a village having a population of 4000, requires 150 litres of water per head per day. it has a tank measuring 20m x 15m x 6m. for how many days will the water of this tank last?

Answer:

4x+60 or 4(x+15)

Step-by-step explanation:

1/2x+4x-1/2x+60

1/2x-1/2x+4x+60

4x+60

Answer: It’s 4(x+60)

Step-by-step explanation: hope this helps

Answer:

D

Step-by-step explanation:

it is the only figure that looks like a transformation from P

Answer:

slope = - 3

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (0, - 3) ← 2 points on the line

m = [tex]\frac{-3-0}{0+1}[/tex] = [tex]\frac{-3}{1}[/tex] = - 3

Step-by-step explanation:

first distribute the 5.

10x-40=90

then get rid of the 4o and add it to 90

10x=130

then divide by 10 to get x alone

x= 13

Answer:

x = 13

Step-by-step explanation:

5(2x - 8) = 90       Divide by 5 on both sides

2x - 8 = 18            Add 8 to both sides

    + 8  + 8

2x = 26               Divide by 2 on both sides

x = 13

Answer:

D negative four

Step-by-step explanation:

Answer:

d) y= -4

Step-by-step explanation:

Answer:

Therefore , Equation of Line Passing through A with slope 1/3 is

[tex]x-3y=-12[/tex]

Step-by-step explanation:

Given:  

Let,  

point A( x₁ , y₁) ≡ ( 3 , 5)

[tex]Slope = m =\dfrac{1}{3}[/tex]  

To Find:  

Equation of Line Passing through A with slope 1/3 =?  

Solution:  

Equation of a line passing through a points A( x₁ , y₁) and having slope m is given by the formula,  

i.e Equation in point - slope form

[tex](y-y_{1})=m(x-x_{1})[/tex]

Now on substituting the slope and point A( x₁ , y₁) ≡ ( 3 , 5) we get

[tex](y-5)=\dfrac{1}{3}(x-3)\\\\3y-15=x-3\\x-3y=-15+3=-12[/tex]

Therefore , Equation of Line Passing through A with slope 1/3 is

[tex]x-3y=-12[/tex]

Answer:

Step-by-step explanation:

8x - 20.....factor a 4 out

4(2x - 5) <=== this one is correct...not 100% sure who wrote it

8x - 20...factor out a 2

2(4x - 10) <==== this is correct

8x - 20....factor out a -2

-2(-4x + 10) <==== this is correct

8x - 20....factor out a -4

-4(-2x + 5).....nobody did this one......but somebody tried....that person didn't factor correctly

Final answer:

Craig, Ester, and Lisa wrote correct expressions equivalent to 8x - 20. Ali's expression is incorrect due to improper distribution of the negative sign, resulting in an expression equivalent to 8x + 20, rather than 8x - 20.

Explanation:

The expressions provided by the students need to be equivalent to 8x - 20. We can factor out a common factor or distribute and combine like terms to check the equivalence of each expression:

For the incorrect expression (-4)(2x + 5), Ali likely distributed the negative incorrectly. Ali should have distributed the negative sign across the terms inside the parenthesis, producing -8x - 20, which is equivalent to 8x + 20, and not 8x - 20.

Answer:

Domain: {-2, 0, -1,  4}

 Range: { 4, 2,  3, -2}

Step-by-step explanation:

In a set of ordered pairs, the domain is the set of the first number in every pair, and the range is the set of the second number in every pair.

If the set of ordered pairs is { (-2, 4), (0, 2), (-1, 3), (4, -2)},

                       the domain is {  -2,       0,       -1,       4      }

                   and the range is {       4,       2,        3,       -2}

Answer:

Domain: {-2, -1, 0, 4}

Range: { -2, 2, 3, 4}

^in order^

Step-by-step explanation:

Answer: [tex]x^{3}[/tex] - 2[tex]x^{2}[/tex] - 11x + 12 = 0

Step-by-step explanation:

Since the zeros of the polynomials are -3 , 4 and 1 , then the equation will be in the form:

(x+3)(x-4)(x-1) = 0

Expanding (x+3)(x-4) , we have

[tex]x^{2}[/tex] - 4x + 3x - 12

⇒[tex]x^{2}[/tex] -x - 12

combining with (x-1) , we have

([tex]x^{2}[/tex] -x - 12) ( x -1 ) = 0

expanding , we have :

[tex]x^{3}[/tex] - [tex]x^{2}[/tex]-[tex]x^{2}[/tex] + x - 12x + 12 = 0

⇒[tex]x^{3}[/tex] - 2[tex]x^{2}[/tex] - 11x + 12 = 0

Answer:

Step-by-step explanation:

Subtract 2x

from both sides of the equation.

y=8−2x

x−y=2

Replace all occurrences of y

in x−y=2 with 8−2x

.

y=8−2x

x−(8−2x)=2

Simplify the left side.

Tap for more steps...

y=8−2x

3x−8=2

Solve for x

in the second equation.

Tap for more steps...

y=8−2x

x=103

Replace all occurrences of x

in y=8−2x with 103

.

y=8−2(103)

x=103

Simplify 8−2(103)

.

Tap for more steps...

y=43

x=103

The solution to the system of equations can be represented as a point.

(103,43)

Allow me to review before I start.  Inconsistent means there's no solution to the system of simultaneous equations, i.e. parallel lines.  Consistent means there's at least one solution.  Independent and dependent apply to consistent systems.  The former means exactly one solution (two lines in different directions which meet).  Dependent means an infinite number of solution; the two lines are really the same line.

1. We have two different slopes, lines in two different directions, so they'll meet in exactly one place.  That system is consistent and independent, the usual case.

2. We can write the first one y-3x= -2 and the second y-3x=+2.  These are parallel lines that are different, so no solution: inconsistent.

3.  The first equation is x+2y=4, same as the second. An infinite number of solutions.  Consistent and dependent.

By rewriting the 3 given systems, we will see that:

Let's analyze each system.

Let's look at the first one, we can rewrite it as:

y = 2x + 3

y = -x - 3

So, the slopes are different, meaning that we have one solution, so this system is consistent and independent.

Now let's look at the second system, we can rewrite it as:

y = 3x - 2

y = 3x + 2

Here both lines have the same slope, so the lines never do intersect, meaning that the system is inconsistent and independent.

For the final system we have:

y = (-1/2)*x + 2

y = (-1/2)*x + 2

So, we have two equal lines, so this system is dependent.

If you want to learn more about systems of equations:

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To find the length of segment EF, first equate ED and DF as D is the midpoint, solve for x, and then calculate EF as 2 times either ED or DF.

To find the length of segment EF, we need to use the given information: since D is the midpoint of EF, ED is equal to DF. The expressions given for ED (4x + 6) and DF (7x - 9) can therefore be set equal to each other to solve for x:

4x + 6 = 7x - 9

After solving for x, we can find the lengths of ED and DF, which are equal. Finally, we get the total length of EF by adding ED plus DF (or simply 2 times one of them since they're equal).

Here's how you solve for x:
3x = 15
x = 5

Now, substitute x back into one of the original equations to find one of the segment lengths:
ED = 4(5) + 6 = 20 + 6 = 26

Therefore, EF, which is made up of two segments of length 26, is 26 + 26 = 52 units long.

To find the length of EF, use the fact that D is the midpoint of EF. Set ED and DF equal to each other, solve for x, and substitute the value of x back into either ED or DF to find the length of EF.

To find the length of EF, we can use the fact that D is the midpoint of EF. This means that ED is equal to DF.

Given that ED = 4x + 6 and DF = 7x - 9, we can set these two expressions equal to each other:

4x + 6 = 7x - 9

Simplifying the equation:

6 + 9 = 7x - 4x

15 = 3x

Dividing both sides by 3:

x = 5

Now, we can substitute this value of x back into either ED or DF to find the length of EF. Let's use ED:

EF = 4x + 6 = 4(5) + 6 = 20 + 6 = 26

Therefore, EF = 26.

Answer:

  {-1, -1/3, 1/3, 1}

Step-by-step explanation:

The possible rational roots are ...

  ±(divisor of constant)/(divisor of leading coefficient)

Here, that means the rational roots are ...

  ±p/q where p ∈ {1}, and q ∈ {1, 3}

That is, they can be ±1/1 or ±1/3. Arranged from smallest to largest, they are ...

  -1, -1/3, 1/3, 1

_____

A graph shows the roots to be -1 (multiplicity 2) and (+1/3). Then the function factors as ...

  f(x) = (3x -1)(x +1)²

To find the possible rational roots of the function f(x) = 3x^3 + 5x^2 + x - 1, we can use the Rational Root Theorem. The p/q list of possible rational roots is ±1/1, ±1/3, ±1/3, ±1/1.

To find the possible rational roots of the function f(x) = 3x^3 + 5x^2 + x - 1, you can use the Rational Root Theorem. According to the theorem, the possible rational roots are all the possible fractions that can be formed by dividing a factor of the constant term (-1) by a factor of the leading coefficient (3).

Step 1: Find the factors of the constant term (-1), which are ±1.

Step 2: Find the factors of the leading coefficient (3), which are ±1 and ±3.

Step 3: Write out all the possible fractions using the factors found in steps 1 and 2 as p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

The p/q list of possible rational roots for the function f(x) = 3x^3 + 5x^2 + x - 1 is ±1/1, ±1/3, ±1/3, ±1/1.

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To find the total amount of water needed to water all the plants in the house, the amount of water for a part of the plants is used to set up a proportion. After cross-multiplying and calculating, it is determined that 10/3 liters or approximately 3.33 liters of water is required.

If 4/3 liters of water is enough for 2/5 of the plants, then the amount of water required for all the plants can be found by setting up a proportion. We use cross-multiplication to solve for the unknown amount of water needed to water all the plants.

First, we express the given information as a fraction:

(4/3) liters

(2/5) plants

Next, we solve for the total water required (let's call it x):

(4/3) / (2/5) = x / 1

We cross-multiply to solve for x:

4/3 * 1 = x * (2/5)

Multiplying both sides by the reciprocal of (2/5), which is (5/2), to isolate x, we get:

(4/3) * (5/2) = x

Now we calculate:

x = (4 * 5) / (3 * 2) = 20/6 = 10/3 liters

Therefore, 10/3 liters of water, or approximately 3.33 liters, is necessary to water all the plants in the house.

Answer:

The solution set can be given as:

[tex]\{x|x\ \epsilon\ R,x\neq -3\}[/tex]

Step-by-step explanation:

Given function:

[tex]f(x)=\frac{1}{2x+6}[/tex]

To find the domain of the function in set notation.

Solution:

For the function [tex]f(x)[/tex] to exist the denominator must be ≠ 0

We have the denominator [tex](2x+6)[/tex] which  cannot be = 0.

Thus, we can find the domain of the function using the above relation.

The function [tex]f(x)[/tex] will not exist when:

[tex]2x+6=0[/tex]

Solving for [tex]x[/tex]

Subtracting both sides by 6.

[tex]2x+6-6=0-6[/tex]

[tex]2x=-6[/tex]

Dividing both sides by 2.

[tex]\frac{2x}{2}=\frac{-6}{2}[/tex]

∴ [tex]x=-3[/tex]

Thus, the function will not exist at [tex]x=-3[/tex]. This means it has all real number solutions except -3.

The solution set can be given as:

[tex]\{x|x\ \epsilon\ R,x\neq -3\}[/tex]

Answer:

2.15

Step-by-step explanation:

The easiest way to convert a percentage to a decimal is to simply add a decimal on the number (If the number does not already have one), then move that decimal two places to the left.

We can do that like so:

1: Remove the percentage sign: 215% -> 215

2: Add a decimal at the end of the number: 215.

3: Move the decimal two places to the left: 2.15

So 215% converted to a decimal would be 2.15

Answer:

$52

Step-by-step explanation:

90-38

total amount subtracted by the amount she had

Answer:

3 slices each

Step-by-step explanation:

18 people ÷ 6 pizzas = 3 slices each

18÷6=3

The principal to be deposited is $ 11874.6594

Solution:

Given is a simple interest problem

Principal = ?

Simple Interest = $ 2179

[tex]Rate = 3\frac{2}{3} \% = \frac{11}{3} \% = 3.67 \%[/tex]

Number of years = 60 months = [tex]\frac{60}{12} = 5 \text{ years }[/tex]

The simple interest is given by formula:

[tex]Simple\ Interest = \frac{p \times n \times r}{100}[/tex]

Where, "p" is the principal and "r" is the rate of interest and "n" is the number of years

[tex]2179 = \frac{p \times 3.67 \times 5}{100}\\\\217900 = 18.35p\\\\p = \frac{217900}{18.35}\\\\p = 11874.6594[/tex]

Thus the principal to be deposited is $ 11874.6594

Answer:

$39.50

Step-by-step explanation:

Multiply 7.9 by 5 to get 39.5

Answer:

if 10 of them costs $7.90 then 50 would cost $39.50.

there are two different ways of doing this:

1. you could divide $7.90 by 10 which would get you $0.79 (the price of one frozen juice bar) then multiply $0.79 by 50 to get $39.50 (the price of 50 frozen juice bars)

or

2. you could just take $7.90 and multipy it by 5 (b/c 10 x 5 is 50)

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

(x₁, y₁) - point on a line

We have

[tex](-6,\ 3)\to x_1=-6,\ y_1=3,\ m=\dfrac{5}{2}[/tex]

Substitute:

[tex]y-3=\dfrac{5}{2}(x-(-6))\\\\y-3=\dfrac{5}{2}(x+6)[/tex]

Convert to the slope-intercept form

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

[tex]y-3=\dfrac{5}{2}(x+6)[/tex]         use the distributive property

[tex]y-3=\dfrac{5}{2}x+\dfrac{5}{2\!\!\!\!\diagup_1}\cdot6\!\!\!\!\diagup^3[/tex]

[tex]y-3=\dfrac{5}{2}x+15[/tex]           add 3 to both sides

[tex]y=\dfrac{5}{2}x+18[/tex]

Convert to the standard form:

[tex]Ax+By=C[/tex]

[tex]y=\dfrac{5}{2}x+18[/tex]              multiply both sides by 2

[tex]2y=5x+36[/tex]              subtract 5x from both sides

[tex]-5x+2y=36[/tex]          change the signs

[tex]5x-2y=-36[/tex]

Answer:

A) (3, 11)

Step-by-step explanation:

Because 11=2(3)+5.

Answer:

60%

Step-by-step explanation:

so u have 15 players.....6 of them are in 8th grade....meaning (15 - 6) = 9 are not in 8th grade

percent of the team not in 8th grade...

9/15 = 0.6 = 60% <===

Final answer:

The rectangle's width is found to be 7.3 cm, and the length is approximately 10.47 cm, both measured to three significant figures. This was determined by setting up equations based on the given perimeter and the relationship between the rectangle's length and width.

Explanation:

To find the dimensions of the rectangle, we need to set up an equation based on the given perimeter and the relationship between length and width.

Let's denote the width of the rectangle as w centimeters. According to the problem, the length l is 3 1/6 cm longer than the width, so l = w + 3 1/6 cm. The perimeter P of a rectangle is given by the formula P = 2l + 2w. Substituting the given perimeter 15 1/3 cm and the expression for l into the formula, we get:

15 1/3 = 2(w + 3 1/6) + 2w

To solve, first convert the mixed numbers to improper fractions:

46/3 = 2((6w + 19)/6) + 2w

Multiply through by 6 to clear the fractions, resulting in:

92 = 4w + 19 + 6w

Combine like terms and solve for w:

92 = 10w + 19

73 = 10w

w = 7.3 cm

Now that we have the width, calculate the length:

l = w + 3 1/6

l = 7.3 + 3 1/6

l = 7.3 + 19/6

l = 7.3 + 3.1667

l = 10.4667 cm

So the width of the rectangle is 7.3 cm, and the length is approximately 10.47 cm, to three significant figures.

Answer:19.7

Step-by-step explanation:

Sin‐(7.5/22.3) on your calculator

The answer to 3 significant figures is 19.7

The question seeks to find the size of angle YZX in a triangle but lacks the necessary information to provide an accurate answer. By using the sum of the angles in a triangle (180 degrees), we could find the angle YZX if we had the other two angle measurements.

Your question is a mathematical one, specifically within the study of geometry, but it seems to be missing information needed to provide a specific answer. Determining the size of Angle YZX would depend on other given angles or measurements within the triangle. For example, if we know the other two angles, we could calculate Angle YZX by subtracting the sum of the other two angles from 180 (as the total degrees in a triangle is 180). Furthermore, the number of significant figures doesn't affect the calculation of an angle, it only refers to how precise your final answer should be represented. In this case, the answer should be given to three significant figures. Let's say that the value of Angle YZX was calculated to be 123.456 degrees, then presenting this to three significant figures would result in 123 degrees.

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Answer:

[tex]\dfrac{1}{6}[/tex] hour or [tex]10[/tex] minutes

Step-by-step explanation:

Lisa:

Rate = 10 mph

Time = t hours

Distance = x miles

[tex]x=10\cdot t[/tex]

Jen:

Rate = 4 mph

Time = t hours

Distance = x - 1 miles

[tex]x-1=4\cdot t[/tex]

Hence,

[tex]10t-1=4t\\ \\10t-4t=1\\ \\6t=1\\ \\t=\dfrac{1}{6}\ hour[/tex]

Answer:

Step-by-step explanation: the sender below is not correct

ANSWER=  square root(-1) =  i

STEP-BY STEP EXPLANATION:

Imaginary number. An imaginary number is the square root of a negative real number. (The square root of a number is a second number that, when multiplied by itself, equals the first number.)

Answer:

x = 45/7

Step-by-step explanation:

Write as an algebraic equation.

Look at each part in the word question : 0.7 of what number is 4 1/2

"0.7 of what number" can be written as 0.7x

The word "is" means equals.

0.7x = 4 1/2     <= The equation, using 'x' to represent the number.

To find the number, isolate 'x'.

0.7x = [tex]4\frac{1}{2}[/tex]    Convert mixed fraction to improper fraction

0.7x = [tex]\frac{(4*2)+1}{2}[/tex]     Multiply the whole number by the denominator and add it to the numerator

0.7x = [tex]\frac{9}{2}[/tex]     Now isolate 'x'

0.7x/0.7 = [tex]\frac{9}{2}/0.7[/tex]     Divide both sides by 0.7

x = [tex]\frac{9}{2}/0.7[/tex]     Simplify right side

x = [tex]\frac{9}{2}/\frac{7}{10}[/tex]     Rewrite 0.7 as a fraction

x = [tex]\frac{9}{2}*\frac{10}{7}[/tex]     To divide, you multiply a flipped fraction

x = [tex]\frac{9*10}{2*7}[/tex]     Multiply across the top and across the bottom

x = 90/14      Reduce to lowest terms. Top and bottom are divisible by 2

x = 45/7        Answer

Each guest will get [tex]\frac{1}{2}\ pound[/tex] of meat on their sandwich.

Step-by-step explanation:

Given,

Number of guests = 15

Meat bought by Susie = [tex]7\frac{1}{2}=\frac{15}{2}[/tex] pounds

Therefore;

[tex]15\ guests = \frac{15}{2}\ pounds[/tex]

For 1 guest, we will divide the pounds by number of guest

Quantity of meat 1 guest gets= [tex]\frac{15}{2}\ divide \frac{15}{1}[/tex]

The fraction is reciprocated when division sign is changed into multiplication.

Quantity of meat 1 guest gets = [tex]\frac{15}{2}*\frac{1}{15}[/tex]

Quantity of meat 1 guest gets = [tex]\frac{1}{2}\ pound[/tex]

Each guest will get [tex]\frac{1}{2}\ pound[/tex] of meat on their sandwich.

Keywords: fraction, division

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