what is the solution to the system of equations graphed below

Answer:

V = 4(5)(7) + 6(5)(15) = 140 + 450 = 590 cm³

In 12 years, Maxwell will deposit $290 into the savings account each month.

To calculate how much money Maxwell will deposit into the account each month in 12 years, we need to determine the pattern of increasing deposits over time.

Maxwell deposits $125 into the savings account each month this year, which we can consider as Year 1. Starting from Year 2, he plans on increasing the monthly deposit by $15.

In Year 2, the monthly deposit will be $125 + $15 = $140.

In Year 3, the monthly deposit will be $140 + $15 = $155.

This pattern continues, increasing the deposit by $15 each year.

Therefore, in Year 12, the monthly deposit will be $125 + ($15 * 11) = $125 + $165 = $290.

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Rhe point-slope equation of a line with the labeled point (3, -4) is y + 4 = m(x - 3), where 'm' represents the slope of the line.

To find the point-slope equation of a line using the coordinates of a labeled point, you can use the following formula:
y - y₁ = m(x - x₁)
In this formula, (x₁, y₁) represents the coordinates of the labeled point, and m represents the slope of the line.
Given the coordinates (3, -4) of the labeled point, we can substitute these values into the formula:
y - (-4) = m(x - 3)
Simplifying this equation, we get:
y + 4 = m(x - 3)
This is the point-slope equation of the line.
Now, it's important to note that the problem does not provide information about the slope of the line. Therefore, we cannot determine the exact point-slope equation without knowing the slope. The point-slope equation requires the slope value to be defined.
If you have the slope of the line, let's say it is represented by the variable 'm', you can substitute that value into the equation to get the specific point-slope equation. For example, if the slope is 2, the equation becomes:
y + 4 = 2(x - 3)

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The steps to solving these differential equations are:

1) x^6 - 2x^5 + x^4/2x^2 = (x^4)(x^2) - 2(x^5) + x^4/(2(x^2)) = x^4 (x^2 - 2x + 1/2)

2) Sec^3x + e^xsecx + 1/sec x = Sec^3x + e^x*cscx + cscx

3) cot^2 x = 1/tan^2 x

4) x^2 - 2x^3 + 7/ cube root x = x^2 - 2x^3 + 7 *x

5) y = x^(1/2) - x^2 +2x is the derivative of the function (factored form)

The important variables are the two types of test questions which can be represented as :

Variables are used to represent unknown values which could be worked out in a mathematical expression or problem.

The variables or unknown in this case are the type of test questions. which are : m for multiple choice, s for short answer

Therefore, the correct option is C. m for multiple choice, s for short answer

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The correct algebraic expression for the reduced price of the computer is p - 250, as stated in option B. It signifies subtracting $250 from the original price, 'p.' Option B

To determine the algebraic expression that represents the reduced price of a computer, let's consider the given information. It states that the original price of the computer was reduced by $250.

Let's represent the original price of the computer as 'p' in dollars. Since the price was reduced by $250, we need to subtract $250 from the original price.

The expression that represents the reduced price is obtained by subtracting $250 from 'p.' Therefore, the algebraic expression for the reduced price is p - 250, which corresponds to option B.

Option A, 250 + p, suggests adding $250 to the original price, which would result in a higher value, contrary to the information given.

Option C, 250 - p, represents subtracting the original price from $250, which is not correct as we are reducing the price, not subtracting it from a fixed value.

Option D, 250p, represents multiplying the original price by $250, which does not align with the given scenario of reducing the price by $250.

Option B

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Note: The complete question is:

The original price of a computer was reduced by $250.If p = the computer's original price in dollars, which algebraic expression represents the reduced price? A.250 + p B.p – 250 C.250 – p D.250p

The correct step that comes after constructing a circle when constructing an inscribed square is to use a straightedge to draw a diameter of the circle (option C).

When constructing an inscribed square by hand, the step that comes after constructing a circle is to use a straightedge to draw a diameter of the circle. Therefore, the correct answer is C.

To understand why drawing a diameter comes after constructing a circle, let's review the steps involved in constructing an inscribed square:

1. Start by constructing a circle: To do this, you would use a compass and a fixed point as the center to draw a circle.

2. Draw a diameter of the circle: A diameter is a line segment that passes through the center of the circle and divides it into two equal parts. Using a straightedge, you can draw a straight line that passes through the center of the circle.

3. Find the midpoint of the diameter: The midpoint is the point on the diameter that divides it into two equal parts. You can use a compass or measure the distance from each end of the diameter to find the midpoint.

4. Draw a perpendicular bisector: With the midpoint as the center, use a compass to draw an arc that intersects the diameter on both sides. This arc will create two points on the diameter.

5. Connect the points: Use a straightedge to connect the two points on the diameter. This line segment will be one side of the inscribed square.

6. Repeat the process: Repeat steps 2 to 5 to draw the other three sides of the square, using the circle as a guide.

By drawing a diameter of the circle, you establish a reference line that will be the base for constructing the sides of the inscribed square. It allows you to accurately position the square within the circle and ensure that its vertices lie on the circumference.

Therefore, the correct step that comes after constructing a circle when constructing an inscribed square is to use a straightedge to draw a diameter of the circle (option C).

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The equation of the tangent line at (3, 324) is y = 288x - 540.

To find y' (the derivative of y), we can differentiate the given function y = [tex](x^2 + 2x + 3)^2[/tex] using the chain rule.

y' = [tex]2(x^2 + 2x + 3) \times (2x + 2) = 4(x^2 + 2x + 3)(x + 1)[/tex]

Now, to find the slope of the tangent line at (3, 324), we substitute x = 3 into y' and evaluate it:

y' = [tex]4(3^2 + 2(3) + 3)(3 + 1) = 4(9 + 6 + 3)(4) = 4(18)(4) = 288[/tex]

So, the slope of the tangent line at (3, 324) is 288.

To find the y-intercept of the tangent line, we substitute the coordinates (3, 324) and the slope (288) into the point-slope form equation: y - y1 = m(x - x1).

Using (x1, y1) = (3, 324) and m = 288, we have:

y - 324 = 288(x - 3)

y - 324 = 288x - 864

y = 288x - 540

Therefore, the equation of the tangent line at (3, 324) is y = 288x - 540.

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The correct answer is: OD. (x+7)(x-7)

To find the area of the combined rectangles, we need the dimensions (length and width) of each rectangle. However, the provided text and numbers do not seem to correspond to a clear description of the rectangles or their dimensions. Could you please provide more specific information or clarify the question?

A recent survey conducted on a sample of 425 individuals revealed that 102 of them had visited the cinema within the past month.

This data suggests that approximately 24% of the surveyed population had engaged in movie going activities during the specified period.

The findings highlight a significant proportion of the respondents who have recently enjoyed the cinematic experience.

However, it is important to note that this data is based on a limited sample size and may not be representative of the entire population.

Further research and surveys involving a larger and more diverse sample are recommended to obtain a more accurate understanding of movie attendance trends.

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Answer: rotation of 90 counter clockwise about the origin

Step-by-step explanation:

We need to apply a translation of 3 units up.-

We can see that both of them have almost the same slope, but the line d starts at y = 0, while the data starts at y = 3.

Then we could apply a translation up of 3 units, so if the line is:

d = f(x)

Then the translated line is:

d = f(x) + 3

And that translates the line 3 units upwards.

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Answer:

explanation provided in the picture

Step-by-step explanation:

the answer is x= 55°

hopefully this helps ! :)

Answer:

The area of this triangle is (1/2)(9)(8) = 36.

The solution to the equation 2(x - 6) + 25 = 49 - 2x is x = 9.

To solve the equation 2(x - 6) + 25 = 49 - 2x for x, we will simplify and isolate the variable x.

Let's start by simplifying both sides of the equation:

2(x - 6) + 25 = 49 - 2x

Expanding the parentheses:

2x - 12 + 25 = 49 - 2x

Combining like terms:

2x + 13 = 49 - 2x

Now, let's isolate the variable x by moving the terms involving x to one side of the equation. We can do this by adding 2x to both sides:

2x + 2x + 13 = 49 - 2x + 2x

Simplifying:

4x + 13 = 49

Next, we'll get rid of the constant term on the left side by subtracting 13 from both sides:

4x + 13 - 13 = 49 - 13

Simplifying:

4x = 36

To solve for x, we'll divide both sides of the equation by 4:

4x/4 = 36/4

Simplifying:

x = 9

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According to the information, we can infer that the frog must take 4 hops to travel the same distance as a cat's jump.

Since the cat's jump covers a distance of 1 meter, we need to determine how many hops the frog needs to take to cover the same distance.

The frog's jump covers 1/4 meter, and we want to find the number of hops needed to reach 1 meter (the distance of the cat's jump).So, to do this, we can set up a proportion:

By cross-multiplying, we have:

So, the correct answer is 4 because the frog has to jump 4 times to cover the same distance of the rabbit.

Note: This question is in a different language. Here is in English:

How many hops must the frog take to travel the same distance as a cat's height?

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The linear relationship illustrated in the provided table can be effectively described by the equation Y = -4x + 2. Option D.

To determine the equation that represents the given table with the values of x and y, we can observe the pattern and find the equation of the line that fits these points.

Given the table:

X: 2 0 4

Y: -4 3 1

We can plot these points on a graph and see that they form a straight line.

Plotting the points (2, -4), (0, 3), and (4, 1), we can see that they lie on a line that has a negative slope.

Based on the given options, we can now evaluate each equation to see which one represents the line:

Y = 1/2x + 5

When we substitute the x-values from the table into this equation, we get the following corresponding y-values: -3, 5, and 6. These values do not match the given table, so this equation does not represent the table.

Y = -1/2x + 3

When we substitute the x-values from the table into this equation, we get the corresponding y-values: 4, 3, and 2. These values also do not match the given table, so this equation does not represent the table.

Y = 2x - 3

When we substitute the x-values from the table into this equation, we get the corresponding y-values: -4, -3, and 5. These values do not match the given table, so this equation does not represent the table.

Y = -4x + 2

When we substitute the x-values from the table into this equation, we get the corresponding y-values: -6, 2, and -14. Interestingly, these values match the y-values in the given table. Therefore, the equation Y = -4x + 2 represents the table.

In conclusion, the equation Y = -4x + 2 represents the linear relationship described by the given table. So Option D is correct.

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The factored form of 3x^2 - 5x - 18x + 30 is (3x - 5)(x - 6).

To factor the expression3x^2 - 5x - 18x + 30, we can group the terms and then factor out common factors.

Step 1: Group the terms.

3x^2 - 5x - 18x + 30,

Step 2: Factor out the common factors from each group.

x(3x - 5) - 6(3x - 5)

Step 3: Notice that we now have a common binomial factor of (3x - 5).

(3x - 5)(x - 6)

Therefore, the factored form of the expression 3x^2 - 5x - 18x + 30 is (3x - 5)(x - 6).

In this factored form, (3x - 5) and (x - 6) are the factors of the expression. To check if the factoring is correct, you can multiply the factors back together to see if you get the original expression:

(3x - 5)(x - 6) = 3x(x) - 3x(6) - 5(x) + 5(6)

=3x^2 - 18x - 5x + 30

= 3x^2 - 23x + 30  

The result matches the original expression, so the factoring is correct.

Therefore, the factored form of 3x^2 - 5x - 18x + 30 is (3x - 5)(x - 6).

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The correct answer is: d. x → -1 Simplifying further, we get: [tex]\frac{1}{2}+7[/tex] Which equals [tex]\frac{15}{2}[/tex]. d. x → -1

To find the limit of the expression [tex](\frac{x^2}{2} ) - (\frac{7}{x} )[/tex] as x approaches a specific value, we substitute that value into the expression.

a. x → 0:

[tex]lim (\frac{x^2}{2} ) - (\frac{7}{x} ) x \rightarrow 0[/tex]

Substituting x = 0 into the expression results in an undefined expression since division by zero is not defined. Therefore, the limit in this case is undefined.

b. x → 0:

[tex]lim (\frac{x^2}{2} ) - (\frac{7}{x} ) x \rightarrow 0[/tex]

Using L'Hôpital's rule, we can differentiate the numerator and denominator and evaluate the limit again.

[tex]lim[/tex]([tex]\frac{2x}{2}[/tex]) - ([tex]\frac{7}{1}[/tex]) as x → 0

Simplifying further, we get:

lim x - 7 as x → 0

Substituting x = 0, we find that the limit is -7.

c. x → 3/14:

lim ([tex](\frac{x^2}{2} ) - (\frac{7}{x} ) x\rightarrow \frac{3}{14}[/tex]

Substituting x = 3/14 into the expression gives:

[tex]\frac{\frac{3}{14}^2 }{2}-\frac{ 7}{\frac{3}{14} }[/tex]

Simplifying this expression, we find that the limit evaluates to [tex]\frac{-77}{6}[/tex]

d. x → -1:

[tex]lim (\frac{x^2}{2} ) - (\frac{7}{x} ) x \rightarrow 0[/tex]

Substituting x = -1 into the expression gives:

[tex]\frac{-1^2}{2} - (\frac{7}{-1} )[/tex]

Simplifying further, we get:

[tex]\frac{1}{2}+7[/tex]

Which equals [tex]\frac{15}{2}[/tex]

Therefore, the correct answer is:

d. x → -1

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Answer:

the property of a material of undergoing elastic deformation or (of a gas) change in volume when subjected to an applied force. It is equal to the reciprocal of stiffness.

a. Triangle 3 is a right triangle.

b. For any triangles that are not right triangles, we can use any two of the sides to create a right triangle by applying the Pythagorean theorem.

a Let's apply the Pythagorean theorem to each triangle:

Triangle 1:

Side lengths: √519 units, 27 units, √210 units

Checking the squares of the side lengths:

(√519)² = 519

27² = 729

(√210)² = 210

In this case, 519 + 210 is not equal to 729. Therefore, Triangle 1 is not a right triangle.

Triangle 2: Side lengths: 21 units, √109 units, √420 units

Checking the squares of the side lengths:

21² = 441

(√109)² = 109

(√420)² = 420

Similarly, the sum of the squares of the two shorter sides should be equal to the square of the longest side if it is a right triangle. However, 441 + 109 is not equal to 420. Therefore, Triangle 2 is not a right triangle.

Triangle 3: Side lengths: √338 units, 26 units, √338 units

Checking the squares of the side lengths:

(√338)² = 338

26² = 676

(√338)² = 338

Here, 338 + 338 is equal to 676, which satisfies the Pythagorean theorem. Therefore, Triangle 3 is a right triangle.

b. For any triangles that are not right triangles, we can use any two of the sides to create a right triangle by applying the Pythagorean theorem.

Let's take Triangle 1 as an example:

Side lengths: √519 units, 27 units, √210 units

Let's choose the first and third side:

(√519)²+ (√210)² = 519 + 210 = 729

Now, we take the square root of 729 to find the length of the missing side:

√729 = 27

By doing this, we have formed a right triangle with side lengths of 27 units, √519 units, and √210 units.

Similarly, you can apply this process to Triangle 2 or any other triangle that is not initially a right triangle to create a right triangle using two of its sides.

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Answer: 3√11.

Step-by-step explanation:

To simplify the radical expression √99, we can look for perfect square factors of 99.

The prime factorization of 99 is 3 * 3 * 11.

We can rewrite √99 as √(3 * 3 * 11).

Taking out the perfect square factors, we get:

√(3 * 3 * 11) = 3√11.

Therefore, the simplified radical expression for √99 is 3√11.

The correct answer is: Starting with one, every consecutive line has two more marbles than the previous line. This is the result inferred using deductive reasoning.

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The function f(x) = √3x - 3 could be the one graphed.

From the given information, we can deduce the following about the graph of the square root function:

The graph is a square root function, which means it has the form f(x) = √(ax + b), where a and b are constants.

The graph is shifted horizontally by a certain amount.

The graph is shifted vertically by a certain amount.

Using this information, we can analyze each function option to determine if it matches the graph:

Of(x) = √x - 3: This function is a square root function shifted vertically downward by 3 units. It does not match the given graph, as it is shifted vertically, not horizontally.

Of(x) = √x - 1: This function is a square root function shifted vertically downward by 1 unit. It also does not match the given graph, as it is shifted vertically, not horizontally.

Of(x) = √x + 1: This function is a square root function shifted vertically upward by 1 unit. It does not match the given graph, as it is shifted vertically, not horizontally.

f(x) = √3x - 3: This function is a square root function with a coefficient of 3 in front of x, causing a horizontal compression. It is also shifted vertically downward by 3 units. This function matches the given graph, as it represents a horizontal and vertical shift of the square root function.

Therefore, the function f(x) = √3x - 3 could be the one graphed.

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Answer:

The 2nd option is correct, a 90 degree counterclockwise rotation about the origin and then a reflection across the y-axis

Step-by-step explanation:

The following sequences of transformations do not show congruency by mapping shape I onto shape II:

These sequences of transformations do not map shape I onto shape II because they either change the size or shape of the figure. The second sequence of transformations reflects shape I across the x-axis, rotates it 90° clockwise, and then translates it 4 units down.

This results in a figure that is flipped sideways and shifted down. The third sequence of transformations reflects shape I across the x-axis, rotates it 90° counterclockwise, and then translates it 6 units down. This results in a figure that is flipped upside down and shifted to the left.

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Answer:

Minimum=60

First Quartile(Q1)=79

Median=86

Third Quartile (Q3)=89

Interquartile range (IQR)=10

To determine the type of correlation between two variables on a graph, we can examine the pattern or relationship exhibited by the data points.

If the data points on the graph form a roughly linear pattern with a positive slope, it indicates a positive correlation. This means that as one variable increases, the other variable also tends to increase.

Conversely, if the data points on the graph form a roughly linear pattern with a negative slope, it indicates a negative correlation. In this case, as one variable increases, the other variable tends to decrease.

Additionally, the strength of the correlation can be assessed by how closely the data points align with the overall trendline. If the points are tightly clustered around the trendline, it suggests a strong correlation, while scattered points indicate a weaker correlation.

By visually inspecting the graph and observing the direction and pattern of the data points in relation to the trendline, we can determine the type of correlation exhibited by the variables.

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