Word Problem On Division
1. a cup can hold 2/9 ( fraction) litres of water. how many cups of water can be filled with 3 litre bottle?

Answer: C

Step-by-step explanation:

The red graph is the result of reflecting the graph of y=f(x) across the x-axis and then translating 1 unit to the right.

Option C is correct (y + z = 6) ⋅ −3

What is a linear equation in math?

As per the statement -

A student is trying to solve the system of two equations given below:

Equation P:   y + z = 6              ....[1]

Equation Q:  3y + 4z = 1           ....[2]

Multiply the equation [1] by -3 to both sides we have;

-3 .( y + z = 6 ) ⇒ -3y -3z = -18..........(3)

Add equation [2] and [3] to eliminate the y-term;

z = -17

Therefore, the  possible step used in eliminating the y-term is, (y + z = 6) ⋅ −3

Learn more about linear equation

brainly.com/question/11897796

#SPJ4

The complete question is -

A student is trying to solve the system of two equations given below: Equation P: y + z = 6 Equation Q: 3y + 4z = 1 Which of these is a possible step used in eliminating the y-term?

(y + z = 6) ⋅ 4

(3y + 4z = 1) ⋅ 4

(y + z = 6) ⋅ −3

(3y + 4z = 1) ⋅ 3

Let hats be x

Let shirts be y

We can set up a system of equations to figure out the cost of one hat.

5x+3y = 176 and 3x+5y = 208

Since we are finding the cost of the hats, we will need to isolate x from the equation. We can first get rid of y. One way we can do that is by multiplying the first equation with 5 and the second one with -3, effectively making y add up to 0 when we solve for x.

5(5x+3y = 176) --> 25x+15y = 880

-3(3x+5y = 208) --> -9x-15y = -624

We can now add the 2 equations together and solve for x.
25x+15y = 880

-9x-15y = -624

+>>>>>>>>>>>>>>>

16x = 256

x = 16

So the the cost of one hat is 16 dollars.

Answer:

$16

Step-by-step explanation:

Define the variables:

Create two equations using the defined variables and the given information.

Equation 1

Five hats and three shirts cost $176.

⇒ 5x + 3y = 176

Equation 2

Three hats and five shirts cost $208.

⇒ 3x + 5y = 208

Rewrite Equation 2 to make y the subject:

[tex]\implies \sf 3x+5y-3x=208-3x[/tex]

[tex]\implies \sf 5y=208-3x[/tex]

[tex]\implies \sf \dfrac{5y}{5}=\dfrac{208-3x}{5}[/tex]

[tex]\implies \sf y=\dfrac{208-3x}{5}[/tex]

Substitute the found expression for y into Equation 1 and solve for x:

[tex]\implies \sf 5x+3\left(\dfrac{208-3x}{5} \right)=176[/tex]

[tex]\implies \sf 5x+\dfrac{624-9x}{5}=176[/tex]

[tex]\implies \sf 5x+124.8-1.8x=176[/tex]

[tex]\implies \sf 3.2x+124.8=176[/tex]

[tex]\implies \sf 3.2x+124.8-124.8=176-124.8[/tex]

[tex]\implies \sf 3.2x=51.2[/tex]

[tex]\implies \sf \dfrac{3.2x}{3.2}=\dfrac{51.2}{3.2}[/tex]

[tex]\implies \sf x=16[/tex]

Therefore, the cost of one hat is 16 dollars.

Learn more about systems of equations here:

https://brainly.com/question/28093918

https://brainly.com/question/21447811

The value of the given trigonometry function is 2√15/15

Half angles are trigonometric identities used to express sine, cosine and tangent of half angles.

For instance the value of cos theta is expressed as shown below;

cosФ = cos(Ф/2+Ф/2)

cosФ = cos²Ф/2-sin²Ф/2
cosФ = cos²Ф/2-(1-cos²Ф/2)
cosФ  = 1 - 2cos²Ф/2

Given the following parameters

cosФ = -7/15

Substitute

cosФ  = 1 - 2cos²Ф/2

-7/15  = 1 - 2cos²Ф/2

-2cos²Ф/2 = -7/15 - 1

-2cos²Ф/2 = -8/15

cos²Ф/2 = 4/15
cosФ/2 = 2/√15

Rationalize

2/√15 * √15/√15

2√15/15

Hence the value of the given trigonometry function is 2√15/15

Learn more on trigonometry function here: https://brainly.com/question/2254074

#SPJ1

The Created cone  with the possible record  of the the values of the radius, and  height is given in the image attached.

A scale factor is known to be a number that is known to often multiplies (doubles or triples, etc.,“scales”) a given quantity.

Since the volume is not attached, it will be manually created here.

Note that the resulting volumes must be in terms of 7.

Hence:

Volume  Formula:   V=V  x  k³

When scale factor is 2, radius  = 4, height  = 8,  then volume will be:

7π x 2³

=  56π

When scale factor is 3, radius  = 6, height  = 18,  then volume will be:

7π x 3³

= 189π

When scale factor is 4, radius  = 8, height  = 24,  then volume will be:

7π x 4³

= 448π

Hence the volume that will be fixed into the scale factor diagram will be:

Learn more about scale factor from

https://brainly.com/question/17093741

#SPJ1

Answer:

8-18=n

-10=n

therefore

n=-10

-------------------------------------------------------------------------------------------------------------

Answer:  [tex]\textsf{n = -11}[/tex]

-------------------------------------------------------------------------------------------------------------

Given:  [tex]\textsf{-19 = -8 + n}[/tex]

Find:  [tex]\textsf{Solve for n}[/tex]

Solution: In order to solve for n we need to add 8 to both sides which would cancel -8 on the right side and isolate n giving us the value of n.

Add 8 to both sides

Therefore, the final answer would be that n is equal to -11.

Answer:

slope

(0, 6) and (-9, 0)

0 - 6 / -9 - 0 = -6/-9 = 2/3

y intercept is when the line intercepts the y axis and x = 0

The slope of the line shown in the graph is 2/3 and the y-intercept of the line is 6

Answer:

slope is 2/3

y intercept is 6

Step-by-step explanation:

We can find the slope of the line by using two point

(-9,0) and (0,6)

The slope formula is

m = ( y2-y1)/(x2-x1)

   = ( 6 - 0) /( 0 - -9)

   = (6-0)/(0+9)

  = 6/9

  = 2/3

The y intercept is where it crosses the y axis ( the value where x is 0)

The y intercept is 6

The coordinates of point r(-8,0).

The coordinates of the point r(x,y) which divides the line segment joining the points p([tex]x_{1}[/tex],[tex]y_{1}[/tex]) and q([tex]x_{2}[/tex],[tex]y_{2}[/tex]) internally in the ratio :[tex]m_{1}[/tex][tex]m_{2}[/tex] are

[tex]\left(\frac{m_{1}x_{2}+ m_{2}x_{1} }{m_{1}+m_{2} } ,\frac{m_{1}y_{2}+ m_{2}y_{1} }{m_{1}+m_{2} }\Rifgt)[/tex]

Given that,

Two end points on the line q(-14,0) and s(2,0). point r(x,y) is the partition of the line segment from q to s in a ratio 3:5

[tex]m_{1}[/tex] = 3 and [tex]m_{2}[/tex] = 5

By using the midpoint formula

[tex]\left(\frac{m_{1}x_{2}+ m_{2}x_{1} }{m_{1}+m_{2} } ,\frac{m_{1}y_{2}+ m_{2}y_{1} }{m_{1}+m_{2} }\Rifgt)[/tex]

[tex]\left(\frac{3(2)+ 5(-14) }{3+5 } ,\frac{3(0)+ 5(0) }{3+5 }\Rifgt)[/tex]

[tex]\left(\frac{-64}{8 } ,\frac{0 }{8 }\Rifgt)[/tex]

[tex]\left(-8 ,0\Rifgt)[/tex]

Hence, The coordinates of point r(-8,0).

To learn more about midpoint formula from the given link:

https://brainly.com/question/4429656

#SPJ4

Answer:

below

Step-by-step explanation:

2) 10², the second power of ten

3) 10⁴, the fourth power of ten

4) 1000

5) 400

6) 90,000

7) 10

8) 100,000

9) 50

10) 7000

11) 8

12) 24 x 10⁴

13) 93,000,000

Answer + Step-by-step explanation:

Answer:

$591.10

Step-by-step explanation:

First, add up $475.88 and $609.00 together. Then, subtract it from $1675.88. They need $591.10 more for their vacation.

It would take 2 months for the membership of both clubs to be the same

An equation is an expression that shows the relationship between two numbers and variables.

The standard form of a linear equation is:

y = mx + b

Where m is the rate of change and b is the y intercept

Let y represent the total cost of dues over x months, hence given that:

y = 3x - 5     (1)

Also:

4x - 3y = 5

y = (4x - 5)/3      (2)

For the membership of both clubs to be the same:

3x - 5 = (4x - 5)/3    

9x - 15 = 4x - 5

x = 2

It would take 2 months for the membership of both clubs to be the same

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Answer: 2

Step-by-step explanation:

remember y=mx^2+c

where m = gradient = slope

∴ expand and simplify y-5=2(x+3)

y-5=2x+6

y=2x+11

m=2  ∴ slope: 2

The maximum height is; 180 ft and the Total time in the air is 12 seconds

We are given the equation that represents the height of the rocket as;

d = 60t - 5t²

Taking the derivative of the formula gives us;

d' = 60 - 10t.  

-10t represents the acceleration.  The 60 represents the initial velocity.

Set 60 - 10t = 0 and solve for t to get;

t = 60/10 = 6seconds.  

That's when the maximum height occurs. Plug that value of t into the original quadratic equation to get the maximum height.

d(6) = 60t - 5t²

d(6) = 60(6) - 5(6²)

d(6) = 180

So,  maximum height is about 180 ft.  

Thus, total time in air = 2 * 6 = 12 seconds

Read more about Projectiles at; https://brainly.com/question/1130127

#SPJ1

Answer:

0.012

Step-by-step explanation:

We know the standard notation of table salt is 0.003, so we simply multiply 40 by this.

answer - 0.0003 X 40 = 0.012

The issue of too many proficient business-savvy programmers is least likely to arise in machine learning(ml) and artificial intelligence(ai).

What is machine learning?

The process by which computers learn to recognize patterns, or the capacity to continuously learn from and make predictions based on data, then make adjustments without being specifically programmed to do so, is known as machine learning (ML), a subcategory of artificial intelligence.

The operation of machine learning is quite complicated and varies according to the task at hand and the algorithm employed to do it. However, at its foundation, a machine learning model is a computer that analyzes data to spot patterns before using those realizations to better fulfill the work that has been given to it. Machine learning can automate any task that depends on a set of data points or rules, even the more difficult ones.

To learn more about machine learning.........

https://brainly.com/question/25523571

#SPJ4

It's tempting to say that increasing the speed limit has led to higher accident rates, but you have to be careful because other variables (e.g. cheaper gas or time of year the change was introduced) can also affect accident rates. The option C is correct.

Given the impact of the speed limit increase from 55 to 65 mph, there are more crashes in the 6 months after the speed limit change than in the 6 months before the speed limit change. speed.

The dependent variable is the variable that is attempted and expected in a survey and is "dependent" on the free aspect. In a survey, the scientist tries to find the conceivable influence on the reliable variable, which can be approximated by changing the free thing. The free aspect is the variable that the experimenter adjusts or controls, and should directly affect the dependent variable. Therefore, increasing the speed limit from 55 to 65 mph resulted in higher accident rates, you have to be careful with other variables.

Learn more about quasi-experiment from here brainly.com/question/15875054

#SPJ1

Question 1

[tex]x^3 + x^2 - 4x-4=0\\\\x^2 (x+1)-4(x+1)=0\\\\(x^2 -4)(x+1)=0\\\\(x-2)(x+2)(x+1)=0\\\\x=-2, -1, 2[/tex]

Question 2

By inspection, we know that [tex]x=2[/tex] is a root.

[tex]\frac{2x^3 - 11x^2 + 17x-6}{x-2}=2x^2 - 7x+3[/tex].

So, we can factor the equation as

[tex](x-2)(2x^2 - 7x+3)=0\\\\(x-2)(x-3)(2x-1)=0\\\\x=\frac{1}{2}, 2, 3[/tex]

So, the value of x is 1.19

The question is an exponential equation

An exponential equation is a mathematical expression between two quantities in which one variable is raised to a power of the other variable.

Since [tex]4^{x} + 6^{x} = 9^{x}[/tex],

Dividing through by 4ˣ, we have

[tex]\frac{4^{x} }{4^{x} } + \frac{6^{x} }{4^{x} } = \frac{9^{x} }{4^{x} } \\1 + (\frac{6}{4})^{x} } = (\frac{9}{4})^{x} } \\1 + (\frac{3}{2})^{x} } = (\frac{3^{2} }{2^{2} })^{x} } \\1 + (\frac{3}{2})^{x} } = (\frac{3}{2})^{2x} }[/tex]

Let y = (3/2)ˣ

So,

1 + y = y²

y² - y - 1 = 0

Using the quadratic formula to find y,

[tex]y = \frac{-b +/- \sqrt{b^{2} - 4ac} }{2a}[/tex]

where a = 1 b = -1 and c = -1

Substituting the values of the variables into the equation, we have

[tex]y = \frac{-(-1) +/- \sqrt{(-1)^{2} - 4\times 1 \times (-1)} }{2\times 1}\\= \frac{1 +/- \sqrt{1 + 4} }{2}\\= \frac{1 +/- \sqrt{5} }{2}\\= \frac{1 - \sqrt{5} }{2} or \frac{1 + \sqrt{5} }{2}\\= \frac{1 - 2.236}{2} or \frac{1 + 2.236}{2}\\= \frac{- 1.236}{2} or \frac{3.236}{2}\\= -0.618 or 1.618[/tex]

Since y = (3/2)ˣ

Takung logarithm of both sides, we have

㏒y = ㏒(3/2)ˣ

㏒y = x㏒(3/2)

x = ㏒y/㏒(3/2)

x = ㏒y/㏒1.5

Since we do not have logarithm of a negative number, we use y = 1.618.

So, x = ㏒y/㏒1.5

x = ㏒1.618/㏒1.5

x = 0.2090/0.1761

x = 1.19

So, the value of x is 1.19

Learn more about exponential equation here:

https://brainly.com/question/11832081

#SPJ1

An expression for the amount of the money left = (5n-7900) cedis

The minimum amount she needs to save each week to be able to afford the gift: n = 7900/5.

The term "word problem" refers to a type of math question where the answer is written as one or more sentences and asks students to use their mathematical understanding to solve a problem from "real world."

Read the problem in its full to get a clear understanding of what you need to do in order to solve it before you start. Following reading it, you may choose which components of the issue need to be resolved the most and which ones are not.

She gets n cedis a week.

she will get n x 5 cedis for 5 wks =5n cedis.

She buys a present worth 7900.

An expression for the amount of the money left = (5n-7900) cedis.

The minimum amount she needs to save each week to be able to afford the gift.

5n-7900 = 0

 n = 7900/5.

 7900/5 = ____ per week

To know more about word problem visit:

https://brainly.com/question/11240316

#SPJ4

Answer: [tex]\Large\boxed{f(x-1)=x}[/tex]

Step-by-step explanation:

Given function

f(x + 1) = x + 2

Isolate [ x + 1 ] on the right-hand side

f(x + 1) = x + 1 + 1

f(x + 1) = (x + 1) + 1

Substitute [ x + 1 ] with x

f(x) = x + 1

Substitute [ x ] with [ x - 1 ]

f(x - 1) = (x - 1) + 1

[tex]\Large\boxed{f(x-1)=x}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

An equivalent system of equations using the sum of the system and the first equation is:

[tex]x+4y=8\\5x+5y=10[/tex]

Given:

[tex]x+4y=8\\4x+y=2[/tex]

Add the above equations to get:
[tex]x+4y+4x+y=8+2\\x+4y+4x+y=10\\5x+5y=10[/tex]

Therefore, an equivalent system of equations using the sum of the system and the first equation is:

[tex]x+4y=8\\5x+5y=10[/tex]

Know more about equations here:

https://brainly.com/question/2972832

#SPJ4

The correct question is given below:
Create an equivalent system of equations using the sum of the system and the first equation.

x + 4y = 8

4x + y = 2

x + 4y = 8

5x + y = 2

x + 4y = 8

5x + 5y = 2

x + 4y = 8

4x + 5y = 10

x + 4y = 8

5x + 5y = 10

Answer: 2 and -10 respectively

Step-by-step explanation:

m in the equation is 2 as it is parallel to a line with a slope of 2

Both point A and B are on the x-axis so both of them have a y value of 0

To find the x value of A, we have to substitute y = 0 into the equation

2x + 8 = 0

x = -4, so the coordinate for A is A(-4,0)

As AB is 9 units, we can figure out that B(5,0)

Substitute x = 5 and y = 0 into the equation y = 2x + c to find c

0 = 2(5) + c

c = -10

So m = 2 and c = -10

Answer:

0.13 inches.

Step-by-step explanation:

1 inch = 2.54 cm

So 1 cm = 1/ 2.54 in

0.33 cm = 0.33/2.54 in

= 0.13 inches.

The equation of the parabola given in the graph is:

(x - 5)² = -8(y + 4).

The equation of a quadratic function, of vertex (h,k), is given by:

a(y - k) = (x - h)²

In which a = 4p is the leading coefficient.

In this problem, the vertex is at point (5,-4), hence h = 5, k = -4, and the equation is:

a(y + 4) = (x - 5)²

The focus is at y = -6, which means that p = -6 - (-4) = -2, hence the leading coefficient is:

a = 4p = 4(-2) = -8

Hence the equation is:

(x - 5)² = -8(y + 4).

More can be learned about the equation of a parabola at https://brainly.com/question/24737967

#SPJ1

The height of the second square base prism is 50 cm.

The volume of the first square base prism is represented as follows:

v = ha²

where

Therefore, the height of the prism is 10 cm.

v = 10a²

Hence, the volume of the initial prism is 5 times the volume. Therefore,

v = 5(10a²)

v = 50a²

Therefore,

50a² = ha²

divide both sides by a²

50a² / a² = ha² / a²

50 = h

h = 50  cm

Therefore, the height of the second square base prism is 50 cm.

learn more on volume here: https://brainly.com/question/3600642

#SPJ1

Answer:724

Step-by-step explanation: Let us go through trail and error method.

Question: Need to find N, so that 2020+ N should be a perfect cube, as well as a multiple of 56.

2744 is the first number we get after 2020 and it is a cube of 14. ___ equation -01

Let us divide, 2744 with 56.

i.e., 2744/56= 49. ___ equation -02

As per 1st and 2nd equation 2744 meets with the condition. And we can consider it as 2020+ N.

i.e., 2020+N= 2744

N= 2744-2020

Therefore; N= 724.

Answer:

724,

Step-by-step explanation:

14^3 = 2744 is the next perfect cube > 2020.

2744 / 56 = 49.

So that fits the requirements in the question.

So N = 2744 - 2020

= 724,

The solution to the system of equations is x = 3 and y = 11

Linear equations are equations that have constant average rates of change, slope or gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

y equals x plus 8

y equals 3 x plus 2

Rewrite properly as

y = x + 8

y = 3x + 2

Substitute y = x + 8 in y = 3x + 2

x + 8 = 3x + 2

Evaluate the like terms

2x = 6

Divide by 2

x = 3

Substitute x = 3 in y = x + 8

y = 3 + 8

Evaluate

y = 11

Hence, the solution to the system of equations is x = 3 and y = 11

Read more about system of equations at

https://brainly.com/question/14323743

#SPJ1

The solution to the system of equation is as follows:

x = 3

y = 11

y = x + 8

y = 3x + 2

Using substitution method,

3x + 2 = x + 8

subtract x from both sides

3x - x + 2 = x - x + 8

2x + 2 = 8

subtract 2 from both sides

2x + 2 - 2 = 8 - 2

2x = 6

divide both sides by 2

2x / 2  = 6 / 2

x = 3

y = 3 + 8 = 11

y = 11

learn more on equation here: https://brainly.com/question/13575946

#SPJ1

The minimum cost to produce the product is $7.

What are functions?

To determine the minimum cost:

We have to determine the minimum cost of producing this product.

Since [tex]f(x) = 5x^{2} -70x+258[/tex].

Now, consider the equation [tex]5x^{2} -70x+258= 0[/tex].

Dividing the above equation by 5, we get

[tex]x^{2} -70x/5+258/5=0\\x^{2} -14x+258/5=0[/tex]

Now, considering the coefficient of 'x', dividing it by '2' and then adding and subtracting the square of the number which we got after dividing.

Since the coefficient of 'x' is 14, and half of 14 is '7'.

So, adding and subtracting from the above equation.

[tex]x^{2} -14x+(7)^{2} -(7)^{2}+258/5=0\\x^{2} -14x+49 -49+258/5=0\\(x-7)^{2} -49+258/5=0\\(x-7)^{2} +258-245/5=0\\(x-7)^{2} +13/5=0\\5(x-7)^{2} +13=0[/tex]

Now, we have to determine the minimum cost to produce the product.

Since [tex]f(x) = 5x^{2} -70x+258[/tex].

[tex]f'(x) = 10x-70[/tex]

Now, let f'(x)=0

[tex]10x-70=0\\10x=70[/tex]

Therefore, x=7

Now, consider which is greater than 0.

Therefore, x= 7 is the minimum cost.

Know more about functions here:

https://brainly.com/question/25638609

#SPJ4

Answer: The minimum cost to produce the product is $13.

I apologize for the late answer, hope this helps in the future!

Step-by-step explanation:

To complete the square, we need to rewrite the given function in the form:

f(x) = a(x - h)^2 + k

where (h, k) is the coordinates of the vertex of the parabola defined by the function, and a is a positive constant that determines the shape of the parabola.

We start by factoring out the coefficient of x^2:

f(x) = 5(x^2 - 14x + 51.6)

To complete the square, we need to add and subtract a constant inside the parentheses that will allow us to write the expression inside the parentheses as a perfect square. The constant we need to add and subtract is half of the coefficient of x, squared:

f(x) = 5(x^2 - 14x + 51.6 + (7)^2 - (7)^2)

= 5((x - 7)^2 + 13)

Now we have the function in the desired form, with a = 5, h = 7, and k = 13. Since a is positive, we know that the vertex of the parabola is a minimum. Therefore, the minimum cost of producing the product is $13. So the correct answer is:

5(x − 7)2 + 13

Answer:

1/1000 = 0.001

Step-by-step explanation:

Out of the 1000 tickets only one will be chosen. And since you only bought one ticket you would get a 1/1000 chance to get chosen. If you turn 1/1000 into a decimal you get 0.001 or 0.1%. Say if you bought 2 tickets you would get a 2/1000 chance which would be a 0.2% chance and so on.