15-36 Find the limit. 1 15. lim *-** 2x + 3 1 - x - x2 17. lim ** 2x2 - 7 x3 + 5x 2x3 – x2 + 4 19. lim

If Sandy works at a clothing store. She makes $9 per hour plus earns 15% commission on her sales. The amount that is closest to how much she will earn in hourly wages and commission for those two weeks is A $592.

Earnings can be defined as the money a person earn as wages or as salary.

First step is to find the amount that Sandy earns per hours

Earnings per hour = 9+ (0.15×9)

Earnings  = $10.35 per hour

Second step is to find her earnings

Earnings =73 × $10.35

Earnings = $755.55

Closest amount is $592.

Therefore  the correct option is A.

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The complete question is:

Sandy works at a clothing store. She makes $9 per hour plus earns 15% commission on her sales. She worked 73 hours over the last two weeks and had a total of $2,830 in sales before taxes.

Which of the following is closest to how much she will earn in hourly wages and commission for those two weeks?

A $592

B $890

C $386

D $298

Answer:

P: y=-4x

N: y=x-1

L: y=4

M: y=-2x+4

Step-by-step explanation:

p: y=-4x

because the line intercepts only x

L: y=4

because the line intercepts only y

N: y=x-1

(0,-1),(1,0)

(x1,y1),(x2,y2)

M: y=-2x+4

(0,4),(2,0)

(x1,y1),(x2,y2)

eqn of aline y2-y1/x2-x1

the turning point(s) of a polynomial function by using below steps

To find the turning point of a polynomial function, follow these steps:

1. Determine the degree of the polynomial. The turning point will occur in a polynomial of odd degree (1, 3, 5, etc.) or at most one turning point in a polynomial of even degree (2, 4, 6, etc.).

2. Write the polynomial function in the form f(x) = axⁿ + bxⁿ⁻¹ + ... + cx + d, where n represents the degree of the polynomial and a, b, c, d, etc., are coefficients.

3. Find the derivative of the polynomial function, f'(x), by differentiating each term of the function with respect to x. This will give you a new function that represents the slope of the original polynomial function at any given point.

4. Set f'(x) equal to zero and solve for x to find the x-coordinate(s) of the turning point(s). These are the values where the slope of the polynomial function is zero, indicating a potential turning point.

5. Substitute the x-coordinate(s) obtained in step 4 into the original polynomial function, f(x), to find the corresponding y-coordinate(s) of the turning point(s).

6. The turning point(s) of the polynomial function is given by the coordinates (x, y), where x is the x-coordinate(s) found in step 4 and y is the y-coordinate(s) found in step 5.

By following these steps, you can find the turning point(s) of a polynomial function.

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The blood test for determining coagulation activity defects is called the Prothrombin Time (PT) test.

The blood test for determining coagulation activity defects is called the Prothrombin Time (PT) test. This test measures the time it takes for blood to clot and is used to assess the functioning of the clotting factors in the blood. It is commonly used to evaluate the extrinsic pathway of the coagulation cascade, which involves factors outside of the blood vessels.

The PT test is an important diagnostic tool in hematology and is used to diagnose or monitor conditions that affect blood clotting, such as bleeding disorders or the effectiveness of anticoagulant medications. By measuring the PT, healthcare professionals can determine if there are any abnormalities in the coagulation process and make appropriate treatment decisions.

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Given that

The Venn diagram will be shown below

Therefore,

From the calculations done above, we can see that there is no intersection between the students that took algebra and biology.

Hence, the correct option is Option B.

Yes, this could be true if there were 113 students taking algebra but not biology, and there were 87 students taking biology but not algebra.

The attached figures represent the transformations of the triangle ABC

From the figure, the coordinates of the triangle ABC are:

A =  (-2, 3)

B = (0, 2)

C = (3, 4)

Next, we carry out the required transformations on the above coordinates of the triangle ABC

The rotation

Here, we rotate the triangle 90 degrees clockwise across the origin

The rule of this transformation is:

(x, y) = (y, -x)

So, we have:

A' =  (3, 2)

B' = (2, 0)

C' = (4, -3)

See figure (1) in the attachment for the graph of the rotation transformation

The translation

Here, we translate the triangle up by 3 units

The rule of this transformation is:

(x, y) = (x, y + 2)

So, we have:

A' =  (-2, 5)

B' = (0, 4)

C' = (3, 6)

See figure (2) in the attachment for the graph of the reflection transformation

The reflection

Here, we reflect the triangle across the y-axis.

The rule of this transformation is:

(x, y) = (-x, y)

So, we have:

A' =  (2, 3)

B' = (0, 2)

C' = (-3, 4)

See figure (3) in the attachment for the graph of the reflection transformation

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Answer:

v=20π ft/s

Step-by-step explanation:

Given:

Distance from the security car to the movie theater, D=25 ft

Distance of the reflection from the car, d=30 ft

Speed of rotation of the strobe lights, 2 rev/s

To find the speed at which the reflection of the security strobe lights is moving along the wall of the movie theater, we need to calculate the linear velocity of the reflection when it is 30 ft from the car.

We can start by finding the angular velocity in radians per second. Since the strobe lights rotate at 2 revolutions per second, we can convert this to radians per second.

ω=2πf

=> ω=2π(2)

=> ω=4π rad/s

The distance between the security car and the reflection on the wall of the theater is...

r=30-25= 5 ft

The speed of reflection is given as (this is the linear velocity)...

v=ωr

Plug our know values into the equation.

v=ωr

=> v=(4π)(5)

∴ v=20π ft/s

Thus, the problem is solved.

The speed of the reflection of the security strobe lights along the wall of the movie theater is 2π ft/s.

To solve this problem, we can use the concept of related rates. Let's consider the following variables:

x: Distance between the security car and the movie theater wall

y: Distance between the reflection of the security strobe lights and the security car

θ: Angle between the line connecting the security car and the movie theater wall and the line connecting the security car and the reflection of the strobe lights

We are given:

x = 25 ft (constant)

y = 30 ft (changing)

θ = 2 revolutions per second (constant)

We need to find the speed at which the reflection of the security strobe lights is moving along the wall (dy/dt) when the reflection is 30 ft from the car.

Since we have a right triangle formed by the security car, the movie theater wall, and the reflection of the strobe lights, we can use the Pythagorean theorem:

x^2 + y^2 = z^2

Differentiating both sides of the equation with respect to time (t), we get:

2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)

Since x is constant, dx/dt = 0. Also, dz/dt is the rate at which the angle θ is changing, which is given as 2 revolutions per second.

Plugging in the known values, we have:

2(25)(0) + 2(30)(dy/dt) = 2(30)(2π)

Simplifying the equation, we find:

60(dy/dt) = 120π

Dividing both sides by 60, we get:

dy/dt = 2π ft/s

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Answer: the answer is x=0

Step-by-step explanation:

The linear equation doesn't have a solution.

The linear equation given is illustrated as: 4x-(2x-1) = x+5+x-6

This will be solved thus:

4x - 2x + 1 = x+5+x-6

4x - 2x + 1 = 2x - 1.

2x + 1 = 2x - 1

Collect like terms

2x - 2x = -1 - 1

0 = -2

This illustrates that the equation doesn't have a solution.

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Answer:

Step-by-step explanation:

Convert 84lbs to kg (mass is measured in kg ).

\(1 \: lb = 0.453592kg \\ 84 \: lb = x \: kg\)

Cross Multiply

\(x = 84 \times 0.453592 \\ x = 38.1018\)

Answer:

D. 38kg

Step-by-step explanation:

A boy weighs 84 lbs, what is his mass 38kg

The total price of the shoes, including tax is $39.944.

Given is that a pair of shoes usually sells for $56. The shoes are 40% off, and sales tax is 6%.

We can write the total cost of shoes as -

{x} = 56 - {40% of 56} + 6% of {40% of 56}

{x} = 56 - {40/100 x 56} + 6/100 x {40/100 x 56}

{x} = 56 - 22.4 + 1.344

{x} = 56 - 21.056

{x} = 34.944

Therefore, the total price of the shoes, including tax is $39.944.

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Parametrization of equations x=x(t), y=y(t) for f(x)=x^8−x^2−6 from (5,−4) to (9,−1) is that parametrization does indeed connect the points (5, -4) and (9, -1).

A parametrization for the curve that connects the points (5, -4) and (9, -1) given by the function f(x) = \(x^8 - x^2 - 6.\)

To do this, we can use the parameter t to represent points on the curve as follows:

x(t) = 5 + 4t, since we want x to start at 5 and end at 9, so we need to add 4 to x over the interval [0, 1].

Substituting this into our function f(x), we get:

y(t) = f(x(t)) = \((5 + 4t)^8 - (5 + 4t)^2 - 6\).

Therefore, our parametrization is:

x(t) = 5 + 4t

y(t) = (5 + 4t)^8 - (5 + 4t)^2 - 6

To verify that this parametrization does indeed connect the points (5, -4) and (9, -1), we can check that x(0) = 5, x(1) = 9, y(0) = f(5) = -4, and y(1) = f(9) = -1.

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Answer:

  B.  False

Step-by-step explanation:

You want to know if it is true that when each of seven persons in a group shakes hands with each of the other six persons, a total of forty-two handshakes occurs.

The count of 42 handshakes includes every one of 7 shaking hands with each of the remaining 6, without regard to whether they met before.

The count will include A shaking hands with B, and B shaking hands with A. That handshake will be counted twice, so the number 42 overstates the actual number of handshakes by a factor of 2.

It is false that there will be 42 handshakes. (There will be only 21.)

The net income (or loss) for: (a) Net income for 2019: $165,000. (b) Net income for 2020: $52,000. (c) Net income for 2021: $45,000.

To calculate the net income (or loss) for each year, we need to analyze the change in owner's equity. The owner's equity is the residual interest in the assets of the company after deducting liabilities. It represents the owner's investment and the accumulated net income (or loss) over time.

(a) For 2019:

The change in owner's equity can be calculated as follows:

Owner's Equity (2019) = Owner's Equity (2018) + Additional Investment - Drawings + Net Income (or Loss)

$493,000 = $100,000 + $0 - $24,000 + Net Income (or Loss)

Solving for Net Income (or Loss), we find:

Net Income (or Loss) for 2019 = $493,000 - $100,000 - $0 + $24,000 = $165,000

(b) For 2020:

The change in owner's equity can be calculated as follows:

Owner's Equity (2020) = Owner's Equity (2019) + Additional Investment - Drawings + Net Income (or Loss)

$553,000 = $493,000 + $40,000 - $0 + Net Income (or Loss)

Solving for Net Income (or Loss), we find:

Net Income (or Loss) for 2020 = $553,000 - $493,000 - $40,000 + $0 = $52,000

(c) For 2021:

The change in owner's equity can be calculated as follows:

Owner's Equity (2021) = Owner's Equity (2020) + Additional Investment - Drawings + Net Income (or Loss)

$683,000 = $553,000 + $15,000 - $25,000 + Net Income (or Loss)

Solving for Net Income (or Loss), we find:

Net Income (or Loss) for 2021 = $683,000 - $553,000 - $15,000 + $25,000 = $45,000

Therefore, the net income (or loss) for 2019 is $165,000, for 2020 is $52,000, and for 2021 is $45,000.

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Answer:

x is 46.67

y is 28.4°

Step-by-step explanation:

To solve for x we use sine

sin ∅ = opposite / hypotenuse

AC is the opposite

x is the hypotenuse

so we have

sin 59° = 40 / x

x sin 59 = 40

Divide both sides by sin 59

x = 40/sin 59

x = 46.67

To solve for y we also use sine

sin y = 30/ 63

y = sin^-1(30/63)

y = 28.4°

Hope this helps you

The numeric value of the expression √7 x√2/√2 is given as follows:

√7.

The expression for this problem is defined as follows:

√7 x√2/√2

For the second factor of the multiplication, we have a fraction in which the numerator and the denominator are the same. As the fraction is equivalent to a division operation, the quotient is of pone, as follows:

√2/√2 = 1.

Then the numeric value of the expression is obtained with the multiplication by 1, as follows:

√7 x 1 = √7.

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Answer: 1

Step-by-step explanation: the lowest number they divide into evenly is 1

The solutions to the quadratic equation \(2x^2 + 6x - 1 = 0\), obtained by completing the square, are x = -3 + √10 and x = -3 - √10.

To solve the quadratic equation\(2x^2 + 6x - 1 = 0\)by completing the square, follow these steps:

Ensure that the coefficient of \(x^2\) is 1. In this case, it is already 2, so we don't need to make any changes.

Move the constant term to the other side of the equation. Add 1 to both sides:

\(2x^2 + 6x = 1\)

Divide the coefficient of x by 2 and square it. In this case, (6/2)^2 = 9.

Add the result from step 3 to both sides of the equation:

\(2x^2 + 6x + 9 = 1 + 9\)

Simplifying, we get:

\(2x^2 + 6x + 9 = 10\)

Write the left side of the equation as a perfect square trinomial. In this case, it is \((x + 3)^2.\)

\((x + 3)^2 = 10\)

Take the square root of both sides:

\(√[(x + 3)^2] = ±√10\)

Simplifying:

\(x + 3 = ±√10\)

Solve for x by subtracting 3 from both sides:

x = -3 ± √10

So, the solutions to the quadratic equation \(2x^2 + 6x - 1\)= 0, obtained by completing the square, are x = -3 + √10 and x = -3 - √10.

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the final answer is that if f(x) = -i and 9(x) = 2x³ - i - 3√x, we cannot find f(x) = g(x).To find f(x) = g(x), we need to first find the value of g(x). Given that 9(x) = 2x³-√ - I, we can simplify this expression by first adding the square root terms:
9(x) = 2x³ - √(I) - √(9x)

Next, we can simplify the square roots:
9(x) = 2x³ - i - 3√x
Now we can see that g(x) = 2x³ - i - 3√x.
To find f(x), we need to solve the equation f(x) = -√I. Since f(x) is not given, we can use any function that satisfies this equation. For example, we can let f(x) = -i.

To solve this problem, we need to apply basic algebraic manipulations and solve for the given functions f(x) and g(x). First, we can simplify the expression for 9(x) by adding the two square roots:
9(x) = 2x³ - √(I) - √(9x)
Next, we can simplify the two square roots by taking their values:
9(x) = 2x³ - i - 3√x
Now we can see that g(x) = 2x³ - i - 3√x.
To find f(x), we need to solve the equation f(x) = -√I. However, the function f(x) is not given explicitly in the problem. Therefore, we can use any function that satisfies this equation. For example, we can let f(x) = -i.
Now we can compare the expressions for f(x) and g(x) to see if they are equal.
f(x) = -i
g(x) = 2x³ - i - 3√x
Since f(x) is a constant function and g(x) is a polynomial function, we can see that f(x) = g(x) is not true in this case.

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Answer:

the equation of this line is x = -5

Step-by-step explanation:

To write an exponential function in the form y = ab^x that goes through the points (0,11) and (2,396), we can use the fact that the exponential function is defined as y = ab^x, where a is the initial value and b is the growth factor.

First, we can find the growth factor by using the following equation: b = y2/y1.

In this case: b = 396/11 = 36

Next, we can use the point (0,11) and the growth factor to find the value of a.

Since we know that y = ab^x, we can substitute the point (0,11) and the growth factor into the equation:

11 = a(36)^0

a = 11

So, the exponential function that goes through the points (0,11) and (2,396) is: y = 11 * 36^x

It is important to note that the above function will pass through the points (0,11) and (2,396) but it may not pass through any other points. It is also a good practice to check the function by substituting the point (0,11) and (2,396) to confirm it gives the correct output.

Elina's GPA is greater than 2.0. If this condition is met, the formula returns "OK standing". If neither of the conditions is met, the formula returns "Bad standing".

To determine Elina's standing based on her GPA, you can use the following formula:

=IF(G6 > 3.0, "Good standing", IF(G6 > 2.0, "OK standing", "Bad standing"))

In this formula, we use the IF function to evaluate different conditions. The first condition checks if Elina's GPA (in cell G6) is greater than 3.0. If it is, the formula returns "Good standing". If the first condition is not met, it moves to the second condition, which checks if Elina's GPA is greater than 2.0. If this condition is met, the formula returns "OK standing". If neither of the conditions is met, the formula returns "Bad standing".

By using nested IF statements, we can evaluate multiple conditions and return the corresponding standing based on Elina's GPA.

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The root of the graph of f(x) = \((x-5)^{3} (x+2)^{2}\) touches the x axis at -2 and 5.

What is root of graph ?

A rooted graph is a graph in which one node is labeled in a special way so as to distinguish it from other nodes. The special node is called the root of the graph. The rooted graphs on nodes are isomorphic with the symmetric relations on nodes.

Have given,

f(x) = \((x-5)^{3} (x+2)^{2}\)

If a curve touches the x-axis then f(x) = 0

⇒\((x-5)^{3} (x+2)^{2}\) = 0.

But if ab = 0 ⇒ either a = 0 or b = 0 or both zero.

⇒\((x - 5)^{3}\) = 0 and \((x + 2)^{2}\) = 0

⇒ (x - 5) = 0 and x + 2 = 0

⇒ x = 5 and x = - 2.

The root of the graph of f(x) = \((x-5)^{3} (x+2)^{2}\) touches the x axis at -2 and 5.

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Answer:

The first two.

Step-by-step explanation:

See that L is 600mm MORE than W.

From there, you can note that L = W+600  

or rearrange the formula and get W= L-600

Then, see that the perimeter of a flag is 2L + 2W

(Because there are two four sides to a rectangle, 2 width, 2 length)

It must total to be 5 meters, or 5000mm

Thus,

2L + 2W = 5000

First, we need to calculate the total amount of time the machine runs each day:

Starting time: 09:30

Ending time: 16:10

We can convert the starting time and ending time to minutes:

09:30 = 9 x 60 + 30 = 570 minutes

16:10 = 16 x 60 + 10 = 970 minutes

The total running time of the machine is:

970 - 570 = 400 minutes

Since the machine produces a bolt every 8 seconds, we need to convert the running time from minutes to seconds:

400 x 60 = 24,000 seconds

Finally, we can calculate the number of bolts produced by dividing the total running time by the time it takes to produce one bolt:

24,000 / 8 = 3,000

Therefore, the machine produces 3,000 bolts each day.

Step-by-step explanation:

Prime factors of 105 is

105 = 3 × 5 × 7

Answer:

3

Step-by-step explanation:

use the formula

y2-y1/x2-x1

1-7/5-7= -6/-2=3

The angle between the stick and the base of the box is 77. 9 degrees

To determine the angle between the stick and the base, we have to know the trigonometric identities.

These identities are;

From the information given, we have;

sin A = FB/AB

Given that;

GB = 14.5cm

AB = 18. 6cm

substitute for the length of the sides, we have;

sin A = 14.5/18. 6

Divide the values, we have;

sin A = 0. 7796

Find the inverse sine

A = 77. 9 degrees

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Step-by-step explanation:

58 +38 = 96 degree

so we do 180 - 96 = 84 degree valur of x for one triangle

so opposite side angke x will be 96

so again we do 96 +15 = 111 degree

180 - 111 = 69 degree

Using factors, K has a value of -7.

A divisor of an integer n, also known as a factor of n, is an integer m that may be multiplied by another integer to create n. In this case, it is also possible to assert that n is a multiple of m.

Given,

f(x) = 3x³ + kx- 10

Given factor of the equation is (x - 2)

Let us assume:

x - 2 = 0

x = 2

Since, x-2 is a factor of f(x)

∴ By factor theorem

f(2) = 0

3(2)³ + k(2) - 10 = 0

3(8) + 2k - 10 = 0

24 + 2k - 10 = 0

14 + 2k = 0

2k = -14

k = -14/2

k = -7

Hence, The value of k is -7

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