Write the equation of the function graphed below:

Ricky should place the ball along 2nd diamond of top rail from right.

Aim should be towards the 2nd diamond of right rail.

Distance-angle commonly refers to the horizontal distance of an angle that reaches a certain height, which in turn forms a triangle.

Given,

In the Diagram,

Shot of Montana Mike is shown,

Montana started the shot with the ball against the top rail and the ball hit the bottom rail three diamonds from the right rail.

By the figure,

To repeat Montana shot,

Hence, the shot will be repeated by Ricky if ball is placed along the 2nd diamond of top rail from right and aim towards 2nd diamond of right rail.

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The constant term is 6 and the numerical coefficient of g, s and t are 1, -2 and -5.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division. The terms involved in an expression in math are:

Constant: A constant is a fixed numerical value.

Variable: A variable is a symbol that doesn't have a fixed value.

The given expression is g-2s-5t+6.

In the expression there are 4 terms.

Here, 6 is the constant and the numerical coefficient of g is 1, the numerical coefficient of -2s is -2 and the numerical coefficient of -5t is -5.

Therefore, the constant term is 6.

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The function rule describes the connection between the input or domain and the output or range and we know that the required function rule is x=y-7.

The relationship between the input or domain and the output or range is known as the function rule.

If and only if there is a single value in the range for each domain value, then a relation is a function.

Consequently, the expression f (x) = 3 x + 1 can be used to represent the function rule y = 3 x + 1.

Function notation is the name for this method of expressing a function rule.

We can read the function notation above as A function exists that is "expressed in terms of the variable" in such a way that it equals 3 x + 1 or of equals 3 x + 1.

So, Y is the result, and x is the input.

According to the provided information, the output is 7 less than the input.

Since the output is y and the input is x, y is therefore 7 less than x.

Since y is 7 less than x, you may express that as an equation, giving you x = y -7.

Therefore, the function rule describes the connection between the input or domain and the output or range and we know that the required function rule is x=y-7.

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Complete question:

Write a function rule for "The output is 7 less than the input." Let x be the input and let y be the output.

Cramer's rule is a method of calculating the solution to a system of linear equations by finding the "Quotient" of the determinants.

Hence, option (a) is correct choice.

Cramer's rule is one of the most significant strategies for solving a system of equations. The values of the system's variables are to be computed using determinants of matrices in this technique. As a result, Cramer's rule is frequently referred to as the determinant technique.

If unique solutions exist, this approach is utilized to find them. Cramer's rule cannot be used if the determinant of the coefficient matrix is zero.

To use Cramer's Rule to solve a system of three equations in three variables, substitute a variable column with the constant column for each desired solution: x=DxD, y=DyD, z=DzD.

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The missing option be:

(a) Quotient

(b) Divisor

(c) Factor

(d) Multiple

Answer:

12 and 18

Step-by-step explanation:

60 miles in 2 hours, so that means together the cyclists are traveling at 30mph,

one is traveling at 6mph more so 30mph-6mph =24

24/2=12

so the slower one is going at 12mph and the other at 18mph

Answer: This is True.

Answer:

You should use  [tex]\frac{1}{3}[/tex] orange juice.

Step-by-step explanation:

Set up a proportion

[tex]\frac{3}{5}[/tex] = [tex]\frac{\frac{1}{5} }{x}[/tex]  
This is lime juice  to orange juice.  Cross multiply and solve for x.

3x = [tex]\frac{5}{1 }[/tex] x [tex]\frac{1}{5}[/tex]

3x = 1  Divide both sides by 3

x = [tex]\frac{1}{3}[/tex]

Answer: 1/3 cup of oj

Step-by-step explanation:

Answer:

There are only 4, 11/2 ounce of medication in a 24 ounce bottle

Step-by-step explanation:

11/2 = 5.5, 24/5.5=4.4

James needs to invest $83226.33 as his principal in order to achieve this goal.

How to Work Out How Much

An asset or item purchased with the intention of generating income or appreciation is referred to as an investment. The term "appreciation" describes a rise in an asset's value over time. When a person buys a product as an investment, they don't intend to use it right away; instead, they plan to use it to make money later on.

Here is the basic interest calculation formula:

I, or simple interest, is equal to PRT/100.

Where:

P represents the primary amount.

R represents the rate.

The letter T represents time.

Modify the values.

2496.79 = P × 1 × 3/ 100

Multiplying by two

3 P = 249679

Create "P" as the formula's

P = 249679/ 3

Count through

P = $ 83226.33

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The population of the nation as per the provisional figures of Census 2011 is 1210.19 million of which 623.7 million (51.54%) are males and 586.46 million (48.46%) are females.

Canada is larger than the United States, making it the second-largest country in the world. However, despite this vast territory for a relatively small population, more than 90 percent of Canadians live within 150 miles of the US border.

The population of the country as per the provisional figures of Census 2011 is 1210.19 million of which 623.72 million (51.54%) are males and 586.46 million (48.46%) are females. The provisional figures of Census 2011 were released in New Delhi today by Union Home Secretary Shri G.K.Pillai and RGI Shri C. Chandramouli.

Canada contains the world's seventh-largest Indian diaspora. The highest concentrations of Indian Canadians are found in the provinces of Ontario and British Columbia, followed by growing communities in Alberta and Quebec as well, with the majority of them being foreign-born.

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Answer: A. x < 2

Step-by-step explanation:

         We will isolate the variable with inverse operations.

Given:

  3x – 2 < 4

Add 2 to both sides of the equation:

  3x < 6

Divide both sides of the equation by 3:

  x < 2

        A. x < 2

The work W required to pump the water out of the spout is  6, 115, 200 Joule.

The product of the displacement and the component of the applied force of the object in the displacement direction is the work done by a force. Work is accomplished when we push a block with some force; the body moves more quickly. Work completed is noted as.

Given:

The first step is to compute the work against gravity performed on a thin layer of the liquid of width Δ y.

A thin layer at height y is a rectangular box of volume 18y Δy and to lift it , we must exert a force against gravity equal to

So, Force on layer = g [ density] [ volume]

                               ≈ 9.8 (1000 ) 18y Δy

and, The layer has to be lifted a vertical distance of 7−y , so

Work on layer ≈  176400 yΔy [ 7−y ]

Then W= [tex]\int\limits^3_0[/tex] 176400 yΔy [ 7−y ]

             = 176400  [ 7 (4)² /2 - 4³/3 - 7 (0)² /2 + 0³/3]

             =  176400  x (56 - 64/3)

              =  6, 115, 200 Joules

Hence, the work done is 6, 115, 200 Joules.

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x=-224/229, y=296/229, Gaussian elimination approach is z=118/229.

The row reduction strategy for solving linear equation systems in mathematics is also referred to as the Gaussian elimination method. A series of procedures are carried out on the corresponding coefficients matrix to create it.

Gaussian elimination is the name of this process, which entails the gradual removal of the variables. Sample 1 Make this system work: The variable x is removed from the second equation by multiplying the first equation by 3, then adding the result. This last formula, 5 y = 5, suggests y = 1 right away.

Systems of linear equations are resolved using the Gaussian elimination (also known as row reduction) approach. It bears the name of Carl Friedrich Gauss, a well-known German mathematician who discussed this approach but did not create it.

-5x-7y-4z=-6

6x+2y+3z=-2

-x+2y-7z=0

(Multiply with -5 and add the result to the first equation; multiply with 6 and add the result to the second equation)

-x+2y-7z=0

-17y+31z=-6.....(mult with 14) (mult with 14)

the sum of 14y-39z=-2 (mult with -17)

-x+2y-7z=0

We have z=118/229 since -229z=-118.

14y-39*(118/229)=-2, thus y=296/229 follows.

-x+2*(296/229)-7*(118/229)=0, hence x=-234/229 is the result.

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Answer:

After the second quarter, the Cavaliers' score would be 25 points and the Hornets' score would be 45 points. The score for each team would not have changed if the Hornets scored 25 points in the first quarter and 20 points in the second quarter because the total number of points scored by each team would still be the same. The order in which the points were scored does not affect the final score of the game.

The point charges placed 0.500 m apart are 10.4 nC and 43.9 nC. Then, the electric field halfway between these charges will be -4824 N/C.

The physical field that surrounds particles with an electrical charge is called an electric field. All other charged particles in the field are affected by it, either being attracted to it or being repelled by it.

The electric field because of a point charge q is written as [tex]E=\frac{kq}{r^2}[/tex]

Positive point charges cause the electric field to point away from the point, whereas negative point charges cause the electric field to point in the direction of the point. Then, the electric field of the midpoint p in the diagram is written as,

[tex]\begin{aligned}E_p&=\mathrm{\frac{k(10.4\;nC)}{(0.25\;m)^2}-\frac{k(43.9\;nC)}{(0.25\;m)^2}}\\&=\mathrm{\frac{k(10.4-43.9)\times10^{-9}\;C}{(0.25\;m)^2}}\\&=-\mathrm{\frac{9\times 10^9\;Nm^2/C^2\times 33.5\times10^{-9}\;C}{(0.25\;m)^2}}\\&=-\mathrm{4824\;N/C}\end{aligned}[/tex]

The required answer is -4824 N/C.

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Lines r and s have the same slope of 4/9, therefore, they are parallel.

To determine if two lines are parallel or perpendicular, you can use the slope formula. If the slopes of the two lines are equal, the lines are parallel. If the product of the slopes of the two lines is -1, the lines are perpendicular.

The slope formula is: m = (y2 - y1) / (x2 - x1)

For line r:

m = (4 - 8) / (1 - 10) = -4 / -9 = 4/9

For line s:

m = (5 - 9) / (1 - 10) = -4 / -9 = 4/9

Since the slopes of the two lines are equal, they are parallel.

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The word sentence as an inequality is -4y ≤ -2/3

An inequality can be defined as a mathematical relation that makes a non-comparison between two expressions, equations or numbers.

It is also important to note that algebraic expressions can be defined as expressions that are composed of terms, coefficients, variables, constants and factors.

The signs in an inequality are;

From the information given, we have that

The variable is y

The fraction is -4

This can be represented as;

y × -4 ≤ -2/3

multiply the values

-4y ≤ -2/3

Hence, the expression is -4y ≤ -2/3

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The polynomial representing the total amount of electricity produced by geothermal and wind power between 2002 and 2007 is 847x2 + 103x + 24,610.

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The equation that best represents the relationship is 7x - 4y = -20

From the question, we have the following parameters that can be used in our computation:

x      y

5     13.75

10    22.50

15    31.25

In the above table, we can see that

As x increases by 5

y increases by 8.75

So, the slope is

m = 8.75/5 = 1.75

A linear equation is represented as

y = mx + c

so, we have

y = 1.75x + c

Using the ordered pair, we have

1.75 * 5 + c = 13.75

Evaluate

c = 5

So, we have

y = 1.75x + 5

Express as

4y = 7x + 20

This gives

7x - 4y = -20

Hence, the relaionship is 7x - 4y = -20

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The value of b for the cost function F(x)

= mx + b, of a membership plan in car sharing offer ( picewise function) is -64.

We have, yaster car sharing offers a membership plan, the fee of complete month = $42 includes 13 hours of driving each month.

Additional charges for each hour = $8

Let F(x) be the cost for a month in which member uses a car for x hours. F(x) is Piecewise function defined as F(x)= 42, for 0≤x≤ 13,

F(x) = mx+b, for x> 13 for some scalars m and b. We have to determine value of b.

When member uses a car for more than 13 hours, x> 13, For 13 hours monthly fee would be $42 and for hours after 13 hours (x- 13) hours the fee would be $8 for each hour. So, the cost would be

= (x - 13)8+ (42)

Simplify the expression,

= 8x - 104 + 42

F(x) = 8x - 64

Now, comparing the above expression of f(x) with F(x) = mx + b, we get m= 8 , b = - 64 . Hence the required value is - 64.

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Complete question:

Yaster Car Sharing offers a membership plan with a $42 per month fee that includes 9 hours of driving each month and charges $8 for each additional hour. Let F(x) be the cost for a month in which a member uses a car for x hours. Then F(x) is the piecewise function

F(x)= 42, for 0≤x≤ 13

F(x)=mx+b, for x> 13 for some scalars m and b. Find b. Round to the nearest whole number.

Answer:

see below

Step-by-step explanation:

$4500

simple interest 1.9% per year

20 years = 20*1.9%=38%

4500*(1+38%) = 6210

Answer:

  y = 7/25x² +42/25x +5 13/25

Step-by-step explanation:

You want the general form of the equation for the quadratic function that has (-3, 3) as its vertex and (2, 10) as a point on the graph.

The vertex form equation is ...

  y = a(x -h)² +k

where (h, k) is the vertex and 'a' is a vertical scale factor.

For the given vertex, this becomes ...

  y = a(x +3)² +3

We want to find 'a' such that the point (x, y) =(2, 10) satisfies the equation:

  10 = a(2 +3)² +3

  7/25 = a . . . . . . subtract 3, divide by 25

The expanded equation is ...

  y = 7/25(x +3)² +3 = 7/25(x² +6x +9) +3

  y = 7/25x² +42/25x +5 13/25

General form of the equation of the quadratic function:

y = (7/25)x² + (42/25)x + 138/25

A quadratic function is a polynomial function with one or more variables in which the highest exponent of the variable is two.

Given

vertex (h,k) = (−3,3)

Point (x,y) = (2,10)

Standard Form Equation for a Parabola:

a(x-h)² = y-k

for vertex (h,k)

(h,k) = (−3,3)

a(x - -3)² = y - 3

a(x + 3)² = y - 3               ______(1)

(x,y)=(2,10)

a(2+3)² = 10 - 3

25a = 7

a = 7/25

Substituting value of a in equation 1

(7/25)(x+3)² = y - 3

(7/25) (x² + 9 + 6x)  = y - 3

7x² + 63 + 42x = 25y - 75

7x² + 63 + 75 + 42x = 25y

7x² + 42x + 138 = 25y

⇒ y = (7/25)x² + (42/25)x + 138/25

Hence, y = (7/25)x² + (42/25)x + 138/25 is the general form of the equation of the quadratic function.

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Answer:5.29 seconds to hit ground 30.86 feet in air

Step-by-step explanation:

The first equation, y = 7.16t^2 - 40t + 45, represents the vertical position of the cargo as a function of time.

The second equation, y = -0.047x^2 + 45, represents the height of the cargo as a function of horizontal distance traveled.

To find the time it takes for the cargo to hit the ground, we need to find when y = 0 in the first equation.

Setting y = 0, we have:

0 = 7.16t^2 - 40t + 45

Solving for t, we can use the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / (2a)

where a = 7.16, b = -40, and c = 45.

t = (40 ± √(40^2 - 4 * 7.16 * 45)) / (2 * 7.16)

t = (40 ± √(1600 - 322.2)) / (2 * 7.16)

t = (40 ± √1277.8) / (2 * 7.16)

t = (40 ± 35.62) / 14.32

t = (75.62 / 14.32, 4.38 / 14.32)

Since t must be positive, t = (75.62 / 14.32) = 5.29 s

Now that we have the time it takes for the cargo to hit the ground, we can use that time in the second equation to find the horizontal distance the cargo traveled.

x = √((45 - 0) / -0.047)

x = √(45 / -0.047)

x = √(45 * -21.28) = √(957) = 30.86 ft

So, it takes the cargo 5.29 seconds to hit the ground, and it travels 30.86 feet horizontally.

[tex]\therefore[/tex] Leonel will play on his soccer field with a perimeter of 110 m.

Data to then substitute into the equation:

Before starting to solve, I will show you the formula for the perimeter of the rectangle:

[tex]\bold{ \: P= 2(a) + 2(b)}[/tex]

We substitute equation:

[tex]\bf \: P = 2(15) + 2(40)[/tex]

We multiply:

[tex]\bf \: P= 15 * 2 = 30[/tex]

[tex]\bf \: P= 40 * 2 = 80[/tex]

We add both resultants to obtain the perimeter:

[tex]\bf \: P= 80 + 30[/tex]

[tex]\large\boxed{ \bf \:P = 110 \: m}[/tex]

Rpt: Leonel will play on his soccer field with a perimeter of 110 m.

The equation that has infinite number of solutions is A: 5x = 4x + 1.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

When certain requirements are met, an equation can have an unlimited number of solutions. In the case of coinciding lines with the same y-intercept, the number of solutions to the equation system is unlimited. The two lines are actually in the same line if they share the same slope and y-intercept.

The first equation is 5x = 4x + 1.

Solve the equation -

5x - 4x = 1

x = 1

The x value is obtained as 1 which means the line is made parallel to the y-axis at point x = 1.

Therefore, this line has infinite number of solutions.

The second equation is 2 - 2x = -2(x - 1).

Solve the equation -

2 - 2x = -2x + 1

-2x + 2x = 1 - 2

0 = -1

This equation doesn't exist.

Therefore, there are no solutions for the equation.

The third equation is 2x + 7 = 2x - 7.

Solve the equation -

2x - 2x = -7 + 7

0 = 0

This equation doesn't exist.

Therefore, there are no solutions for the equation.

The fourth equation is 5x + 4 = 5(x + 4).

Solve the equation -

5x + 4 = 5x + 4

5x - 5x = 4 - 4

0 = 0

This equation doesn't exist.

Therefore, there are no solutions for the equation.

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Answer: [tex]10\sqrt{2}[/tex]

Step-by-step explanation:

Angles in an isosceles right triangle are: 90, 45, 45.

The ratio of the sides are: [tex]1:1:\sqrt{2}[/tex]

Side of 90° = 20

Side of 45° = [tex]\frac{20}{\sqrt{2} }[/tex]

[tex]\frac{20}{\sqrt{2} } =[/tex] [tex]\frac{20\sqrt{2} }{\sqrt{2} ^{2} } = \frac{20\sqrt{2} }{2} = 10\sqrt{2}[/tex]

The interest rate for the basic account is 10% and the interest rate for the higher yield account is 30%.

Let the basic account interest rate be r, then the higher yield account interest rate is 3r.

The total interest earned ($460) is

$1000r + $3600r = $460

$460 = $4600r

Dividing both sides by $4600:

r = 0.1

This gives

r - 10%

So, the interest rate for the basic account is 10%

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Answer:

Step-by-step explanation:

The cost has two parts; a fixed cost of $29 and a variable cost of $0.12 per minute. So, the total monthly cost for 50 minutes is $35.

Answer:

I think it's [tex]\frac{12}{5}[/tex]

Step-by-step explanation:

[tex]\frac{4}{5} * \frac{3}{1} = \frac{4}{1} *\frac{3}{5}[/tex]

= [tex]\frac{12}{5}[/tex]

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{\dfrac{4}{5}\times 3}[/tex]

[tex]\mathsf{= \dfrac{4}{5}\times \dfrac{3}{1}}[/tex]

[tex]\mathsf{= \dfrac{4\times3}{5\times1}}[/tex]

[tex]\mathsf{= \dfrac{12}{5}}[/tex]

[tex]\mathsf{= 2\dfrac{2}{5}}[/tex]

[tex]\star\star\star\star\star\star\start\star\star\star\star \star\star\star\star\star\star\start\star\star\star\star \star\star\star\star\star\star\start\star\star\star\star \star\star\star\star\star\star\start\star\star\star\star \star\star\star\star\star\star\start\star\star\star\ \star[/tex]
[tex]\mathsf{4\times\dfrac{3}{5}}[/tex]

[tex]\mathsf{= \dfrac{4}{1}\times\dfrac{3}{5}}[/tex]

[tex]\mathsf{= \dfrac{4\times3}{1\times5}}[/tex]

[tex]\mathsf{= \dfrac{12}{5}}[/tex]

[tex]\mathsf{= 2\dfrac{2}{5}}[/tex]

[tex]\huge\text{Therefore your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{\dfrac{12}{5}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

The approximation is: A1 = f(0) * 2, A2 = f(2) * 2, A3 = f(4) * 2, A4 = f(6) * 2.

To calculate the approximate integral using a Riemann sum with right rectangles, we need to calculate the area of each rectangle and then add them all together. The area of each rectangle is given by the formula A = f(x) * Δx, where f(x) is the value of the function at a given x and Δx is the width of the rectangle.

For a rectangle approximation with Δx=20:

Calculate the x-coordinates of the right endpoints of the rectangles:

Calculate the values of f(x) at each x-coordinate:

Calculate the area of each rectangle using the formula A = f(x) * Δx, where

Add up the areas of all the rectangles to get the approximate integral:

For a rectangle approximation with Δx=2:

Calculate the x-coordinates of the right endpoints of the rectangles:

Calculate the values of f(x) at each x-coordinate:

Calculate the area of each rectangle using the formula A = f(x) * Δx, where

Add up the areas of all the rectangles to get the approximate integral:

∫0 5 f(x) dx ≈ A1 + A2 + A3 + A4, where:

A1 = f(0) * 2, A2 = f(2) * 2, A3 = f(4) * 2, A4 = f(6) * 2.

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