If you know a point on a line and you know the equation of a line parallel to this line, explain how to write the line’s equation.

The water will last for 3 days

Solution:

Given that, village having a population of 4000, requires 150 litres of water per head per day

Let us first find the volume of tank

The tank measuring 20m x 15m x 6m

Length = 20 m

Breadth = 15 m

Height = 6 m

[tex]volume\ of\ tank = length \times breadth \times height[/tex]

[tex]Volume\ of\ tank = 20 \times 15 \times 6 = 1800[/tex]

Thus volume of tank is 1800 cubic meter

From given,

Water required per person per day = 150 liters

Therefore, water required for 4000 people per day is:

[tex]\rightarrow 4000 \times 150 = 600000 \text{ liters }[/tex]

Convert to meters

[tex]600000 \text{ liters } = 600000 \times \frac{1}{1000}\ m^3\\\\600000 \text{ liters } = 600\ m^3[/tex]

How many days will the water of this tank last?

[tex]\text{Number of days water will last } = \frac{\text{volume of tank}}{\text{total water required per day}}[/tex]

[tex]\text{Number of days water will last } = \frac{1800}{600} = 3[/tex]

Thus the water will last for 3 days

The range of function is { -1, 1 }

Solution:

Given that, the function is:

[tex]f(x) = \frac{x^2-2}{2}[/tex]

Domain is {0, 2 }

We have to find the range of function

The domain refers to the set of possible input values

The range is the set of possible output values

Here domain is x = 0 and x = 2

Substitute x = 0 in given function

[tex]f(0) = \frac{0-2}{2}\\\\f(0) = \frac{-2}{2}\\\\f(0) = -1[/tex]

Substitute x = 2 in given function

[tex]f(2) = \frac{2^2-2}{2}\\\\f(2) = \frac{4-2}{2}\\\\f(2) = \frac{2}{2} = 1[/tex]

Thus the range of function is { -1, 1 }

Answer: y = 5

Step-by-step explanation:

This triangle is isosceles.

So, ∠ABC = ∠ACB = 75°

Now,

sum of interior angles of a triangle = 180°

∠ABC + ∠ACB + ∠BAC = 180°

75° + 75° + (4y + 10)° = 180°

160° + 4y° = 180°

4y° = 20°

y = 5

Answer:

y = 150 - 11x

Step-by-step explanation:

Janelle is starting out with 150 surveys and if she is conducting 11 surveys an hour, then that means you need to subtract 11x from 150 because that will give you how many surveys she has left.

Answer:

The solution of the system is the point (-1,-2)

Step-by-step explanation:

The question is

Enter the coordinates of the solution to the system of equations

we have

[tex]y=x-1[/tex] ----> red line

[tex]y=-2x-4[/tex] ----> blue line

Solve the system by graphing

Remember that the solution of the system of equations is the intersection point both graphs. The solution is a point that satisfy both equations

using a graphing tool

The intersection point is (-1,-2)

The intersection point satisfy both equations

therefore

The solution of the system is the point (-1,-2)

see the attached figure to better understand the problem

Answer:

[tex]\frac{8}{3}[/tex]

Step-by-step explanation:=

= [tex]\frac{56}{21}[/tex]  ( Divide both sides by 7)

= [tex]\frac{8}{3}[/tex]

21 is 3/8 fraction of 56.

A fraction describes a part of a whole. For example, one slice of a pizza is a fraction of the whole pizza.

Given that, what fraction of 56 is 21,

Finding the fraction, we get,

21 / 56 = 7(3) / 7(8)

= 3 / 8

Hence, 21 is 3/8 fraction of 56.

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Answer:

The equation of the line in point slope form is equal to

[tex]y+2=(x+2)[/tex]

Step-by-step explanation:

The picture of the question in the attached figure

step 1

Find the slope

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

we have

(-2,-2) and (2,2)

substitute the values

[tex]m=\frac{2+2}{2+2}=1[/tex]

step 2

Find the equation of the line in point slope form

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=1\\(x1,y1)=(-2,-2)[/tex]

substitute the values in the formula

[tex]y-(-2)=(1)(x-(-2))\\y+2=(x+2)[/tex]

The hypotenuse length is D. 2√29

Step-by-step explanation:

Here apply the Pythagorean relationship were the sum of squares of the sides equals the square of the hypotenuse.

Mathematically,

a²+b²=c²

a=10 ,b=4 ,c=hypotenuse

10²+4²=c²

100+16=c²

116=c²

√116=c

√4*29=c

√4 *√29=c

2√29 =c

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Kim's gross pay for this week is $292.50.

To calculate Kim's gross pay for this week,

we multiply the number of hours she worked by her hourly rate.

In this case, Kim worked 39 hours and her hourly rate is $7.50.

So, we can multiply 39 by $7.50 to find her gross pay.

39 * $7.50 = $292.50

Therefore, Kim's gross pay for this week is $292.50.

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Answer:

2

Step-by-step explanation:

(20÷4)-3

20÷4=5

5 x -3= 2

Answer:

2

Step-by-step explanation:

20 /4=5

5-3=2

Answer:

7-3n

Step-by-step explanation:

3 less than 7.................. 7-3

times a number ............ n

Together ......................... 7-3n

Step-by-step explanation:

To find, an algebraic expression for the given phrase = ?

6 times the length x = 6x

and

7 inches shorter than 6 times the length x

= 6x - 7

∴ 7 inches shorter than 6 times the length x of a table in inches = 6x - 7

Hence, the required "option d) 6x – 7" is correct.

Answer:

19 L

Step-by-step explanation:

Given that the volume (V) varies inversely with the pressure (P) then the equation relating them is

V = [tex]\frac{k}{P}[/tex] ← k is the constant of variation

To find k use the condition V = 5 when P = 304

k = VP = 5 × 304 = 1520

V = [tex]\frac{1520}{P}[/tex] ← equation of variation

When P = 80, then

V = [tex]\frac{1520}{80}[/tex] = 19 L

Answer: 2/3

Step-by-step explanation:

Answer:

15/11

Step-by-step explanation:

Because the GCF is 20

Hope this helps:)

Answer:

15/11

Step-by-step explanation:

Answer:

420 cm

Step-by-step explanation:

Answer: 29 m

Step-by-step explanation: First find the width

Since Area = Length x Width

Width = Area/Length = 232/8 = 29

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Answer:

4 x 11 + 3 = 47

Step-by-step explanation:

n = 11

The equation that represents the situation will be 4n + 3 = 47. And the solution of the equation is 11.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Four times a number, n, added to 3 is 47. Then the equation is given as,

4n + 3 = 47

Simplify the equation, then we have

4n + 3 = 47

4n = 47 - 3

4n = 44

n = 11

The equation that represents the situation will be 4n + 3 = 47. And the solution of the equation is 11.

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Answer:

13

Step-by-step explanation:

First find the number of children attending elementary school

= 1349*2

= 2698 children

Now each school can accommodate 220 children so divide the number of children by 220

=  

= 12.26 which is the closest to 13 in the options so the answer is 13

Step-by-step explanation:

Context?                                                                                                                      

??????????????                              

Answer:

Step-by-step explanation:

y - y1 = m(x - x1)

(1,9)...x1 = 1 and y1 = 9

slope(m) = 2

now we sub

y - 9 = 2(x - 1) <===

The point-slope equation of the line with slope 2 that passes through the point (1, 9) is y - 9 = 2(x - 1).

To find the point-slope form equation of a line with a given slope and a point, use the formula y - y1 = m(x - x1),

where (x1, y1) is the point on the line and m is the slope.

In this case, the slope is given as 2 and the point is (1,9).

Substituting these values into the point-slope form formula yields the equation y - 9 = 2(x - 1), which represents the linear relationship between x and y corresponding to the described line.

Step-by-step explanation:

To find a improper fraction, you must multiply the denominator by the whole number, then add the numerator to the product.

6 x 8 = 48 + 1 = 49.

Our numerator for the improper fraction is 49, we keep the denominator as the same as the whole number fraction, which is 8.

Therefore, your improper fraction is 49/8.

The improper fraction equivalent of 6 1/8 is 49/8.

Given that a mixed fraction 6 1/8, we need to convert it into improper fraction,

To change a mixed number like 6 1/8 into an improper fraction, you need to convert the whole number and the fraction into a single fraction.

Step 1: Multiply the whole number by the denominator of the fraction.

6 x 8 = 48

Step 2: Add the product from Step 1 to the numerator of the fraction.

48 + 1 = 49

Step 3: Write the result from Step 2 over the original denominator.

The original denominator is 8.

Therefore, the improper fraction equivalent of 6 1/8 is 49/8.

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Answer:

The area of a the parallelogram is 88meers squared

Answer:

Therefore the final elevation of the butterfly is 4 m.

Step-by-step explanation:

i) initial elevation = 20 m

ii) change in elevation = -16m

iii) therefore final elevation = initial elevation + change in elevation

               =   20 m + (-16 m)  

              =   (20 - 16) m

               =    4 m

Therefore the final elevation of the butterfly is 4 m.

Answer:

4

Step-by-step explanation:

Answer:

x = -2

Step-by-step explanation:

Answer: Its 2

Step-by-step explanation: PEMDAS Keep.Change.Flip.

5/6×3/2=15/12=1 3/12

1 3/12+3/4(3/3)

1 3/12+9/12=1 12/12=2. BOOM!

Answer:

1/8

Step-by-step explanation:

Check: 12.5 * 8 = 100

Answer:

1/8 is the simplest form

Step-by-step explanation:

12.5% = 12.5/100 = 125/1000

125/125 = 1

1000/125 = 8

= 1/8

Answer:

90 yards a minute

Step-by-step explanation:

The way to figure this out is simple. Just do the amount of yards he or she did total, which is 450, then divided it by the amount of time it took him or her to do so, which is 5 minutes, meaning the equation is 450 divided by 5 equaling 90.

Answer:i think its 90

Step-by-step explanation:

450 / 5 = 90

Answer:

If the input is n then the output f(n) will be 4n - 8.

Step-by-step explanation:

Let the input of the function is denoted by x and the output is denoted by y.

Then, two ordered pairs of the linear function i.e.(x,y) are (2,0) and (3,4).

Therefore, the relation between x and y i.e. the equation of the straight line will be given by

[tex]\frac{y - 4}{4 - 0} = \frac{x - 3}{3 - 2}[/tex]

⇒ y - 4 = 4(x - 3)

⇒ y = 4x - 8

⇒ f(x) = 4x - 8

Therefore, if the input is n then the output f(n) will be 4n - 8. (Answer)