Mathematics High School

If a rope 36 feet long is cut into two pieces in such a way that one piece is twice as long as the other piece, how long must the long piece be

Answers

Answer 1

rope = 36 feet

first piece = x

2nd piece = 2x ( twice as long as the first piece)

3x=36

x=12

first piece = 12 feet

2nd piece = 2 x 12 = 24 feet

Related Questions

a plane intersects a prism parallel to the base of the prism. the cross section is a polygon with eight sides. The base of the prism had how many sides

Answers

eight sides, hope this helps!

The answer is eight sides.

What is the domain of f(x) = 3^x – 2?

Answers

All real numbers. No restrictions

Answer: In fact tis D. Is all real numbers

Step-by-step explanation: your welcome?

The factory produces sewing machine parts. During one week, they produced 345, 298, 452 and 388 parts per day.
What was the average number of parts produced each day?

Answers

to find the average, add up ur numbers, then divide by how many numbers there are.

(345 + 298 + 452 + 388) / 4 = 1483/4 = 370.75 per day <=

Answer:

The produced parts average each day were 370.75.

Step-by-step explanation:

We have to find the average of parts produced by day, to calculate it we have sum all the parts produced by day and divide it by the number of days (4 days). In the equation we have:

[tex]Average=\frac{345+298+452+388}{4}=\frac{1483}{4}=370.75[/tex]

The produced parts average each day were 370.75.

Find the measures of two angles, one positive and one negative, that are coterminal with pi divided by seven.

Answers

check the picture below.

you simply come "clockwise" to get the negative angle.

and to get the positive angle, simply go around 2π and then add π/7 to it.

Answer? Multiple choice?

Answers

Given fraction is
[tex]f(x) = \frac{x^2 + 4x + 3}{x^2 - 9} [/tex]

As we know fraction is not defined where denominator is equal to zero.

So let's find where denominator is zero.

[tex]x^2 - 9 = 0[/tex]

We can factorize it as [tex]a^2 - b^2 = (a+b)(a - b)[/tex]

So we can write given equation as

[tex](x+3)(x-3) = 0[/tex]

So x = 3 or x = -3.

So function is undefined at x = 3 and x = -3.

So option 3 is correct.

A house is advertised as having 1 420 square feet under roof. what is the area of this house in square meters? (a) 115 m 2

Answers

Final answer:

To convert square feet to square meters, we multiply the number of square feet (1,420) by the conversion factor (0.092903), resulting in approximately 132 square meters as the area of the house.

Explanation:

To convert the area of a house from square feet to square meters, we use the conversion factor where 1 square foot equals 0.092903 square meters. The house in question has 1,420 square feet, so we multiply this number by the conversion factor to find the area in square meters.a

1,420 square feet * 0.092903 square meters/square foot = 131.92186 square meters.

We can round the final result to the nearest whole number, which gives us approximately 132 square meters as the area of the house.

x plus 20% = 1980
what is x

Answers

20% = 20/100 = 0.2

x + 0.2x = 1980
1.2x = 1980
x = 1980/1.2
x = 1650 ← unknown number

[tex]20\%=0.2\\\\ x+0.2x=1980\\ 1.2x=1980\\ x=1650[/tex]

The table shows the ages and weights of babies at a hospital.

What is the correlation between age and weight as shown in the table?

A.) none

B.) positive

C.) negative

D.) constant

Answers

Answer:

Option (b) is correct.

The correlation between age and weight shown in the table is positive.

Step-by-step explanation:

Given: The table shows the ages and weights of babies at a hospital.

We have to determine the correlation between age and weight as shown in the table.

We first Plot these points to obtain the graph as show in attachment below.

Since, Using correlation calculator , we find the correlation as 0.83113

Which is positive

Thus, The correlation between age and weight shown in the table is positive.

As age increases the weight increase.Hence, positive.

The correlation between age and weight as shown in the table is positive, This is further explained below, Option B is correct

What is correlation?

Correlation is simply a relationship that exists between events or objects, A relationship between mathematical variables that are subject to variation.

In conclusion, Therefore we look at the table to decipher the correlation between age and weight.

Answers

a(4) = 1/2 a(n - 1) + 12 = 36
1/2 * 3a + 12 = 36
3/2 a = 24
a = 16

so first term = 1/2 * 16 (1 - 1) + 12 = 12
which is different from any of the choices.

you sure you have the question right? Or maybe i misread it.

What is the discriminant of 3x2-10x=-2 ?

Answers

The discriminant of [tex]3x^2-10x=-2[/tex] is 76

To find the discriminant of [tex]3x^2-10x=-2[/tex], we have to recall the quadratic formula.

Further Explanation

The formula of the quadratic equation can be expressed as [tex]ax^2+bx+c=0[/tex] and discriminant also expressed as [tex]D=b^2-4ac[/tex]

Using the quadratic formula, the given question can be expressed as:

[tex]3x^2-10x+2=0[/tex]

Where a = 3, b = -10, and c = 2

If we substitute the values, then the discriminant would be:

Recall the discriminant is [tex]D=b^2-4ac[/tex]

Therefore, we have

[tex]D=(-10)^2-4(3)(2)[/tex]

[tex]D=100-24[/tex]

[tex]D=76[/tex]

Thus, the discriminant of [tex]3x^2-10x=-2[/tex] is 76.

Discriminant is very helpful in quadratic equation as it helps reveals the number of real solutions to a given quadratic equation. In other words, it helps you to solve quadratic equation.

While discriminant only tells only reveals the number of real solutions, it doesn’t reveal what the solutions are. The determinant would only give you hint as regards the number of real solution to look for.

LEARN MORE:

Find the discriminent of the equation 3x2- 10x https://brainly.in/question/11507036Find the discriminent of the equation 3x2+10x+3=0 https://brainly.in/question/5897002

KEYWORDS:

discriminantquadratic formula3x2-10x=-2solutionquadratic equation

Shaun and Trudy are selling raffle tickets. So far, Shaun has sold x tickets. Trudy has sold 3 more tickets than half the number of tickets that Shaun sold. Which expression represents the number of raffle tickets that Shaun and Trudy have sold altogether?

Answers

S=x,

T=s/2+3, using s from above we have:

T=x/2+3

t=T+S

t=x+x/2+3 make all term have a common denominator of 2

t=(2x+x+6)/2

t=(3x+6)/2 or if you prefer

t=1.5x+3

Answer:

3/2x+3

Step-by-step explanation:

cos y = 0.02034 ; y°=?

Answers

Cos y = 0.02034
y°= cos^-1 (0.02034)
= 88.834°

That's it

monique deposited 1800 at the beginning of each quarter for 6 years into an ira. given an interest rate of 6% compounded quarterly find the value

Answers

Use the formula of the future value of annuity due because the amount of 1800 is deposited at the (beginning) of each quarter
The formula is
Fv=pmt [((1+r/k)^(kn)-1)÷(r/k)]×(1+r/k)
Fv future value?
PMT amount deposited 1800
R interest rate 0.06
K compounded quarterly 4
N time 6years
Fv=1,800×((((1+0.06÷4)^(4×6)
−1)÷(0.06÷4))×(1+0.06÷4))
=52,313.44....answer

Line segment AB has a length of 3 units. It is translated 2 units to the right on a coordinate plane to obtain line segment A′B′. What is the length of A′B′?

1 unit
2 units
3 units
5 units

Answers

the length of a'b' is the same as ab because it is the same image so it is 3 units

Answer:

It is still 3.

Step-by-step explanation:

We only translated it, so we just moved it over to the side. Translating cannot take away length.

- Bruce added some chlorine to the water in a pool. The chlorine evaporated at a fixed rate every week... ... The table below shows the amount of chlorine f(n), in ounces, that was left in the pool after n weeks: n f(n) 1 54 2 27 3 13.5 4 6.75 Which function best shows the relationship between n and f(n)?.

Answers

To solve this problem, let us first remember that the formula for rate is:

rate = f (n) = A (r)^(n-1)

Where,

A = the 1st term

r = fractional rate of evaporation

n = number of terms

Now let us calculate for the fraction rate of evaporation, r. Since it is stated that the evaporation is happening at a fixed rate, therefore we can use any two given f (n) values to find for r. In this case, let us use when n=1 and 2.

r = 27 / 54

r = 0.5

The first term in the series is when n = 1 and that is:

A = 54

Therefore substituting all known values to the equation:

f (n) = 54 (0.5)^(n-1) (ANSWER)

A point in the form (x, y) has two dimensions. is this correct

Answers

False.

A point has no dimension or you could say zero dimensions.

A point in the form (x, y) is simply a location on a plane.

Which one of the following characteristics of a solid is of concern to geometry? A. Weight B. Shape C. Color D. Substance

Answers

B. Shape; The answer is shape because weight isn't a factor of Geometry due to the measurement being more scientific, color is a mere hue that would matter more in an artistic perspective, and substance is a more scientific characteristic than geometric as well.

What is the amplitude, period, and phase shift of f(x) = -3 cos (4x + pi) +6?

Answers

The given signal is
(x) = -3 cos(4x + π) + 6

The amplitude is |-3| = 3
If T is the period, then
(2π)/T = 4
4T = 2π
T = π/2
The period is π/2.
The phase shift is -π/4.
The vertical shift is 6.

A graph of the function is shown below.

Answer:
Amplitude = 3.
Period = π/2.
Phase shift = -π/4

The amplitude, period, and phase shift are 9, [tex]\dfrac{\pi }{2} [/tex] and [tex]\dfrac{\pi }{4} [/tex] respectively.

Periodic function

A periodic function is a function that repeats itself after a definite time interval.

Given

[tex]f(x) = -3cos(4x+\pi ) +6[/tex]

The cosine function is a periodic function that repeats itself in the interval of [tex]2\pi [/tex].

Step by step explanation

For maximun amplitude

[tex]cos(4x+\pi )=-1\\ [/tex]

Then

[tex]f(x)=3+6\\ f(x)= 9[/tex]

For time period

The cosine function repeats itself in the interval of [tex]2\pi [/tex].

[tex]\begin{aligned} \frac{2\pi }{T} &= 4 \\\\ T &=\dfrac{\pi }{2}\\ \end{aligned}[/tex]

For phase shift

Phase is [tex]\dfrac{\pi }{4} [/tex]

Thus, the amplitude, period, and phase shift are 9, [tex]\dfrac{\pi }{2} [/tex] and [tex]\dfrac{\pi }{4} [/tex] respectively.

To more about the Period function link is given below.

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Suppose someone opens the valve on a large water tank so that water drains out. Choose a starting volume of water in the tank (from 100 to 500 gallons), and choose how much water drains out each day (from 2 to 5 gallons). Write the equation that models the relationship between time (x) and water volume (y) in slope-intercept form.

Answers

If we are to choose any number from 100 to 500, you may take any other number but for the purpose of showing how things are done here, let me choose 100 gallons. Similarly, we choose 2 gallons to be drain out each day.

The equation that would best represent the relationship between the given parameters is,
y = 100 - 2x

where y is the volume of water after x days.

A restaurant earns $1073 on Friday and $1108 on Saturday. Write and solve an equation to find the amount xx (in dollars) the restaurant needs to earn on Sunday to average $1000 per day over the three-day period. Write your equation so that the units on each side of the equation are dollars per day

Answers

(1073 + 1108 + x) / 3 = 1000
(2181 + x) / 3 = 1000 ....multiply both sides by 3
2181 + x = 1000 * 3
2181 + x = 3000
x = 3000 - 2181
x = 819 <== they would need to earn $ 819 on Sunday

the volume of a gas varies inversely as the pressure upon it. if the volume of the gas is 160 cubic centimeters at a pressure of 108 centimeters find the volume when the pressure is 87 centimeters

Answers

It was stated in the problem that a given volume of a is inversely proportional with the pressure of the system. It means that the as the volume increases, the pressure would decrease and as the volume decreases, the pressure would increase. We would express it as:

V α 1/P

To change it to an equality, we introduce a proportionality constant, k. We do as follows:

V = k/P

So, to determine what is asked, we need to first calculate for the value of k.

V = k/P
At V = 160 m^3 P = 108 cmHg
160 = k / (108)
k = 17280

Thus, at P = 87 cmHg
V = 17280 / 87
V = 198.62 m^3

A binomial is defined as what?

Answers

A [tex]Binomial [/tex] is defined as: [tex]like[/tex] [tex]the [/tex] [tex]expression[/tex] [tex]that's [/tex] [tex]a [/tex] [tex]sum (addition) [/tex] [tex]or [/tex] [tex]even[/tex] [tex]the [/tex] [tex]difference(subtraction)[/tex] [tex]with[/tex] [tex]the[/tex] [tex]number 2 [/tex][tex]terms [/tex]

If two lines are perpendicular, then they form?

Answers

If two lines intersect to form a linear pair of congruent angles

If two lines are perpendicular, that mean that they intersect to form a RIGHT ANGLE. All perpendicular lines form a 90 degrees angle.
hope this helps:)

Find the value of each variable for the right triangles. Make sure all answers are in reduced radical from. Shoe your work.

Answers

Denote each of the triangles ABC, where B is the right angle.

a.

[tex] t^{2}+ 12^{2}= 13^{2} [/tex]

instead of taking the square of 12 and 13, , take 12 squared to the right side and apply the difference of squares formula: [tex] a^{2}- b^{2}=(a-b)(a+b)[/tex]

[tex]t^{2}= 13^{2}- 12^{2}=(13-12)(13+12)=1*25[/tex]

so t is square root of 25, which is 5

b.

[tex] a^{2}+9 ^{2} = 12^{2} [/tex]

[tex]a^{2}= 12^{2} -9 ^{2}=(12-9)(12+9)=3*21=3*3*7 [/tex]

[tex]a= \sqrt{3*3*7}=3 \sqrt{7} [/tex]

b.

[tex] 6^{2} + 9^{2} = x^{2} [/tex]

[tex]36+81= x^{2} [/tex]

here we can factorize 9, to work with small numbers:

[tex]9(4+9)= x^{2}[/tex]

[tex]9*13= x^{2} [/tex]

[tex] x^{2} =3*3*13[/tex]

[tex]x= \sqrt{3*3*13}=3 \sqrt{13} [/tex]

Alex is making a rectangular garden and wants a fence around it. He wants the length of the garden to be 3 feet longer than the width. 150 feet of fence is all he can afford. What is the greatest possible width he can have for his garden?

Answers

Since it's rectangular, there is a length and width. Let the width be w, and the length is then w+3. The total length of the fence is the perimeter, so 150 = 2*w + 2*(w+3) = 4w+6. Solving for w, this becomes w=(150-6)/4 = 144/4 = 36 feet.

Choose the graph below that correctly represents the equation 15x − 5y = 30.

will give brainiest to best answer!!

PLEASE HELP!!!

Answers

You didn't give us a picture but I'll help you as best as I can.

First, convert the equation into the form y=mx+b:
15x-5y=30
-5y=-15x+30

Divide both sides by -5.
y=-3x-6

Below is a graph of that equation:

Final answer:

To choose the correct graph that represents the equation 15x - 5y = 30, isolate y, find the slope and y-intercept, and compare to the given graphs.

Explanation:

In order to choose the correct graph that represents the equation 15x - 5y = 30, we need to solve the equation for y.

First, let's isolate y by subtracting 15x from both sides of the equation:

15x - 5y - 15x = 30 - 15x

-5y = -15x + 30

Next, divide both sides of the equation by -5 to find the value of y:

-5y/-5 = (-15x + 30)/-5

y = 3x - 6

Now that we have the equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, we can determine the graph that represents the equation. The slope of the equation is 3, which means that for every 1 unit increase in x, y increases by 3 units. The y-intercept is -6, which means that the graph intersects the y-axis at the point (0, -6).

Based on this information, we can determine that the graph that correctly represents the equation 15x - 5y = 30 is the one where the slope is 3 and it intersects the y-axis at (0, -6).

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Words that came from the same ancestral language and originated from the same word are called

Answers

Words that came from the same ancestral language and originated from the same word are called COGNATE WORDS.

In linguistics, cognates are words that have a common etymological origin. These are words in two languages that share a similar meaning, spelling, and pronunciation. For an instance, English words have lots of related words in Spanish.

The words that came from the same ancestral language and originated from the same word are called COGNATE WORDS.

What is ancestral language?

In the historical linguistics tree model, a protolanguage is a hypothetical ancestral language from which several documented languages are thought to have evolved, constituting a language family. In most cases, protolanguages are unattested or, at most, only partially attested.

The languages of Norway, Sweden, Denmark, and Iceland descend from Old Norse. Numerous Indian languages, including Bengali, Hindi, Marathi, and Urdu, have their roots in Sanskrit. Each of these ancestral languages had a single common progenitor further back in time.

The term "cognates" in linguistics refers to words with the same etymological background. These are words that have the same pronunciation, spelling, and meaning in two different languages. For instance, Spanish has many words that are similar to English words.

Therefore, Words that came from the same ancestral language and originated from the same word are called COGNATE WORDS.

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Use a normal approximation to find the probability of the indicated number of voters. in this case, assume that 114 eligible voters aged 18-24 are randomly selected. suppose a previous study showed that among eligible voters aged 18-24, 22% of them voted. probability that exactly 27 vote

Answers

The random variable X ≈ B(n, p)

Where n is the number of samples. If the value of n is huge, calculating binomial coefficient can be difficult and calculator won't be able to perform the nCr calculation for a big value of n (try ⁶⁰⁰C₁₂₃ on the calculator).

If p, which is the probability, is close to 0.5, the binomial distribution will be fairly symmetric.

We have n = 114 and p = 22% = 0.22

We first need to approximate X by Y ≈ N(np, np(p-1))

np = 114×0.22 = 25.08
np(1-p) = 114×0.22×0.78 = 19.6

Therefore, Y ≈ N(25.08, 19.6)
and since the standard deviation, б = √np(1-p) = √19.6
We then have, Y≈N(25.08, (√19.6)²)

We aim to find the probability of X is exactly 27, mathematically written as P(X=27)

Applying the continuity correction we have P(26.5<Y<27.5) ⇒ This correction, in other words, is applying a range to X that will definitely include the value of X=27

The next step is standardising
We have the mean, μ=25.08 and σ=√19.6

P(26.5<Y<27.5) = P([tex] \frac{26.5-25.08}{ \sqrt{19.6} } [/tex]<Z<[tex] \frac{27.5-25.08}{ \sqrt{19.6} } [/tex])
P(26.5<Y<27.5) = P(0.32<Z<0.55)
P(26.5<Y<27.5) = P(Z<0.55) - [1 - P(Z<0.32)] ⇒ Read the values for these z-score on the z-table
P(26.5<Y<27.5) = 0.7088 - [1-0.6255]
P(26.5<Y<27.5) = 0.3343

What positive number is the same as its reciprocal?

Answers

1 It's the only positive number whose reciprocal is its equal

Final answer:

The only positive number that is the same as its reciprocal is 1. This is achieved by setting up the equation x = 1/x and solving it.

Explanation:

In mathematics, a number and its reciprocal are the same when the number is 1. If you denote the mysterious number we are looking for as 'x', then its reciprocal would be 1/x. Since the number and its reciprocal are the same, we can set up the equation x = 1/x. Solving this equation, we cross multiply to get x^2 = 1. The positive solution to this equation is x = 1, which confirms that the only positive number that is the same as its reciprocal is 1.

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tristen is a saleman whose base pay plus commissions amounted to $59,238 last year. if his base pay was $31,050 and he made $97,200 is sales last year what was his rate of commission?

Answers

subtract base pay from what he made

59238-31050 = 28188

so he made 28188 in commissions

now divide that by 97200

28188/97200 = 0.29

so he makes 29% commision

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