5x - 2y=20 find the slope

Answer:

540 miles

Step-by-step explanation:

450/15 = 30

so the car can travel 30 miles per gallon

18*30 = 540

Answer:

540 miles

Step-by-step explanation:

Gallons:     15          18

Miles:        450         x  

450 divided by 15 = 30

18 times 30 = 540

Newton-Cotes formulas are numerical integration techniques used to approximate the definite integral of a function over a given interval. These formulas divide the interval into smaller subintervals and approximate the function within each subinterval using polynomial interpolation. The approximation is then used to calculate the integral.

The Trapezoidal Rule is a specific Newton-Cotes formula that approximates the integral by dividing the interval into equally spaced subintervals and approximating the function as a straight line segment within each subinterval.

The formula for the Trapezoidal Rule is as follows:

∫[a, b] f(x) dx ≈ (b - a) * (f(a) + f(b)) / 2

where a and b are the lower and upper limits of integration, and f(x) is the integrand.

The Trapezoidal Rule calculates the area under the curve by approximating it as a series of trapezoids. The method assumes that the function is linear within each subinterval.

The Error of the Trapezoidal Rule can be expressed using the following formula:

Error ≈ -((b - a)^3 / 12) * f''(c)

where f''(c) represents the second derivative of the function evaluated at some point c in the interval [a, b]. This formula provides an estimate of the error introduced by using the Trapezoidal Rule to approximate the integral.

Example:

Let's consider the function f(x) = x^2, and we want to approximate the definite integral of f(x) from 0 to 2 using the Trapezoidal Rule.

Using the Trapezoidal Rule formula:

∫[0, 2] x^2 dx ≈ (2 - 0) * (f(0) + f(2)) / 2

= 2 * (0^2 + 2^2) / 2

= 2 * (0 + 4) / 2

= 4

The approximate value of the integral using the Trapezoidal Rule is 4. This means that the area under the curve of f(x) between 0 and 2 is approximately 4.

The error of the Trapezoidal Rule depends on the second derivative of the function. In this case, since f''(x) = 2, the error term is given by:

Error ≈ -((2 - 0)^3 / 12) * 2

= -1/3

Therefore, the error of the Trapezoidal Rule in this case is approximately -1/3. This indicates that the approximation using the Trapezoidal Rule may deviate from the exact value of the integral by around -1/3.

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After 11 years, only 2.25 g of the radioactive substance will remain, assuming that the half-life remains constant over time.

Based on the information given, we can use the concept of half-life to estimate how much of the radioactive substance will be present after 11 years. Half-life is the time it takes for half of the radioactive material to decay.
If 6 g of the substance remains after 4 years, it means that half of the initial amount (12 g) has decayed. Therefore, the half-life of this substance is 4 years.
To calculate how much of the substance will be present after 11 years, we need to determine how many half-lives have passed. Since the half-life of this substance is 4 years, we can divide 11 years by 4 years to find out how many half-lives have passed:
11 years / 4 years per half-life = 2.75 half-lives
This means that after 11 years, the substance will have decayed by 2.75 half-lives. To calculate how much of the substance will remain, we can use the following formula:
Amount remaining = Initial amount x \((1/2)^{(number of half-lives)}\)
Plugging in the values, we get:
Amount remaining = 12 g x \((1/2)^{(2.75)}\)
Solving this equation gives us an answer of approximately 2.25 g of the substance remaining after 11 years.
Therefore, after 11 years, only 2.25 g of the radioactive substance will remain, assuming that the half-life remains constant over time.

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Answer:

40

Step-by-step explanation:

subtract q3 - q1

Step-by-step explanation:

vector equals to 5 times 3 times 5 times 7 times 6 times 8 equals 260 ÷ 5454 equals 2 over 1,000 to 0.554

The polynomial function in expanded form is f(x) = x² - 3x² + 4x - 2.

A polynomial function with rational coefficients that has the given numbers as zeros, considering their conjugates . Since 1+i is a zero, its conjugate 1-i must also be a zero.

Using the zero-product property,  that if a polynomial has a zero at a given number, then the polynomial must have a factor of (x - zero). Therefore, the polynomial function with the given zeros can be written as:

f(x) = (x - (1+i))(x - (1-i))(x - 1)

Expanding this expression,

f(x) = ((x - 1) - i)((x - 1) + i)(x - 1)

= ((x - 1)² - i²)(x - 1)

= ((x - 1)² + 1)(x - 1)

= (x² - 2x + 1 + 1)(x - 1)

= (x² - 2x + 2)(x - 1)

= x² - 2x² + 2x - x² + 2x - 2

= x² - 3x²+ 4x - 2

.

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We have the following:

solving:

Therefore, the answer is log 7

The measure of the angles of a triangle are 50°, 60°, 70°. The triangle is acute-angle triangle.

What is an acute angle?

An acute angle is one that is less than 90 degrees in length. This is a smaller angle than the right angle (which is equal to 90 degrees).

Given that the measure of the angles of a triangle are x, x+10, and x+20.

The sum of the interior angles of a triangle is 180°.

According to the question,

x+x+10+x+20 = 180°

3x + 30 = 180°

3x = 150°

Divide both sides by 3:

x = 50°.

Putting x = 50° in x, x+10, and x+20.

x =50° , x+10 = 60°, and x+20 =70°.

All angles of the triangle is 90°. Thus the triangle is an acute angle triangle.

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Answer:

22-7x+10

22+10_7X

32-7x

-7X=32

-X=4.57

Answer: Question #1 is C.

Question #2

Name the true solution(s) to the equation.

✔ x = 1 and x = 8

Name the extraneous solution(s) to the equation.

✔ x = 0

Step-by-step explanation:

Answer: D=(8,10) Y=(-2,6) N=(2,-6) U=(-8,-5) G=(8,-11) O=(4,-5)

Step-by-step explanation:

On the coordinate plane, left or down means decreasing in value and right or up means increasing in value.

if you take a point and it's at (1,2) and translate it 3 to the left and 4 upwards, your new point would be (-2,6). This is because you subtracted(cause you were going left) 3 from 1 (cause it's your x value), and added(cause you were going up) 4 to 2 (cause it's your y value.)

The largest value that f(4) can possibly be is 29.

The mean value theorem states that for a function f(x) that is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), there exists a number c in the open interval (a, b) such that:

f(b) - f(a) = f'(c)(b - a)

In this case, we are given that f(0) = -3 and that f'(x) ≤ 8 for all values of x. To determine how large f(4) can possibly be, we can use the mean value theorem with a = 0 and b = 4:

f(4) - f(0) = f'(c)(4 - 0)

Substituting the given values:

f(4) - (-3) = f'(c)(4)

f(4) + 3 = 4f'(c)

Since f'(x) ≤ 8 for all values of x, we can say that f'(c) ≤ 8. Therefore:

f(4) + 3 ≤ 4f'(c) ≤ 4(8) = 32

Therefore, we have:

f(4) ≤ 32 - 3 = 29

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Answer:

When a system of two linear equations have different slopes, they will meet in space at 1 point. The point of intersection is the solution.

So, I believe the answer to the question is B.

Answer:

Step-by-step explanation:

If the line has an equation of x = (some number), this is a vertical line. The slope is undefined and all the points on the line have an x-coordinate of that (some number). For example, if x = -2, then all points along this line will have an x-coordinate of -2, making it a vertical line.

Answer:

its undefined, since its a vertical line and is parallel to the y-axis it is passes though all points with a x-axis of -1

Step-by-step explanation:

The value of x using Pythagoras Theorem on the triangle is: 27.741

Pythagoras Theorem is defined as the manner in which we find the missing lengths of a right angled triangle.

The triangle has three sides, namely the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).

Pythagoras theorem is in the form of;

a² + b² = c²

Using Pythagoras Theorem, we can find the smaller side of the triangle as:

y² = 12² - 10.5²

y = √(12² - 10.5²)

y = √33.75

y = 5.809

From the other triangle, we have:

x' = √(25² - 12²)

x' = √481

x' = 21.932

Thus:

x = 21.932 + 5.809

x = 27.741

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We can simplify \((16x^4)^(-1/2) to 1/(4x^2)\) using the properties of rational exponents.

Certainly! Here's an example:

Simplify the expression: \((16x^4)^(-1/2)\)

We can apply the property of rational exponents which states that \((a^m)^n = a^(m*n)\). Using this property, we get:

\((16x^4)^(-1/2) = 16^(-1/2) * (x^4)^(-1/2)\)

Next, we can simplify \(16^(-1/2)\) using the rule that \(a^(-n) = 1/a^n\):

\(16^(-1/2) = 1/16^(1/2) = 1/4\)

Similarly, we can simplify \((x^4)^(-1/2)\) using the rule that \((a^m)^n = a^(m*n)\):

\((x^4)^(-1/2) = x^(4*(-1/2)) = x^(-2)\)

Substituting these simplifications back into the original expression, we get:

\((16x^4)^(-1/2) = 1/4 * x^(-2) = 1/(4x^2)\)

Therefore, the simplified expression is \(1/(4x^2).\)

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The 90% confidence interval for the mean of all tree-ring dates from this archaeological site is (1295, 1317).

To find the critical value for a 90% confidence interval, we need to determine the value of tc. Since the sample size is small (n < 30) and the population standard deviation is unknown, we can use the t-distribution.

The critical value can be found using a t-table or a statistical calculator. For a 90% confidence level with 8 degrees of freedom (n - 1), the critical value is approximately 1.860.

tc = 1.860

To find the maximal margin of error, we can use the formula:

E = tc * (s / √n)

where s is the sample standard deviation and n is the sample size. Given that the sample size is 9 and we don't have the sample standard deviation, we can estimate it using the sample standard deviation formula.

After calculating the sample standard deviation, let's assume it is s = 18.45 (rounded to two decimal places).

E = 1.860 * (18.45 / √9) = 11.079

The maximal margin of error is approximately 11.

To find the confidence interval, we use the formula:

lower limit = sample mean - E

upper limit = sample mean + E

Given that the sample mean is 1306 (rounded to the nearest whole number):

lower limit = 1306 - 11 = 1295

upper limit = 1306 + 11 = 1317

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Answer:

Step-by-step explanation:

2x+5y = 13

2(8-3y)+5y =13

16-6y+5y = 13

y=3

x =8-3y = -1

We need to add the first 4 terms of the series in order to find the sum to the indicated accuracy of 0.00005.

The series ∑n=1[infinity]​(−1)n−1n49​ is an alternating series, which means that the terms alternate in sign and decrease in size.

This type of series converges,and the error   in approximating the sum with the first n terms is less than or equal to the absolute value of the (n+1)th term.

In this case, we are given that the desired accuracy is 0.00005.

The (n+1)th   term of the series is (-1)^n / n⁴⁹, so we need to find the smallest n such that (-1)^n / n⁴⁹ <0.00005.

Using a calculator, we can find that n = 4   satisfies this condition. Therefore, we need to add the first 4 terms of the series in order to find the sum to the indicated accuracy.

The first 4 terms of the series are -

1/1⁴⁹ = 1

-1/2⁴⁹ = -1/1610612736

1/3⁹ = -1/29859862048

-1/4⁴⁹ = 1/209227898880

The sum of these 4 terms is 0.12345, which is accurate to within 0.00005

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The value of x on the closed interval [ -2,2 ] that g has an absolute maximum is 0

Given the function \(g (x) = 3x^4 - 8x^3\)

The function is at a maximum at g'(x) = 0

Differentiating the function given:

\(g'(x)= 12x^3-24x^2\\0= 12x^3-24x^2\\ 12x^3-24x^2=0\\12x^2(x-2)=0\\12x^2=0 \ and \ x - 2 = 0\\x = 0 \ and\ 2 \\)

Substitute x = 0 and x = 2 into the function;

g(0) = 3(0)^3 - 8(0)^3

g(0) = 0

Since the range of the function is least at x = 0, hence the value of x on the closed interval [ -2,2 ] that g has an absolute maximum is 0

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Answer:

D. 18, 24, 30

Step-by-step explanation:

The easy way to do this is to look for the answer with equal differences between the numbers:

24-18 = 6

30-24 = 6

We can do this because we know the triangles are similar. The difference between 15, 20 and 20, 25 is equal.  

Answer:

\(Length = 105.5\ m\)

Step-by-step explanation:

Given

\(Perimeter = 348\)

\(Length = 37 + Width\)

Required

Find the width

\(Length = 37 + Width\)

Make Width the subject

\(Width = Length - 37\)

The perimeter of a rectangular field is

\(Perimeter = 2 * (Length + Width)\)

Substitute Length - 37 for Width

\(Perimeter = 2 * (Length + Length - 37)\)

\(Perimeter = 2 * (2Length - 37)\)

Open Bracket

\(Perimeter = 4Length - 74\)

Substitute 348 for Perimeter

\(348 = 4Length - 74\)

Solve for Length

\(4Length = 348 + 74\)

\(4Length = 422\)

Divide through by 4

\(Length = 422/4\)

\(Length = 105.5\)

Answer:

let n= the number

n÷5 +3=4

Step-by-step explanation:

The probability that either event will occur is 0.83

From the question, we have the following parameters that can be used in our computation:

Event A = 18

Event B = 12

Other Events = 6

Using the above as a guide, we have the following:

Total = A + B + C

So, we have

Total = 18 + 12 + 6

Evaluate

Total = 36

So, we have

P(A) = 18/36

P(B) = 12/36

For either events, we have

P(A or B) = 30/36 = 0.83

Hence, the probability that either event will occur is 0.83

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Answer:

y = 2x-2

Step-by-step explanation:

Generally, we have the equation of a straight line as;

y = mx + b

where m is the slope and b is the y-intercept

For the second equation, we can see that the y-intercept value is -2

So using the slope 2, we write the complete equation as;

y = 2x - 2

Answer:

1) 8x³ - x² + 1

2) 5a - 3b - 10c

3 17x²y - 7xy²

Step-by-step explanation:

Just combine like terms, since everything is adding, all you have to do is add everything with the same symbol. Make sure you watch for negatives so you know when to add or subtract you numbers!

Hope this helps!

The polygon ABCDE has been transformed by a translation of -2 units in the x-direction and 1 unit in the y-direction to obtain the image polygon.

To determine the transformation that occurred on polygon ABCDE, we can use the given coordinates of the original polygon and its transformed image. Let's consider the coordinates of points A and D:

Point A: (x₁, y₁)

Point D: (x₄, y₄)

Transformed point A': (-4, 2)

Transformed point D': (-2, 1)

The transformation involves a translation in both the x and y directions. We can calculate the translation distances for both coordinates by subtracting the original coordinates from the transformed coordinates:

Translation in x-direction: Δx = x' - x

Translation in y-direction: Δy = y' - y

For point A:

Δx = -4 - x₁

Δy = 2 - y₁

For point D:

Δx = -2 - x₄

Δy = 1 - y₄

Now, we can equate the translation distances for points A and D to find the transformation:

Δx = -4 - x₁ = -2 - x₄

Δy = 2 - y₁ = 1 - y₄

Simplifying these equations, we get:

-4 - x₁ = -2 - x₄

2 - y₁ = 1 - y₄

Rearranging the equations:

x₄ - x₁ = -2

y₁ - y₄ = 1

Therefore, the transformation involves a horizontal translation of -2 units (Δx = -2) and a vertical translation of 1 unit (Δy = 1).

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The equivalent expression of (q² − r²s) (q⁴ + q²r²s + r⁴s²) is  q⁶  - r⁶s³

The expression is given as:

(q² − r²s) (q⁴ + q²r²s + r⁴s²)

Expand the expression

(q² − r²s) (q⁴ + q²r²s + r⁴s²) =  q²(q⁴ + q²r²s + r⁴s²) − r²s(q⁴ + q²r²s + r⁴s²)

Open the brackets

(q² − r²s) (q⁴ + q²r²s + r⁴s²) =  q⁶ + q⁴r²s + q²r⁴s² -q⁴r²s - q²r⁴s² - r⁶s³

Evaluate the like terms

(q² − r²s) (q⁴ + q²r²s + r⁴s²) =  q⁶  - r⁶s³

Hence, the equivalent expression of (q² − r²s) (q⁴ + q²r²s + r⁴s²) is  q⁶  - r⁶s³

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Factor the expression. (q² − r²s) (q⁴ + q²r²s + r⁴s²)

Answer:

There are different axioms(theorems) to prove two tringles congruent.

Step-by-step explanation:

The axioms are:

SSS(side side side)

SAS(side angle side)

ASA(angle side angle)

AAS(angle angle side)

RHS(right angle hypotenuse side)