Sam has $2,500 in his bank account and withdraws $45 each week. Write the function that models this situation. Let W=weeks and B=bank balance.

Answer:

cindy is 51

Step-by-step explanation:

70 divided by 2 is 45

45+ 6 is 51

The vertex of the equation y = x² + 2x -3 is (-1, -4).

The term vertex in math is known as a point on a polygon where the sides or edges of the object meet or where two rays or line segments meet.

Here we have the expression y = x² + 2x -3

As we all know that the given equation of parabola is written as,

=> y = ax² + bx + c

As we all know that the vertex of the parabola is given by (h, k).

Here we have calculated the value of the x coordinate of vertex as ,

=> h = -b/2a

And the value of y coordinate of vertex k by using the formula,

=> k  = y(h)

Through the given equation we have identified the value of a = 1, b = 2 and c = -3

Then the value of x coordinate is calculated as,

=> h = -2/(2 × 1)

Therefore, the value of h is -1

Then the value of y coordinate is calculated as,

=> k = y (-1)

Here we have to substitute -1 in the equation, then we get

=> k = (-1)2 + 2(-1) - 3

=> k = 1 - 5 = -4

Hence the coordinate of the vertex is (-1, -4).

Complete Question:

Where is the vertex of the parabola of the equation y = x² + 2x -3?

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Answer:

193 minutes

Step-by-step explanation:

We know

Boris paid an $8 fee to start the scooter plus 6 cents per minute of the ride.

Let y represent the total cost and x represent the number of minutes we have the equation

y = 0.06x + 8

Now, put $19.58 in for y and solve

19.58 = 0.06x + 8

11.58 = 0.06x

x = 193 minutes

So, Boris rides the scooter for 193 minutes.

For the given system of equations 4x – 9y = 7 , –2x + 3y = 4 answer of the following question are:

a. To eliminate x-terms we need to multiply 2 to the second equation and add it to the first equation.

b.  To eliminate y-terms we need to multiply 3 to the second equation and add it to the first equation.

As given in the question,

For the given system of equation,

4x – 9y = 7 ___(1)

–2x + 3y = 4  ___(2)

a. To eliminate x-terms multiply by 2 to the (2) equation and add it to (1)

 4x – 9y = 7

–4x + 6y = 8

-3y = 15

⇒ y = -5

b. To eliminate y-terms multiply by 3 to the (2) equation and add it to (1):

4x – 9y = 7

–6x + 9y = 12

-2x = 19

⇒x = -19/2

Therefore, for the given system of equations 4x – 9y = 7 , –2x + 3y = 4 :

a. To eliminate x-terms we need to multiply 2 to the second equation and add it to the first equation.

b.  To eliminate y-terms we need to multiply 3 to the second equation and add it to the first equation.

The above question is incomplete , the complete question is:

Use this system of equations to answer the questions that follow.

4x – 9y = 7 , –2x + 3y = 4

a. What number would you multiply the second equation by in order to eliminate the x-terms when adding to the first equation?

b. What number would you multiply the second equation by in order to eliminate the y-terms when adding to the first equation?

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Answer:

30 tiles

Step-by-step explanation:

We know

First store

$0.59 per tile

Rent a tile saw for $18

Second store

1 tile = $1.19

We have the equation

0.59x + 18 = 1.19x

18 = 0.6x

x = 30 tiles

So, she must buy 30 tiles for the same cost at both stores.

Answer:

Margo must purchase 30 tiles for the cost to be the same at both stores.

Step-by-step explanation:

By analyzing the "real-world" problem, we can convert the words into two algebraic equations.

Store 1:

"$0.59 per tile and rent a tile saw for $18."

y = 0.59x + 18

y = the price of the tiles bought

0.59 = price of one tile

x = number of tiles

18 = the fixed cost of a saw

Store 2:

"At another store, she can borrow the tile saw for free if she buys tiles there for $1.19 per tile."

In this case, the saw is free. Thus, we don't need to add a price to the equation.

y = 1.19x

y = the price of the tiles bought

1.19 = price of one tile

x = number of tiles

Now that we have both equations, we can write down the equations that equate other. This formula will indicate that the equations would intersect at a certain point on the x and y values. Hence, this step will answer how many tiles are required for both stores to equal the same price.

[tex]0.59x+18=1.19x[/tex]

Now solve for x:

[tex]0.59x-0.59x+18=1.19x-0.59x\\\\18=0.6x\\\\\frac{18}{0.6} =\frac{0.6x}{0.6}\\\\30=x[/tex]

Margo can buy 30 tiles from both stores for the cost to be equal.

You might ask, "But what about the price?" This is where we solve for y; this variable will answer how much the tiles would cost at 30 tiles. So, we can take the answer for "x" and plug it into any of the two equations.

[tex]y=1.19x\\y=1.19(30)[/tex]

For this equation, all you have to do is multiply both numbers to get your answer.

[tex]y=35.7[/tex]

Therefore, Margo can buy 30 tiles for the cost to be same at both stores at $35.70.

Answer:

15 nickels and 8 dimes

Step-by-step explanation:

Let N = number of nickels and D = number of dimes

N - D = 7   (the number of nickels exceeds the number of dimes by 7.)

or

N = D + 7

Total value of N nickels = 5N

Total value of D nickels = 10D

Combined total value => 5N + 10D = 155

Substitute for N in terms of D
==> 5(D + 7) + 10D = 155

5D + 35 + 10D = 155

15D + 35 = 155

15D = 155 - 35

15D = 120

D = 120/15

D = 8

N = D + 7 = 8 + 7 = 15

15 nickels and 8 dimes

A fraction share that Tiana share with her brother called half part. This because the part is split into two where the first part is called first half and other called as second half.

To name a piece of an object that split into several you have to:

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A linear inequality in two variables is an inequality that can be written in the form "ax + by < c" or "ax + by > c" or "ax + by = c", where a, b, and c are constants and x and y are variables. This inequality represents a boundary line and all the solutions of the inequality make up a region of the xy-plane.

For example, the inequality "2x + 3y < 6" represents the region of the xy-plane that is on one side of line 2x + 3y = 6. To graph this inequality, one can find the boundary line by setting the inequality equal to zero and then shading in the region that satisfies the inequality.

A linear equation in two variables is an equation that can be written in the form "ax + by = c", where a, b, and c are constants and x and y are variables. This equation represents a straight line in the xy-plane and all the solutions of the equation are the coordinates of the points on that line.

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Answer:

1.  Y = -1/4x + 1

3. Y = 2/5x + 1

5. Y = 4/5x + 5

7. Y = -x + 5

9. Y = -5/2x - 16

Step-by-step explanation:

Find the slope using the formula

Use the slope and one of the points to find the y-intercept

Once you know the value for m and the value for b, you can plug these into the slope-intercept form of a line (y = mx + b) to get the equation for the line.

ok

0 is the smallest value or X is the smallest value

The angle e between vectors u and v to the nearest tenth of a degree is

≈ 3.14°.

An angle in plane geometry is a shape created by two rays or lines that have a shared termination. The name "angle" originates from the Latin word "angulus," which means "corner. "The common terminus of two rays is known as the vertex, and the two rays are known as sides of an angle.

When u and v's two vectors are at an angle, if, then cosθ = (u·v) / [llull llvll]

u·v = (5)(4) + (2)(-3)

       = 20 - 6

        = 14

llull = √[(5)2 + (2)2]

= √29    

llvll = √[(4)2+(-3)2]

= √25

So, cosθ = 14 / [√725]

            = 0.51

θ = cosθ-(0.51) ≈ 3.14°

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Answer:

48

Step-by-step explanation:

AB+CB=AC which is 18+30 which is 48

Answer:

C. 48

Step-by-step explanation:

This distance of AC is the same as the distance between BC plus the distance between AB. In other words: AB + BC = AC

AB = 18

BC = 30

30 + 18 = AC

AC = 48

It is option D (f-¹ (x) = x-3/5

The cost of a book bought by Russell is found in in dollars is $7.

For the stated question-

Let the price of the each book be 'x'.

Let the price of movie  be 'y'.

Then,

11x + 12y = 245  ...eq 1

10x + 26y = 434  ...eq 2

Solving both eq 1 and 2 using calculator.

x = 7 and y = 14

Thus, the cost of a book bought by Russell is found in in dollars is $7.

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A horizontal straight line at the -7 point.

A straight line can be formed between two points also but both ends extend to infinity.

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined on both sides of a point.

A straight line does not have any curve in it. It can be horizontal, vertical, or slanted. If we draw an angle between any two points on a straight line, we will always get a 180-degree.

With no other values other than -7, the only value possible must be -7. Thus, we get a straight line.

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Domain and range of a square root of a quadratic function is as [ 0, ∞ ) , and  [ 0 ,∞ ) respectively which is find by simplification.

Let us consider a square root quadratic function y = √x.

Domain of a square root quadratic function is :

All input values of x are domain of a function.

y = √x

⇒ x = y²

⇒ x ≥ 0

All the input values representing the domain are x > 0.

This implies domain is [0 , ∞ ).

And range of a square root quadratic function is:

All output values of y are range of a function.

y = √x

As we know x = y²

√y² = y > 0 .

Range is [ 0, ∞ ).

Therefore, domain and range of square root of a quadratic function is calculated by simplifying the function.

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The mean and standard deviation of a discrete distribution can be found by calculating the sum of all the values in the distribution multiplied by their respective probabilities and then dividing the result by the total probability.

To calculate the standard deviation, the sum of the squares of the differences between the values and the mean has to be multiplied by the corresponding probabilities and divided by the total probability.

The square root of this outcome is then the standard deviation. The standard deviation is a measurement of the spread or dispersion of the data, whereas the mean of a discrete distribution is a measure of the central tendency of the data.

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Answer:

7500

Step-by-step explanation:

15/100×50000

750000/100

=7500

To see the steps of linear and non linear system of equation.

Now, According to the question:

Steps to solve non linear equation are:

To solve a system of linear equations using substitution:

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A function argument is a value supplied to achieve the Range function's outcome. This is often alluded to as a latent variable.

This is an optional argument that determines the sequence's point of reference. The default assumption is 0.

A mathematical function includes one or much more arguments in the form of the independent variables that are specified in the definition and can also include parameters.

This is a necessary argument that determines the sequence's final chapter location.

This is an optional argument that specifies the adjustment between both sequence members. The default mode is 1.

A domain of the sum of two or multivalued argument values is considered to be the domain of a function with two or more variables.

A cyclical function's argument is angular. A hyperbolic perspective is the input of a hyper equation.

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An x-y (or bivariate) plot is any graph or plot with two axes. The "x-axis" is typically the horizontal axis, whereas the "y-axis" is typically the vertical axis.

Your plot's axes should be identified, and the scale should be chosen (if the graph is not already labeled). Plot the first two pairs of numbers first (the top row of numbers).

Finding the number a on the horizontal, or x-, axis and tracing up or down from there while maintaining a parallel path to the vertical, or y-, axis, will allow you to draw the point at (a, b) on the Cartesian plane.

The position of the point is this area (a, b). The intersection of the two axes defines the plane's center. It is referred to as the beginning or point (0,0).

Each axis is further subdivided into equal units starting at the origin: rising, positive numbers on the x-axis and up the y-axis; falling, negative numbers on the x-axis and down the y-axis.

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Answer:

Step-by-step explanation:

-4,+ infinity symbol which I can’t find

The set of all the outputs of a function is known as the range of the function or after substituting the domain, the entire set of all values possible as outcomes of the dependent variable.

For e.g. the range of the function F is {1983, 1987, 1992, 1996}.

On the other hand, the whole set B is known as the codomain of the function.

It is the set that contains all the outputs of the function.

So, the set of real numbers is a codomain for every real-valued function. The codomain of the function F is set B.

How to Find the Range of a Function

Consider a function y = f(x).

The spread of all the y values from minimum to maximum is the range of the function.

In the given expression of y, substitute all the values of x to check whether it is positive, negative or equal to other values.

Find the minimum and maximum values for y.

Then draw a graph for the same.

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The solution of the given linear equations is (x,y) = (1,-1).

The given linear equations are

8x + 3y = 5 - - - ( 1 )

3x - 2y = 5 - - - ( 2 )

As the RHS of both equations is equal, equating the LHS of both equations, we get,

8x + 3y = 3x - 2y

⇒ 8x - 3x = - 2y - 3y

⇒ 5x = - 5y

⇒ x = - 5y ÷ 5

⇒ x = - y

By substituting x = - y in equation ( 1 ), we get,

8x + 3y = 5 - - - ( 1 )

⇒ 8 ( - y ) + 3y = 5

⇒ - 8y + 3y = 5

⇒ - 5y = 5

⇒ y = - 5 ÷ 5

⇒ y = - 1

Now,

x = - y

⇒ x = - ( - 1 )

⇒ x = 1

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Lance and Alberto cycled along the same 75 km route. Speed of Alberto is 30 km/ hr

Since, Lance takes 3 hours to complete 75km, his speed will be

v= [tex]\frac{75}{3}[/tex]

v= 25 km/hr

The amount of time taken by Lance to complete 10 km is

t= 10/25

t =0.4 hr

t= 0,4×60 min

t=24 min.

Since Alberto started 4 min late and  time taken by Alberto to complete 10 km is

t= 24-4

t=20 min.

Hence, speed of Alberto is v=10/0.33

v=30 km/hr.

A measure of how quickly something is moving is speed. The distance an object travels in a single time unit is its speed. The speed formula is: Distance times speed. Meters per second (m/s), kilometres per hour (km/h), and miles per hour (mph) are the most common units of speed.

Speed is calculated by dividing distance by time. You must be familiar with the distance and time units in order to determine the units of speed. The units will be measured in meters per second (m/s) because distance is measured in meters (m) and time is measured in seconds (s).

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The prime factorization of the number 21 is:

21 = 3*7

We want to write the prime factorization of 21.

To do so, we just need to divide the number by prime numbers.

The first prime number we can try is 2, if we divide by 2 we get:

21/2 = 10.5

This is not an integer, so 2 is not a factor.

The next one is 3:

21/3 = 7

Now we can rewrite:

21 = 3*7

Where 3 and 7 are prime numbers, so that is the prime factorization.

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The quotient of the rational expressions is 4(x+2) / 5(x-1) (x-1)

The quotient of the rational expressions is

4(x+2) / 5(x-1) (x-1)

The quotient of the rational expressions shown below

Explanation in detail:

Two expressions are shown here.

Expression 1 : 2x/x-1

Expression II for 5x/2x+4.

The product of expressions I and II must be calculated.

(2x / x-1 ) ÷ (5x / 2x+4)

applying the upcoming regulation

a ÷ b = a× 1/b

(2x/x-1)×( 2x+4 / 5x)

(2x) (2x+4) / (x-1)(5x) (5x)

(2) (2) (x+2) / (x-1)(5) (5)

The solution to the previous question is 4(x+2) / 5(x-1).

The quotient of the rational expressions is 4(x+2) / 5(x-1) (x-1)

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The area will be 1/4 of the original.

The area is the region defined by an object's shape. The area of a shape is the space covered by a figure or any two-dimensional geometric shape in a plane.

The area of all shapes is determined by their dimensions and attributes. Different shapes have various areas. The perimeter of a shape is defined as the total distance around the shape.

Given that,

[scale factor]=1/2

[dilated area of circle]=[original area of circle]*[scale factor]²

so

[dilated area of circle]=[original area of circle]*[1/2]²

[dilated area of circle]=[original area of circle]*[1/4]

Thus, The area will be 1/4 of the original.

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