Janet is comparing the functions h(x) and g(x), the graph shows that the function g(x) is defined as -x^2-2x+6, Which statement is correct?

A) h(x) has a larger maximum value than g(x), and h(x) has a larger value
at x=3.
B) h(x) has a larger maximum value than g(x), and h(x) has a smaller value
at x=3.
C) h(x) has a smaller maximum value than g(x), and h(x) has a smaller value
at x=3.
D) h(x) has a smaller maximum value than g(x), and h(x) has a larger value
at x=3.

1) How many functions is the question referring to?
2) Do you know the functions? Do you have a way to visually compare the functions?
3) What is the question asking?
4) In the answer choices what are they talking about?
5) Identify the maximum of h(x) and g(x).
6) Identify the value of x=3 of h(x) and g(x).
7) which answer choice would be best based on your findings?

Answer:

0

Step-by-step explanation:

If x ≥ 4, then the equation simplifies to x+4 = x-4, which gives 8=0, which is not true. Therefore, there are no solutions in this case.

If x < -4, then the equation becomes -(x+4) = -(x-4), which simplifies to -x-4 = -x+4. Simplifying further gives -8 = 0, which is not true. Therefore, there are no solutions in this case either.

If -4 ≤ x < 4, then the equation becomes x+4 = -(x-4), which simplifies to 2x = 0. Therefore, x = 0 is a solution.

If we plug x = 0 back into the original equation, we can see that it works:

|0+4| = |0-4|,

which simplifies to 4 = 4.

Therefore, the solution to the equation |x+4|=|x-4| is x = 0.

Answer:

x = 0

Step-by-step explanation:

Because |-4| = |4| = 4, then the only way x+4 can be -4 is if x=0, and the only way x-4 can be -4 is if x=0 as well. x can't be 4 for instance because then we have |8|≠|0|.

Answer:

  (d)  none of the lines fit the data

Step-by-step explanation:

You want to know if any of the lines shown on the graph represents a good fit to the data.

The line of best fit for the data shown would be one that passes through the points (0, 5.3) and (9, 0.4). It would lie somewhat below line A and somewhat above line B.

None of the lines shown fit the data.

__

Additional comment

Line A seems to ignore the data that is fit by Line B, and vice versa. A line of best fit will minimize the measure of distance to all the data points, not just some of them.

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The diameter of the circle is 24 units.

To find the diameter of the circle, we can use the formula that relates the length of an arc to the circumference of a circle.

The formula is:

Length of arc = (Measure of arc/360) × Circumference

Given that the length of arc AB is 14π and the measure of arc AB is 210 degrees, we can plug these values into the formula:

14π = (210/360) × Circumference

To solve for the circumference, we multiply both sides of the equation by (360/210):

14π × (360/210) = Circumference

Simplifying the right side of the equation:

Circumference = 24π

The circumference of a circle is equal to π times the diameter. Therefore,

we can write:

24π = π × diameter

To solve for the diameter, we divide both sides of the equation by π:

diameter = 24

Hence, the diameter of the circle is 24 units.

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Answer:

sandwich = $4. bottle = $2

Step-by-step explanation:

let's A = sandwich, B = bottle

elimination method:

10A + 6B = 52   (call this equation '1.' or just call it '1')

A + 3B = 10     (call this '2')

'2' X 2:   2A + 6B = 20     (call this '3')

'1' - '3':

8A + 0B = 32

A = 32/8 = 4

Sandwich costs $4.

go back to '2.'

3B = 10 - A = 10 - 4 = 6.

B = 6/3 = 2.

bottled water costs $2.

substitution method:

6B = 52 - 10A

3B = 26 - 5A.

'2.'

A + 3B = 10

A + (26 - 5A) = 10

-4A = -16

A = 4.

A + 3B = 10

3B = 10 - 4 = 6

B = 6/3 = 2.

There is no specific minimum amount he needs to earn on the last day to meet the goal because it has already been achieved.

We have,

To find the minimum amount Gil must earn on the last day of the week to meet his weekly goal,

We need to calculate the total earnings for the first 6 days and subtract it from the target weekly goal of $500.

Given the daily earnings for the first 6 days:

425, 515, 475, 620, 525, 415

We can calculate the total earnings:

Total earnings = 425 + 515 + 475 + 620 + 525 + 415 = 2975

Now, we subtract the total earnings from the weekly goal:

Minimum amount needed on the last day.

= 500 - 2975

= -2475

Since the calculated value is negative (-2475), it implies that Gil has already exceeded his weekly goal based on the earnings from the first 6 days.

Therefore,

There is no specific minimum amount he needs to earn on the last day to meet the goal because it has already been achieved.

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The surface area of the cylinder B is 2.5 cm square.

The surface area of the cylinder can be found as follows:

Cylinder A and cylinder B are similar. Let's find the surface area of cylinder B.

The radius of cylinder A is 4 cm and the volume of cylinder A is 24π,. Therefore,

volume of cylinder A = πr²h

24π = π2²h

24π = 4πh

4h = 24

h = 24 / 4

h = 6 cm

surface area of the cylinder A = 2πr(r + h) = 3π(1.5 + 6) = 22.5π cm²

Therefore, let's find the surface area of the cylinder B as follows:

(2 / 6) ² = x / 22.5π

4 / 36 = x / 22.5π

cross multiply

36x = 90π

x = 90π / 36

x = 10π / 4

surface area of cylinder B = 5 / 2 π = 2.5π cm²

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The area of the park is 12 square units.

To find the area of the park, we can use the Shoelace Formula (also known as Gauss's area formula). This formula allows us to calculate the area of any polygon given the coordinates of its vertices.

The Shoelace Formula states that if we have the coordinates of the vertices of a polygon in counterclockwise order (x₁, y₁), (x₂, y₂), ..., (xn, yn), then the area (A) of the polygon is given by:

A = 1/2 × |(x₁y₂ + x₂y₃ + ... + xn-1yn + xny₁) - (y₁x₂ + y₂x₃ + ... + yn-1xn + ynx₁)|

In our case, the coordinates of the park's vertices are (-9, -9), (-3, -9), and (-6, -5). Let's calculate the area using the Shoelace Formula:

A = 1/2 × |(-9 × -9 + -3 × -5 + -6 * -9) - (-9 × -3 + -9 × -6 + -5 × -9)|

Simplifying further:

A = 1/2 × |(81 + 15 + 54) - (27 + 54 + 45)|

A = 1/2 × |150 - 126|

A = 1/2 × |24|

A = 12

Therefore, the area of the park is 12 square units.

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Answer:

---------------------

Plot the given vertices and connect.

See attached.

Then add the height CD.

The base is AB, with the length:

The height is CD, with length:

Find the area using equation:

The midpoint of three points with the position vector 1/3(a + b + c) is given by:

P = (b + c - B - C) / 2 + (1/3)(b + c)

The point with the position vector 1/3(a + b + c) is given by:

P = F - (2/3)D - (1/3)E + (1/3)(b + c)

To find the point with the position vector 1/3(a+b+c), we can use the fact that the position vector of a point that divides a line segment in a given ratio can be found by taking the weighted average of the position vectors of the endpoints.

Given that D, E, and F are the midpoints of line segments BC, AC, and AB, respectively, we know that:

D = (B + C) / 2

E = (A + C) / 2

F = (A + B) / 2

To find the point with the position vector 1/3(a+b+c), we can substitute a = 3F - 2D - E into the equation:

1/3(a + b + c) = 1/3((3F - 2D - E) + b + c)

Expanding the equation further:

1/3(a + b + c) = 1/3(3F - 2D - E + b + c)

= (F - (2/3)D - (1/3)E) + (1/3)(b + c)

Therefore, the point with the position vector 1/3(a + b + c) is given by:

P = F - (2/3)D - (1/3)E + (1/3)(b + c)

Substituting the midpoints:

P = (A + B) / 2 - (2/3)((B + C) / 2) - (1/3)((A + C) / 2) + (1/3)(b + c)

= (A + B - 2B - 2C - A - C + b + c) / 2 + (1/3)(b + c)

= (b + c - B - C) / 2 + (1/3)(b + c)

Therefore, the midpoint of three points with the position vector 1/3(a + b + c) is given by:

P = (b + c - B - C) / 2 + (1/3)(b + c)

The point with the position vector 1/3(a + b + c) is given by:

P = F - (2/3)D - (1/3)E + (1/3)(b + c)

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The solution is: the numeric value of (A, B, C, D, E) from the following three formulas are: A = 4, B = 10, C = 2, D = 5, E = 6.

Here, we have,

given that,

Formula:

AC x 1E = 4CD (1)

ADE x 1EC = AB (2)

AB + E9 = 11A (3)

now, we have to find the numeric value of (A, B, C, D, E) from the following three formulas.

However, A, B, C, D, E represent numbers between 0 and 9.

given example: If F = 1, G = 2, then 3FG would be 312.

now, we have,

Let, A = 4 and E = 6

as we have,

A+C = E

B-D = D

A + E = B

so, we get, C = 6 - 4 = 2

B = 6 + 4 = 10

2D = 10 => D = 5

Hence, The solution is: the numeric value of (A, B, C, D, E) from the following three formulas are: A = 4, B = 10, C = 2, D = 5, E = 6.

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Hello !

2 1/4 ÷ 5/8

= 9/4 ÷ 5/8

= 9/4 x 8/5

= 9x8/4x5

= 72/20

= 18/5

= 3 3/5

The Separation Schema is a rule in set theory that allows us to construct a new set from an existing set based on a given property.

For example, if a set of all natural numbers, use the Separation Schema to construct a new set of all even natural numbers. The new set will contain all of the elements of the original set that satisfy the given property, in this case, the property of being even.

The property x ∉ x states that x is not a member of x. If we apply the Separation Schema to this property, we will construct a new set that contains all of the sets that are not members of themselves. This set is called the Russell set, and it is known to be paradoxical.

The Russell paradox shows that the unrestricted Comprehension Schema is inconsistent. This is because the Russell set is a set that can be constructed using the Comprehension Schema, but the Russell set also satisfies the property that it is not a member of itself. This is a contradiction, and it shows that the Comprehension Schema cannot be used to construct all sets.

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To find mADC, we need to examine the given information and the diagram provided. However, without the diagram, it is difficult to determine the specific angles and relationships between the points A, D, and C.

If you can provide more information or a visual representation of the movie reel and the points A, D, and C, I will be able to assist you in finding mADC.

Based on the principle of prudence, Theo should record the transaction, Sarah shouldn't, Jacob should, Jerry shouldn't, and JSL Inc. should record the transaction in the company accounts based on the principle of prudence.

1. Theo estimates that he might have to incur additional expenses for the purchase of raw materials next month.

  - Should record the transaction: It is prudent to anticipate and record potential expenses to reflect a more accurate financial position.

2. Sarah estimates that the market value price of the office building has risen by $50,000.

  - Shouldn't record the transaction: The principle of prudence suggests that gains should only be recorded when they are realized, not based on estimated market value changes.

3. Jacob bought goods for the business on credit.

  - Should record the transaction: Purchasing goods on credit should be recorded to accurately reflect liabilities and the financial position.

4. Jerry buys fuel for his personal car.

  - Shouldn't record the transaction: Personal expenses should not be recorded in the company accounts as they are unrelated to the business.

5. JSL Inc. bought stocks of another company.

  - Should record the transaction: Buying stocks of another company should be recorded as an investment to reflect the company's financial holdings.

Note: It's important to consider specific accounting regulations and policies that may vary depending on the jurisdiction and the nature of the business.

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Answer:

Step-by-step explanation:

distribute the 3

you get 3x+24=15

subtract 24 from both sides

you get 3x=-9

divide 3 from both sides

you get x=-3

Answer:

y = 3. last option is correct answer for 2nd question.

Step-by-step explanation:

f(x) just means y.

horizontal asymptote is y = 'something.'

the graph crosses y = 4, so y = 4 cannot be asymptote.

y = 3 is since the graph never quite touches it.

as for ∞, we see that as x approaches -∞, y almost reaches 3. but not quite. also, as x approaches +∞, y approaches +∞.

so the last option is the correct answer.

This axiom says that there is no upper bound to the number of elements that a set can have, thus, sets with infinite elements do exist.

First, we need to give the definition of an axiom. This is a proposition that is assumed to be true, and don't need a demonstration.

Axioms are the logical base of mathematics, so these are usually used to define concepts or basic rules.

In set theory,  the axiom of infinity just claims (and because it is an axiom, it must be true) that there are sets that have a infinite number of elements.

A trivial case is the set of real numbers, which we know has infinite elements because there are infinite real numbers.

So there is not a maximum for the number of elements that a set can have.

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When 0.50 is written out in full, the first seven digit after the decimal point is

5 0 5 0 5 0 5

A recurring decimal also known as a repeating decimal  is a decimal representation of a number where one or more digits repeat infinitely after a certain point. In other words  there is a repeating pattern of digits that continues indefinitely.

Recurring decimals are typically denoted by placing a horizontal line or a dot above the repeated portion of the digits.

In this case the repeating decimal is represented by dot above. therefor we have 5 and 0 repeating.

The umber in fraction is 50/99

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a) Population: All students who attended the college last year.

b) Population: All students who graduated from the college last year.

c) Data: 3.65, 2.80, 1.50, 3.90.

d) Sample: Group of students randomly selected from the population.

e) Variable: Cumulative GPA.

f) Sample: All students who graduated.

g) Sample: Students in the study who graduated from the college last year.

a) Population: All students who attended the college last year

Statistic: Not applicable (no specific data)

Parameter: Not applicable (no specific data)

Variable: Cumulative GPA

Data: Not applicable (no specific data)

Sample: Not applicable (no specific data)

b) Population: All students who graduated from the college last year

Statistic: Cumulative GPA of one student

Parameter: Not applicable (one student's GPA)

Variable: Cumulative GPA

Data: GPA of the specific student

Sample: Not applicable (one student)

c) Population: Not applicable (no specific population mentioned)

Statistic: Not applicable (no sample data)

Parameter: Not applicable (no population parameter)

Variable: Cumulative GPA

Data: 3.65, 2.80, 1.50, 3.90

Sample: Not applicable (no specific sample mentioned).

d) Population: All students who graduated from the college last year

Statistic: Not applicable (no specific data)

Parameter: Not applicable (no specific data)

Variable: Cumulative GPA

Data: Not applicable (no specific data)

Sample: Group of students randomly selected from the population

e) Population: All students who graduated from the college last year

Statistic: Average cumulative GPA of students

Parameter: Not applicable (no specific data)

Variable: Cumulative GPA

Data: Cumulative GPAs of students who graduated

Sample: Not applicable (no specific sample mentioned)

f) Population: All students who graduated from the college last year

Statistic: Not applicable (no specific data)

Parameter: Not applicable (no specific data)

Variable: Cumulative GPA

Data: Not applicable (no specific data)

Sample: All students who graduated

g) Population: Students in the study who graduated from the college last year

Statistic: Average cumulative GPA of students in the study

Parameter: Not applicable (no specific data)

Variable: Cumulative GPA

Data: Cumulative GPAs of students in the study

Sample: Students in the study who graduated

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Answer:

The correct answer is C. $68.35.

Here's the breakdown of the total cost:

* 4 large pizzas at $13.99 each = $55.96

* 7.85% sales tax on $55.96 = $4.38

* $8.00 delivery charge

Total: $55.96 + $4.38 + $8.00 = $68.35

To determine the amount of binding Erin needs to cover the outside edges of the kite, we need to add up the lengths of all the sides of the kite.

Looking at the pattern, we can see that there are two sides with a length of 13 inches each, and two sides with a length of 15 inches each.

Therefore, the total length of the binding needed is:

13 inches + 13 inches + 15 inches + 15 inches = 56 inches.

Based on this calculation, Erin needs approximately 56 inches of binding to cover the outside edges of the kite.

Among the options given, the closest measurement to 56 inches is 52 inches.

Answer:

Point where the line crosses the y-axis is (0, -8)

Gradient: 3

Step-by-step explanation:

The slope-intercept form of the equation of a straight line is
y = mx + b

where m =slope or gradient

b is the y-intercept ie the y-value where the line crosses the y-axis. This is also the value of y when x = 0

Comparing the general equation with y = 3x - 8

we get the y-intercept as -8 and therefore the point (0, -8) is the point where the line crosses the y-axis

The gradient is 3 which is the coefficient of x

Answer:

30

Step-by-step explanation:

y = ( a + b ) ( a - b )

Let a = 6.5 and b = 3.5

y = ( 6.5 + 3.5 ) ( 6.5 - 3.5 )

Simplify the terms in the parentheses.

y = (10)(3)

y= 30

Answer:

(i) x ≤ 1

(ii) ℝ except 0, -1

(iii) x > -1

(iv) ℝ except π/2 + nπ, n ∈ ℤ

Step-by-step explanation:

(i) The number inside a square root must be positive or zero to give the expression a real value. Therefore, to solve for the domain of the function, we can set the value inside the square root greater or equal to 0, then solve for x:

[tex]1-x \ge 0[/tex]

[tex]1 \ge x[/tex]

[tex]\boxed{x \le 1}[/tex]

(ii) The denominator of a fraction cannot be zero, or else the fraction is undefined. Therefore, we can solve for the values of x that are NOT in the domain of the function by setting the expression in the denominator to 0, then solving for x.

[tex]0 = x^2+x[/tex]

[tex]0 = x(x + 1)[/tex]

[tex]x = 0[/tex]     OR     [tex]x = -1[/tex]

So, the domain of the function is:

[tex]R \text{ except } 0, -1[/tex]

(ℝ stands for "all real numbers")

(iii) We know that the value inside a logarithmic function must be positive, or else the expression is undefined. So, we can set the value inside the log greater than 0 and solve for x:

[tex]x+ 1 > 0[/tex]

[tex]\boxed{x > -1}[/tex]

(iv) The domain of the trigonometric function tangent is all real numbers, except multiples of π/2, when the denominator of the value it outputs is zero.

[tex]\boxed{R \text{ except } \frac{\pi}2 + n\pi} \ \text{where} \ \text{n} \in Z[/tex]

(ℤ stands for "all integers")

Answer:

(i)  x ≤ 1

(ii)  All real numbers except x = 0 and x = -1.

(iii)  x > -1

(iv)  All real numbers except x = π/2 + πn, where n is an integer.

Step-by-step explanation:

The domain of a function is the set of all possible input values (x-values).

[tex]\hrulefill[/tex]

[tex]\textsf{(i)} \quad f(x)=\sqrt{1-x}[/tex]

For a square root function, the expression inside the square root must be non-negative. Therefore, for function f(x), 1 - x ≥ 0.

Solve the inequality:

[tex]\begin{aligned}1 - x &\geq 0\\\\1 - x -1 &\geq 0-1\\\\-x &\geq -1\\\\\dfrac{-x}{-1} &\geq \dfrac{-1}{-1}\\\\x &\leq 1\end{aligned}[/tex]

(Note that when we divide or multiply both sides of an inequality by a negative number, we must reverse the inequality sign).

Hence, the domain of f(x) is all real numbers less than or equal to -1.

[tex]\boxed{\begin{aligned} \textsf{Inequality notation:} \quad &x \leq 1\\\textsf{Interval notation:} \quad &(-\infty, 1]\\\textsf{Set-builder notation:} \quad &\left\{x \in \mathbb{R}\left|\: x \leq 1 \right\} \end{aligned}}[/tex]

[tex]\hrulefill[/tex]

[tex]\textsf{(ii)} \quad g(x) = \dfrac{1}{x^2 + x}[/tex]

To find the domain of g(x), we need to identify any values of x that would make the denominator equal to zero, since division by zero is undefined.

Set the denominator to zero and solve for x:

[tex]\begin{aligned}x^2 + x &= 0\\x(x + 1) &= 0\\\\\implies x &= 0\\\implies x &= -1\end{aligned}[/tex]

Therefore, the domain of g(x) is all real numbers except x = 0 and x = -1.

[tex]\boxed{\begin{aligned} \textsf{Inequality notation:} \quad &x < -1 \;\;\textsf{or}\;\; -1 < x < 0 \;\;\textsf{or}\;\; x > 0\\\textsf{Interval notation:} \quad &(-\infty, -1) \cup (-1, 0) \cup (0, \infty)\\\textsf{Set-builder notation:} \quad &\left\{x \in \mathbb{R}\left|\: x \neq 0,x \neq -1 \right\} \end{aligned}}[/tex]

[tex]\hrulefill[/tex]

[tex]\textsf{(iii)}\quad h(x) = \log_7(x + 1)[/tex]

For a logarithmic function, the argument (the expression inside the logarithm), must be greater than zero.

Therefore, for function h(x), x + 1 > 0.

Solve the inequality:

[tex]\begin{aligned}x + 1 & > 0\\x+1-1& > 0-1\\x & > -1\end{aligned}[/tex]

Therefore, the domain of h(x) is all real numbers greater than -1.

[tex]\boxed{\begin{aligned} \textsf{Inequality notation:} \quad &x > -1\\\textsf{Interval notation:} \quad &(-1, \infty)\\\textsf{Set-builder notation:} \quad &\left\{x \in \mathbb{R}\left|\: x > -1\right\} \end{aligned}}[/tex]

[tex]\hrulefill[/tex]

[tex]\textsf{(iv)} \quad k(x) = \tan x[/tex]

The tangent function can also be expressed as the ratio of the sine and cosine functions:

[tex]\tan x = \dfrac{\sin x}{\cos x}[/tex]

Therefore, the tangent function is defined for all real numbers except the values where the cosine of the function is zero, since division by zero is undefined.

From inspection of the unit circle, cos(x) = 0 when x = π/2 and x = 3π/2.

The tangent function is periodic with a period of π. This means that the graph of the tangent function repeats itself at intervals of π units along the x-axis.

Therefore, if we combine the period and the undefined points, the domain of k(x) is all real numbers except x = π/2 + πn, where n is an integer.

[tex]\boxed{\begin{aligned} \textsf{Inequality notation:} \quad &\pi n\le \:x < \dfrac{\pi }{2}+\pi n\quad \textsf{or}\quad \dfrac{\pi }{2}+\pi n < x < \pi +\pi n\\\textsf{Interval notation:} \quad &\left[\pi n ,\dfrac{\pi }{2}+\pi n\right) \cup \left(\dfrac{\pi }{2}+\pi n,\pi +\pi n\right)\\\textsf{Set-builder notation:} \quad &\left\{x \in \mathbb{R}\left|\: x \neq \dfrac{\pi}{2}+\pi n\;\; (n \in\mathbb{Z}) \right\}\\\textsf{(where $n$ is an integer)}\end{aligned}}[/tex]

Step-by-step explanation:

Angle 1 and 2 are vertical angles and are equal

Angle 2 and three are equal....   they are corresponding angles

therefore   angle 1 = angle 3  because alternating interior angles are equal

Step-by-step explanation:

to find f(5)   in f(x) , just put in '5' where 'x' is in the equation

f(5) = 3 (5) + 2 = 17

Answer:

f(5) = 17

Step-by-step explanation:

Let's evaluate the function for f(5)

Insert 5 everywhere x appears:

Therefore f(5) = 17

Solution of the given expression is,

 x = 6/5 or x = -4

Given that,

|2x+5| + |3x+1| = 10

Add -|3x-1| both sides,

⇒ |2x+5| + |3x+1| - |3x+1| = 10 -  |3x+1|

⇒                          |2x+5| = 10 -  |3x+1|

Either 2x+5 = -  |3x+1| + 10 or 2x + 5 = -(-|3x-1| + 10)

Proceed:

2x+5 = -  |3x+1| + 10

⇒ -|3x-1| + 10 = 2x + 5

⇒ -|3x-1| + 10 - 10 = 2x + 5 - 10             [subtract 10 both sides]

⇒                -|3x-1| = 2x - 5

⇒                -|3x-1|/-1 = (2x - 5)/-1           [ divide both sides by -1]

We know either 3x - 1 = -2x + 5 or 3x - 1 = - (-2x+5)

       3x - 1 = -2x + 5

3x - 1 + 2x = -2x + 5 + 2x                        [ adding 2x both sides]

           5x = 6

              x = 6/5

Now,

      3x - 1 = -(-2x+5)

3x - 1 - 2x = 2x - 5 - 2x                           [ subtracting 2x both sides]

             x = -4

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The number of fossils after 10 years is equal to 2333.59 fossils.

In order to determine the number of fossils on this barren land after 10 years, we would have to solve the given differential equation [tex]\frac{dN}{dt} =\frac{5000}{6\;+\;5t}[/tex] by applying an integration in order to create an equation that models N(t) with respect to the number of years or time (t) as follows.

First of all, we would rewrite the equation as follows;

[tex]dN =\frac{5000}{6\;+\;5t}dt[/tex]

By integrating both sides of the equation with respect to t, we have the following:

[tex]\int dN =\int \frac{5000}{6\;+\;5t}dt\\\\N=\frac{5000}{5} ln|6+5t|+C\\\\N=1000 ln|6+5t|+C[/tex]

Since the initial number of fossils (N) is equal to 100 when time (t) = 0, we would substitute the parameters into the equation as follows;

N = 1000ln(6 + 5t) + C

100 = 1000ln(6 + 5(0)) + C

C = 100 - 1000ln6

Next, we would rewrite the equation for the number of fossils (N) in terms of time (t) as follows;

N = 1000ln(6 + 5t) + 100 - 1000ln6

By simplifying the equation using the quotient log rule, we have:

N = 1000ln(6 + 5t) - 1000ln6 + 100

N = 1000ln[(6 + 5t)/6] + 100

Therefore, the number of fossils (N) after 10 years can be calculated as follows;

N = 1000ln[(6 + 5(10))/6] + 100

N = 1000ln[(6 + 50)/6] + 100

N = 1000ln(56/6) + 100

N = 2333.59 fossils.

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Check the picture below.

the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

how fast is it traveling? or what's its average rate or slope?

to get the slope of any straight line, we simply need two points off of it, let's use those two in the picture below

[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{6}-\stackrel{y1}{2}}}{\underset{\textit{\large run}} {\underset{x_2}{6}-\underset{x_1}{4}}} \implies \cfrac{ 4 }{ 2 } \implies \cfrac{2~meters}{1~second}\qquad \textit{2 meters per second}[/tex]

Type I error is "Megan's results show significant improvements in health associated with a whole foods diet."

A Type I error occurs when the null hypothesis is rejected, even though it is true.

In this case, the null hypothesis states that a whole foods diet would not have any impact on general health.

Therefore, a Type I error would occur if Megan's results show significant improvements in health associated with a whole foods diet.

This means that Megan would reject the null hypothesis and conclude that a whole foods diet does have an impact on general health, even though it is not true.

So, the statement that would indicate a Type I error is "Megan's results show significant improvements in health associated with a whole foods diet."

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Answer:

24

Step-by-step explanation:

the lengths are in proportion to one another, between triangles.

(x - 4)/12  =  5/(x +7)

(x - 4)(x + 7) = 5 X 12

x² + 7x - 4x - 28 = 60

x² + 3x - 28 = 60

x² + 3x - 88 = 0.

(x + 11) (x - 8) = 0

x = -11, 8.

x cannot be -11 since both x +7 and x - 4 would be negative lengths!!

so x = 8.

AB = 12, DE = x - 4 = 8 -4 = 4. 12/4 = 3.

the lengths of triangle ABC are 3 times longer than the lengths of DEF.

we can confirm this: AC = x + 7 = 8 + 7 = 15. DF = 5

AC is 15/5 = 3 times longer than DF.

so we expect BC to be 3 times longer than x. x = 8.

so BC = 3 X 8 = 24.