7. Solve the inequality. (1 point)
d-6>-4

Od>-2
Od>-10
Od>2
Od> 10

A(5,0), B(3,2), C(0,5), and D(-6,1) are all located in the first quadrant. D(-6,1) is located within the second quadrant.

A coordinate system within geometry is a way to use one or more integers, or coordinates, to determine the exact placement of points and other geometrical objects over a manifold, such Euclidean space. The order of the coordinates is crucial, and they are frequently identified by their position within an arranged tuple or through a letter, such as "the x-coordinate."  Within the first quadrant is A(5,0). The first quadrant is occupied by B(3,2), followed by C(0,5) with the first quadrant, D(-6,1) with the second quadrant, E(-4,4) from the second quadrant, and F(2,-3) with the fourth quadrant.

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The distance d between A and B is √(68), and the square of the distance in the y direction is 64.

To find the distance d between points A and B, we can use the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Substituting the values of A and B, we get:
d = sqrt((4 - 2)^2 + (5 - (-3))^2)
d = sqrt(2^2 + 8^2)
d = sqrt(4 + 64)
d = sqrt(68)
Next, to calculate the square of the distance in the y direction, we need to find the difference between the y-coordinates of A and B and square it. So:
(y2 - y1)^2 = (5 - (-3))^2 = 8^2 = 64
Therefore, the square of the distance in the y direction is 64.
I'm here to help you with your question. To find the distance d between two points A(x1, y1) and B(x2, y2), we can use the distance formula:
d = √((x2-x1)² + (y2-y1)²)
Given the points A(2, -3) and B(4, 5), let's plug in the values:
d = √((4-2)² + (5-(-3))²)
Now, calculate the difference for each coordinate:
d = √((2)² + (8)²)
Next, square the differences:
d = √(4 + 64)
Finally, calculate the square root:
d = √(68)
ow, let's find the square of the distance in the y direction, which is (y2-y1)²:
(y2-y1)² = (5-(-3))²
Calculate the difference:
(y2-y1)² = (8)²
Square the difference:
(y2-y1)² = 64
So, the distance d between A and B is √(68), and the square of the distance in the y direction is 64.

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The required forms of the equation are;

(x+(-4))²= - 5 + ((-4))²

(x -4)²= 11

Completing the square is a method used to rewrite a quadratic expression in standard form by adding and subtracting a constant to make it a perfect square trinomial. Completing the square is a useful method to solve quadratic equations and to rewrite quadratic expressions in standard form.

The standard form of a quadratic equation  is ax² + bx + c = 0

We have that;

x²-8x+5=0

(x+(-4))²= - 5 + ((-4))²

(x -4)²= 11

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The total payment required to pay off a promissory note issued for $400.00 is $412.

Using this formula

Total payment=Promissory note+(Promissory note× Ordinary interest× 90 day term/360)

Where:

Promissory note=$400

Ordinary interest=12%

Let plug in the formula

Total payment= $400 + ($400 × 12% × 90 days ÷ 360 days)

Total payment= $400 + $12

Total payment= $412

Hence, the total payment required to pay off a promissory note issued for $400.00 is $412.

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Answer:

f(- 5) = 10

Step-by-step explanation:

the absolute value function always gives a positive value, that is

| - a | = | a | = a

given

f(x) = 5 + | x |

to find f(- 5) substitute x = - 5 into f)x)

f(- 5) = 5 + | - 5| = 5 + | 5 | = 5 + 5 = 10

The probability of a random person on the street having an IQ score of less than 99 is 0.4729.

We have,

We need to standardize the IQ score using the formula:

z = (x - μ) / σ

So,

For x = 99,

z = (99 - 100) / 15

z = -0.067

We can then use a standard normal distribution table or calculator to find the probability of a z-score less than -0.067.

Using a standard normal distribution table, we find that the probability of a z-score less than -0.067 is 0.4729

Therefore,

The probability of a random person on the street having an IQ score of less than 99 is 0.4729.

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The coordinates of the image after the rotation are given as follows:

The five more known rotation rules are given as follows:

The coordinates of the original image are given as follows:

The rotation is a 90º counterclockwise about the origin, hence the rule is given as follows:

(x,y) -> (-y, x).

Meaning that the coordinates of the rotated image are given as follows:

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The inverse of the function f(x) = 1/x is B. f⁻¹(x) = 1/x

The inverse of a function f(x) written as f⁻¹(x) is such that ff⁻¹(x) = f⁻¹f(x)

Given the function f(x) = 1/x,we desire to find its inverse. We proceed as follows.

Since f(x) = 1/x

Let f(x) = y

So,we have that

y = 1/x

Now, multiplying both sides by x,we have that

x × y = 1/x × x

xy = 1

Dividing though by y, we have that

xy/y = 1/y

x = 1/y

Now, relacing y with x and x with f⁻¹(x), the inverse of f(x), we have that

x = 1/y

x = 1

f⁻¹(x) = 1/x

So, the inverse is B. f⁻¹(x) = 1/x

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The actual side length of the house is 240 feet long.

The scale factor is 1 inch on the blueprint represents 60 actual feet.

The side of the house measures 4 inches on the blueprint. To find the actual length, we multiply the blueprint length by the scale factor:

Actual side length = 4 inches * 60 feet/inch = 240 feet

So, the actual side length of the house is 240 feet.

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Based on the Tuesday rate, $100 United States dollars is equal to 843.64 French francs.

One hundred US dollars are equivalent to 834.3664 French francs at the exchange rate on Tuesday. Accordingly, you can swap eight hundred forty-three point 64 years old French francs for every one hundred dollars in the United States.

1. From the tables, the Tuesday rate is 0.119 US dollars to 1 French franc.

2. To find the exchange rate, multiply the number of US dollars by the exchange rate: 100 x 0.119 = 11.90.

3. To find the amount in French francs, divide the US dollars by the exchange rate: 11.90 / 0.119 = 843.64 French francs. Based on the Tuesday rate, $100 United States dollars is equal to 843.64 French francs.

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Answer:

the answer is: 258

How?:

Area:

2(wl+hl+hw)

2(9×6 + 5×6 + 5×9) = 258

The segment lengths are given as follows:

The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

The theorem is expressed as follows:

c² = a² + b².

In which:

Considering the geometric mean theorem, the triangle has bases of 7 and 14 - 7 = 7, hence the altitude BD is given as follows:

BD² = 7 x 7

BD² = 7²

BD = 7.

The segment BC is the hypotenuse of a right triangle of two sides with length 7, hence:

(BC)² = 7² + 7²

[tex]BC = \sqrt{2 \times 49}[/tex]

[tex]BC = 7\sqrt{2}[/tex]

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Answer: 15cm?

Step-by-step explanation: I am doing this assignment right now, after i submit it i will reply with the answer. Edit: 15cm is correct.

The distance from point A (tangent point on clock) to point B (the hanger) is approximately 10 cm, based on the principles of right-angle triangles and Pythagorean theorem.

In this geometry problem, we're looking at a situation where a circular clock is hung by wires connected to a tangential point on the clock. By using right-angle triangle principles and the given radius of 15 cm from E to D, it''s key to recognize that triangle AED is a right triangle (since a radius perpendicular to a tangent at its point of contact forms a right angle).

So, the distance from A to E (the radius) is 15 cm. The distance from E to D is also a radius, hence is 15 cm as well. Now, by Pythagoras theorem for right triangle AED, the distance AD (the hypotenuse) is square root of (15^2 + 15^2), which is approximately 21.21 cm.

The distance BD from the top of the clock at point D to the hanger at point B is given as 10 cm. Since the clock is hanging from point B, this creates another right triangle ADB. The length from point A to B is found by subtracting BD (10 cm) from the hypotenuse AD (21.21 cm), which is roughly 11.21 cm. However, this option is not offered in the question, meaning a rounding must be made, so the answer is approximately 10 cm.

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To use the substitution method to solve the system, we need to solve one of the equations for x or y in terms of the other variable, and then substitute that expression into the other equation to get an equation in one variable that we can solve.

Let's solve the first equation for x in terms of y:

x + 4y = -9

x = -4y - 9

Now we substitute this expression for x into the second equation:

2x + 5y = -6

2(-4y - 9) + 5y = -6

Simplifying this expression, we get:

-8y - 18 + 5y = -6

-3y = 12

y = -4

Now we can substitute this value of y into either of the original equations to find x. Let's use the first equation:

x + 4y = -9

x + 4(-4) = -9

x - 16 = -9

x = 7

Therefore, the solution to the system is x = 7, y = -4.

Now let's look at the answer choices and see which one matches the equation we got by substituting x = -4y - 9 into the second equation:

A) 2(4-9)+ 5y-6 = -10 + 5y - 6 = 5y - 16

B) 21-4y-9)+5% -6 = -4y + 6

C) 2x+5(4-9)=-6 = 2x - 25 = -6

D) 2x+5(-4y-9)=-6 = 2x - 20y - 45 = -6

The answer choice that matches our equation is D), 2x + 5(-4y - 9) = -6.

Answer:

The equation of a line that is perpendicular to y = 3x + 3 is option A y equals negative one-third times x plus 1(-1/3x + 1)Given,The equation of line, y = 3x + 3The line passes through (-6, 3)We have to find the equation of the line that is perpendicular to y = 3x + 3Slope of the line, m = 3Here, in perpendicular case, slope is negative of its reciprocal.That is, m = -1/3Now, we can find the equationy - y₁ = m(x - x₁)

Here,

y₁ = 3x₁ = -6m = -1/3

So,y - 3 = -1/3(x - (-6))

y - 3 = -1/3(x + 6)

y - 3 = -1/3x + -1/3(6)

y - 3 = -1/3x - 6/3

y - 3 = -1/3

x - 2y = -1/3

x - 2 + 3

y = -1/3x + 1

That is, the equation of a line that is perpendicular to y = 3x + 3 is y equals negative one-third times x plus 1(y = -1/3x + 1)

Step-by-step explanation:

Answer:

midsegment = 23

Step-by-step explanation:

the midsegment is half the sum of the bases, that is

midsegment = [tex]\frac{18+28}{2}[/tex] = [tex]\frac{46}{2}[/tex] = 23

The pythagorean theorem says a^2 + b^2 = c^2 when a and b are the sides of the right triangle and c is the hypotenuse (longest side, opposite the 90 degree angle).

so if  8^2 + 6^2 = 10^2, then it's a right triangle.

8^2 + 6^2 = 64 + 36 = 100 = 10^2, so yes, this is a right triangle.

The approximate length of the diagonal to the nearest tenth of an inch is 32.52 inches.

To find the length of the diagonal, we can use the Pythagorean theorem, which states that the square of the length of the diagonal is equal to the sum of the squares of the lengths of the sides.

In this case, since the sides of the square television screen are 23 inches, we can calculate the length of the diagonal using the following formula

So, if the sides of the square television screen are 23 inches, then:

[tex]Diagonal^2 = Side^2 + Side^2[/tex]

[tex]Diagonal^2 = 23^2 + 23^2[/tex]

[tex]Diagonal^2[/tex]= 529 + 529

[tex]Diagonal^2[/tex] = 1058

Diagonal = √1058

Diagonal ≈ 32.52 inches

Rounding to the nearest tenth of an inch, the approximate length of the diagonal is 32.52 inches.

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If the temperature of a chemical mixture is tan√x degree celsius after x hours then the rate of change of temperature after π /4 hours is 0.141099

We are given that the temperature of the chemical mixture after x hours is given by:

T(x) = tan(√x)

To find the rate of change of temperature after π/4 hours, we need to find the derivative of T(x) with respect to x and evaluate it at x = π/4.

T'(x) = sec²(√x)/2√x

So, the rate of change of temperature after π/4 hours is given by:

T'(π/4) = sec²(√(π/4))/2√(π/4)

= sec²(π/2)/2√(π/4)

= 1/2√(π/4)

We can simplify this expression as:

T'(π/4) = 1/2(π/2)⁰⁵

= 0.141099

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The trinomial expression when factored is (3x - 3)² & A = 3 and B = 3

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

9x² - 18x + 9 = (Ax − B)²

Factor out 9 in the expression

So we have

9(x² - 2x + 1) = (Ax − B)²

When the above expression is factored

We have

9(x - 1)² = (Ax − B)²

Express 9 as 3²

3²(x - 1)² = (Ax − B)²

So, we have

(3x - 3)² = (Ax − B)²

This means that

A = 3 and B = 3

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"The correct answer is: g(x), f(x), h(x)."To determine the correct order of the functions from least to greatest according to the average rate of change on the interval from x = 0 to x = 4, we need to calculate the average rate of change for each function.

The average rate of change is calculated by finding the difference in the function's values at the endpoints of the interval (x = 4 and x = 0) and dividing it by the difference in the corresponding x-values.

For function f(x), we have:

Average rate of change = (f(4) - f(0))/(4 - 0) = (64 - 0)/(4 - 0) = 64/4 = 16

For function g(x), since it is a linear graph, the average rate of change is constant throughout. Therefore, the average rate of change for g(x) is the same as the slope of the line, which is determined by the ratio of the change in y to the change in x. In this case, it would be the slope between the given x-intercept (-2) and y-intercept (-1), which is -1/2.

For function h(x), we need to find the average rate of change between x = 0 and x = 4. Substituting the values, we get:

Average rate of change = (h(4) - h(0))/(4 - 0) = (36 - 6)/(4 - 0) = 30/4 = 7.5

Now, let's compare the average rates of change for each function:

f(x): 16

g(x): -1/2

h(x): 7.5

From least to greatest, the correct order according to the average rate of change is:

g(x), f(x), h(x).

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The area of the triangle in the shaded region is derived to be 12.5 square units.

For any triangle, the area is calculated as half the base multiplied by the height of the triangle, that is;

Area of triangle = 1/2 × base × height

For the triangle in the shaded region;

base = 5 units

height = 5 units

area of the triangle = 1/2 × 5 units × 5 units

area of the triangle = 25/2

area of the triangle = 12.5 square units

Therefore, the area of the triangle in the shaded region is derived to be 12.5 square units.

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The derivative of the inverse trigonometric function is equal to f'(x) = (2 · e²ˣ) / √(1 - e⁴ˣ). (Correct choice: D)

In this problem we find the case of the inverse trigonometric function, whose derivative must be found. This can be done by means of derivative rules and chain rules. First, write the entire function:

f(x) = sin⁻¹ (e²ˣ)

Second, find the derivative of the inverse trigonometric function:

f'(x) = [1 / √[1 - (e²ˣ)²]] · (2 · e²ˣ)

f'(x) = (2 · e²ˣ) / √(1 - e⁴ˣ)

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The 6-digit number A is 419065.

To find the least 6-digit number A that is divisible by 495, we need to follow these steps:
Step 1: Find the prime factors of 495.
495 = 3 × 3 × 5 × 11 = 3^2 × 5 × 11
Step 2: Determine the lowest 6-digit number divisible by the prime factors.
The lowest 6-digit number is 100000, so we find the next multiple of 495 above 100000.
100000 ÷ 495 ≈ 202.02
The next integer value is 203, so:
203 × 495 = 100485
Step 3: Substitute the given digits (4, 9, and 6) into the 6-digit number.
The least 6-digit number divisible by 495 is 100485. To make A the smallest possible number, we will place the given digits in the following order: 4, 9, and 6. The missing digits in A are 1, 0, and 5.
So, the 6-digit number A is 419065.

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a. The concentration of the drug after 8 hours is equal to 24 mg/L.

b. The interval over which the concentration increases is 0 < t < 2. The interval over which the concentration decreases is 2 < t < ∞.

c. The drug is at its maximum concentration when t = 2 hours and the maximum concentration is 64 mg/L.

d. After the drug reaches its maximum concentration, the number of hours that are required for the concentration to decrease to 16 mg/L is 8 hours.

e. After 1 week and 1 month, we can predict that the concentration of the drug kept decreasing after reaching 20 hours.

f. After the drug is taken orally, it took exactly 2 hours to reach a maximum concentration of 64 mg/L.

By critically observing the graph, the time and concentration of the drug after 8 hours is represented by the order pair (8, 24). Therefore, the concentration is equal to 24 mg/L.

Part b.

For any given function, y = f(x), if the output value (range or y-value) is decreasing when the input value is increased, then, the function is generally referred to as a decreasing function.

For any given function, y = f(x), if the output value (range) is increasing when the input value is increased, then, the function is generally referred to as an increasing function.

By critically observing the graph of the given function, we can reasonably infer and logically deduce the following:

Part c.

The vertex (2, 64) of the graph represent the point where the drug is at its maximum concentration, which is time (t) = 2 hours and the maximum concentration is y = 64 mg/L.

Part d.

After the drug reaches its maximum concentration, the number of hours that are required for the concentration to decrease to 16 mg/L can be calculated from the graph as follows;

Number of hours = 10 - 2

Number of hours = 8 hours.

Part e.

After 1 week and 1 month, it can be predicted that the concentration of the drug kept decreasing after reaching 20 hours.

Part f.

After the drug is taken orally, it took exactly 2 hours to reach a maximum concentration of 64 mg/L. Subsequently, the level of the drug in the bloodstream drops after reaching its maximum concentration, reaching approximately 10 mg/L after 12 hours.

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A) the average speed  of the journey from my home town to A is 30 miles per hour

B) the average speed of the journey from my home town to B is 40 miles per hours.

C) The average time is 36 miles per hours.

Average speed = distance /   time

So the answers is

A) Average speed = 10 miles ÷ (1/3 hour) = 30 miles per hour

B) Average speed = 20 miles ÷ 0.5 hours = 40 miles per hour.

C) Average speed = 30 ÷ (50/ 60) = 30 ÷ 0.8333 = 36 miles per hour.

Average Speed is essential for understanding the rate at which a travel occurs.

The speed of a vehicle may change from time to time throughout a travel. In that instance, determining the average speed is critical in order to determine the pace at which the voyage will be completed.

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Full Question:

The diagram shows the distance between my home, H, and two towns, A and B. It also shows information about journey times. See same attached.

The mean absolute deviation for the data-set in the table is given as follows:

1.52 million.

The mean of a data-set is given by the sum of all observations divided by the cardinality of the data-set, which is the number of observations in the data-set.

Hence the mean for the data-set in this problem is given as follows:

(1.5 + 3.8 + 1.3 + 1.6 + 2.9 + 1.4 + 0.9 + 2.3 + 8.4 + 1.3)/10 = 2.54.

The deviations are given as follows:

Hence the mean absolute deviation is given as the sum of the deviations divided by the number of observations, hence:

(1.04 + 1.26 + 1.24 + 1.06 + 0.46 + 1.14 + 1.64 + 0.24 + 5.86 + 1.24)/10 = 1.52 million.

The table is given by the image presented at the end of the answer.

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