Find the focus of the parabola defined by the equation 100 points.

Answer:

Therefore, the cost of a pen is $2.30.

Step-by-step explanation:

Let's assign variables to represent the cost of a calculator and the cost of a pen.

Let c represent the cost of a calculator.

Let p represent the cost of a pen.

Based on the given information, we can form the following pair of simultaneous equations:

Equation 1: 4c + 2p = 20.60   (Mia buys 4 calculators and 2 pens for $20.60)

Equation 2: 5c + 3p = 26.90   (Heidi buys 5 calculators and 3 pens for $26.90)

To solve for the cost of a pen, we'll eliminate the variable c by multiplying Equation 1 by 5 and Equation 2 by 4. Then we'll subtract Equation 1 from Equation 2:

5 * (4c + 2p) = 5 * 20.60

4 * (5c + 3p) = 4 * 26.90

20c + 10p = 103.00

20c + 12p = 107.60

Subtracting Equation 1 from Equation 2:

(20c + 12p) - (20c + 10p) = 107.60 - 103.00

20c - 20c + 12p - 10p = 4.60

2p = 4.60

p = 4.60 / 2

p = 2.30

Therefore, the cost of a pen is $2.30.

Answer:

Let's assume that the cost of a calculator is x and the cost of a pen is y. Then we can write the following pair of equations:

4x + 2y = 20.60    (equation 1)

5x + 3y = 26.90    (equation 2)

To solve for the cost of a pen, we need to eliminate x from the equations. We can do this by multiplying equation 1 by 5 and equation 2 by -4, and then adding them:

(5)(4x + 2y = 20.60)  becomes  20x + 10y = 103    (equation 3)

(-4)(5x + 3y = 26.90) becomes -20x - 12y = -107.60    (equation 4)

Adding Equation 3 and Equation 4 gives:

-2y = -4.60

Divide both sides by -2:

y = 2.30

Therefore, the cost of a pen is $2.30.

Step-by-step explanation:

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Answer:

Step-by-step explanation:

Akira has 3 cheeses to arrange on a cheese board. She would like to arrange them in a row

The number of permutations of n distinct objects is given by n! (n factorial). In this case, Akira has 3 cheeses to arrange in a row. Therefore, the number of different orders she can arrange them is 3! = 6¹⁴.

So Akira can arrange the 3 cheeses in 6 different ways.

The measure of the arc DGF which substends the angle DEF at the circumference of the circle is equal to 190°

The angle subtended by an arc of a circle at it's center is twice the angle it substends anywhere on the circles circumference.

Given that the arc DGF = (62x + 4)°

62x + 4 = 2(30x + 5)

62x + 4 = 60x + 10

62x - 60x = 10 - 4 {collect like terms}

2x = 6

x = 6/2

x = 3

arc DGF = 62(3) + 4 = 190°

Therefore, the measure of the arc DGF which substends the angle DEF at the circumference of the circle is equal to 190°

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Step-by-step explanation:

a)  23.6 (1.08)^x        for 2016    x = 26   ('x' is the number of years past 1990)

        23.6 (1.08)^(26) = 174.6  billion

b)  109 = 23.6 ( 1.08)^x

    4.6186 = 1.08^x

          x =   log 4.6186 / log1.08   = 19.88 yrs  

                                         means  1990 + 19.88 yrs = year 2010

Answer: c. known

Step-by-step explanation:

In random sampling, the probability of selecting an item from the population is known. This probability can be calculated based on the sampling method and the characteristics of the population being sampled. Random sampling ensures that each item in the population has an equal chance of being selected, making the probability of selection known and calculable.

The period of the trigonometric function is -2π/3.

To determine the period of the trigonometric function based on the given information, we need to consider the pattern of the graph and identify the interval over which it repeats.

Given that the maximum point is at (-π, 7.7) and the minimum point is at (-1/3π, -6.7), we can observe that the graph completes one full oscillation between these two points.

The distance between the maximum and minimum points corresponds to half of the period. Therefore, the full period of the function can be found by doubling this distance.

The distance between (-π, 7.7) and (-1/3π, -6.7) can be calculated as follows:

Δx = -1/3π - (-π) = π/3π - π = -π/3

Since the full period is twice this distance, we multiply by 2:

2 * (-π/3) = -2π/3

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Answer:

(2, -1)

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases}y=-2x+3\\y+9=4x\end{cases}[/tex]

To solve the given system of equations, we can use the method of substitution.

Substitute the first equation into the second equation to eliminate the y term:

[tex](-2x+3)+9=4x[/tex]

Solve for x:

   [tex]-2x+3+9=4x[/tex]

       [tex]-2x+12=4x[/tex]

[tex]-2x+12+2x=4x+2x[/tex]

                  [tex]12=6x[/tex]

                 [tex]\dfrac{12}{6}=\dfrac{6x}{6}[/tex]

                   [tex]2=x[/tex]

                   [tex]x=2[/tex]

Substitute the found value of x into the first equation and solve for y:

[tex]y=-2(2)+3[/tex]

[tex]y=-4+3[/tex]

[tex]y=-1[/tex]

Therefore, the solution to the system of equations is (2, -1).

To verify the solution by graphing the system, find two points on each line by substituting two values of x into each equation. Plot the points and draw a line through them. The solution is the point of intersection.

Graphing y = -2x + 3

[tex]\begin{aligned} x=0 \implies y&=-2(0)+3\\y&=0+3\\y&=3\end{aligned}[/tex]            [tex]\begin{aligned} x=-2 \implies y&=-2(-2)+3\\y&=4+3\\y&=7\end{aligned}[/tex]

Plot points (0, 3) and (-2, 7) and draw a straight line through them.

Graphing y + 9 = 4x

[tex]\begin{aligned} x=0 \implies y+9&=4(0)\\y+9&=0\\y&=-9\end{aligned}[/tex]                 [tex]\begin{aligned} x=3 \implies y+9&=4(3)\\y+9&=12\\y&=3\end{aligned}[/tex]

Plot points (0, -9) and (3, 3) and draw a straight line through them.

The solution to the graphed system of equations is the point of intersection of the two lines: (2, 1).

Answer:

$4929

Step-by-step explanation:

I assume the cost is proportional to the area.

15 ft × 20 ft = 300 ft²

25 ft × 26 ft = 650 ft²

650/300 = x/$2275

300x = 650 × $2275

x = $4929

Answer: $4929

The polynomial [tex](x^2 + 3x + 3) * (-2x^2 - x + 6)[/tex] simplifies to [tex]-2x^4 - 7x^3 - 3x^2 + 33x + 18.[/tex]

A polynomial is a mathematical expression consisting of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication operations. It is defined as a sum of terms, where each term consists of a variable raised to a non-negative integer exponent, multiplied by a coefficient.

The general form of a polynomial is:

P(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₂x² + a₁x + a₀

To simplify the expression[tex](x^2 + 3x + 3) * (-2x^2 - x + 6)[/tex], we need to perform the multiplication and combine like terms.

First, we multiply each term in the first polynomial by each term in the second polynomial:

[tex](x^2 + 3x + 3) * (-2x^2 - x + 6) = x^2 * (-2x^2 - x + 6) + 3x * (-2x^2 - x + 6) + 3 * (-2x^2 - x + 6)[/tex]

Expanding each term, we get:

=[tex](-2x^4 - x^3 + 6x^2) + (-6x^3 - 3x^2 + 18x) + (-6x^2 - 3x + 18)[/tex]

Now, we combine like terms:

=[tex]-2x^4 + (-x^3 - 6x^3) + (6x^2 - 3x^2 - 6x^2) + (18x + 18x - 3x) + 18[/tex]

Simplifying further:

=[tex]-2x^4 - 7x^3 - 3x^2 + 33x + 18[/tex]

The simplified expression in polynomial standard form is:

-2x^4 - 7x^3 - 3x^2 + 33x + 18

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Answer:

Step-by-step explanation:

When the equation is in the slope intercept form of y = mx + b, you know that the m is the slope and the b is the y-intercept (0, b)

By looking at the equation  y=2x + 2, you can determine that the y-intercept will be at the point (0, 2)  and the slope is 2.

To graph, start with the point of (0, 2) then go up 2 units and to the right 1 unit.  So the next point will be at (1, 4)

You can also, substitute and number in for the x and calculate the y value.   For example, if x is 3, then  y=2(3)+2; y = 8 so the point (3, 8) is on the line.

Answer:

Step-by-step explanation:

a. To write an equation describing the total cost of RV rental, we can use the given information:

Let x be the number of days of rental.

Let y be the number of miles driven.

The total cost of RV rental can be calculated as follows:

Total cost = (125 * x) + (0.32 * y) + 2500

b. To compare the cost of the two options, we need to calculate the total cost for each option.

Option 1:

x = 11 days

y = 3500 miles

Total cost = (125 * 11) + (0.32 * 3500) + 2500

Option 2:

x = 14 days

y = 3000 miles

Total cost = (125 * 14) + (0.32 * 3000) + 2500

Compare the total costs of both options to determine which one is cheaper.

c. To compromise and keep the rental cost under $5,000, we can adjust either the number of miles driven or the number of days of rental.

For the first compromise (lessening the miles), let's assume the new number of miles driven is y1.

The domain for the compromise in miles would be 0 ≤ y1 ≤ 3500, as you cannot drive more miles than the original option or negative miles.

For the second compromise (lessening the days of rental), let's assume the new number of days of rental is x1.

The domain for the compromise in days would be 0 ≤ x1 ≤ 14, as you cannot have more days of rental than the original option or negative days.

The justification for these domains is that they restrict the values within the range of the original options while allowing for adjustments in the desired direction.

d. To find out how many miles or how many days need to be eliminated to stay under the $5,000 budget, we can set up and solve equations.

For the compromise in miles (y1):

(125 * x) + (0.32 * y1) + 2500 ≤ 5000

For the compromise in days (x1):

(125 * x1) + (0.32 * y) + 2500 ≤ 5000

Solve each equation by isolating the variable to determine the maximum allowed value for y1 or x1, respectively.

Finally, after solving the equations, compare the maximum allowed values for y1 and x1 and consider other factors like practicality, time constraints, and preferences to make a recommendation to your parents about which compromise is best.

Answer:

Step-by-step explanation:

I understand your confusion. Let's go through the steps together to solve the equation correctly:

Given equation: 5 + x - 12 = 2x - 7

Combine like terms on the left side and the right side of the equation:

x - 7 = 2x - 7

Now, let's isolate the variable x. Subtract x from both sides of the equation:

x - x - 7 = 2x - x - 7

Simplifying:

-7 = x - 7

Next, add 7 to both sides of the equation:

-7 + 7 = x - 7 + 7

Simplifying:

0 = x

Therefore, the solution to the equation is x = 0.

If you need to use the values x = -4, 0, and 5, you can substitute each value into the original equation to check if it satisfies the equation. Let's do that:

For x = -4:

5 + (-4) - 12 = 2(-4) - 7

-11 = -15 - 7

-11 = -22

The equation is not satisfied for x = -4.

For x = 0:

5 + 0 - 12 = 2(0) - 7

-7 = -7

The equation is satisfied for x = 0.

For x = 5:

5 + 5 - 12 = 2(5) - 7

-2 = 3

The equation is not satisfied for x = 5.

Therefore, the correct solution to the equation is x = 0. The values x = -4 and x = 5 do not satisfy the equation.

The area of the shaded part is 640.56 m²

The area of a shape is the space occupied by the boundary of a plane figures like circles, rectangles, and triangles.

The figure is a concentric circle, i.e a circle Ina circle. Therefore to calculate the area of the shaded part,

Area of shaded part = area of big circle - area of small circle

area of big circle = 3.14 × 20²

= 1256

area of small circle = 3.14 × 14²

= 615.44

Area of shaded part = 1256 - 615.44

= 640.56m²

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The cost of 2.5 liters of petrol in the United Kingdom is £1.70. The cost of 1 US gallon of petrol in the United States is $3.30. £1 = $1.42 and 1 liter = 0.26 US gallons. So, is petrol cheaper in the United Kingdom or the United States.

Let's find out the cost of 2.5 liters of petrol in the United States dollars;Cost of 1 litre of petrol in the United Kingdom = £1.70/2.5 = £0.68Cost of 1 liter of petrol in the United States = $3.30/3.78 (as 1 US gallon = 3.78 liters) = $0.87We know that £1 = $1.42£0.68 = $0.68 x 1.42 = $0.96So, the cost of 1 liter of petrol in the United Kingdom is $0.96 (approximately)The cost of 1 liter of petrol in the United States is $0.87 (approximately)

Therefore, petrol is cheaper in the United States than the United Kingdom.

So, the answer is that petrol is cheaper in the United States than in the United Kingdom.

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The composite functions for this problem are given as follows:

a) (f ∘ g)(x) = 4x² + 24x + 32.

b) (g ∘ f)(x) = 2x² - 8x

The composite function of f(x) and g(x) is defined by the function presented as follows:

(f ∘ g)(x) = f(g(x)).

For the composition of two functions, we have that the output of the inner function, which in this example is given by g(x), serves as the input of the outer function, which in this example is given by f(x).

The functions for this problem are given as follows:

Hence the function for item a is given as follows:

(f ∘ g)(x) = f(2x + 8)

(f ∘ g)(x) = (2x + 8)² - 4(2x + 8)

(f ∘ g)(x) = 4x² + 32x + 64 - 8x - 32

(f ∘ g)(x) = 4x² + 24x + 32.

For item b, the function is given as follows:

(g ∘ f)(x) = g(x² - 4x)

(g ∘ f)(x) = 2(x² - 4x)

(g ∘ f)(x) = 2x² - 8x

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The graph of the trigonometric function is the first one.

Here we have the trigonometric function:

y = 15*sin(x/2).

So, the amplitud if 15, thus, the distance between a maximum and a minimum must be of 15*2 = 30 units.

Also, for x =0 we have:

y = 15*sin(0/2) = 0

y = 0

So the fourth graph can be discarded.

Also, when x increases also does the function (near x = 0), so the third graph is discarded.

Finally, sin(pi) = 0, in this case when x = 2pi we will get:

15*sin(2pi/2) = 0

Then we have an x-intercept at 2pi, thus, the correct option is the first one.

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Answer:

(-4,4)

Step-by-step explanation:

You rewrite the terms:

(x + 4)^2 => [x - (-4)]^2

(y - 4)^2 => [y - (4)]^2

so h = -4 and k = 4

so center of ellipse is (h,k) or (-4,4)

Answer:

Center = (-4, 4)

Step-by-step explanation:

The standard form of the equation of an ellipse with center (h, k) is:

[tex]\boxed{\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1}[/tex]

The given equation is:

[tex]\dfrac{(x+4)^2}{25}+\dfrac{(y-4)^2}{9}=1[/tex]

Comparing the given equation with the standard form, we can see that h = -4 and k = 4. Therefore, the center (h, k) of the ellipse is (-4, 4).

The graph of the linear inequality is given by the image presented at the end of the answer.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The function for this problem is given as follows:

y = -3x/4 + 2.

Hence the graph crosses the y-axis at y = 2, and when x increases by 4, y decays by 3.

The inequality is given as follows:

y < -3x/4 + 2.

Meaning that points below the dashed line are the solution to the inequality.

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Hello!

V

= (18cm * 15cm * 6cm) + ((13cm - 6cm) * 15cm * 6cm)

= 1,620cm³ + 630cm³

= 2,250cm³

The value of tan(80°) × tan(10°) + sin(70°) + sin(20°) ​= 2.28171276

Trigonometry is the branch of mathematics concerned with specific functions of angles and their application to calculations. There are six functions of an angle commonly used in trigonometry. Their names and abbreviations are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc). These six trigonometric functions in relation to a right triangle are displayed in the figure.

Given:

tan(80°) × tan(10°) + sin(70°) + sin(20°)

Using Trigonometric identity

sin (A · B) = sin A cos B - cos A sin B

So, tan(80°) × tan(10°) + sin(70°) + sin(20°)

[tex]\rightarrow \tan (80 \times 10)=1[/tex]

[tex]\rightarrow\sin(70^\circ+20^\circ)=1.28171276[/tex]

[tex]\rightarrow 1.28171276+1=\bold{2.28171276}[/tex]

Hence,  tan(80°) × tan(10°) + sin(70°) + sin(20°) = 2.28171276

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By analyzing the temperature-altitude relationship on a mountain, we can establish a linear model that describes how temperature changes with varying altitudes.

Step-by-step explanation:

a) Knowing the altitude and temperature data, we can use the formula for the slope of a line:

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

where (x1, y1) and (x2, y2) are two points on the line.

Using the altitude and temperature values provided:

(x1, y1) = (4800, 79) and (x2, y2) = (6400, 67),

we can calculate the slope:

m = (67 - 79) / (6400 - 4800)

= -12 / 1600

= -0.0075.

Now, to find the y-intercept (b), we can substitute one of the points (4800, 79) into the equation:

79 = (-0.0075)(4800) + b.

Solving for b, we have:

b = 79 + 0.0075(4800)

= 79 + 36

= 115.

Therefore, the linear model is T(x) = -0.0075x + 115.

b) The units of the slope (m) can be determined by looking at the units of the y values (temperature) and x values (altitude). In this case, the units of temperature are degrees, and the units of altitude are feet. Therefore, the units of the slope (m) are degrees per foot.

c) To find T(5800), we can substitute x = 5800 into the linear model:

T(5800) = -0.0075(5800) + 115

= -43.5 + 115

= 71.5.

Answers:

a) T(x) = -0.0075x + 115.

b) The units of the slope (m) can be determined by looking at the units of the y values (temperature) and x values (altitude). In this case, the units of temperature are degrees, and the units of altitude are feet. Therefore, the units of the slope (m) are degrees per foot.

c) 71.5 degrees.

Group A is performing most consistently in terms of quality and associate engagement compared to last month.

To determine which performance area the groups are performing most consistently compared to last month, we need to compare the scores of each performance area between the two months.

Let's analyze each performance area:

Quality:

For Group A, the quality score increased from 90 to 94, indicating an improvement in quality performance. However, for Group B, the quality score decreased from 74 to 70, indicating a decline in quality performance. Therefore, Group A is performing more consistently in terms of quality compared to last month.

Productivity:

For Group A, the productivity score decreased from 79 to 62, showing a significant decline in productivity performance. Similarly, for Group B, the productivity score decreased from 86 to 58, indicating a notable decline as well. Both groups experienced a decrease in productivity performance, but Group A had a larger decline. Therefore, neither group is performing consistently in terms of productivity compared to last month.

Associate Engagement:

For Group A, the engagement score increased from 68 to 70, suggesting a slight improvement in associate engagement. Conversely, for Group B, the engagement score increased from 76 to 72, indicating a slight decline. Both groups had minor changes in engagement scores, but Group A had a smaller change. Therefore, Group A is performing more consistently in terms of associate engagement compared to last month.

Based on the analysis, Group A is performing most consistently in terms of quality and associate engagement compared to last month. However, neither group is performing consistently in terms of productivity. It is important to address the productivity decline and identify areas for improvement to ensure consistent performance across all categories.

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Answer:

Option C is correct.

The kind of growth model is shown in the table is exponential

Step-by-step explanation:

Exponential growth function is in the form of :    ......[1];   where a is the initial value and b> 0.

Consider any two point from the table:

(1 , 5) and ( 2 , 25)

Substitute these in the equation [1] we get;

        ......[2]

     ......[3]

Divide equation [3] by [2] we have;

Simplify:

Now substitute this value in equation [2] we get;

Divide both sides by 5 we get;

Simplify:

1=a or a = 1

Therefore, the table shown the  exponential growth function y=5^x

Answer:

P(Colin) = 20/38

P(Paul) = 18/38

Step-by-step explanation:

Colin won 20 times out of 38, so the probability that he wins would be 20/38 (or 10/19 simplified).

Paul won 18 times out of 38, so the probability that he wins would be 18/38 (or 9/19 simplified).

Answer:

a) Probability of Colin winning = 10/19

b) Probability of Paul winning = 9/19

Step-by-step explanation:

Total number of matches = 38

Colin won 20,

Paul won the rest so, 38 - 20 = 18

Paul won 18 matches,

From this data, we calculate the probabilities of Colin or Paul winning,

a) Estimate the probability that Colin wins.

Colin won 20 out of 38 matches, so his probability of winning is,

20/38 = 10/19

Probability of Colin winning = 10/19

b) Estimate the probability that Paul wins

Paul won 18 out of 38 matches, so his probability of winning is,

18/38 = 9/19

Probability of Paul winning = 9/19

Rounding to the nearest tenth of a meter, the distance from marker A to marker B (side AB) is approximately 5.7 meters.

To find the distance from marker A to marker B in triangle ABC, we need to calculate the length of side AB.

The distance between two points (x1, y1) and (x2, y2) can be found using the distance formula:

d = √[tex]((x2 - x1)^2 + (y2 - y1)^2)[/tex]

In this case, let's assume that the coordinates of marker A are (x1, y1) and the coordinates of marker B are (x2, y2).

Given that the coordinates of marker A are not provided in the question, we would need the coordinates of both marker A and marker B to calculate the distance between them accurately.

Once we have the coordinates of marker A and marker B, we can substitute them into the distance formula to calculate the distance AB.

For example, if the coordinates of marker A are (x1, y1) = (3, 4) and the coordinates of marker B are (x2, y2) = (7, 8), we can calculate the distance as follows:

d = [tex]\sqrt{((7 - 3)^2 + (8 - 4)^2)}[/tex]

= √[tex](4^2 + 4^2)[/tex]

= √(16 + 16)

= √32

≈ 5.66

Rounding to the nearest tenth of a meter, the distance from marker A to marker B (side AB) is approximately 5.7 meters.

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The central angles for the categories with the numbers 40, 100, 50, and 50 are 60 degrees, 150 degrees, 75 degrees, and 75 degrees, respectively.

To calculate the central angles for each category based on the given numbers 40, 100, 50, and 50, we need to find the proportion of each value to the total sum of all the values. Let's proceed with the following steps:

Step 1: Calculate the total sum of the given numbers: 40 + 100 + 50 + 50 = 240.

Step 2: Find the proportion of each value by dividing it by the total sum and multiplying it by 360 (since a full circle has 360 degrees).

Central angle for the first category: (40/240) * 360 = 60 degrees.

Central angle for the second category: (100/240) * 360 = 150 degrees.

Central angle for the third category: (50/240) * 360 = 75 degrees.

Central angle for the fourth category: (50/240) * 360 = 75 degrees.

The central angles for each category based on the given numbers are 60 degrees, 150 degrees, 75 degrees, and 75 degrees, respectively.

These central angles represent the relative proportions of each category's spending in relation to the total spending. They can be used to create a pie chart or visualize the distribution of expenses in a circular graph.

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Note the search engine cannot find the complete question

The cost of a single unit is given as follows:

$1.05.

El costo de un plátano es el seguiente:

$1.05.

The cost of a single unit is obtained applying the proportions in the context of the problem.

The cost of 22 units is of $23.10, hence the cost of a single unit is obtained dividing the total cost by the number of units, as follows:

23.1/22 = $1.05.

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To solve this problem, we can set up a system of equations based on the given information.

Let's assume the amount of money Ralph Chase will receive through the short-term note is represented by "x" and the amount through the long-term note is represented by "y".

According to the problem, the total amount Ralph plans to sell the property for is $145,000. Therefore, we have the equation:

[tex]\displaystyle x+y=145000[/tex] ...(1)

Now let's consider the interest paid annually. The interest paid on the short-term note at 10% is calculated as [tex]\displaystyle 0.10x[/tex], and the interest paid on the long-term note at 8% is [tex]\displaystyle 0.08y[/tex]. The total annual interest paid is given as $13,100. Therefore, we have the equation:

[tex]\displaystyle 0.10x+0.08y=13100[/tex] ...(2)

We now have a system of two equations (1) and (2). We can solve this system to find the values of "x" and "y".

Multiplying equation (2) by 100 to eliminate decimals, we get:

[tex]\displaystyle 10x+8y=1310000[/tex] ...(3)

Now we can solve equations (1) and (3) simultaneously using any method such as substitution or elimination.

Multiplying equation (1) by 10, we get:

[tex]\displaystyle 10x+10y=1450000[/tex] ...(4)

Subtracting equation (3) from equation (4), we can eliminate "x" and solve for "y":

[tex]\displaystyle 2y=140000[/tex]

Dividing both sides by 2, we find:

[tex]\displaystyle y=70000[/tex]

Now substituting the value of "y" back into equation (1), we can solve for "x":

[tex]\displaystyle x+70000=145000[/tex]

Subtracting 70000 from both sides, we have:

[tex]\displaystyle x=75000[/tex]

Therefore, the amount of money Ralph Chase will receive through the short-term note is 75,000 and through the long-term note is $70,000.