a wire 30 cm long is cut into two pieces. the longer piece is 6 cm longer than the shorter piece. find the length of the shorter piece of wire
Answers
The length of the shorter piece of wire is 12 cm, which is found by setting up the equation x + (x + 6) = 30, where x is the length of the shorter piece.
The student has asked to find the length of the shorter piece of wire when a 30 cm long wire is cut into two pieces, with the longer piece being 6 cm longer than the shorter piece. To solve this, we need to set up a simple equation based on the information given.
Let's represent the length of the shorter piece as x cm. Since the longer piece is 6 cm longer than the shorter piece, we can represent the longer piece as (x + 6) cm
We are told that the total length of the wire before it was cut was 30 cm. Therefore, the sum of the lengths of both pieces must equal 30 cm. This gives us the equation:
x + (x + 6) = 30
Simplifying the equation, we get:
2x + 6 = 30
Subtracting 6 from both sides of the equation gives us:
2x = 24
Dividing both sides by 2 to solve for x gives us:
x = 12
Related Questions
When does a barbershop Quartet have 16 legs
Answers
A traditional barbershop quartet has 8 legs since it consists of four people. Female quartets exist alongside male quartets, with popular female groups like The Sweet Adelines International and The Chordettes. The scenario of a quartet having 16 legs is hypothetical and humorous, similar to a comedic tale from 'Only Fools and Horses' regarding a constantly replaced broom.
The question "When does a barbershop quartet have 16 legs?" seems to contain a riddle rather than a direct inquiry into the makeup of a barbershop quartet. Traditionally, a barbershop quartet comprises four individuals, each with two legs, totaling eight legs. This would shift to 16 legs if the quartet consisted of eight people. However, if we're speaking about the traditional four-person quartet, they would only have 16 legs if each member had four legs, which is not characteristic of human anatomy.
It is important to clarify that despite the common misconception that barbershop quartets are exclusively male, there are female quartets as well, such as those associated with The Sweet Adelines International or popular groups like The Chordettes. Neither of these situations normally results in 16 legs unless for comedic or hypothetical scenarios, akin to the tale shared in the comedy "Only Fools and Horses" where Trigger's broom maintains the same identity despite numerous replacements of its parts.
Examples in Pop Culture and Misconceptions
A blend of humor and play on the concept of identity similar to the aforestated barbershop quartet conundrum is seen in the television sitcom "Only Fools and Horses," where a character humorously remarks on the extensive replacement of broom parts, posing a philosophical question of identity and perception.
Drag the correct tiles that match.?
Answers
<EOB = 360- (90+90+58) = 122
<COB = 360 - (90+90+66) = 114
<COE = 360 - (90+90+56) = 124 so arcCE = 124
answer
<DFA = 58
<EOB = 122
<COB = 114
arc CE = 124
Simplify
19 - 1.67 + (-2.4)
Answers
14.93
hope this helps
How do you subtract 7.6 from 20.39
Answers
20.39 -7.6
your answer is 12.79
hope this helps
Imagine a model shaded to show 0.001 How much would be shaded?
Answers
A model being 0.001 shaded would be 0.1% or 1/1000 of the whole model.
How to identify the place value of a digit in a number?The place values on left of decimal point start as ones, tens, hundreds, and so on.....
The place value on right of decimal point starts from point and goes to right as tenths, hundreths and so on....
The tens means multiply by 10..
The tenth means tenth part of that digit which is that digit divided by 10...
A model being 0.001 shaded would be 0.1% or 1/1000 of the whole model.
One would equal the whole model being shaded, but that’s not the case. Instead it is in the thousandths,
So, that’s 1/1000 or 0.1% of the whole model shaded.
Therefore, A model being 0.001 shaded would be 0.1% or 1/1000 of the whole model.
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Find the length of l on the curve r(t)=5cos(3t)i-5sin(3t)j+3tk over the interval [3,7]
Answers
[tex]\mathrm d\mathbf r(t)=\mathbf r'(t)\,\mathrm dt=(-15\sin3t\,\mathbf i-15\cos3t\,\mathbf j+3\,\mathbf k)\,\mathrm dt[/tex]
[tex]\displaystyle\int_C\mathrm d\mathbf r(t)=\int_{t=3}^{t=7}\|\mathbf r'(t)\,\mathrm dt\|=\int_{t=3}^{t=7}\sqrt{225\sin^23t+225\cos^23t+9}\,\mathrm dt[/tex]
[tex]=\displaystyle3\sqrt{26}\int_{t=3}^{t=7}\mathrm dt[/tex]
[tex]=12\sqrt{26}[/tex]
To find the length of the curve, use the formula for arc length and integrate over the given interval. The integrals can be calculated using the derivatives of the curve's components.
Explanation:To find the length of the curve, we need to calculate the arc length. The formula for arc length is given by:
L = ∫√(dx/dt)² + (dy/dt)² + (dz/dt)² dt
In this case, dx/dt = -15sin(3t), dy/dt = -15cos(3t), and dz/dt = 3. We can use these formulas to calculate the integrals over the interval [3, 7] and find the length of the curve.
simplify 5 + 4 • (8 – 6)2
Answers
Sari has 3 times as many pencil erasers as Sam. Together they have 28 erasers. How many erasers does Sari have?
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let x represent the amount of erases Sam has
3x + x = 28
4x = 28
4x/4 = 28/4
x = 7
Sam has 7 erasers and Sari has 3 times more than Sam.
so 7 x 3 =21
Answer: Sam has 21 eraser i believe so
twelve is six times the difference between a number and three. find the number.
Answers
12=6x-18
30=6x
5=x
A square pyramid has a height h and a base with side length b. The side lengths of the base increase by 50%. Write a simplified expression that represents the volume of the new pyramid in terms of b and h.
Answers
Final answer:
The volume of the new pyramid, after a 50% increase in base side length, is expressed as V = 0.75b²h. This comes from applying the formula for the volume of a square pyramid and substituting the new base length of 1.5b into the formula.
Explanation:
The student is asked to write a simplified expression for the volume of a new pyramid after the side lengths of the base increase by 50%. The formula for the volume of a square pyramid with a base side length b and height h is V = (1/3)b²h.
When the side lengths of the base increase by 50%, the new base side length becomes 1.5b. Plugging this into the volume formula, we have:
V' = (1/3)(1.5b)²h
= (1/3)(2.25b²)h
= (2.25/3)b²h
= 0.75b²h
This is the simplified expression for the volume of the pyramid after the increase in base side length.
The volume of the new pyramid is [tex]\(0.75b^2h\), where \(b\)[/tex] is the base side length and [tex]\(h\)[/tex] is the height.
To find the volume of a square pyramid, we use the formula:
[tex]\[ V = \frac{1}{3} \times (\text{area of base}) \times \text{height} \][/tex]
For a square pyramid, the area of the base is [tex]\( b^2 \), where \( b \)[/tex] is the side length of the base.
So, the volume [tex]\( V \)[/tex] of the original pyramid can be written as:
[tex]\[ V = \frac{1}{3} \times b^2 \times h \][/tex]
Now, if the side lengths of the base increase by 50%, the new side length of the base becomes [tex]\( 1.5b \)[/tex] (since increasing by 50% is the same as multiplying by [tex]\( 1.5 \))[/tex].
Therefore, the new area of the base is [tex]\( (1.5b)^2 = 2.25b^2 \).[/tex]
So, the volume \( V' \) of the new pyramid can be written as:
[tex]\[ V' = \frac{1}{3} \times (2.25b^2) \times h \][/tex]
[tex]\[ V' = \frac{2.25}{3} \times b^2 \times h \][/tex]
[tex]\[ V' = 0.75 \times b^2 \times h \][/tex]
So, the simplified expression representing the volume of the new pyramid in terms of [tex]\( b \) and \( h \) is \( 0.75b^2h \)[/tex].
How do the number line graphs of the solutions sets of mc011-1.jpg and mc011-2.jpg differ? One graph uses an open circle, but the other graph uses a closed circle. Also, the rays use arrows that point in opposite directions, but they have the same endpoint. They use arrows that point in opposite directions, the rays have different endpoints, and both graphs use open circles. One graph uses an open circle, but the other graph uses a closed circle. Also, the rays have different endpoints, but they use arrows that point in the same direction. They use arrows that point in opposite directions, the rays have different endpoints, and both graphs use closed circles
Answers
Answer:A. One graph uses an open circle, but the other graph uses a closed circle. Also, the rays use arrows that point in opposite directions, but they have the same endpoint.
Earth travels about 10^9 kilometers in its year-long orbit around the sun. About how far does it travel in 100 years?
Answers
100 = 10^2
so 10^9 * 10^2 = 10^11 kilometers in 100 years
Find the four real zeros of the polynomial. f(x) = x4 + 6x3 - 3x2 -52x - 60
A. 2, -2, -5, -3
B. -2, -2, -5, 3
C. -2, -2, 5, 3
D. 2, -2, -5, 3
Answers
[tex]f(x)=x^4+6x^3-3x^2-52x-60[/tex]
The "zeros" of a function, are the values of x, for which f(x)=0
According to the "Rational Root Theorem", the rational roots of f, are factors of 60.
That is, when trying to find the roots of a polynomial function, it is a very good idea to first check the factors of the constant term.
All numbers shown in the choices are factors of 60, so we will solve the problem by trial:
[tex]f(2)=2^4+6\cdot2^3-3\cdot2^2-52\cdot2-60=16+48-12-104-60 \neq 0[/tex]
2 is not a root, so we eliminate choices A and D,
Choices B and C are almost equal, with only 1 different number, so let's check whether 5 is a root or not:
[tex]f(5)=(5)^4+6\cdot(5)^3-3\cdot(5)^2-52\cdot(5)-60[/tex]
[tex]=625+750-75-160-60=60[/tex]
but
[tex]f(-5)=(-5)^4+6\cdot(-5)^3-3\cdot(-5)^2-52\cdot(-5)-60[/tex]
[tex]=625-750-75+160-60=0[/tex]
So the right choice is B
To find the zeros of the polynomial f(x) = x^4 + 6x^3 - 3x^2 -52x - 60, we can test different values and find that x = 2, -2, -5, -3 are the four real zeros.
Explanation:To find the zeros of the polynomial f(x) = x^4 + 6x^3 - 3x^2 -52x - 60, we need to solve the equation f(x) = 0. We can do this by factoring or using synthetic division. By testing different values, we find that x = 2, -2, -5, -3 are the four real zeros of the polynomial. Therefore, the correct answer is A. 2, -2, -5, -3.
You have $37 to spend at the music store. Each cassette tape costs $10 and each CD costs $13. Write a linear inequality that represents this situation. Let x represent the number of tapes and y the number of CDs.
Answers
13 times how ever many CD's plus 10 times how ever many cassettes has to equal to the amount of money that you have to spend that's $37
An equation of the form ax+b=0 is called a __________ equation or a ________________ equation.
Answers
Answer:
Sloose intercept or a strait line
Step-by-step explanation:
Evaluate the following expression. 10−9×5+6×(−2)
Answers
10-45+-12
Then add and subtract from left to right
-35-12
-47
Final answer: -47
A colony of bacteria triples in link every 10 minutes. It's length is now 1 mm. How long will be in 40 minutes
Answers
[tex]\bf \textit{Periodic Exponential Growth}\\\\ A=I(1 + r)^{\frac{t}{p}}\qquad \begin{cases} A=\textit{accumulated amount}\\ I=\textit{initial amount}\to &1\\ r=rate\to 2\%\to \frac{200}{100}\to &2.00\\ t=\textit{elapsed time}\to &40\\ p=period\to &10 \end{cases} \\\\\\ A=1(1 + 2)^{\frac{40}{10}}[/tex]
There is an alien machine which produces seven aliens every two seconds. At this rate how many aliens will produces in one hour?
Answers
the machine makes 7 aliens in 2 seconds, how many will it make in 3600 seconds?
[tex]\bf \begin{array}{ccll} aliens&seconds\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 7&2\\ a&3600 \end{array}\implies \cfrac{7}{a}=\cfrac{2}{3600}\implies \cfrac{7\cdot 3600}{2}=a[/tex]
that many.
Set up a proportion.
Let A = number of aliens in one hour
7/A = 2/3600
2A = 7(3600)
2A = 25,200
A = 25,200 ÷ 2
A = 12,600
So, 12,600 aliens are produced in one hour.
A eighteen-sided die is rolled three times. In how many ways can this happen?
Answers
Number of ways it can happen is 5832.
What is Multiplication?Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.
a × b means that a is added to itself b times or b is added to itself a times.
We have eighteen-sided die is rolled three times.
When the die is first rolled, there are 18 possibilities of outcomes.
Again when the die is rolled, again there are 18 possibilities.
In the third rolling also, there are 18 possibilities.
Each die has 18 possibilities of numbers for a number for the other die.
Total number of sets = 18 × 18 × 18
= 5832
Hence the total number of ways that the numbers can be formed is 5832.
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You are working as a caterer and need 20 gallons of lemonade for an upcoming event. The bottles of lemonade you are purchasing are in liters.
Answers
Multiply: 3.78541 liters x 20 gallons = 275.7082 liters
there are 275.7082 liters in 20 gallons.
You would need approximately 75.7 liters of lemonade for your event. This is calculated by using the conversion factor of 3.78541 liters per gallon.
Explanation:To calculate how many liters of lemonade you need for 20 gallons, we first need to know the conversion rate. There are about 3.78541 liters in 1 gallon. Thus, if you need 20 gallons, we can use multiplication to find this.
So, if we multiply 20 (gallons) by 3.78541 (liters per gallon), the result is approximately 75.7 liters. You would therefore need about 75.7 liters of lemonade for your event. This is a simple application of conversion factors, where the given quantity (gallons) is multiplied by a conversion factor (liters per gallon) to obtain the desired quantity (liters).
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simplify the following expression. one-fourth(24 – 16x)
Answers
6 - 4x
What is the standard form of five and three hundred fifty- two thousandths?
Answers
expanded form is
5 + 0.3 + 0.05 + 0.002
hope this helps
what is the answer to 15/4 in improper fraction s
Answers
3 3/4
That's what I think you're asking...
Find all real zeros of the function y=-7x+8
Answers
Set y=0 since on the x-axis y=0 and that is where we need to see when it crosses or touches.
y=-7x+8
0=-7x+8
-8+0=-7x+8-8
-8=-7x
-8/-7=-7x/-7
8/7=x
Real zeros 8/7
The zero of the function y = -7x + 8 is 8/7.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
y = -7x + 8
y = 0 to find the zeroes.
0 = -7x + 8
7x = 8
x = 8/7
Thus,
The zero of the function is 8/7.
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Catherine likes to go ice fishing. She has learned from experience that she stays warm about 20 minutes for every undershirt she wears. If she wants to stay out for 120 minutes, how many undershirts should she put on?
Answers
Answer:
She need to put on 6 underpants
Step-by-step explanation:
She has learned from experience that she stays warm about 20 minutes for every undershirt she wears.
Time warmed by 1 undershirt = 20 minutes.
Total time she wants to stay out = 120 minutes
Number of underpants required [tex]=\frac{120}{20}=6\texttt{ underpants}[/tex]
So she need to put on 6 underpants
Can you please explain how the answer is 24 for this Problem 60÷5(7-5)
Answers
do order of operations:
60 / 5*(7-5)=
do parenthesis first: 7-5=2
60 / 5*2 =
now do division: 60/5 =12
12*2 =
now multiply: 12 *2 = 24
answer is 24
Find the sum of 5m + 3n + p, -5p + 3n, and 2n - m.
Answers
= 4m + 8n - 4p
Answer:
4m+8n -4p
Step-by-step explanation:
hello
you can just sum like a normal addition, just put similar terms on each other
5m + 3n +p
+3n -5p (second expression)
-m +2n ( third expression)
_____________
(5-1)m (3+3+2)n+(1-5)p = 4m+8n -4p
I hope it helps you
Have a great day
Sara set off on a bicycle trip at 6:30 am at an average rate of 24 miles per hour. Her friend, Jayne, promised to bring her some lunch, and she set off by motorcycle 2 hours after Sara left, driving at an average speed of 40 miles per hour. At what time did Jayne catch up with Sara?
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What is 8.478 in expanded form
Answers
The formula for glue says to add 45mL of hardener to each container of resin. How much hardener should be added to 18 containers of resin?
Answers
18 * 45 is 810.
So 810 mL should be added to each container of resin.