he graph for the equation y = x minus 4 is shown below. On a coordinate plane, a line goes through (0, negative 4) and (4, 0). Which equation, when graphed with the given equation, will form a system that has an infinite number of solutions? y minus x = negative 4 y minus x = negative 2 y minus 4 = x y + 4 x = 1

we find that the numerical approximation using Euler's method gives y(2) ≈ 1.865, while the analytical solution gives y(2) = 2.5.

Using the formula y(n+1) = y(n) + Δx * f(x(n), y(n)), where f(x, y) = x² √y, we can calculate the values of y at each step. Here's the step-by-step calculation:

Step 1: For x = 0, y = 1 (initial condition).

Step 2: For x = 0.2, y = 1 + 0.2 * (0.2)² * √1 = 1.008.

Step 3: For x = 0.4, y = 1.008 + 0.2 * (0.4)² * √1.008 = 1.024.

Step 4: For x = 0.6, y = 1.024 + 0.2 * (0.6)² * √1.024 = 1.052.

Step 5: For x = 0.8, y = 1.052 + 0.2 * (0.8)² * √1.052 = 1.094.

Step 6: For x = 1.0, y = 1.094 + 0.2 * (1.0)² * √1.094 = 1.155.

Step 7: For x = 1.2, y = 1.155 + 0.2 * (1.2)² * √1.155 = 1.238.

Step 8: For x = 1.4, y = 1.238 + 0.2 * (1.4)² * √1.238 = 1.346.

Step 9: For x = 1.6, y = 1.346 + 0.2 * (1.6)² * √1.346 = 1.483.

Step 10: For x = 1.8, y = 1.483 + 0.2 * (1.8)² * √1.483 = 1.654.

Step 11: For x = 2.0, y = 1.654 + 0.2 * (2.0)² * √1.654 = 1.865.

Therefore, using Euler's method with a step size of Δx = 0.2, we approximate y(2) to be 1.865.

To obtain the analytical solution to the ODE, we can separate variables and integrate both sides:

∫(1/√y) dy = ∫x² dx

Integrating both sides gives:

2√y = (1/3)x³ + C

Solving for y:

y = (1/4)(x³ + C)²

Using the initial condition y(0) = 1, we can substitute x = 0 and y = 1 to find the value of C:

1 = (1/4)(0³ + C)²

1 = (1/4)C²

4 = C²

C = ±2

Since C can be either 2 or -2, the general solution to the ODE is:

y = (1/4)(x³ + 2)² or y = (1/4)(x³ - 2)²

Now, let's evaluate y(2) using the analytical solution:

y(2) = (1/4)(2³ + 2)² = (1/4)(8 + 2)² = (1/4)(10)² = 2.5

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Answer:

75.08

Step-by-step explanation:

Focus on the 2nd digit to the right of the decimal point (it is 7).  The next digit is 9.  Because of this (nex digit 5 or greater), we round the 7 up to 8 and obtain the answer

75.08

this is the Answer:

18

Since y_1(0) = 1, it satisfies the initial condition. However, y_2(0) = 0 does not satisfy the initial condition, as it should be y(0) = 1. Therefore, only y_1(t) is a solution of the initial value problem.

To verify that both y_1(t) = 1 - t and y_2(t) = -t^2/4 are solutions of the initial value problem, we first need to understand what the problem is. An initial value problem is a differential equation that includes an initial condition. In this case, we can assume that the initial condition is y(0) = 1.
Now, let's substitute both y_1(t) and y_2(t) into the differential equation and see if they satisfy the initial condition. The differential equation is not provided, but assuming it is y'(t) = -t/2, we have:
y_1'(t) = -1
y_2'(t) = -t/2
Substituting y_1(t) and y_2(t) into the differential equation gives:
y_1'(t) = -1

= -t/2 (when t = 2)
y_2'(t) = -t/2

= -t/2 (for all t)
Thus, both y_1(t) and y_2(t) satisfy the differential equation. Now, let's check if they satisfy the initial condition.
y_1(0) = 1 - 0

= 1
y_2(0) = -0^2/4

= 0
In conclusion, y_1(t) = 1 - t is the only solution that satisfies the differential equation and initial condition, while y_2(t) = -t^2/4 is not a solution since it does not satisfy the initial condition.

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Answer:

it's the first one

Step-by-step explanation:

it's equation f(x) over g(x), so it's the first one

The initial 50 miles distance from the lighthouse and the N 30° W and N 40° W bearing of the ship before and after traveling due east, using the law of sines, indicates.

The law of sines states that in a triangle, the ratio of the length of a side to the sine of the angle opposite that side is the same for each of the three sides of the triangle.

The distance of the ship from the lighthouse = 50 miles

Bearing of the lighthouse from the ship = N 30° W

The direction in which the ship travels = due east

The new bearing to the lighthouse = N 40° W

In the triangle formed by the initial and new locations of the ship and the lighthouse, the interior angles, A, B, C are;

m∠A = 30° + 90° = 120°

m∠B = 90° - 40° = 50°

Therefore; m∠C = 180° - (120° + 50°) = 10°

Angle opposite the initial distance of the ship from the lighthouse = ∠B = 50°

The angle opposite the new distance of the ship from the lighthouse = m∠A = 120°

The law of sines indicate that we have;

\(\dfrac{50}{sin(50^{\circ})} = \dfrac{New \, distance}{sin(120^{\circ})}\)

50 × sin(120°) = The new distance of the lighthouse × sin(50°)

The new distance of the lighthouse = 50 × sin(120°)/(sin(50°)) ≈ 56.53

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Answer:

$12.50

Step-by-step explanation:

Look at the graph down below \/

U can also mark where the pounds is so right at 25 pounds it would be about $12~

The inequality x - 4 ≥ 8 represents the sentence "  the sum of a number and -4 is at least 8" and the solution of the inequality is the value of variable x is x ≥ 12.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

Let's assume that the number would be x

The sum of a number and -4 is at least 8

According to the given question, translate the phrase into an algebraic form :

x - 4 ≥ 8

Add 4 both sides of the above inequality,

x - 4 + 4 ≥ 8 + 4

x ≥ 12

Therefore, the inequality x - 4 ≥ 8 represents the sentence "  the sum of a number and -4 is at least 8" and the solution of the inequality is the value of variable x is x ≥ 12.

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Adding and subtracting polynomials worksheets assist pupils in becoming acquainted with the idea of polynomial addition and subtraction.

Adding and subtracting polynomial worksheets provide pupils with a platform to access a variety of well-structured problems. Because these worksheets progress in complexity, they are simple to use and allow pupils to reinforce their concepts.

Children must study in accordance with their learning curve, and these worksheets are designed to allow young brains to work at their own speed. These math worksheets also address the logical and reasoning aspects of arithmetic, assisting pupils in real-life situations.

Students may have a better grasp and explore these worksheets more quickly with the aid of pictures. These worksheets' step-by-step approach helps pupils better comprehend ideas and reinforce their comprehension.

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Answer:

-6.29

Step-by-step explanation:

Add two negative integers together is just as simple as two positive integers together.

Let's for a little bit ignore that negative. What is 4.058 + 2.232? 6.290 or just 6.29. Now slap a negative in front of it!

Your answer is -6.29.

Different rules arise when adding a negative integer with a positive integer. We can cross the bridge when we get there :)

The evidence does not strongly support the claim that women with above-average looks earn significantly more than women with average looks.

To understand the findings, we need to discuss a few key concepts. First, let's clarify the null hypothesis (H0) and the alternative hypothesis (H1). In this case, the null hypothesis states that there is no relationship between physical appearance and income (β2 = 0), while the alternative hypothesis suggests that there is a relationship (β2 ≠ 0).

In this scenario, the one-sided p-value of 0.272 means that there is a 27.2% chance of observing a relationship between physical appearance and income as strong or stronger than what was found in the study, purely by chance, if there is actually no relationship (β2 = 0). Since this p-value is relatively high (greater than the commonly used threshold of 0.05), it implies weak evidence against the null hypothesis.

Therefore, based on the given information, the evidence does not provide sufficient statistical support to reject the null hypothesis that there is no relationship between physical appearance and income (H0: β2 = 0).

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Answer:

2 is the answer your welcome!!!!!!!!!! :)

Step-by-step explanation:

Answer:

There's no table but

Step-by-step explanation:

4 tickets = $32

8 tickets = $64

Sorry if I didn't help:/.

Answer:

8 1/2

or 8.5

Step-by-step explanation:

Answer:

The second one, √4^9

Sorry lol i posted the answer in the questions section by accident

Answer:

x = 0 & y = 2. Hope this helped <3

The value of x and y from the equation is 1/6 and 5/6 respectively

x = 1/6

y = 5/6

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the first equation be A

11x - 7y = -4   be equation (1)

Let the second equation be B

-14x - 2y = -4   be equation (2)

On simplifying , we get

Multiply equation (2) by 7 , we get

-98x - 14y = -28   be equation (3)

Multiply equation (1) by 2 , we get

22x - 14y = -8   be equation (4)

Subtract equation (4) from equation (3) , we get

-120x = -20

Divide by 120 on both sides , we get

x = 1/6

Now , substituting the value of x in equation (1) , we get

11x - 7y = -4  

11 ( 1/6 ) - 7y = -4

Adding 7y on both sides , we get

7y - 4 = 11/6

Adding 4 on both sides , we get

7y = 11/6 + 4

7y = 35/6

Multiply by 7 on both sides , we get

y = 5/6

Hence , the value of x is 1/6 and value of y is 5/6

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It is true that If two lines meet at a 90 angle, they are perpendicular. If two lines are perpendicular, they have opposite reciprocal slopes.

In geometry, perpendicular lines are two lines that intersect at a 90-degree angle. A right angle is formed where the lines cross each other, so that one line is at a 90-degree angle to the other. This means that the lines are orthogonal to each other, and their slopes are negative reciprocals of each other. For example, consider the Cartesian plane where the x-axis and y-axis are perpendicular lines. The slope of the x-axis is 0, and the slope of the y-axis is undefined, so their negative reciprocals are also undefined and 0, respectively. Perpendicular lines are used extensively in mathematics, physics, and engineering to describe relationships between objects and forces. In construction, perpendicular lines are important for building structures that are stable and level. In computer graphics, perpendicular lines are used to create images and animations with precise angles and proportions.

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Complete question:

If two lines meet at a 90 angle, they are perpendicular. If two lines are perpendicular, they have opposite reciprocal slopes. True or False.

The height of the right cone is \(7 \ units\).

To find the height of the right cone, we can use the formula for the volume of a cone:

Volume = \(\frac{1}{3} \times \pi \times r^{2} \times h\)

where \(\pi\) is the mathematical constant pi (approximately \(3.14159\)), r is the radius of the base of the cone, and h is the height of the cone.

Given that the volume is \(21 \ \pi\) units and the diameter is \(6\) units, we can find the radius:

Radius (r) =

\(\frac{diameter}{2} \\= \frac{6}{2} \\= 3\)

Substituting the known values into the formula, we have:

\(21 \pi = \frac{1}{3} \times \pi \times 3^{2} \times h\)

Simplifying the equation:

\(21 = (\frac{1}{3}) \times 9 \times h\)

Multiplying both sides by \(3\):

\(63 = 9h\)

Dividing both sides by \(9\\\):

\(h = \frac{63}{9} \\ = 7 units\)

Therefore, the height of the right cone is \(7 \ units\).

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Answer:

1) (x + 1)(2x + 3) | 2) (3x + 4)(x + 2) | 3) (2x+3)(x+2) | 4) (3x + 4)(2x + 3)

Step-by-step explanation:

Question 1: (x + 1)(2x + 3)

Question 2: (3x + 4)(x + 2)

Question 3: (2x+3)(x+2)

Question 4: (3x + 4)(2x + 3)

(If you need explanation reply to the message)

Answer:

-6/5

Step-by-step explanation:

it is also -1.2 as a decimal

Hey there!

(0 + -3) * (-1 + 5) / (12 + -2)

= (0 - 3) * (-1 + 5) / (12 - 2)

= -3(4) / 10

= -12 / 10

= -12 ÷ 2 / 10 ÷ 2

= -6 / 5

≈ - 1 1/5

≈ -1.2

Therefore, your answer is: -6/5 or -1 1/5

{EITHER OF THOSE SHOULD WORK BECAUSE THEY ARE EQUIVALENT TO EACH OTHER}

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

Leslie has 13 quarters and 23 half-dollars.

Step-by-step explanation:

You can write the following equations from the information given and considering that a quarter is $0.25 and half-dollar is $0.50:

x+y=36 (1)

0.25x+0.50y=14.75 (2), where:

x=amount of quarters

y=amount of half-dollars

First, you can isolate x in (1):

x=36-y (3)

Then, you can replace (3) in (2):

0.25(36-y)+0.50y=14.75

9-0.25y+0.50y=14.75

0.25y=5.75

y=5.75/0.25

y=23

Finally, you can replace the value of y in (3) to find the value of x:

x=36-23

x=13

According to this, the answer is that Leslie has 13 quarters and 23 half-dollars.

Answer:

The correct answer is: 2. t=0.45a

Step-by-step explanation:

Let t be the price of apples

and a be the number of apples

The price and quantity are directly proportional

\(t \propto a\)

Removing the proportionality symbol introduces a proportionality constant in the equation

\(t = ka\)

So far we know that cost of 6 apples is $2.70

Putting in the equation

\(2.70 = k (6)\\k = \frac{2.70}{6}\\k = 0.45\)

Putting the values of k will give us:

\(t = 0.45a\)

Hence,

The correct answer is: 2. t=0.45a

To find the water-level height (feet) as a function of time (hours), we need to know the volume of the pool and how much water is being pumped in per hour.

The volume of the rectangular pool can be found by multiplying its length, width, and height:

Volume = Length x Width x Height

Since we know the dimensions of the pool are 20 feet by 10 feet, we can assume the height is 5 feet (half the length of the pool).

Volume = 20 ft x 10 ft x 5 ft = 1000 cubic feet

This means the pool can hold 1000 cubic feet of water.

If 50 cubic feet of water is pumped into the pool per hour, we can write the water-level height (h) as a function of time (t) as follows:

h(t) = (50t) / 1000

where t is the time in hours.

For example, after 1 hour, the water-level height would be:

h(1) = (50 x 1) / 1000 = 0.05 feet

After 2 hours, the water-level height would be:

h(2) = (50 x 2) / 1000 = 0.1 feet

And so on.

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Answer: 1.90

Step-by-step explanation:

9/4.72= 1.90

Answer:

1.90

Step-by-step explanation:

9/4.72= 1.90

Answer:

Step-by-step explanation:

The first one has a median of 5, because 5 is the middle number of a set when they are in order of least to greatest, or in this case 0, 1, 2, 3, 4, 5, 6, 6, 7, 7, 9.

The second one is 3, because it is in the middle when it is 0, 2, 3, 3, 3, 4, 6.

The third one is 2, 3, 6, 7, 25 and the median is 6.

The fourth one is is 4, and is already ordered properly.

The last one is 2, and is also ordered properly.

Answer:

Update on

Step-by-step explanation:

shay hit me....

gooo

Answer:

d=7

Step-by-step explanation:

Answer:

The roots of x^3 −2=2x^2 −x can be found by using the cubic formula to solve this polynomial equation. The roots are -2, 1, and 2/3.

Step-by-step explanation:

Answer:

31

Step-by-step explanation:

Answer: 31

Step-by-step explanation:

1. Multiply 28+6-12/4

2. Divide 28+6-3

3. Add 34-3

4. Subtract 31

The odd cubic function f(x) = x³ - 4x² + 5 is approaching (x → ∞, y → ∞).

A polynomial function's final behavior is how its graph behaves as x gets closer to positive or negative infinity.

The graph's final behavior is determined by a polynomial function's degree and leading coefficient.

The function f(x) = x³ - 4x² + 5 is an odd cubic function that is symmetric about the origin.

As x approaches negative infinity the function f(x) also approaches negative infinity but at a faster rate and as approaches positive infinity the function f(x) also approaches positive infinity at a faster rate.

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