Find the slope of the line going through the points (-4, 2) and
(3,5).

Answer:

560

Step-by-step explanation:

Given:

A line passes through (-2,-6) and has a slope of \(\dfrac{1}{3}\).

To find:

The point slope form of the given line.

Solution:

If a line passes through a point \((x_1,y_1)\) with slope m, then the slope intercept form of the line is

\(y-y_1=m(x-x_1)\)

The line passes through (-2,-6) and has a slope of \(\dfrac{1}{3}\). So, the point slope form of the line is

\(y-(-6)=\dfrac{1}{3}(x-(-2))\)

\(y+6=\dfrac{1}{3}(x+2)\)

Therefore, the correct option is A.

Answer:

The answer is B, Domain: −2≤x≤2 Range: −2≤y≤3

Step-by-step explanation

Answer  

1,863.5

Step-by-step explanation: add 165.85 +20.50 =186.35 the do 186.35 x 10 =1,863.5

The limit of |a_(n+1)/a_n| is 7.

To apply the ratio test to the series ∑ \((n!)/(7n^3)\), we need to evaluate the limit: lim(n→∞) |a_(n+1)/a_n| = lim(n→∞) \([(n+1)!/(7(n+1)^3)] * [(7n^3)/(n!)]\)

= lim(n→∞)\([(n+1)/(7(n+1))^3] * [7n^3/n]\)

= lim(n→∞) \([(n+1)/7(n+1)^3] * [7n^3/n]\)

= lim(n→∞)\((n+1)/(7(n+1))^3 * 7n^3/n\)

= lim(n→∞) \((n+1)/(7n+7)^3 * 7n^3/n\)

Next, we simplify the expression:

= lim(n→∞)\([(n+1)/(7n+7)]^3 * 7n^2/n\)

= lim(n→∞)\((n+1)^3/(7n+7)^3 * 7n^2/n\)

As n approaches infinity, the terms with n in the numerator and denominator dominate, and we can neglect the constant terms:

= lim(n→∞) (n/n)² * 7 = 7

According to the ratio test, if the limit is less than 1, the series converges. If the limit is greater than 1, the series diverges. If the limit is exactly 1, the test is inconclusive.

Since the limit in this case is 7, which is greater than 1, the ratio test tells us that the series ∑ \((n!)/(7n^3)\) diverges.

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Step-by-step explanation:

\( {3}^{2} + {3}^{2} = 2 \times {3}^{2} = 18 \\ \sqrt{18} = 4.24 \: km\)

Answer:

\(1.345 * 10^{10\)

Step-by-step explanation:

= 13450000000

Putting the decimal point after first non-zero digit

=> \(1.345 * 10^{10\)

Answer:

1.345 × 10^10

Step-by-step explanation:

Put the decimal point after 1.

1.345

Multiply by a number that makes the decimal to 13450000000.

That number is 10^10.

We will solve as follows:

*First: We determine the minimum number of triangles that should go in a row [Taking into account that there will be 1 empty triangular space of identical measurements but rotated 180°], that is:

*We determine the minimum number of triangles of the base dividing the length of the base of the rectangle by the length of the base of the triangle:

So, from this we will have that we would need 15 triangles for the base.

*We determine the number of triangles for the heigth of the rectangle:

*Now, we determine the total number of triangles we would need:

So we would need 1080 triangles to create the whole rectangular shape.

a) The equation:

Here "t" represents the number of triangles needed on the horizontal line and in the vertical line, but not taking into account the empty spaces due to them being triangles.

b)The area of the triangle:

The area of the rectangle:

c)The variable for the unkown quantity is "t".

d)We solve the equation.

Answer:

a and d are parallel

Step-by-step explanation:

The conclusions that can be made about the two distributions are:

Options A and D are correct.

The means-to-MAD ratio is found by dividing the mean of a dataset by its Mean Absolute Deviation (MAD).

We have that in Data Set 1, the means-to-MAD ratio is 54/4 = 13.5, and in Data Set 2, the means-to-MAD ratio is 60/2 = 30.

Since the means-to-MAD ratio in Data Set 1 is 13.5 and in Data Set 2 is 30, we can conclude that the two distributions are not similar.

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By the radius-tangent theorem, the radius is equal to 39/10 units.

In Euclidean geometry, Pythagorean's theorem is given by this mathematical expression:

a² + b² = c²

Where:

a, b, and c represents the side lengths of a right-angled triangle.

Since CB is tangent to OA at point C and line segment CB is perpendicular to line segment AC by the radius-tangent theorem, we would determine the radius by applying Pythagorean's theorem as follows;

r^2 + 8^2 = (r + 5)^2

r^2 + 64 = r^2 + 10r + 25

r^2 - r^2 = -10r + 64 - 25

10r = 39

r = 39/10 units.

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Answer:

\(8)79 + .3y |1| 5131x - 2884 \frac{ {8 - { { - 44 - {516}^{ |?| } }^{?} }^{?} }^{2} }{?} 5 - {1 {y {1 {40091 - \times \frac{?}{?} }^{?} }^{2} }^{2} }^{2} 444 = .3 = 547 - 274\)

Any non-empty subset of Rⁿ, where any linear combination of vectors in S is again a vector in S, is a subspace of Rⁿ.

Given that S is a non-empty subset of Rⁿ such that any linear combination of vectors in S is again a vector in S. Therefore, to prove that S is a subspace of Rⁿ, we have to show that S satisfies three conditions. These conditions are as follows;

The condition for being a subspace of Rⁿ

Firstly, a subspace must be closed under addition. In other words, if x and y are any two vectors in S, then their sum x + y must be in S.

Secondly, a subspace must be closed under scalar multiplication. In other words, if x is any vector in S and c is any scalar, then cx must be in S.

Finally, a subspace must contain the zero vector, denoted by 0.S is a subspace of Rⁿ

From the conditions mentioned above, we can show that S is indeed a subspace of Rⁿ, since S satisfies all the required conditions.

Therefore, we can say that any non-empty subset of Rⁿ, where any linear combination of vectors in S is again a vector in S, is a subspace of Rⁿ.

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Answer:

d=6 & p=13

Step-by-step explanation:

1. P+d=19

×9

2. 9p +5.50d=150

×1

9p+9d=171

-

9p +5.50d=150

3.5d=21

d=6

Substituting d=6 in 1.

P+6=19

P=13

Answer:

there is no picture

Step-by-step explanation:

in this demonstration you need visual aid

The slopes are negative for all points in the xy-plane where y is less than 2.

I am not able to create a visual representation of a slope field on this platform. However, I can describe how to interpret a slope field and provide an answer to the second part of the question.

For the given differential equation dy/dx = x^4(y-2), we can draw a slope field by plotting short line segments with slopes equal to the value of the right-hand side of the equation at each point.

To determine the points in the xy-plane for which the slopes are negative, we need to look for regions where the right-hand side of the differential equation is negative.

Since x^4 is always nonnegative, the sign of the right-hand side of the equation is determined by the term (y-2).

Therefore, the slopes are negative for all points in the xy-plane where y is less than 2. In other words, the solutions of the differential equation are decreasing below the line y = 2, and increasing above it.

This makes sense because when y is less than 2, the right-hand side of the equation is negative, indicating that the solutions are decreasing. Conversely, when y is greater than 2, the right-hand side of the equation is positive, indicating that the solutions are increasing.

Therefore, the answer to the question is that the slopes are negative for all points in the xy-plane where y is less than 2.

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The equations could be made the same by dividing both sides of Equation A by-3 gives x + 7 = -8.

The term equation has to do with a mathematical relationship that involves the equality sign. Let us now look at the equations that have been put forth and see how they can be made to be equivalent;

• Equation A: -3 (x + 7) = 24

• Equation B: x + 7 = -8

If we want to convert equation A into B, what we need to do is simply to divide the both sides of equation A with -3.

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Missing parts;

Mai says x is a number that makes Equation A true and also a number that makes Equation B true.

• Equation A: -3 (x + 7) = 24

• Equation B: x + 7 = -8

Which statement explains why this is true?

O A) Adding 3 to both sides of Equation A gives x + 7 = -8.

O B) Applying the distributive property to Equation A gives x + 7 = -8.

© C) Subtracting 3 from both sides of Equation A gives x + 7 = -8.

OD) Dividing both sides of Equation A by-3 gives x + 7 = -8.

When interpreting the expression as \((tanx)^{(sinx)\), the limit using L'Hospital's Rule is -∞ as x approaches 0+. However, when interpreting the expression as\(tan(x^{sinx})\), the limit is not well-defined due to the indeterminate form of 0^0.

To calculate the limit using L'Hospital's Rule, let's consider both interpretations of the expression and find the limits for each case:

Case 1: lim\((tanx)^{(sinx)\) as x approaches 0+

Taking the natural logarithm of the expression, we have:

\(ln[(tanx)^{(sinx)}] = sinx * ln(tanx)\)

Now, we can rewrite the expression as:

\(lim [sinx * ln(tanx)]\)as x approaches 0+

Applying L'Hospital's Rule, we differentiate the numerator and denominator:

\(lim [(cosx * ln(tanx)) + (sinx * sec^{2}(x))] / (1 / tanx)\) as x approaches 0+

Simplifying the expression:

\(lim [cosx * ln(tanx) + sinx * sec^{2}(x)] * tanx\) as x approaches 0+

\(lim [cosx * ln(tanx) + sinx * sec^{2}(x)] * (sinx / cosx)\) as x approaches 0+

\(lim [(cosx * ln(tanx) + sinx * sec^{2}(x)) / cosx] * sinx\) as x approaches 0+

\(lim [ln(tanx) + (sinx / cosx) * sec^{2}(x)] * sinx\) as x approaches 0+

\(lim [ln(tanx) + tanx * sec^{2}(x)] * sinx\) as x approaches 0+

Since lim ln(tanx) as x approaches 0+ = -∞ and\(lim (tanx * sec^{2}(x))\) as x approaches 0+ = 0, we have:

\(lim [ln(tanx) + tanx * sec^{2}(x)] * sinx\) as x approaches 0+ = -∞

Therefore, the limit of \((tanx)^{(sinx)\) as x approaches 0+ using L'Hospital's Rule is -∞.

Case 2: lim\(tan(x^{sinx})\)as x approaches 0+

We can rewrite the expression as:

lim\(tan(x^{(sinx)})\) as x approaches 0+

This expression does not have an indeterminate form of \(0^0\), so we do not need to use L'Hospital's Rule. Instead, we can substitute x = 0 directly into the expression:

lim \(tan(0^{(sin0)})\) as x approaches 0+

lim\(tan(0^0)\)as x approaches 0+

The value of \(0^0\) is considered an indeterminate form, so we cannot determine its value directly. The limit in this case is not well-defined.

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Answer:

\(-6x^5+8x^4-14x^3\)

Step-by-step explanation:

\(-2x^3(3x^2-4x+7)\)   Use distributive property

\(-2x^3\) · \(3x^2\) = \(-6x^5\)      

\(-2x^3\) · \(-4x\) = \(8x^4\)       Product becomes positive because of two negatives

\(-2x^3\) · \(7\) = \(-14x^3\)

Group all of those numbers together (in order)

\(-6x^5+8x^4-14x^3\)

Suppose that the correlation between educational level attained and yearly income is +0.68. This indicates that there is a positive and strong relationship between educational level and yearly income.

It means that as the level of education attained increases, the yearly income also tends to increase. However, it is important to note that correlation does not imply causation, and there could be other factors that contribute to the relationship between education and income.

Based on the provided correlation coefficient of +0.68 between educational level attained and yearly income, we know that there is a positive and moderately strong relationship between the two variables. As a person's education level increases, their yearly income is also likely to increase.

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After expansion the expression is,

⇒ 65x/4 + 39/16

We have to given that;

Expression is,

⇒ 13/4 (5x + 3/4)

Now, We can simplify the expression by expansion,

⇒ 13/4 (5x + 3/4)

⇒ 5x × 13/4 + 13/4 × 3/4

⇒ 65x/4 + 39/16

Thus, After expansion the expression is,

⇒ 65x/4 + 39/16

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Based on the calculation below, Bristol's next minimum monthly payment is $167.99.

This can be calculated as follows:

Monthly interest rate = APR / 12 = 29.99% / 12 = 0.2999 / 12 = 0.0249916666666667

Balance at the end of the current month = Current balance + Purchases - Current minimum monthly payment = $4,919.21 + $360.00 - $157.41 = $5,121.80

Bristol's next minimum monthly payment = (Balance at the end of the current month + (Balance at the end of the current month * Monthly interest rate)) * Minimum monthly payment rate

Bristol's next minimum monthly payment = ($5,121.80 + ($5,121.80 * 0.0249916666666667)) * 3.2%

Bristol's next minimum monthly payment = $167.99

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Answer: the answer is: A student needs to take 10 dance classes to learn the routine.

Step-by-step explanation: 7 1/2 DIVIDED by 3/4=10

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If 09 people can complete the job in 75 days then 25 people needs 45 days to complete the job.

Let T be the time and L be the Labor (Number of people working on the bridge).

T ∞ 1/√L  (Inverse relationship)

T = K/√L                   ----------------------------- (1)

Since, Constant "K" is introduced once the variation sign (∞) changes to equality (=) sign.

According to the question,

Time (T) = 75 days    and

labor (L) = 09

From the equation (1), we get,

    T = K / √L

⇒ 75   = K/√9

⇒ 75= K/3

⇒ K= 225

First, the relationship between these variables is:

                       T = 225/√L

Therefore, how long it will take 25 people to do it means that we should look for the time.

                           T=225/√L

                      ⇒  T= 225/√25

                      ⇒  T= 225/5

                      ⇒  T= 45 days.

therefore, 25 people needs 45 days to complete the job.

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Answer:

neither they are both equal

Step-by-step explanation:

Answer: there equal/ the same.

Step-by-step explanation:

Answer:

70 degrees

Step-by-step explanation:

(360 - 90 - 130)/2=70

Answer:

16x-2

Step-by-step explanation:

Perimeter is 2w+2l

so we plug it in

2(3x+1) + 2(5x-2)

now we distribute

6x+2 + 10x -4

now we add like terms

6x+10x+2-4

16x-2

(a) The expression (p ∨¬q)∧(¬p∨q)∧(¬p∨¬q) is satisfiable, and one satisfying assignment is when p is true and q is false.

(b) The expression (p → q)∧(p → ¬q)∧(¬p → q)∧(¬p →¬q) is not satisfiable because it leads to a contradiction, specifically a logical inconsistency.

(a) The expression (p ∨¬q)∧(¬p∨q)∧(¬p∨¬q) can be satisfied by assigning truth values to the propositions p and q.

In this case, if we assign p as true and q as false, the expression evaluates to true.

This means that the expression is satisfiable.

(b) The expression (p → q)∧(p → ¬q)∧(¬p → q)∧(¬p →¬q) can be examined to determine its satisfiability.

By analyzing the implications in the expression, we find that if p is true, then q must be both true and false, leading to a contradiction.

Similarly, if p is false, then q must be both true and false, which is again a contradiction.

Therefore, it is impossible to find a satisfying assignment for this expression, making it unsatisfiable.

In summary, the expression (p ∨¬q)∧(¬p∨q)∧(¬p∨¬q) is satisfiable with the satisfying assignment p = true and q = false.

On the other hand, the expression (p → q)∧(p → ¬q)∧(¬p → q)∧(¬p →¬q) is not satisfiable due to logical inconsistencies.

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