what is the equasion for this line

Therefore, it would take approximately 36 minutes for 14 workers to complete the job.

To solve this inverse variation problem, we'll use the formula: t = k/w, where t represents the time needed, w represents the number of workers, and k is the constant of variation.

We can find the value of k by plugging in the given values of 9 workers and 56 minutes into the formula:

56 = k/9

To find the value of k, we multiply both sides of the equation by 9:

k = 504

Now that we know the constant of variation, we can determine the time it would take for 14 workers to complete the job. Plugging in the values into the formula:

t = 504/14

t ≈ 36

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To factor the expression 4x^2 - 25, we can use the difference of squares formula, which states that a^2 - b^2 can be factored as (a + b)(a - b).

In this case, we have 4x^2 - 25, which can be written as (2x)^2 - 5^2. Comparing it with the difference of squares formula, we can identify that a = 2x and b = 5. Therefore, the correct option is:

b. (2x)^2 - (5)^2

Using the difference of squares formula, we can factor it as follows:

(2x + 5)(2x - 5)

Hence, the correct factorization of 4x^2 - 25 is (2x + 5)(2x - 5), which is equivalent to option b.

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The given passage provides a proof that the Separation Axioms follow from the Replacement Schema.

The proof involves introducing a set F and showing that {a: e X : O(x)} is equal to F (X) for every X. Therefore, the conclusion is that the Separation Axioms can be derived from the Replacement Schema.In the given passage, the author presents a proof that demonstrates a relationship between the Separation Axioms and the Replacement Schema.

The proof involves the introduction of a set F and establishes that the set {a: e X : O(x)} is equivalent to F (X) for any given set X. This implies that the conditions of the Separation Axioms can be satisfied by applying the Replacement Schema. Essentially, the author is showing that the Replacement Schema can be used to derive or prove the Separation Axioms. By providing this proof, the passage establishes a connection between these two concepts in set theory.

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Answer:

Step-by-step explanation:

g'(x) = 0.5*[(3x)^(-0.5)]*3 (By the power and chain rule)

And then just plug in 3, 0, and 2 into the given equation for g'(x)

Each child will get 1 orange, and there will be one orange left over.

If you have five oranges and you need to distribute them among four children, then you need to find out how many oranges each child will get.

To do this, you can divide the total number of oranges by the number of children.

Let's see how to do this: Divide the number of oranges by the number of children.5 ÷ 4 = 1.25This means that each child will get 1.25 oranges.

However, since you can't give a child a fraction of an orange, you will need to round this number to the nearest whole number.

If the decimal is less than 0.5, you round down; if it's 0.5 or greater, you round up.

In this case, 1.25 is closer to 1 than to 2, so you round down to 1.

Therefore, Each child will receive one orange, with one orange remaining.

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Answer:

[tex]\frac{g^{125}}{2h^{8}}[/tex]

Step-by-step explanation:

[tex]2g^{5^{3}} =2g^{125}[/tex]

[tex]4h^{2^3} = 4h^{8}[/tex]

[tex]\frac{2g^{125}}{4h^8} = \frac{g^{125}}{2h^8}[/tex]

Answer: x=2, y=4

Step-by-step explanation:

Since the lines are parallel, we can say that the larger triangle and the smaller triangle are similar. Thus. x+3/(2y-1) = (3/2x+2)/(3y-5). Also, note that there are hash lines, telling us that 2y-1 and 3y-5 are equal. Thus 2y-1=3y-5, and y=4. Plugging y=4 into the first equation yields: (x+3)/(7)=(3/2x+2)/(7), or x+3=3/2x+2. Then 1/2x=1, x=2.

Thus: x=2, and y=4

Answer:

x = 2

y = 4

Step-by-step explanation:

If a line parallel to one side of a triangle intersects the other two sides, then this line divides those two sides proportionally.

As the line bisects the side of the triangle with the y-variables, then the line is the midsegment of the triangle. This means that the line also bisects the side of the triangle with the x-variables.

Therefore, the two expressions with the x-variable are equal.

Similarly, the two expressions with the y-variable are equal.

Solving for x:

[tex]\boxed{\begin{aligned}\dfrac{3}{2}x+2&=x+3\\\\\dfrac{3}{2}x+2-x&=x+3-x\\\\\dfrac{1}{2}x+2&=3\\\\\dfrac{1}{2}x+2-2&=3-2\\\\\dfrac{1}{2}x&=1\\\\2 \cdot \dfrac{1}{2}x&=2 \cdot 1\\\\x&=2\end{aligned}}[/tex]

Solving for y:

[tex]\boxed{\begin{aligned}3y-5&=2y-1\\\\3y-5-2y&=2y-1-2y\\\\y-5&=-1\\\\y-5+5&=-1+5\\\\y&=4\end{aligned}}[/tex]

Work Shown:

y = 5x+8

0 = 5*8+8

0 = 40+8

0 = 48

The last equation is false, so the original equation is false when x = 8 and y = 0. This means the point (8,0) is NOT found on the line.

Visual confirmation is shown below.

The implicit derivative is given as follows:

dx/dt(x = 4)  = 1/12.

The function in this problem is given as follows:

y = 3x² + 1.

The implicit derivative, relative to the variable t, is given as follows:

dy/dt = 6x dx/dt.

(the derivative of the constant 1 is of zero).

The parameters for this problem are given as follows:

x = 4, dy/dt = 2.

Hence the derivative is obtained as follows:

2 = 6(4) dx/dt

dx/dt = 2/24

dx/dt = 1/12.

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Answer:

True

Step-by-step explanation:

The easiest way to understand this problem is to first breakdown the notation. In words, the problem is stating 9 is NOT an element of the set containing the elements 4, 1, 8, and 7. Since 4[tex]\neq[/tex]9, 1[tex]\neq[/tex]9, 8[tex]\neq[/tex]9, and 7[tex]\neq[/tex]9 then 9 is not an element of this set and the statement is true.

6a. The equation for the graph is y = 2√(x + 5).

6b. The equation for the graph is y = -|x + 1| + 5

In Mathematics and Geometry, the standard form of a square root function can be modeled as follows;

y = a√(x - h) + k

Part 6a.

Next, we would determine value of a as follows;

4 = a√(-1 + 5) + 0

4 = a√4

4 = 2a

a = 2

Therefore, the required square root function is given by;

y = 2√(x + 5)

Part 6b.

Since the line representing the absolute value function has a y-intercept at (0, 4) and vertex at (-1, 5), the absolute value equation for the graph is given by:

y = a|x - h| + k

y = -|x + 1| + 5

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The amount of inches that the plant grows in 14 days is given as follows:

420 inches.

The proportional relationship that models the situation is given as follows:

i = 30d.

This means that the plant grows by 30 inches every day.

After 14 days, we have that d = 14, hence the size of the plant after 14 days is given as follows:

i = 30 x 14

i = 420 inches.

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Answer:

x = 2

Step-by-step explanation:

P = [tex]\frac{x-2}{x+1}[/tex]

P will equal zero when the numerator is equal to zero , that is

x - 2 = 0 ( add 2 to both sides )

x = 2

P = 0 when x = 2

Answer: 2.8

Step-by-step explanation:

2x^2+6=10

2x^2=10-6

x^2=16 divided by 2

x= square root of 8

x=2.8

Answer:

1/216

Step-by-step explanation:

6×6×6=216

negative exponents meaning reciprocal

so 216/1 means 1/216

The vertex (25, 2400) of the parabola reveals the optimal ticket price (25 dollars) that maximizes the profit (2400 dollars) for the theater during the comedy show.

To find the vertex of the parabola, we can use the formula:

x = -b / (2a)

In this case, the function is p(d) = -4d² + 200d - 100, which can be rewritten in the form of ax² + bx + c.

Comparing it with the standard form ax² + bx + c, we can see that a = -4, b = 200, and c = -100.

Now, let's substitute these values into the formula to find the vertex:

d = -200 / (2 * -4)

d = -200 / -8

d = 25

The x-coordinate of the vertex is 25. To find the corresponding y-coordinate, we substitute this value back into the original function:

p(25) = -4(25)² + 200(25) - 100

p(25) = -4(625) + 5000 - 100

p(25) = -2500 + 5000 - 100

p(25) = 2400

The y-coordinate of the vertex is 2400.

Therefore, the vertex of the parabola is (25, 2400).

The vertex reveals important information about the situation. In this case, it represents the optimal point for maximizing profit. The x-coordinate (25) represents the price at which the theater should set the tickets to maximize their profit. The y-coordinate (2400) represents the maximum profit achievable at that price.

Additionally, since the coefficient of the quadratic term (a) is negative (-4), it indicates that the parabola opens downwards, forming a concave shape. This means that as the ticket price increases or decreases from the optimal price, the profit will decrease. Therefore, setting the tickets at a price other than the one corresponding to the vertex would result in a lower profit for the theater.

In summary, the vertex (25, 2400) of the parabola reveals the optimal ticket price (25 dollars) that maximizes the profit (2400 dollars) for the theater during the comedy show.

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The equation of the linear relationship in slope-intercept form is y = 2x - 8. Option A is the correct answer.

To determine the equation of the linear relationship in slope-intercept form based on the table, we need to find the slope and y-intercept.

By observing the table, we can calculate the slope by selecting any two points. Let's choose the points (0, -8) and (4, 0).

Slope (m) = (change in y) / (change in x)

= (0 - (-8)) / (4 - 0)

= 8 / 4

= 2

Now that we have the slope, we can find the y-intercept by substituting the values of one point and the slope into the equation y = mx + b and solving for b.

Using the point (0, -8):

-8 = 2(0) + b

b = -8

Therefore, the equation of the linear relationship in slope-intercept form is: y = 2x - 8. Option A is the correct answer.

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To determine how the mean changes when a value of 98° is added to the data, we need to calculate the mean before and after the addition.

Before adding 98°, the given data set has 12 values. We can calculate the mean by summing all the values and dividing by the total number of values:

Mean = (58 + 61 + 71 + 77 + 91 + 100 + 105 + 102 + 95 + 82 + 66 + 57) / 12

Mean ≈ 83.67°

After adding 98° to the data set, the total number of values becomes 13. To calculate the new mean, we sum all the values, including the added 98°, and divide by the total number of values:

New Mean = (58 + 61 + 71 + 77 + 91 + 100 + 105 + 102 + 95 + 82 + 66 + 57 + 98) / 13

New Mean ≈ 86.15°

Therefore, the mean increases by approximately 2.48° when a value of 98° is added to the data. None of the provided answer choices accurately reflects this change, as they all mention different values (8.2° and 1.4°) that do not correspond to the actual change in the mean.

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The domain cannot be (–∞, ∞) as it includes values that are not valid inputs for the inverse cosine function.

The domain of the inverse cosine function, y = cos^(-1)(x) or y = arccos(x), is the set of values for which the function is defined.

In this case, the range of the cosine function, which is the set of values that x can take, is [-1, 1]. Therefore, the domain of the inverse cosine function is the range of the cosine function.

Hence, the correct answer is [–1, 1]. This is because the inverse cosine function is only defined for values of x that fall within the range of the cosine function, which is from -1 to 1.

To clarify further, the inverse cosine function is defined as the inverse of the restricted cosine function. The restricted cosine function is defined on the interval [0, π], which means that its range is [–1, 1]. The inverse cosine function "undoes" the cosine function and maps values from [-1, 1] back to the corresponding input values in [0, π]. Therefore, the domain of the inverse cosine function is [-1, 1].

The options [0, π] and (–∞, ∞) are not correct because they do not correspond to the domain of the inverse cosine function. The range of the inverse cosine function is [0, π], and the inverse cosine function is not defined for values outside the range of the cosine function. Therefore, the domain cannot be (–∞, ∞) as it includes values that are not valid inputs for the inverse cosine function.

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The two considered triangles JKL and MNP are similar by the AA rule of similarity as the two angles that is ∠K = ∠N and ∠L = ∠P are there.

Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion. We denote the similarity of triangles here by ‘~’ symbol.

It is given that two triangles that are JKL and MNP are considered in which:

Now, from ΔJKL and ΔMNP, we have

∠K = ∠N (Given in the question)

∠L = ∠P(Given in the question)

Thus, by AA rule of similarity,

ΔJKL is similar to ΔMNP.

Therefore, the two considered triangles JKL and MNP are similar by the AA rule of similarity as the two angles that is ∠K = ∠N and ∠L = ∠P are there.

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To solve the savings plan balance, we have to calculate the interest for 19 months. The formula for calculating interest for compound interest is given below:$$A = P \left(1 + \frac{r}{n} \right)^{nt}$$where A is the amount, P is the principal, r is the rate of interest, t is the time period and n is the number of times interest compounded in a year.

The given interest rate is 11% per annum, which will be converted into monthly rate and then used in the above formula. Therefore, the monthly rate is $r = \frac{11\%}{12} = 0.0091667$.

The monthly payment is $PMT = $250. We need to find out the amount after 19 months. Therefore, we will use the formula of annuity.

$$A = PMT \frac{(1+r)^t - 1}{r}$$where t is the number of months of the plan and PMT is the monthly payment. Putting all the values in the above equation, we get:

$$A = 250 \times \frac{(1 + 0.0091667)^{19} - 1}{0.0091667}$$$$\Rightarrow

A = 250 \times \frac{1.0091667^{19} - 1}{0.0091667}$$$$\Rightarrow

A =250 \times 14.398$$$$\Rightarrow A = 3599.99$$

Therefore, the savings plan balance after 19 months with an APR of 11% and monthly payments of $250 is $3599.99 (approx).

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The interval to the solution is (a) the interval from -7 to 6

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

log(x + 9) + log(x - 9) = 0.47712

Apply the rule of logarithm

So, we have

log(x² - 9) = 0.47712

Take the exponent of both sides

x² - 9 = [tex]10^{0.47712[/tex]

So, we have

x² = 9 + [tex]10^{0.47712[/tex]

Evaluate

x² ≈ 12

Take the square root of both sides

x ≈ ±3.46

This value is between the interval -7 to 6

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Isabella's possible numbers can be represented by the compound inequality 15 ≤ 5n - 5 ≤ 50, which in interval notation is [4, 11].

Based on the given information, we can set up a compound inequality to represent the range of numbers that Isabella might be thinking of.

Let's denote the number Isabella is thinking of as 'n'.

The clue states that "5 less than 5 times his number is at least 15 and at most 50."

We can express this as:

15 ≤ 5n - 5 ≤ 50

To solve this compound inequality, we add 5 to all three parts of the inequality:

15 + 5 ≤ 5n - 5 + 5 ≤ 50 + 5

20 ≤ 5n ≤ 55

Finally, dividing all parts of the inequality by 5:

20/5 ≤ n ≤ 55/5

4 ≤ n ≤ 11

Therefore, Isabella's number, 'n', lies in the range [4, 11] in interval notation. In summary, the compound inequality 15 ≤ 5n - 5 ≤ 50 represents the range of numbers that Isabella might be thinking of. The interval notation [4, 11] indicates that her number could be any value between 4 and 11, inclusive.

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The estimated mean salary in the neighborhood at a 90% confidence level based on the given sample is {1798.94, 1801.06}.

Given data:

Since we know the sample variance (s²), the standard deviation is:

s = √(s²)

s = √(10)

s = 3.16 pesos

Confidence Interval = Sample Mean ± (Critical Value * Standard Error)

The critical value is obtained from the t-distribution table based on the desired confidence level and degrees of freedom (n-1). For a 90% confidence level and 25 degrees of freedom, the critical value is 1.708.

SE = s / √n

SE = 3.16 / √26

SE = 0.618 pesos

Confidence Interval = 1800 ± (1.708 * 0.618)

= 1800 ± 1.055544

= {1798.94, 1801.06}.

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The number of subsets in the given set is as follows:

16.

Considering a set with n elements, the number of subsets in the set is the nth power of 2, that is:

[tex]2^n[/tex]

The set in this problem is composed by integers between 2 and 5, hence it has these following elements:

{2, 3, 4, 5}.

The set has four elements, meaning that n = 4, hence the number of subsets is given as follows:

[tex]2^4 = 16[/tex]

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Answer:

(x+3)^2 + (y+1)^2 = 16

Step-by-step explanation:

The equation of a circle is (x – h)^2 + (y – k)^2 = r^2, where h is the x value of the center, k is the y value of the center, and r is the radius.

We can see from the picture that the radius is at about (-3, -1) and the radius is about 4, so we can plug those in:
(x – (-3))^2 + (y – (-1))^2 = 4^2

Simplify:
(x+3)^2 + (y+1)^2 = 16

Answer:

Equation of circle:[tex](x + 3)^2 + (y + 1)^2 = 16[/tex]

Step-by-step explanation:

Given:

Center of the circle = (-3, -1)

Point on the circle = (1, -1)

In order to find the radius of the circle, we can use the distance formula.

distance =[tex] \boxed{\bold{\sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}}}[/tex]

where:

In this case, the distance formula becomes:

radius = [tex]\sqrt{(-3 - 1)^2 + ((-1) - (-1))^2}= \sqrt{16}=4[/tex]

Therefore, the radius of the circle is 4 units.

Now that we know the radius of the circle, we can find the equation of the circle using the following formula:

[tex]\boxed{\bold{(x - h)^2 + (y - k)^2 = r^2}}[/tex]

where:

In this case, the equation of the circle becomes:

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

=[tex](x + 3)^2 + (y + 1)^2 = 16[/tex]

This is the equation of the circle.

Answer:

Yes, the triangle are similar.

Step-by-step explanation:

To prove that 2 triangle are similar you only need to prove that 2 corresponding angles are equal.

The sum of the interior angles add to 180.

< m on the left measures 30 degrees.

80 - 90 - 60 = 30

> t on the right measures 60 degrees.

180 - 90 - 30 = 60

If two corresponding angles of two triangles are equal that forces the third pair to be congruent, since the total of the angles must add up to 180.

Although we are not given the corresponding sides, there are proportional because the angles are equal.

Helping in the name of Jesus.

Answer:

Similar triangles are triangles that have the same shape but different sizes. In other words, if two triangles are similar, then their corresponding angles are congruent and their corresponding sides are in equal proportion.

For Question:

In Δ MSK and ΔQRT

∡S=∡R right angle

∡K=∡T=180°-90°-30°=60° Given

∡M=∡Q=180°-90°-60°=30° Given

Therefore,

Δ MSK  [tex]\bold{\sim}[/tex]  ΔQRT

By AA similarity.

Hence Proved:

Therefore, the slope-intercept equation of the line passing through the points (2,3) and (6,11) is y = 2x - 1.

To find the slope-intercept equation of the line passing through the points (2,3) and (6,11), we can use the formula for slope:

slope (m) = (change in y) / (change in x)

First, calculate the change in y and change in x using the given points:

change in y = 11 - 3 = 8

change in x = 6 - 2 = 4

Now, substitute the values into the slope formula:

slope (m) = 8 / 4 = 2

Next, we can use the point-slope form of the linear equation:

y - y1 = m(x - x1)

Choose one of the given points, let's use (2,3), and substitute the values into the equation:

y - 3 = 2(x - 2)

Simplifying the equation:

y - 3 = 2x - 4

Rearranging the equation to the slope-intercept form (y = mx + b):

y = 2x - 1

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Answer: $227,226.51

Step-by-step explanation:

First, we need to convert the period to weeks.

9 1/2 years = 9.5 years

1 year = 52 weeks

9.5 years = 494 weeks

Next, we can use the formula for the future value of an annuity:

FV = (PMT x (((1 + r/n)^(n*t)) - 1)) / (r/n)

where:

PMT = payment amount per period

r = annual interest rate

n = number of compounding periods per year

t = number of years

Plugging in the given values:

PMT = $300

r = 0.055 (5.5% expressed as a decimal)

n = 52 (compounded weekly)

t = 9.5 years = 494 weeks

FV = ($300 x (((1 + 0.055/52)^(52*494)) - 1)) / (0.055/52)

FV = $227,226.51

Therefore, the future value of the annuity is approximately $227,226.51.

Answer:

x < –18 or x > 10

Step-by-step explanation:

|x + 4| – 2 > 12

x + 4 - 2 > 12

x + 2 > 12

x > 10

-x - 4 - 2 > 12

-x - 6 > 12

-x > 18

x < 18

So, the answer is x < –18 or x > 10

Answer: D:  x < –18 or x > 10

Step-by-step explanation: