David has a checking account at City center Bank. During the month of April, he made deposits totaling $985.89 and wrote checks totaling $454.27 .He paid a maintenance fee of $18 and earned $2.95 in interest. His balance at the end of the month was $3,005.32. What was the balance at the beginning of April?

The equation of the line that passes through the point (3,2) and has a slope of 4 is; y = 4x - 10

The equation of the straight line has its slope and given point.

If we have a non-vertical line that passes through any point(x1, y1) and has a gradient m. then general point (x, y) must satisfy the equation

y-y₁ = m(x-x₁)

Which is the required equation of a line in a point-slope form.

Point (3,2)

Then Slope m = 4

Now Write the equation as;

y - 2 = 4(x - 3)

y = 4x - 10

Hence, The equation of the line is; y = 4x - 10

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Answer:

A

Step-by-step explanation:

A

Answer:

Q9 -  Option 1---- A -  15.6 Square Units

Q10 --Option --- (B) RECTANGLE

Step-by-step explanation:

Q9 --

we know area of triangle  = 1/2 ab sin theta

Where theta is the angle included between sides A and side B

A  = 5.2

B = 7

theta  = 121 degrees

1/2 * 5.2 * 7 * sin 121 degrees = 15.6 Square Units

Conclusion

The area of the triangle is 15.6 Square Units

Option --- (B) RECTANGLE

Hope this helps!

9514 1404 393

Answer:

  y = x² +x -6

Step-by-step explanation:

The graph shows the zeros of the function to be -3 and +2. This means the factored form of the function can be written as ...

  y = (x -(-3))(x -(+2)) = (x+3)(x-2)

Multiplying this out, we get the desired standard form:

  y = x² +x -6

We note that y=-6 when x=0, which matches the y-intercept. Nothing else needs to be done to this equation.

3rd picture shows correct representation of transformed angle X'Y'Z'.

In mathematics, translation is a type of transformation that moves every point of a geometric figure the same distance in the same direction. It is a rigid transformation, which means that the size and shape of the figure are preserved during the transformation.

In two-dimensional geometry, a translation involves moving every point of a figure horizontally, vertically, or diagonally, without changing its orientation.

Old coordinate of angle XYZ= (-5,-2))

Angle XYZ is translated 10 units right

New coordinate of angle XYZ=(5,-2)

Now angle is reflected about x-axis

New coordinate of angle X'Y'Z'= (5,2)

Hence, third picture shows correct representation of transformed angle X'Y'Z'.

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The function f(x) = -2(4)ˣ⁺¹ +140 represents the number of tokens a child has x hours after arriving at an arcade. The practical domain and range of the function are x ≥ 0 and The practical range of the situation is [140, ∞).

The given function is f(x) = -2(4)ˣ⁺¹+ 140, which represents the number of tokens a child has x hours after arriving at an arcade.

To determine the practical domain and range of the function, we need to consider the constraints and limitations of the situation.

For the practical domain, we need to identify the valid values for x, which in this case represents the number of hours the child has been at the arcade. Since time cannot be negative in this context, the practical domain is x ≥ 0, meaning x is a non-negative number or zero.

Therefore, the practical domain of the situation is x ≥ 0.

For the practical range, we need to determine the possible values for the number of tokens the child can have. Looking at the given function, we can see that the term -2(4)ˣ⁺¹represents a decreasing exponential function as x increases. The constant term +140 is added to shift the graph upward.

Since the exponential term decreases as x increases, the function will have a maximum value at x = 0 and approach negative infinity as x approaches infinity. However, due to the presence of the +140 term, the actual range will be shifted upward by 140 units.

Therefore, the practical range of the situation will be all real numbers greater than or equal to 140. In interval notation, we can express it as [140, ∞).

To summarize:

- The practical domain of the situation is x ≥ 0.

- The practical range of the situation is [140, ∞).

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The equation of the parabola that passes through the points (3,-10), (4,-11), and (5,-10) is y = 1/2(x - 4)^2 - 12.

To find the equation of the parabola that passes through the points (3,-10), (4,-11), and (5,-10), we can use the method of finite differences.

First, we need to find the average rate of change between the y-values at each pair of x-values.

Starting with x = 3 and x = 4:

(-11 - (-10)) / (4 - 3) = -1

Next, we use x = 4 and x = 5:

(-10 - (-11)) / (5 - 4) = 1

Since the two average rates of change are different, we know that the parabola is not a straight line.

Next, we need to find the equation of the parabola in vertex form, which is:

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

where (h, k) is the vertex of the parabola.

To find the vertex, we average the x-coordinates and plug them into the equation, using the average rate of change we found above:

h = (3 + 4 + 5) / 3 = 4

k = -11 - (1)(4 - 3)^2 = -11 - 1 = -12

So the equation of the parabola is:

y = a(x - 4)^2 - 12

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Answer:

1/14

Step-by-step explanation:

The ratio is 5:70. The fraction form of that is 5/70. To get the lowest terms, I divided both numbers by 5. So it is 1/14

Answer:

z=16

Step-by-step explanation:

10=z-6

10+6=z-6+6

16=z

Answer:

10=z-6

or, z= 10+6

or, z = 16

the vale of y is 16

Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{1 \frac{2}{15}}}}}} \)

Step-by-step explanation:

\( \sf{1 \frac{7}{10} \times \frac{2}{3} }\)

Convert the mixed number into improper fraction

\( \longrightarrow{ \sf{ \frac{10 \times 1 + 7}{10} \times \frac{2}{3}}} \)

\( \longrightarrow{ \sf{ \frac{17}{10} \times \frac{2}{3}}} \)

To multiply one fraction by another, multiply the numerators for the numerator, and multiply the denominator for its denominator and reduce the fraction obtained after multiplication into lowest term

\( \longrightarrow{ \sf{ \frac{17 \times 2}{10 \times 3}}} \)

\( \longrightarrow{ \sf{ \frac{34}{30}}} \)

\( \longrightarrow{ \sf{ \frac{17}{15} }}\)

Convert the improper fraction into mixed number

\( \longrightarrow{ \sf{1 \frac{2}{15} }}\)

Hope I helped!

Best regards! :D

Step 1: Pick any two points

The points are represented as (x1,y1), (x2,y2).

where x1= -4, y1= -8, x2= 0, y2= 4

Step 2: Write out the formula of the equation to use

Step 3: Substituting the values and to get the equation

The equation that represents the graph is y= 3x+4.

Option A is the correct answer.

Answer:

m<wzx = 71

Step-by-step explanation:

Assuming these are interior angles of a triangle.

The sum of all three interior angles of a triangle is always 180 degrees, therefore:

m<xyz + m<wxz + m<wzx = 180

Substitute our values:

58 + 51 + m<wzx = 180

m<wzx = 180 - 58 - 51

m<wzx = 71

The gradient of the line joining the points (1,-1) and (4,9) is 10/3, while the gradient of the line joining (5,1) and (2,-2) is 1. The x-intercept of the equation 3y = 2x - 2 is 1, and the y-intercept is -2/3. These calculations follow the formula for gradient and the methods for finding intercepts in linear equations.

1) To find the gradient of a line joining two points, you can use the formula: gradient = (change in y)/(change in x).
Given the points (1,-1) and (4,9), the change in y is 9 - (-1) = 10 and the change in x is 4 - 1 = 3.
Therefore, the gradient of the line joining these points is 10/3.
2) Similarly, to find the gradient of a line joining two points (5,1) and (2,-2), we can use the same formula. The change in y is -2 - 1 = -3 and the change in x is 2 - 5 = -3.
Therefore, the gradient of the line joining these points is -3/-3 = 1.
3) To find the x-intercept, we set y to 0 and solve for x.
Given the equation 3y = 2x - 2, if we substitute y with 0, we have 3(0) = 2x - 2, which simplifies to 0 = 2x - 2.
To solve for x, we can add 2 to both sides: 0 + 2 = 2x - 2 + 2, which gives us 2 = 2x.
Dividing both sides by 2, we get x = 1.
Therefore, the x-intercept of the equation 3y = 2x - 2 is 1.
To find the y-intercept, we set x to 0 and solve for y.
Using the same equation, if we substitute x with 0, we have 3y = 2(0) - 2, which simplifies to 3y = -2.
To solve for y, we can divide both sides by 3: (3y)/3 = (-2)/3, which gives us y = -2/3.
Therefore, the y-intercept of the equation 3y = 2x - 2 is -2/3.
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To match the graphs of cylinders a and b to cylinders P and Q, we need to analyze the relationship between the height of the water and the volume of water in each cylinder.

Cylinder P would correspond to graph b, while Cylinder Q would correspond to graph a.

The reasoning behind this is as follows:

Cylinder P, corresponding to graph b, shows a steeper increase in height with increasing volume. This indicates that the water level rises quickly as more volume is added, suggesting that the cylinder has a smaller cross-sectional area. Since height is directly proportional to volume for a cylinder, a smaller cross-sectional area would result in a higher rise in height for the same volume of water.

Cylinder Q, corresponding to graph a, shows a slower increase in height with increasing volume. This implies that the water level rises more gradually as more volume is added, indicating a larger cross-sectional area. A larger cross-sectional area would result in a smaller increase in height for the same volume of water.

In summary, the steeper graph b matches Cylinder P with a smaller cross-sectional area, while the gentler graph a matches Cylinder Q with a larger cross-sectional area.

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I don't need the vbucks, thank you very much

I believe the questions are the same here: https://brainly.com/question/24851003

Answer is there

Answer:

DL/dt = 1000 miles/hour

Step-by-step explanation:

Let´s call A Point for the airplane at 70 miles from the point O (converging point), and point B for the airplane at 240 miles from point O.

Then the three-points A, B, and O shape a right triangle with legs (distances from each of the airplane to point O, and hypotenuse L distance between the two airplanes

Then according to Pithagoras´theorem:

L²  =  (AO)²  + (BO)²

At the moment t when the airplanes are far away as 70 and 240 miles per hour

L²  = (70)²  + ( 240)²

L²  = 4900 + 57600

L = √62500

L = 250 miles

In general

L²  = x² + y²

That equation is always valid for a right triangle if the airplanes are approaching keeping the right triangle shape then:

L² = x² + y²        where x and y are the legs ( that legs change in time then):

Tacking derivatives on both sides of the equation

2*L*DL/dt = 2*x*Dx/dt + 2*y*Dy/dt

By substitution:    since Dx/dt = 280 m/h   and Dy/dt = 960 m/h

2*(250)*DL/dt = 2*70*280 + 2*(240)*960

500*DL/dt  =  39200 + 460800

DL/dt  =  500000/ 500

DL/dt = 1000 miles/hour

Cesar initially had $2,500 in savings.

Let's solve the problem step by step.

Let's assume that the initial amount of money Cesar had is represented by "x" dollars.

According to the problem, Cesar spent 15% of his savings on a cellphone, which means he has 85% of his initial savings left. We can represent this mathematically as:

0.85x = 2,125

To find the initial amount of money Cesar had, we need to solve for x. We can do this by dividing both sides of the equation by 0.85:

x = 2,125 / 0.85

Calculating this value:

x = 2,500

Cesar initially had $2,500 in savings.

Please note that the calculations are done assuming a straightforward interpretation of the problem. If there are additional factors or context that could affect the interpretation, it's important to consider them in order to arrive at an accurate answer.

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Answer:

(-2,8),(-1,2),(0,0)(1,2) and (2,8)

Explanation:

Given the functions, f(x) and g(x) defined below:

First, find the sum (say h(x)) of the functions f(x) and g(x):

Next, we determine 5 ordered pairs for the sum:

The 5 ordered pairs are (-2,8),(-1,2),(0,0)(1,2) and (2,8).

Answer: 334

Step-by-step explanation: Find the steps in the file

Answer:

34

Step-by-step explanation:

1. Expand 5(x - 20):

5x - 100

2. Expand \(\frac{1}{2} (4x + 4)\):

2x + 2

3. Add 100 to both sides:

5x - 100 = 2x + 2

5x - 100+100 = 2x + 2+100

5x = 2x + 102

4. Subtract 2x from both sides:

3x = 102

5. Divide both sides by 3:

x = 34

hope this helps!

1. The relationship as a function r = f(t) is: r = (9 - 2t)/9.

2. The numeric value at t = -9 is: f(-9) = 3.

3. The value of t for which f(t) = 5 is t = -18.

The relationship is given as follows:

9r + 2t = 9.

To write the relationship as a function of t, we have to isolate the variable r as a function of the variable t, hence:

9r = 9 - 2t

r = (9 - 2t)/9.

To find the numeric value at t = -9, we replace the lone instance of t in the relationship by -9, hence:

r = (9 - 2(-9))/9 = 27/9 = 3.

To find when f(t) = 5, we have to find t for which f(t) = 5, hence:

9r = 9 - 2t

2t = 9 - 9r

2t = 9 - 9(5)

2t = -36

t = -36/2

t = -18.

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Answer:

No solution

Step-by-step explanation:

y + 12 = y - 20

=> y = y - 20 - 12

=> y - y = -32

=> No solution

The required ordered pair (x,y) = (3,4) is a solution to the given equation -x+2y=5.

To determine an ordered pair that is a solution to the equation -x+2y=5, we can first solve for y in terms of x by moving all of the terms that contain x to one side of the equation and all of the terms that do not contain x to the other side. We can do this by adding x to both sides of the equation:

-x + 2y = 5

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

2y = 5 + x

Next, we can divide both sides of the equation by 2 to solve for y in terms of x:

2y = 5 + x

y = (5 + x)/2

Now that we have solved for y in terms of x, we can plug in any value of x that we choose to find the corresponding value of y.

For example, if we plug in x = 3, we get:

y = (5 + 3)/2

y = 8/2

y = 4

Therefore, the ordered pair (x,y) = (3,4) is a solution to the equation -x+2y=5.

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Once we have those values, we can plug them into the formula and calculate the area of trapezium PQRS. And that's it!

To start, let's quickly review what a trapezium is. A trapezium, also known as a trapezoid, is a four-sided geometric shape with two parallel sides (called the bases) and two non-parallel sides (called the legs). The distance between the two parallel sides is known as the height.
In order to find the area of a trapezium, we use the formula:
Area = (sum of bases x height) / 2
So for trapezium PQRS, we need to identify the length of its two bases and its height in order to use this formula.
Without any specific measurements given in your question, I'll assume we don't have any numerical values to work with. Instead, let's use variables to represent the length of each base and the height.
We can call the shorter base PQ, and the longer base SR. Let's say PQ has a length of 'a' units, and SR has a length of 'b' units. For the height, let's call it h.
So, the formula for the area of trapezium PQRS becomes:
Area = ((a + b) x h) / 2
This means that to find the area of the trapezium, we simply need to know the lengths of the two bases (a and b) and the height (h).
Once we have those values, we can plug them into the formula and calculate the area of trapezium PQRS. And that's it!

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Answer:

This is the whole process I guess

Answer:

A: Function 1
B: Function 4
C: Function 2

Explanation A:

In order to solve this problem, you will have to find the slope for each function.

1st Function: For the first function, you will need to find 2 points, let's use (0, -4) and (1, 1). Remember slope is rise over run, so you would count the spaces from the first point to the second, it rises (y-axis) 5 points and runs (x-axis) 1 point. Which would give you 5/1 = 5. Function 1's slope is 5.

2nd Function: Same equation, rise over run, or y over x, so we need to find the pattern on each side. For the x-values, we can see starting from the first point that they increase by one, -2 to -1 to 0, and for the whole x-values, so 1 will be our run, since it is the x-value. For the rise, or y-values, we can see a pattern of -1 starting from the top going towards the bottom. Now, we can rise over run, -1/1 = -1

3rd Function: Slope is -4, as the equation is y = mx + b, and m stands for slope.

4th Function: Says slope is 2.

Now that we know all the slopes, we can see that Function 1's slope is the greatest.

Explanation B:
For this problem, we will have to find the y-intercept for all the functions, this means where the x-value is 0, so that the y-value will be right on the y-axis.

Function 1: We can see that the function intercepts the y-axis at (0, -4), it's y-intercept being -4.

Function 2: Where the x-value is 0, we can find the y-intercept, which is (0, 1). Making the y-intercept 1.

Function 3: Following the y = mx + b format, the b is the y-intercept, so it is -2.

Function 4: Gives you the y-intercept as 5.

In the end, the only function with a y-intercept greater than 4 is Function 4.

Explanation C:

Since we already know the y-intercepts from the previous problem, we only need to see which one is closest to 0. In this case, it would be Function 2 with a y-intercept at -1, only 1 unit off of 0, making it the closest.

Answer:

1

Step-by-step explanation:

Hope this helpsss

Answer:

1

Step-by-step explanation:

The equation is 3/10 times 10/3, which is 30/30, which equals 1.

(hope this helps :P)

Answer: 14$

Step-by-step explanation:

let x = number of games, let y = cost of shoe rental

then        Total cost = x•$4 + y

In this case, TC = 3•$4 + $2

TC = $14

The equation of lines are (a) x - 2y + 6 = 0

                                          (b) 2x - y - 4 = 0

                                          (c) x - y + 1 = 0

                                          (d) 4x + 3y + 4 = 0

Slope-intercept form of the equation -> y = mx + c

Slope = m = \(\frac{y2-y1}{x2-x1}\)

(a) A(0,3) and B(6,6)

    m = \(\frac{6-3}{6-0}\)

        = 3/6

        = 1/2

    Putting the value in equation,

     3 = (1/2)*0 + c

     c = 3

   Equation -> y = (1/2)x + 3

                     2y = x + 6

          x - 2y + 6 = 0  

(b) A(0,-4) and B(5,6)

    m = \(\frac{6+4}{5-0}\)

        = 10/5

        = 2

    Putting the value in equation,

     -4 = (2)*0 + c

     c = -4

   Equation -> y = (2)x - 4

          2x - y - 4 = 0  

(c) A(-4,-3) and B(2,3)

    m = \(\frac{3+3}{2+4}\)

        = 6/6

        = 1

    Putting the value in equation,

     3 = (1)*2 + c

      3 = 2 + c

      c = 3 - 2

      c = 1

   Equation -> y = (1)x + 1

                       y = x + 1

             x - y + 1 = 0  

(d) A(-6,4) and B(3,-8)

    m = \(\frac{-8-4}{3+6}\)

        = -12/9

        = -4/3

    Putting the value in equation,

     -8 = (-4/3)*3 + c

     -8 = -4 + c

      c = -8 + 4

      c = -4

   Equation -> y = (-4/3)x - 4

                     3y = -4x - 4

       4x + 3y + 4 = 0  

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Answer:

240 inches cubed

I see you have 4 mins left

The maximum value of the function f (x) = -1.8x² + 7x - 11 to the nearest hundredth is,  - 4.19.

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

We have to given that;

The function is,

⇒ f (x) = -1.8x² + 7x - 11

Now, We can differentiate with respect to x as;

⇒ f ' (x) = - 1.8 × 2x + 7 × 1 - 0

⇒ f ' (x) = - 3.6x + 7

Put f ' (x) = 0

⇒ - 3.6x + 7 = 0

⇒ 3.6x = 7

⇒ x = 1.94

Now, Again differentiate with respect to x as;

⇒ f ' (x) = - 3.6x + 7

⇒ f '' (x) = - 3.6 × 1 + 0

⇒ f '' (x) = - 3.6 < 0

Hence, Substitute x = 1.94 in function to get maximum value,

⇒ f (x) = -1.8x² + 7x - 11

⇒ f (x) = -1.8 (1.94)² + 7 × 1.94 - 11

⇒f (x) = - 6.77 + 13.58 - 11

⇒ f (x) = - 4.19

Thus, The maximum value = - 4.19

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