S
9. Is the square root of -68 a rational number?

The derivative of [tex]f(x) = \sinh{(7e^x + 2)}[/tex] is given as follows:

B. [tex]7e^x\cosh{(7e^x + 2)}[/tex]

The function in this problem is given as follows:

[tex]f(x) = \sinh{(7e^x + 2)}[/tex]

This function is a composite function, hence we use the chain rule for derivatives, which state that:

If f(x) = f(g(x)) then f'(x) = g'(x)f'(g(x)).

The inner and outer functions are given as follows:

The derivative of the hyperbolic sine is given as follows:

cosh(x).

(derivative of the outer function).

The derivative of the exponential is given as follows:

[tex](7e^x + 2)^{\prime} = 7e^x[/tex]

(derivative of the inner function).

Hence the derivative of the function is given as follows:

[tex]7e^x\cosh{(7e^x + 2)}[/tex]

(application of the chain rule).

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The resulting image of Triangle ABC after reflecting it across the line y=-x and rotating it 90 degrees clockwise is Triangle A''B''C'' with vertices at (2, 3), (1, 4), and (5, 1).

To find the resulting image of Triangle ABC after reflecting it across the line y=-x and rotating it 90 degrees clockwise, we can follow these steps:
1. Draw Triangle ABC and the line y=-x on a coordinate plane.
2. Reflect Triangle ABC across the line y=-x to get its image, Triangle A'B'C'.
3. Draw the image Triangle A'B'C' on the coordinate plane.
4. Rotate Triangle A'B'C' 90 degrees clockwise around the origin to get its final image.
5. Draw the final image of Triangle ABC, which is Triangle A''B''C''.
To find the coordinates of the image points, we can use the transformation rules for reflections and rotations.
First, let's find the image points after reflecting Triangle ABC across the line y=-x:
- The point A(-2, 3) is reflected to the point A'(-3, 2) by swapping the x and y coordinates and changing their signs.
- The point B(4, 1) is reflected to the point B'(-1, -4) by swapping the x and y coordinates and changing their signs.
- The point C(1, 5) is reflected to the point C'(-5, -1) by swapping the x and y coordinates and changing their signs.
Now, let's find the image points after rotating Triangle A'B'C' 90 degrees clockwise around the origin:
- To rotate a point (x, y) 90 degrees clockwise around the origin, we can use the formulas (-y, x).
- Applying this formula to each image point, we get:
 - A''(2, 3)
 - B''(1, 4)
 - C''(5, 1)
Therefore, the resulting image of Triangle ABC after reflecting it across the line y=-x and rotating it 90 degrees clockwise is Triangle A''B''C'' with vertices at (2, 3), (1, 4), and (5, 1).

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The measures of the arcs are: 16. m(MN) = 72°;  17. m(NQR) = 180°; 18. m(NQ) = 108°; 19. m(MRP) = 265°; 20. m(QR) = 72°; 21. m(MR) = 108°; 22. m(QMR) = 288°; 23. m(PQ) = 13°; 24. m(PRN) = 265°; 25. m(MQN) = 288°

To determine the measures of each of the arcs, note that the central angle will have the same measure as the arc.

16. m(MN) = m<QRN

Substitute:

m(MN) = 72°

17. m(NQR) = 180° [semicircle is equal to 180 degrees]

18. m(NQ) = 180 - 72

m(NQ) = 108°

19. m(MRP) = 180 + (180 - 95)

m(MRP) = 180 + 85

m(MRP) = 265°

20. m(QR) = 72° [central angle is equal to intercepted arc measure)

21. m(MR) = 180 - 72

m(MR) = 108°

22. m(QMR) = 360 - 72 = 288°

23. m(PQ) = 180 - 95 - 72 = 13°

24. m(PRN) = 360 - 95

m(PRN) = 265°

25. m(MQN) = 360 - 72

m(MQN) = 288°

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Answer: $31.58

Step-by-step explanation:

Let us say that x is equal to the bill's amount before adding the tip. Please note that a percent divided by 100 becomes a decimal, so 22.1% / 100 = 0.221. We will write an equation to represent this situation.

         x + 0.221x = $38.56

Next, we will solve by combining like terms.

        1.221x = $38.56

Lastly, we will divide both sides of the equation by 1.221.

        x = $31.58

      Camille's bill was $31.58 before adding a 22.1% tip.

Based on the Supermarkets Agreement 2012, the normal weekly pay for an adult aged 21 and over is $565.90.

The wage rates for a junior employee are based on a percentage of the adult rate, but the exact percentage is not provided. Therefore, it is impossible to determine how many people aged 16 and under 17 years can be employed for the same cost as one adult employee without knowing the specific percentage and calculating the wages accordingly  Based on the Supermarkets Agreement 2012, the normal weekly pay for an adult aged 21 and over is $565.90. To determine how many people aged 16 and under 17 years can be employed for the same cost as one adult employee, we need to know the percentage of the adult rate for junior employees. Once we have that information, we can calculate the number of junior employees that can be employed for the same cost as one adult employee.

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The water level in the aquarium will rise by 18 cm.

The volume of water in the aquarium before adding the sand is given by:

Volume = (1/2) x 23 cm x 15 cm = 172.5 cm³

When the sand is added, its volume is 2350 cm³. Therefore, the new volume of water and sand in the aquarium is:

 = 172.5 cm³ + 2350 cm³

 = 2522.5 cm³

Let h be the height of the water level after adding the sand. The new volume of water in the aquarium is given by:

Volume = (1/2) x 23 cm x 15 cm x h

Setting this equal to the new total volume, we can solve for h:

(1/2) x 23 cm x 15 cm x h = 2522.5 cm³

h = 2522.5 cm³ / (1/2 x 23 cm x 15 cm) = 18 cm

Therefore, the water level in the aquarium will rise by 18 cm.

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The smallest angle that is in the triangle STU is 9 degrees.

A triangle can be solved by using information provided to determine the triangle's unknown side lengths and angles. Depending on the information at hand, a triangle can be solved in a variety of ways as we see here.

To find the side u

[tex]u^2 = (41b)^2 + (44b)^2 - 2(41b * 44b)Cos 128\\u^2 = 1681b^2 + 1936b^2 - 3608b^2Cos 128\\u^2 = 3617b^2 - 2221b^2\\u^2 = 1396b^2[/tex]

u = 37b

Then Using the sine rule;

a/Sin A = b/Sin B

37b/Sin 128 = 41b/SinB

B = sin-1 (41b * Sin 128/37b)

B = 61 degrees

Then;

C = 180 - (128 + 61)

C = 9 degrees

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Answer: 3. Prism

explanation: An apex is basically, the point where all lines meet at one point, and a prism is the one shape that doesn't have a apex. Hope this helps!

a) A table and a graph for this situation is shown in the image below.

b) You can use the table or graph to predict how many weeks it will take Martha to earn enough money to pay for the new computer by comparing the week when her savings are both equal.

c) Since the x-value and y-value in both the table and the graph increase simultaneously, it is an example of linear growth.

In this scenario, the variable x would represent the number of weeks while the variable y would represent the total amount of savings. Since Martha received $200 for her birthday and makes $150 each week, a linear equation in slope-intercept form that models the situation is given by;

y = mx + c

y = 150x + 200

Next, we would use an online graphing calculator to make a table and a graph for this situation as shown in the image attached below.

Part b.

The table and the graph both have the total amount of savings (y) equal to $1,850 when x is equal to 11 weeks. This ultimately implies that, it would take Martha between 11 weeks to save enough money to buy this new computer.

Part c.

By critically observing the table and the graph, we can logically deduce that there is a linear relationship between the variables because both the x-value and y-value increase simultaneously.

Therefore, this is an example of a linear growth.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The length of segment WK is given as follows:

B. [tex]2\sqrt{5}[/tex]

Suppose that we have two points of the coordinate plane, and the ordered pairs have coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].

The shortest distance between them is given by the equation presented as follows, derived from the Pythagorean Theorem:

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

The endpoints of the segment in this problem are given as follows:

K(-2,0) and W(-6,-2).

Hence the length of the segment is given as follows:

[tex]\sqrt{(2 - (-6))^2 + (0 - (-2))^2} = \sqrt{20} = \sqrt{4 \times 5} = 2\sqrt{5}[/tex]

Meaning that option B is the correct option in the context of this problem.

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The fixed cost per ball went to $4.5 when the company produce 22,500.

fixed cost per ball is three dollars when the company produces 15,000

fixed cost per ball went x to produce 22,500

So,

3 : 15000 = x : 22,500

3/15,000 = x/22,0/500

cross product

3 × 22,500 = 15,000 × x

67,500 = 15,000x

divide both sides by 15,000

x = 67,500 /15,000

x = 4.5

Therefore, the fixed cost per ball to produce 22,500 is $4.5

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The number line with the numbers -4 and 3 graphed is given by the image presented at the end of the answer.

The origin point on the number line is given as follows:

0.

Hence positive numbers and negative numbers are plotted as follows:

The numbers for this problem are given as follows:

-4 and 3.

Hence they are plotted as follows:

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Answer: 4+9=10+3

Step-by-step explanation:

We can subtract the number, 4 to get 3. The extra one from the 4 would go to the nine.

The equation of L2 is y = 2x/3 + 23/3.

The equation of L3 is y = -3x/2 - 7.

The equation of L2 in standard form is 2x/3 - y = -23/3.

The x and y intercepts of L3 are (-4.667, 0) and (0, -7) respectively.

The point of intersection between L2 and L3 is (-6.769, 3.154).

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + c

Where:

Based on the information provided about line 1 (L1) and line 2 (L2), we have the following equation;

Equation of line 1 (L1): 3x + 2y = 12

y = -3x/2 + 12

Since line L2 is perpendicular to L1 at (2, 9) and a slope of 2/3, the equation of L2 can be calculated as follows;

y - y₁ = m(x - x₁)

y - 9 = 2/3(x - 2)

y = 2x/3 + 23/3

Since L3 is parallel to L1 and passes through point (-4, -1), the equation of L2 can be calculated as follows;

y - y₁ = m(x - x₁)

y + 1 = -3/2(x + 4)

y = -3x/2 - 6 - 1

y = -3x/2 - 7

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The theoretical probability of having three dogs or three cats is p^3 + q^3.

The theoretical probability of the family having two dogs or two cats depends on the specific probability of each event. Let's assume that the probability of having a dog is 0.5 and the probability of having a cat is also 0.5 (which is a simplification). In this case, the probability of having two dogs is 0.5 x 0.5 = 0.25, and the probability of having two cats is also 0.5 x 0.5 = 0.25. Therefore, the theoretical probability of the family having two dogs or two cats is 0.25 + 0.25 = 0.5 or 50%.

To simulate which two pets the family has using two different coins, we can assign one pet to each coin face (e.g., heads for dog and tails for cat). Then, we can flip both coins and record the outcome to determine which pets the family has. For example, if the first coin shows heads and the second coin shows tails, the family has one dog and one cat.

After flipping both coins 50 times and recording the outcomes in a table, we can calculate the experimental probability of the family having two dogs or two cats. Let's assume that we observed 12 occurrences of two dogs, 10 occurrences of two cats, and 28 occurrences of other outcomes (e.g., one dog and one cat). The experimental probability of the family having two dogs or two cats is (12 + 10) / 50 = 0.44 or 44%.

If the family has three pets, the theoretical probability of having three dogs or three cats can be calculated using a similar approach. Let's assume that the probability of having a dog is p and the probability of having a cat is q (where p + q = 1). Then, the probability of having three dogs is p x p x p = p^3, and the probability of having three cats is q x q x q = q^3. Therefore, the theoretical probability of having three dogs or three cats is p^3 + q^3.

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The nearest Whole percent, the percent increase of women students is approximately 21%.

The percent increase of women students, we need to compare the number of women students in 2005 and 2006.

In 2005, the number of women students was 123.

In 2006, the number of women students was 149.

To find the increase, we subtract the initial value (2005) from the final value (2006):

Increase = Final Value - Initial Value

Increase = 149 - 123

Increase = 26

Next, we need to calculate the percent increase. The percent increase is given by the formula:

Percent Increase = (Increase / Initial Value) * 100

Plugging in the values:

Percent Increase = (26 / 123) * 100

Calculating the percent increase:

Percent Increase ≈ 21.14%

Rounding to the nearest whole percent, the percent increase of women students is approximately 21%.

Therefore, the answer is 21%.

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The equation of the circle with radius 9 and center ( -1,-8 ) is( x + 1 )² + ( y + 8  )² = 81.

The standard form equation of a circle with center (h, k) and radius r is:

( x - h )² + ( y - k )² = r²

Given that the circle has a center of (-1, -8) and the radius is 9.

Hence; from the standard form of the equation of the circle:

Center ( h , k ) = ( -1, -8 )

h = -1

k = -8

And radius r = 9

Plug these values into the above formula and simplify.

( x - h )² + ( y - k )² = r²

( x - ( -1 ) )² + ( y - ( -8 ) )² = 9²

Simplify

( x + 1 )² + ( y + 8  )² = 81

Therefore, the equation of the circle is ( x + 1 )² + ( y + 8  )² = 81.

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The general equation is y=mx+b

where m is the slope and b is the y intercept.

So substitute the m and the b for the equation.

m=2, b = 5 : y = 2x+5

m=3 b = 5: y = 3x + 5

m = 5 b = 4: y = 5x + 4

Answer:

450 cm in meter is 4.5 meters

Step-by-step explanation:

450cm = 4.5m

Answer:

45.75 mph

Step-by-step explanation:

Let's call Sonya's speed before the rest stop "x" (in miles per hour). Then, we know that her speed after the rest stop was "x-5" miles per hour.

We can use the formula: distance = speed x time, to set up two equations based on the given information:

Equation 1: 170 = x * t1 (where t1 is the time Sonya drove before the rest stop)

Equation 2: 320 = (x-5) * (t1+3) (where t1+3 is the time Sonya drove after the rest stop)

We can solve for t1 in Equation 1 by dividing both sides by x:

t1 = 170/x

Now we can substitute this expression for t1 into Equation 2 and simplify:

320 = (x-5) * (170/x + 3)

320 = 170(x-5)/x + 3(x-5)

Multiplying both sides by x gives:

320x = 170(x-5) + 3x(x-5)

320x = 170x - 850 + 3x^2 - 15x

Simplifying and rearranging terms gives a quadratic equation:

3x^2 - 165x + 850 = 0

We can solve for x using the quadratic formula:

x = [165 ± sqrt(165^2 - 4(3)(850))] / (2*3)

x = [165 ± sqrt(27225 - 10200)] / 6

x = [165 ± sqrt(17025)] / 6

x = [165 ± 130.5] / 6

x = 45.75 or x = 9.25

We can ignore the solution x = 9.25 since it doesn't make sense in the context of the problem (Sonya's speed cannot be negative). Therefore, Sonya's speed before the rest stop was 45.75 miles per hour

Applying the tangent and the circle theorems, we have:

22. x ≈ 9.4;   23. Perimeter of triangle GHI = 168 units

24. m<NSR = 110°;    25. x = 10

22. Based on the tangent theorem, the triangle is a right triangle since the line is tangent to the radius of the circle. Therefore, based on the Pythagorean theorem, we have:

x = √[(7.4 + 4.6)² - 7.4²]

x ≈ 9.4

23. JH and HK are tangents, therefore they are equal. Thus:

7x + 4 = 13x - 20

7x - 13x = -4 - 20

-6x = -24

x = 4

Perimeter = GI + GJ + JH + HK + KI

GI = 52

HK = JH = 7x + 4 = 7(4) + 4 = 32

KI = 15

GJ = 52 - 15 = 37

Perimeter of triangle GHI = 52 + 37 + 32 + 32 + 15 = 168 units

24. Based on the angle of intersecting chords theorem, we have:

m<NSR = 1/2(170 + 50)

m<NSR = 110°

25. Based on the inscribed angle theorem, we have:

2(4x - 5) + 290 = 360

Solve for x:

8x - 10 + 290 = 360

8x = 360 - 280

8x = 80

x = 10

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Answer:

  x = -5 2/3

Step-by-step explanation:

You want the solution to the rational equation ...

  (x+5)/(x+8)=1+(6)/(x+1)

Casting this into the form f(x) = 0, we have ...

  [tex]\dfrac{x+5}{x+8}=1+\dfrac{6}{x+1}\\\\\\1-\dfrac{3}{x+8}=1+\dfrac{6}{x+1}\\\\\\\dfrac{6}{x+1}+\dfrac{3}{x+8}=0\\\\\\\dfrac{3(2(x+8)+(x+1))}{(x+1)(x+8)}=0\\\\\\3x+17=0\qquad\text{the numerator is zero when the fraction is zero}\\\\\\\boxed{x=-\dfrac{17}{3}}[/tex]

__

Additional comment

The attachment shows the left side and right side expressions are equal when x = -17/3 = -5 2/3.

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A) The present value of the lease payments can be computed as $255,294.44, using the lease period, borrowing rate, and the monthly lease payments in the online finance calculator as parameters.

B) The journal entry for the lease on September 1, 2024 is as follows:

September 1, 2024:

Debit Lease Expense $8,000

Credit Lease Payable $8,000

(To record the lease liability, payable on September 30, 2024.)

The present value of the lease payments can be computed using an online finance calculator as follows:

N (# of periods) = 36 months (3 years x 12)

I/Y (Interest per year) = 8%

PMT (Periodic Payment) = $8,000

FV (Future Value) = $0

Results:

Present Value (PV) = $255,294.44

Sum of all periodic payments = $288,000.00

Total Interest = $32,705.56

September 1, 2024:

Lease Expense $8,000 Lease Payable $8,000

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The probability that the product is a multiple of 3 is given as follows:

p = 7/16.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

There are four numbers, hence the total number possible products are given as follows:

4² = 16.

The products that are multiples of 3 are given as follows:

7 products are multiples of 16, out of the 16 products, hence the probability is given as follows:

p = 7/16.

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It is true that the functions f(x) and h(x) share a common x-intercept.

On the definition of a function, the x-intercept is given by the value/values of x for which the function assumes a value of zero.

Function f(x) is defined as follows:

x² + 4x.

Hence the x-intercepts are obtained as follows:

x² + 4x = 0

x(x + 4) = 0

x = 0 and x + 4 = 0 -> x = -4.

On a graph, the x-intercept of a function is the value of x at which the graph of the function crosses the x-axis.

Hence the x-intercept of function h(x) is given as follows:

x = -4.

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You would need to reach home plate in 1.02 seconds before the ball reaches the catcher.

we need to convert the speed from mph to feet per second, since the distance is given in feet.

40 mph = 58.7 feet per second (rounded to one decimal place)

To calculate the time it takes to get from 3rd base to home plate, we can use the formula:

time = distance / speed

Plugging in the given values, we get:

time = 60 feet / 58.7 feet per second

time = 1.02 seconds

Therefore, you would need to reach home plate in 1.02 seconds before the ball reaches the catcher.

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The subtraction of the two matrix is   [31    6     12    -14     57 ]

                                                               [-19  -27  -18     18     27 ]

                                                               [ 47    14     -1    -40     9 ]

                                                               [10     12    -19    -15   -58]

                                                               [-14   -23    10     4       19]

The subtraction of the two matrix is calculated as follows;

The result to 4 multiplied by D is calculated as;

4[D] = [28   -24    12    -32     -36]

        [8      -36   -24     24      36]

        [32     8      20     -40     -12]

        [40   -12      -16    12     - 28]

        [4      -8       16     -20     -8 ]

The result to 3 multiplied by B is calculated as;

3[B] = [-3    -30  -24   -18     21]

        [27    -9    -6      6       9]

        [-15    -6    21     0      -21]

        [30    -24   3    27      30]

        [18     15     6   -24     -27]

The subtraction of the two matrix is calculated as follows;

4[D] - 3[B] =  [31    6     12    -14     57]

                   [-19  -27  -18     18     27 ]

                   [ 47    14     -1    -40     9 ]

                   [10     12    -19    -15   -58]

                   [-14   -23    10     4      19]

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Answer:

Step-by-step explanation:

11+6+21+18=56 ft

squared