that a blue ball has been drawn on the first draw (P(B|A)) from a bag containing 4 blue balls, 7 yellow balls, and 4 white balls, without replacement.
Firstly, we calculate the total number of balls in the bag: 4 blue + 7 yellow + 4 white = 15 balls.
For event A (drawing a blue ball first), there are 4 ways this can happen out of 15 total possibilities, so the probability of A is 4/15. After a blue ball is drawn, there are now 14 balls left in the bag for the second draw.
Since event B is drawing a white ball as the second ball, given that a blue ball has already been drawn on the first draw, there are still 4 white balls left in the bag after event A has occurred. Therefore, the probability of B given A is 4/14, which simplifies to 2/7.
Thus, P(B|A) = 2/7.
In general, the point ___is on the graph of the function f(x) = a×b^x.
Answers
Answer:
Option A (0,a)
Step-by-step explanation:
we know that
[tex]f(x)=a(b^{x})[/tex]
Is a exponential function
where
a is the initial value
b is the base
Remember that
The initial value is the value of the function when the value of x is equal to zero (y-intercept)
therefore
For x=0
[tex]f(0)=a(b^{0})[/tex]
[tex]f(0)=a(1)=a[/tex]
The y-intercept is the point (0,a)
Answer:
(0, a)
Step-by-step explanation:
Write a numerical expression for each verbal phrase? How many more pencils Chet has than Benito if Benito has ten pencils and Chet has seventeen pencils
Answers
Answer:
-10 + 17 [OR 17 - 10]
Step-by-step explanation:
To find out how MANY MORE of something someone has THAN the other, you use the operation of deduction [subtraction].
I am joyous to assist you anytime.
Answer:
Chet has 7 more pencils than Benito.
Step-by-step explanation:
We have to Write a numerical expression for each verbal phrase:
Number of pencils Benito has = 10
Number of pencils Chet has = 17
The number of more pencils Chet has than Benito is = [tex]17-10=7[/tex]
Therefore, Chet has 7 more pencils than Benito.