Write the equation in standard form using integers. Y=4/5 x-6

-1 does not equal 0, the equation is not true for any value of "a". This means that there is no value of "a" for which the function f(x) is continuous at x = 1.

To determine the value of "a" for which the function f(x) is continuous at x = 1, we need to check if the left-hand limit and the right-hand limit of f(x) as x approaches 1 are equal, and if the value of f(x) at x = 1 is equal to these limits.

First, let's calculate the left-hand limit of f(x) as x approaches 1. For x < 1, the function is given by f(x) = (ax² - 1). To find the left-hand limit, we substitute x = 1 into this expression:

lim(x→1-) f(x) = lim(x→1-) (ax² - 1) = a(1²) - 1 = a - 1.

Next, let's calculate the right-hand limit of f(x) as x approaches 1. For x > 1, the function is given by f(x) = (a(x² - 2x + 1)). Substituting x = 1 into this expression, we have:

lim(x→1+) f(x) = lim(x→1+) (a(x² - 2x + 1)) = a(1² - 2(1) + 1) = a(1 - 2 + 1) = a.

For the function f(x) to be continuous at x = 1, the left-hand limit and the right-hand limit should be equal. Therefore, we have:

a - 1 = a.

To solve this equation for "a," we subtract "a" from both sides:

-1 = 0.

Since -1 does not equal 0, the equation is not true for any value of "a". This means that there is no value of "a" for which the function f(x) is continuous at x = 1.

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Answer:

\(360xy^2|xz^3|\)

Step-by-step explanation:

Given expression:

\(12x \sqrt{900x^2y^4z^6}\)

\(\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:\)

\(\implies 12x \sqrt{900}\sqrt{x^2}\sqrt{y^4}\sqrt{z^6}\)

Replace 900 with 30² :

\(\implies 12x \sqrt{30^2}\sqrt{x^2}\sqrt{y^4}\sqrt{z^6}\)

\(\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0:\)

\(\implies 12x \cdot 30|x|\sqrt{y^4}\sqrt{z^6}\)

\(\implies 360x|x|\sqrt{y^4}\sqrt{z^6}\)

(We need to use the absolute value of √x² since the x term was originally to the power of 2, which means the value of x² is always positive since the exponent is even).

\(\textsf{Apply exponent rule} \quad \sqrt{a^m}=a^{\frac{m}{2}}:\)

\(\implies 360x|x|\cdot y^{\frac{4}{2}}\cdot z^{\frac{6}{2}}\)

Simplify:

\(\implies 360xy^2|xz^3|\)

(We need to use the absolute value of z³ since the z term was original to the power of 6, which means the value of z⁶ is always positive since the exponent is even).

hopefully this is correct..

it's either e = 1/3 or 3

Answer:

1/3 or 3^-1

Step-by-step explanation:

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The hip breadth for males that separates the smallest 99% from the largest 1% is determined to be 17.03 inches using the Z-score formula and percentile calculations.

According to the question, the engineers want to design seats in commercial aircraft that can accommodate at least 99% of all males. The mean and standard deviation of male hip breadth are 14.9 in. and 1.1 in., respectively.

To determine P99, we need to find the hip breadth for males that separates the smallest 99% from the largest 1%. The value of P99 can be determined using the Z-score formula, which is given by Z = (X - μ)/σ where X is the raw score, μ is the mean, σ is the standard deviation and Z is the standard score.

Since we are looking for the hip breadth for males that separates the smallest 99% from the largest 1%, we need to find the Z-score for the 99th percentile.

Using a Z-score table, we can find that the Z-score for the 99th percentile is 2.33. Substituting the given values into the Z-score formula, we get 2.33 = (X - 14.9)/1.1. Solving for X, we get:X = 2.33(1.1) + 14.9 = 17.03 inches

Therefore, the hip breadth for men that separates the smallest 99% from the largest 1% is 17.03 inches.

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Step-by-step explanation:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the

10

. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

6.11/104

You list the y coordinates of each point to form the range. The range is the set of all possible y values of a relation or function. Toss out any duplicates. The order of items in a set doesn't matter, but convention is to list the values from smallest to larger.

Extra info: The domain is {-4, -1, 1, 2, 3} which is the list of x coordinates of the points shown.

Answer:

A 19 yard gain

Step-by-step explanation:

Simple the question answers itself

Answer:

38.5 minutes

Step-by-step explanation:

105 divided by 15=7

7 x 5 minutes and 30 seconds is 38.5 minutes

The property illustrated in equation 4(-8+5) = -32 + 20 is the Distributive Property.

The Distributive Property states that when a number is multiplied by a sum or difference in parentheses, it can be distributed or multiplied by each term inside the parentheses separately, and then the results can be added or subtracted.

In this case, the number 4 is multiplied by the sum (-8 + 5). By applying the Distributive Property, we distribute the 4 to each term inside the parentheses:

4(-8 + 5) = (4 * -8) + (4 * 5)

This simplifies to:

4(-8 + 5) = -32 + 20

Finally, we can perform the addition:

-32 + 20 = -12

Therefore, the equation demonstrates the application of the Distributive Property.

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Let's assume David's average speed is S km/h.

A) To find David's average speed, we can use the formula: Speed = Distance / Time.

David completed the race in 5 hours, so his speed is S km/h. Therefore, we have:

S = Distance / 5

B) Ken's average speed is 9.8 km/h less than David's average speed, which means Ken's average speed is (S - 9.8) km/h.

Ken took 7 hours to complete the race, so we have:

S - 9.8 = Distance / 7

Now, we can solve the system of equations to find the values of S and Distance.

From equation (1): S = Distance / 5

Substitute this into equation (2):

Distance / 5 - 9.8 = Distance / 7

Multiply both sides of the equation by 35 to eliminate the denominators:

7 * Distance - 35 * 9.8 = 5 * Distance

7 * Distance - 343 = 5 * Distance

Subtract 5 * Distance from both sides:

2 * Distance - 343 = 0

Add 343 to both sides:

2 * Distance = 343

Divide both sides by 2:

Distance = 343 / 2 = 171.5 km

Therefore, the distance of the cycling race is 171.5 kilometers.

To find David's average speed, substitute the distance into equation (1):

S = Distance / 5 = 171.5 / 5 = 34.3 km/h

So, David's average speed was 34.3 km/h.\(\)

Answer:

A) 34.3 km/h

B) 171.5 km

Step-by-step explanation:

Since Ken's average speed is said to be 9.8km/h less than David's average speed, and we know that Ken's average speed is dependent on him traveling for 7 hours, then we have our equation to get the distance of the cycling race:

\(\text{Ken's Avg. Speed}=\text{David's Avg. Speed}\,-\,9.8\\\\\frac{\text{Distance}}{7}=\frac{\text{Distance}}{5}-9.8\\\\\frac{5(\text{Distance})}{7}=\text{Distance}-49\\\\5(\text{Distance})=7(\text{Distance})-343\\\\-2(\text{Distance})=-343\\\\\text{Distance}=171.5\text{ km}\)

This distance for the cycling race can now be used to determine David's average speed:

\(\text{David's Avg. Speed}=\frac{\text{Distance}}{5}=\frac{171.5}{5}=34.3\text{ km/h}\)

Therefore, David's average speed was 34.3 km/h and the distance of the cycling race was 171.5 km.

The number of tiles needed to cover the surface area of the box excluding the bottom is: 1,046 tiles.

The surface area of a box is the area surrounding all its faces. A box has 6 rectangular faces. Therefore, the total surface area of the box equals the sum of all 6 rectangular faces.

SA = 2(lw + lh + hw), where:

The image attached below shows the box Dmitri wants to cover. Since the bottom of the box would be excluded, therefore:

The surface area to be covered = surface area of the box - area of the bottom rectangular face

The surface area to be covered = 2(lw + lh + hw) - (l)(w)

l = 26

w = 15

h = 8

Substitute

The surface area to be covered = 2(l×w + lh + hw) - (l)(w) = 2·(15·26+8·26+8·15) - (26)(15) =

The surface area to be covered = 1436 - 390 = 1,046 cm

Area of one tile = 1 cm square

Number of tiles needed = 1,046/1

Number of tiles needed = 1,046 tiles.

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Similar means that the figure has the same shape, but not neccesarily the same size. It is said, also, that it is incoungruent, so it definetly doesn't have the same size. A transformation that gives you a similar but incongruent figure is a dialation, rotation and/or translation. I'll do a drawing to illustrate:

Notice that I've done the three of them. I have the same figure, smaller, in another position and rotated.

Answer:

5,700

Step-by-step explanation:

Since 5.7 is multiplied \(10^{3}\), move the decimal point in 5.7 three times to the right. The empty spaces after the 7 in 5.7 will be zeros so the final answer should be 5,700.

The missing ordered pairs that satisfy the equation y = 2x + 4 are (3, 10) and (2, 8).

The equation given is y = 2x + 4. To compute the missing x and y values, we need to substitute the given ordered pairs into the equation and solve for the missing variable.

Let's assume we have an ordered pair (x, y) that satisfies the equation y = 2x + 4.

For example, let's say one missing value is x = 3. We can substitute this into the equation:

y = 2(3) + 4

y = 6 + 4

y = 10

So, the missing ordered pair is (3, 10).

Similarly, if another missing value is y = 8, we can substitute this into the equation and solve for x:

8 = 2x + 4

4 = 2x

x = 2

So, the missing ordered pair is (2, 8).

In summary, the missing x and y values that satisfy the equation y = 2x + 4 are (3, 10) and (2, 8).

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Maureen's pension would be $50,035.20.

What is Percentage?

To compute a percentage, divide the value by the entire amount and multiply the result by 100. A percentage is a quantity or ratio that is stated as a fraction of one hundred. The percent sign, "%," is frequently used to represent it.

First, we need to calculate the average of Maureen's three highest salaries:

Average = (107,000 + 107,800 + 108,198) / 3

Average = 322,998 / 3

Average = 107,666

Next, we need to calculate 1.56% of this average:

Percentage = 1.56% * 107,666

Percentage = 1,667.84

Finally, we multiply this percentage by the number of years worked to find the pension:

Pension = 30 * 1,667.84

Pension = 50,035.20

So, Maureen's pension would be $50,035.20.

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The equation of the line passing through A and B is y = (4/5)x - (2/5).

A straight line's general equation is y = mx + c, where m is the gradient and y = c is the value at which the line intersects the y-axis. The y-axis intercept is denoted by the number c. A straight line with gradient m and intercept c on the y-axis has the equation y = mx + c.

The point-slope form of a linear equation can be used to find the equation of the line passing through points A and B:

y - y1 = m(x - x1) (x - x1)

where m denotes the slope of the line, (x1, y1) denotes the coordinates of point A or B, and (x, y) denotes the coordinates of any other point on the line.

To calculate the slope, we can use points A (3, 2) and B (8, 6).

m = (y2 - y1) / (x2 - x1) = (6 - 2) / (8 - 3)\s= 4 / 5

So the equation for the line connecting A and B is:

y - 2 = (4/5)(x - 3) (x - 3)

This equation can be simplified by multiplying both sides by 5:

5y - 10 = 4x - 12

Then we can rearrange it to form the slope-intercept equation, y = mx + b:

5y = 4x - 2

y = (4/5)x - (2/5)

As a result, the equation for the line connecting A and B is y = (4/5)x - (2/5).

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Answer:  20/3 * $10.50 = &73.5

.

Step-by-step explanation:

Answer:

73.5$

Step-by-step explanation:

21/7=3 so 10.50*7 will give the budget

Answer:

A

Step-by-step explanation:

Answer:

18.5

Step-by-step explanation:

27 rounds up to 30. 53 rounds up to 50

Answer:

19.00

Step-by-step explanation:

½ of a 12 inches pizza represents the bigger portion.

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

Let r be the radius of the circle. Then the area of the circle will be

A = πr² square units

½ of a 12-inch pizza, then the area is given as,

A = (π / 2) x (12 / 2)²

A = 56.52 square inches

30% of a 9-inch pizza. Then the area is given as,

A = 0.30 x π (9 / 2)²

A = 19.0755 square inches

½ of a 12 inches pizza represents the bigger portion.

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The function m(x) = 2tan(3x+4) is obtained by applying a sequence of transformations to the parent tangent function.

To determine the sequence of transformations, let's break down the given function:

1. Inside the tangent function, we have the expression (3x+4). This represents a horizontal compression and translation.

2. The coefficient 3 in front of x causes the function to compress horizontally by a factor of 1/3. This means that the period of the function is shortened to one-third of the parent tangent function's period.

3. The constant term 4 inside the parentheses shifts the function horizontally to the left by 4 units. So, the graph of the function is shifted to the left by 4 units.

4. Outside the tangent function, we have the coefficient 2. This represents a vertical stretch.

5. The coefficient 2 multiplies the output of the tangent function by 2, resulting in a vertical stretch. This means that the graph of the function is stretched vertically by a factor of 2.

In summary, the sequence of transformations applied to the parent tangent function to create the function m(x) = 2tan(3x+4) is a horizontal compression by a factor of 1/3, a horizontal shift to the left by 4 units, and a vertical stretch by a factor of 2.

Example:
Let's consider a point on the parent tangent function, such as (0,0), which lies on the x-axis.

After applying the transformations, the corresponding point on the function m(x) = 2tan(3x+4) would be:
(0,0) -> (0,0) (since there is no vertical shift in this case)

This example helps illustrate the effect of the transformations on the graph of the function.

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a) The rule that represents the height as a function of the number of bounces is described by H(n) = 1.5 · (71 / 100)ˣ⁻¹. (Correct choice: B)

b) The height at the top of the sixth path is equal to 0.27 meters. (Correct choice: B)

In this problem we need to derive the equation that represents maximum height as a function of the number of bounces:

H(n) = a · (r / 100)ˣ⁻¹

Where:

If we know that a = 1.5 m and r = 71, then the rule for the sequence is:

H(n) = 1.5 · (71 / 100)ˣ⁻¹

And the height at the top of the sixth path:

H(6) = 1.5 · (71 / 100)⁶⁻¹

H(6) = 0.27 m

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The graph of y = 3 x 2^x passes through the coordinate points (2,12) and (3,24).

To write a question in the form of y=a x b^x that passes through the coordinate points (2,12) and (3,24), we need to solve for the values of a and b.

First, let's substitute the coordinates (2,12) into the equation:
12 = a x b^2

Next, let's substitute the coordinates (3,24) into the equation:
24 = a x b^3

We now have two equations with two unknowns (a and b), which we can solve using algebra.

From the first equation, we can solve for a:
a = 12 / b^2

We can then substitute this value of a into the second equation:
24 = (12 / b^2) x b^3

Simplifying this equation, we get:
2 = b

We can then substitute this value of b back into the equation for a:
a = 12 / 2^2
a = 3

Therefore, the equation of the graph that passes through the coordinate points (2,12) and (3,24) is:
y = 3 x 2^x

We can check that this equation is correct by plugging in the coordinates:
When x = 2: y = 3 x 2^2 = 12
When x = 3: y = 3 x 2^3 = 24
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A graph of the given piecewise-defined function is shown in the image below.

In Mathematics and Geometry, a piecewise-defined function simply refers to a type of function that is defined by two (2) or more mathematical expressions over a specific domain.

Generally speaking, the domain of any piecewise-defined function simply refers to the union of all of its sub-domains. By critically observing the graph of this piecewise-defined function, we can reasonably infer and logically deduce that it is constant over several intervals or domains such as x > 2 and x < -2.

In conclusion, this piecewise-defined function has a removable discontinuity.

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Answer:

We can solve this problem by:-

Here,

X=38°(Being vertically opposite angle)

So, X=38°

Vertical angles are congruent

The value of x = 38 degrees.

Given :

We are given with two lines that intersects .

we need to find out the vertical angle for the given angle.

When two lines intersects then the opposite angles are equal .

Opposite angles we call it as vertical angles .

Vertical angles are equal when two line intersects.

From the given diagram , vertical angles x  and 38  are congruent .

so \(x=38\)

The value of x is 38 degrees.

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Front-end rounding 10,355 to the nearest ten is 10,360.

Rounding is the process of approximating a number to a specified degree of accuracy or precision. Rounding is useful when we want to simplify numbers or express them in a more manageable or meaningful way. There are various methods of rounding, such as rounding up, rounding down, and rounding to the nearest value.

To round a number to a specified degree of accuracy, we first identify the place value we are rounding to, such as units, tens, hundreds, etc. We then look at the digit in that place value and the digit to the right of it. If the digit to the right is 5 or greater, we round up by adding 1 to the digit in the place value we are rounding, and then replace all the digits to the right with zeros. If the digit to the right is less than 5, we round down by simply dropping all the digits to the right.

To front-end round a number, you look at the digit in the place value you are rounding to and round up or down based on the digit to the right of that place value.

To front-end round 10,355 to the nearest ten, we look at the tens place, which is the second digit from the right. The digit in the tens place is 5, which is greater than or equal to 5, so we round up.

To round up, we add 1 to the digit in the tens place and replace all the digits to the right with zeros. So, rounding up 10,355 to the nearest ten gives us:

10,360

Therefore, front-end rounding 10,355 to the nearest ten is 10,360.

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Answer:

x = 3

Step-by-step explanation:

A vertical line is drawn on a graph paper, which passes through points (3, 3) and (3, -3).  For a vertical line, slope or gradient is undefined.
Therefore, the equation of vertical line is the common x-coordinate of the points along the line. In this case, the common x-coordinate is 3

∴Equation of line

        x = 3

Based on the description provided, the section of the chart that represents the point where a bill is first debated in subcommittees is: C and D

In the given chart, the parallel lines represent the progression of a bill through various stages in the legislative process. The boxes on the top line represent one set of actions or steps, while the boxes on the bottom line represent another set of actions or steps.

Moving from left to right on the chart, the boxes A and B are paired, representing a particular stage in the process. Similarly, the boxes C and D are paired, indicating another stage in the process.

In the context of the question, the stage where a bill is first debated in subcommittees is represented by the boxes C and D.

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