if three buckets of capacities 15 litre,18 litre and 24 litre can fill a drum in exact number of times, find the least capacity of the drum.

Answer:

  the trip represented by f(x) takes less time

Step-by-step explanation:

Given a table of time and distance to go, and a function f(x) = 210-60x representing the same for a different trip, you want to know which trip takes less time.

The table has values ...

  (time in hours, remaining distance in miles) = (1, 150), (2, 100), (3, 50)

This shows you the remaining distance decreases by 50 miles for every hour added to the travel time. That means the remaining 50 miles will be reduced to zero after 4 hours.

The trip represented by the table takes 4 hours.

The function f(x) = 210-60x will have a value of zero when ...

  0 = 210 -60x

  0 = 3.5 -x . . . . . . divide by 60

  x = 3.5 . . . . . . . . add x

The trip represented by the function f(x) takes 3.5 hours.

The second trip takes less time.

The number of terms in the sequence is 19

The sequence is given as

5, 7, 9 . . . 39, 41

In the above sequence, we can see that

The nth term of an arithmetic sequence is

Tn = a + (n - 1)d

So, we have

5 + (n - 1) * 2 = 41

This gives

(n - 1) * 2 = 36

Divide by 2

n - 1 = 18

Add 1 to both sides

n = 19

Hence, there are 19 numbers in the sequence

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Answer:

Step-by-step explanation:

everything u need is in the picture

Using a system of equations, it is found that:

b) The domain of the solution is that Steve ran 11 miles.

c) Variable S gives the distance ran by Steve.

d) The algebraic expressions are:  K = 4 + S, K + S = 26.

e) The equation is: 4 + S + S = 26.

What is a system of equations?

A system of equations is when multiple variables are related, and equations are built to find the numeric values of each variable, according to the relations built in the problem.

In the context of this situation, the variables are given as follows:

Variable K: Distance ran by Kevin.

Variable S: Distance ran by Steve.

Kevin ran 4 miles more than Steve ran, hence:

K = 4 + S.

The sum of their distances is 26 miles, hence:

K + S = 26.

Replacing the first equation K = 4 + S on the second, we have that:

4 + S + S = 26

2S = 22

S = 11 miles.

It is given that area of rectangle of Kaitlin is 1500 sq.ft. with length 50 ft and a width of 30 ft.

The new area when new length 2 times the current length and the new width 2 times the current width.

a. The size of Kaitlin new patio is

b. The area of new patio is 4 times the area of current patio.

The possible solutions for the given function are as follows:

In the graph,  the real roots are the values when it crosses the x-axis.

Therefore, the possible solutions for the given function are as follows:

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Step-by-step explanation:

[tex] \frac{1}{a + b} \times ( \frac{a + b}{ab}) = \frac{1}{ab} [/tex]

Answer with step-by-step explanation:

[tex](a+b)^-^1*(a^-^1+b^-^1)=(ab)^-^1[/tex]

First, convert these into positive indices.

[tex]\frac{1}{(a+b)} *(\frac{1}{a} +\frac{1}{b})=\frac{1}{ab}[/tex]

And now, let us solve the left side.

[tex]\frac{1}{(a+b)} *(\frac{1}{a} +\frac{1}{b})\\\\[/tex]

First, solve the brackets. That is add the fractions inside the brackets.

[tex]\frac{1}{(a+b)} *(\frac{1}{a} +\frac{1}{b})\\\\\frac{1}{(a+b)}*(\frac{1*b}{a*b} +\frac{1*a}{b*a})\\\\\frac{1}{(a+b)}*(\frac{b}{ab} +\frac{a}{ab})\\\\\frac{1}{(a+b)}*\frac{(a+b)}{ab}[/tex]

Now multiply the fractions.

[tex]\frac{1}{ab}[/tex]

So, it's clear that the left side equals the right side.

Left side = Right side

[tex]\frac{1}{ab}=\frac{1}{ab}[/tex]

∴ [tex](a+b)^-^1*(a^-^1+b^-^1)=(ab)^-^1[/tex]

4 is the numerical length of line segment LN.

A line segment is simply the part of a line that connects two points or is bounded by two points.

Given the data in the question;

Since point M is on line segment LN, segment LN equals to the sum of segment LM and MN.

Hence;

Segment LN = segment LM + segment MN

4x = 3 + x

Solve for x

4x - x = 3

3x = 3

x = 3/3

x = 1

Now, we find the numerical length of segment LN;

Segment LN = 4x

Plug in x = 1 and simplify

Segment LN = 4( 1 )

Segment LN = 4

Therefore, the length of segment LN is 4.

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Answer:

x=0.4

Step-by-step explanation:

Put both equations equal to each other:

16x+2=7x+6

Now, Solve:

16x+2=7x+6   Set the equation

16x-7x=6-2     Move like terms together

9x=4              Subtract like terms

x=4/9             Simplify

x=0.4             Answer

Answer:

x ∠ 40

Step-by-step explanation:

0.5x ∠ 20

Divide both sides by 0.5:

x ∠ 40

Answer:

Given that the information,

Length of a  soccer practice = 90 minutes

Time that has elapsed = m minutes

Let "y" be the minutes left

Expression for the number of minutes left is

[tex]y = (90 - m) min[/tex]

In step 2 addition property is used.

2x + (1 ÷ 4) - (3 ÷ 5)x = 55 ÷ 4

Simplifying x,

2x - (3 ÷ 5)x - (1 ÷ 4) = 55 ÷ 4

(10x - 3) ÷ 5 - (1 ÷ 4) = 55 ÷ 4

(7x ÷ 5) - (1 ÷ 4) = 55 ÷ 4

Add (1 ÷ 4) on both sides,

(7x ÷ 5) - (1 ÷ 4) + (1 ÷ 4) = 55 ÷ 4 + (1 ÷ 4)

(7x ÷ 5) = (55 + 1) ÷ 4

(7x ÷ 5) = 56 ÷ 4

Multiplying (5 ÷ 7) on both sides,

(7x ÷ 5) × (5 ÷ 7) = (56 ÷ 4) × (5 ÷ 7)

x = 10

In step 2 - Add (1 ÷ 4) on both sides, the addition property is being used.

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Answer:

its c step three

Step-by-step explanation:

closed circles are at negative 2 and positive 8. everything between the points is shaded.

We have the equation:

|h - 3| [tex]\leq[/tex] 5

Remember that the equation:

|f(x)| = A

with A > 0

means that:

f(x) = A

or

f(x) = -A

Then for our case, we can rewrite:

|h - 3| [tex]\leq[/tex] 5

as:

(h - 3) [tex]\leq[/tex] 5

or

-(h - 3) [tex]\leq[/tex] 5

Now we can solve these two equations to find the two possible values of p.

From the first one, we get:

h [tex]\leq[/tex] 8

Now from the other equation, we can get the other solution:

h [tex]\geq[/tex] -2

Then the correct option is:

closed circles are at negative 2 and positive 8. everything between the points is shaded.

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Answer:

1 / 121

Step-by-step explanation:

4^0 = 1

11^2 = 121

4^0 / 11^2 = 1 / 121

The point would be the solution (25,40).

Let

The number of tacos sold is represented by x.

x denotes the quantity of burritos sold.

We are aware of this,

⇒ x + y 62

⇒ 3.75x + 6y = 330

The triangle shaded region is the answer

(25,40)

The point is one possible solution (25,40).

Remember that if an ordered pair is a solution to a system of inequalities, then the ordered pair must reside on the solution's region.

That indicates there were 30 tacos sold and 30 burritos sold.

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Answer: The answer is 27

Step-by-step explanation:

if a=5 and b=10 and c=12 then just put the numbers in place of the letters so that's going to be :

P=5+10+12
P=15+12
P=27

The equation of the line that passes through the x-intercept ( -2,0 ) and y-intercept ( 0,1 ) is y = (1/2)x + 1.

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

From the graph, the x and y-intercept are; ( -2,0) and (0,1 )

Point 1 ( -2,0 )

Point 2( 0,1 )

First, we determine the slope of the line.

Slope m = y₂ - y₁ / x₂ - x₁

Slope m = 1 - 0 / 0 - (-2)

Slope m = 1 / 0 +2

Slope m = 1/2

Next, determine the y-intercept b by substituting the slope and a point into the equation of line formula.

y = mx + b

0 = (1/2)(-2) + b

0 = -2/2 + b

0 = -1 + b

b = 1

Now that the values of slope m and y-intercept b is known, plug these into y = mx + b to determine the equation of the line.

y = mx + b

y = (1/2)x + 1

Therefore, the equation of the line is y = (1/2)x + 1.

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We have the following number, we need to simplify:

we can also express this as:

since:

which represents the imaginary number,

then, we get:

Answer:

x+3=2x-61 (corresponding angles)

3+61=2x-x

64=x

x=64

Answer:

x = 64

steps are in the photo

The function which will represent the given Translation will be T(x, y) = (x + 3, y - 2).

Translation may be defined as the shifting of the curve on a graph or shifting of the plotted points on a graph. The translation can be horizontal or vertical. In horizontal direction it can be shifted either left or right and in vertical direction it can be shifted either up or down. Horizontal translation always occurs on the x axis and vertical translation always occurs on the y axis. A function may be defined as an expression in which for input variable x there is output variable y. We need to translate a function T(x, y) 3 units right so the new coordinate will be T(x + 3, y). Now, translation occurs 2 units down. so, new coordinates will be T(x + 3, y -2) which is the required function.

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The measure of the angles x and y are 71 degrees and 109 degrees after applying the concept of vertically opposite angles.

It is defined as the angles when two lines intersect each other and at the intersecting point, some pair of angles are formed which we call vertically opposite angles, as the name describes that they have vertically opposite angles.

From the figure:

The value of y can be found by applying the concept of vertically opposite angles:

y =  109 degrees

x = [360 - 2(109)]/2

x = (360 - 218)/2

x = 71 degrees

Thus, the measure of the angles x and y are 71 degrees and 109 degrees after applying the concept of vertically opposite angles.

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The cost of t shirt is $ 133.

Cost price is the complete sum of money that a manufacturer must spend to create a specific good or render a specific service.

For instance, Cost price equals selling price plus revenue ( when selling price and profit is given ) Cost is equal to Selling price plus Loss ( when selling price and loss is given ) Cost price = 100 Selling Price + 100 + Profit (where the Selling Price and Profit Percentage are supplied)

Given: c = 9.5 t

Sanjay bought 14 t shirts

And t in the above equation stands for the number of t shirts

thus c = 9.5 × 14 = $ 133

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point slope form = y-(-43)=[tex]-\frac{2}{21}[/tex](x-3)

slope intercept form = -[tex]\frac{152}{7}[/tex]=c

Finding the ratio of "vertical change" to "horizontal change" between any two unique locations on a line yields the slope. Occasionally, the ratio is written as a quotient (also known as a "rise over run"), which produces the same number for every two unique points on the same line. Negative "rise" refers to a diminishing line. The line could be functional, established by a road surveyor, or depicted in a graphic that represents a road or a roof as a description or a design.

The absolute value of the slope is used to determine how steep, incline, or grade a line is. The steeper the line, the larger the absolute magnitude of the slope. A line's direction might be either horizontal, ascending, decreasing, or vertical

If a line is rising from left to right, it is increasing. Since m>0, the slope is positive.

If a line decreases from left to right, it is said to be diminishing. The slope is inverse, or m0.

A line has zero slope if it is horizontal. This function has a fixed value.

A line's slope is ambiguous if it is vertical.

Slope= [tex]\frac{x-x1}{y-y1}[/tex]= [tex]\frac{3-5}{-22+43}[/tex]=[tex]\frac{-2}{21}[/tex]

point slope form= y-(-43)=[tex]-\frac{2}{21}[/tex](x-3)

slope intercept formy=mx+c

-22=[tex]-\frac{2}{21}[/tex]*3+c

-22+[tex]\frac{2}{7}[/tex]=c

-[tex]\frac{152}{7}[/tex]=c

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Company B has the best buy with a selling price of $2.79

Given: Company A sells 16 lions for $44.32

Company B sells 18 lions for $50.22

Company C sells 12 lions for $ 32.88

To find : The selling price of each lion

By using unitary method we get,

Company A sells 1 lion for $ 2.77

Company B sells 1 lion for $2.79

Company C sells 1 lion for $ 2.74

From the above statistics it is clear that Company B has the best buy .

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Answer:

Step-by-step explanation:

[tex] \sf \cfrac{8(x + 3)^{2} }{2(x + 3)} [/tex]

Cancel out 2(x+3) in both numerator and denominator:

[tex]\sf 4(x + 3)[/tex]

Use the distributive property to multiply 4 by x+3:

[tex]\sf 4x + 12[/tex]

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Hope this helps!!

Have a nice day

Answer:

F(x)=-(x+4)(x-1)

Step-by-step explanation:

the thing hit both -4 and 1 but in the function -4 become 4 and 1 become-1 so (x+4)(x-1) but we need to make it negative so -(x+4)(x-1)