k Kerboodle - A Lev... aw Find Courses by ... 1- cos 20 sin² 20 where k is a constant to be found. TO TU (b) Hence solve, for --

Answer:

26

Step-by-step explanation:

6+10+10=26

Answer:

80m²

Step-by-step explanation:

area of rectangle-&10m×6m=60m²

10m-6m=4m

10m×4m=40m²

area of triangle->40m²÷2=20m²

area->60m²+20m²=80m²

A- a+b-c²

=2+(-1-1)^2

=1-1

=0

B-a³-b+c

2^3-(-1+1)

=8+1+1

= 10

C-a-b-c

2-(-1-1)

=2+1-1

=2

Answer: The answer is y= -6/7x+1

Answer:

cool thats nice

Step-by-step explanation:

When Partition(numbers, 5, 9) is called in Quicksort for the array (56,25,26,28,81,93,92,85,99,87), the pivot is 92. The low partition is (56,25,26,28,81,85,87).

When Partition(numbers, 5, 9) is called in Quicksort with the array numbers = (56, 25, 26, 28, 81, 93, 92, 85, 99, 87), the element at the midpoint between index 5 and index 9 is chosen as the pivot.  The midpoint index is (5 + 9) / 2 = 7, so the pivot is the element at index 7 in the array, which is 92.

After the partitioning step, all the elements less than the pivot are moved to the low partition, while all the elements greater than the pivot are moved to the high partition. The low partition starts at the left end of the array and goes up to the element just before the first element greater than the pivot.

In this case, the low partition after the partitioning step would be (56, 25, 26, 28, 81, 85, 87), which are all the elements less than the pivot 92. Note that these elements are not necessarily in sorted order yet, as Quicksort will recursively sort each partition of the array.

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for k = 6, the pair of linear equations have infinitely many solutions.

n the above equation a1= k, a2 = 12, b1 = 3, b2 = k, c1 = -(k - 3) and c2 = -k

If a solution has infinitely many solutions, then

⇒ a1 / a2 = b1 / b2 = c1 / c2

For the above pair of equations,

⇒ k / 12 = 3 / k = k - 3 / k

⇒ k/ 12 = 3/ k

⇒ k2 = 36⇒ k = ± 6

Also

⇒ 3/ k = (k - 3)/ k

⇒ 3k = k(k - 3)

⇒ 3k = k2 -3k

Then,

⇒ k2 = 6k

⇒ k = 6

The value of k which satisfies both the equations is 6.

Thus, for k = 6, the pair of linear equations have infinitely many solutions.

The complete question is,

For what values of k will the following pair of linear equations have infinitely many solutions?

kx + 3y - (k – 3) = 0

12x + ky - k = 0

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Answer:

1)  x=16

2) x=15

3) x=10

Step-by-step explanation:

1)  Since the triangles are similar and the ratio of the sides is 1 : 2, 1/2=(3x-4)/(10x-72). Cross multiplying, we get 6x-8=10x-72.

10x-72=6x-8 |+72

10x=6x+64 |-6x

4x=64  |/4

x=16

2) Angles HGJ and KLJ are corresponding (they are equal angles).

So, 5x-2=9x-62.

5x-2=9x-62  |+62

5x+60=9x  |-5x

60=4x |/4

x=15

3) If KM is a perpendicular bisector, KJ=KL.

So, 4x+9=11x-61.

4x+9=11x-61 |-4x

9=7x-61   |+61

70=7x  |/7

x=10

Answer:

x = 11

Step-by-step explanation:

We know that the answer we will get will be the same as BD because BD and AC are congrudent, meaning that they are exactly equal shape and size. To find 'x' our equation would be: 29 = 3x - 4. To figure this out we just add 29 and 4 which gives us 33 and then divide that by 3 which gives us 11 (our answer)

Answer:

12/9 = 4/3

Step-by-step explanation:

write it as a fraction, then simplify by dividing numerator and denominator by 3.

Answer:

4/3 or 1.3

Step-by-step explanation:

12 divided by 9

Answer:The first 1 is 98

The second one I have no idea sorry-

Same with third one

and forth 1 sorry I cant help u with the last 3 I hope someone else does :)

Step-by-step explanation:

The coordinates of the vertices of the image are Q'(x, y) = (- 1.5, 6), T'(x, y) = (0, - 3), R'(x, y) = (1.5, 3) and S'(x, y) = (3, - 3), respectively.

A dilation is a kind of rigid transformation, that is, a transformation applied on geometric loci such that its Euclidean distance is conserved. According to the statement, we must the following dilation to generate the image:

P'(x, y) = (3 / 2) · P(x, y)

If we know that Q(x, y) = (- 1, 4), T(x, y) = (0, - 2), S(x, y) = (2, - 2) and R(x, y) = (1, 2), then the vertices of the images are:

Q'(x, y) = (3 / 2) · (- 1, 4)

Q'(x, y) = (- 1.5, 6)

T'(x, y) = (3 / 2) · (0, - 2)

T'(x, y) = (0, - 3)

R'(x, y) = (3 / 2) · (1, 2)

R'(x, y) = (1.5, 3)

S'(x, y) = (3 / 2) · (2, - 2)

S'(x, y) = (3, - 3)

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The new average speed that the pilot should maintain to complete the trip in 90 minutes is 220 miles per hour.

(a) To find the angle that the pilot should turn to head towards Louisville, we first need to find how far off course the pilot has gone in 15 minutes. At an average speed of 220 miles per hour, the pilot would have flown a distance of:

d = rt = 220 mi/hr × (15 min / 60 min/hr) = 55 miles

Since the pilot was 10 degrees off course, they have effectively traveled 10/360 of the circumference of a circle with radius 55 miles. The length of this arc is:

s = rθ = 55 mi × (10/360) = 1.528 mi

To head towards Louisville, the pilot needs to turn to a heading that is 10 degrees in the opposite direction. The angle θ that the pilot needs to turn is given by:

θ = 2arctan(s/2d) = 2arctan(1.528 mi / 2(330 mi)) ≈ 0.266 radians ≈ 15.26 degrees

So the pilot needs to turn approximately 15.26 degrees to head towards Louisville.

(b) Let's call the distance the pilot needs to travel after correcting course "x". We can use the formula for distance to find "x":

x = 330 mi - 2(55 mi) = 220 mi

To complete the trip in a total time of 90 minutes, the pilot must spend 75 minutes flying at the new speed and 15 minutes turning to the correct heading. Therefore, the time spent flying at the new speed is 75 minutes - 15 minutes = 60 minutes. The new speed can be found using the formula for average speed:

average speed = total distance / total time

We want the new speed to cover a distance of 220 miles in 60 minutes:

average speed = 220 mi / (60 min / 60) = 220 mi/hr

So the new average speed that the pilot should maintain to complete the trip in 90 minutes is 220 miles per hour.

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Answer:

Unlikely

Step-by-step explanation:

There are more chances that tomorrow there will be no rain than the raining we can say that it is unlikely to rain tomorrow.

It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have:

The weather forecast calls for a 20% chance of light rain tomorrow.

Probability of rain:

P(rain) = 20% = 0.2

Complement event: Not rain tomorrow

Probability of complement event P(not rain) = 1 – 0.2 = 0.8 or 80%

P(not rain) > P(rain)

Thus, there are more chances that tomorrow there will be no rain than the raining we can say that it is unlikely to rain tomorrow.

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Answer:

(14, - 3 )

Step-by-step explanation:

Under the translation < 6, 0 >

Add 6 to the x- coordinate and 0 to the y- coordinate, that is

B(8, - 3 ) → B'(8 + 6, - 3 + 0 ) → B'(14, - 3 )

For the given scenario: the Probability of making both shots are A. 0.64 and B. 0.72

a) If a player makes 80% of his foul shots, the probability of making a single foul shot is 0.8. Since the two shots are considered independent events, the probability of making both shots is the product of the individual probabilities.

Therefore, the probability of making both shots is 0.8 * 0.8 = 0.64.

To calculate the probability of making exactly one shot, we need to consider two scenarios: making the first shot and missing the second, or missing the first shot and making the second. Each scenario has a probability of 0.8 * 0.2 = 0.16.

Therefore, the probability of making exactly one shot is 0.16 + 0.16 = 0.32.

Similarly, the probability of missing both shots is 0.2 * 0.2 = 0.04.

b) In this case, the outcome of the second shot depends on the outcome of the first shot. If the player makes the first shot (with a probability of 0.8), the probability of making the second shot is 0.9.

Therefore, the probability of making both shots is 0.8 * 0.9 = 0.72.

If the player misses the first shot (with a probability of 0.2), the probability of making the second shot is 0.7.

Therefore, the probability of making exactly one shot is 0.2 * 0.7 = 0.14.

Since there are only two possible outcomes (making both shots or making exactly one shot), the probability of neither shot being made is 1 - (0.72 + 0.14) = 0.14.

Therefore, for the given scenario:

a) Probability of making both shots: 0.64

  Probability of making exactly one shot: 0.32

  Probability of missing both shots: 0.04

b) Probability of making both shots: 0.72

  Probability of making exactly one shot: 0.14

  Probability of missing both shots: 0.14

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The statement "Quadrilaterals A and B are both squares" does not provide enough information to determine whether A and B are scale copies of one another.

To determine if two quadrilaterals are scale copies of each other, we need to compare their corresponding sides and angles. If the corresponding sides of two quadrilaterals are proportional and their corresponding angles are congruent, then they are scale copies of each other.

In this case, since both A and B are squares, we know that all of their angles are right angles (90 degrees). However, we do not have any information about the lengths of their sides. Without knowing the lengths of the sides of A and B, we cannot determine if they are scale copies of each other.

Therefore, the statement cannot be determined as true or false based on the given information.

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Answer:

\(\textsf{A)} \quad \left(-\dfrac{1}{2} , 0\right) \textsf{ and } (2, 0)\)

\(\textsf{B)} \quad \left(\dfrac{3}{4},25 \right)\)

C)  see explanation

Step-by-step explanation:

Given function:

\(f(x) =-16x^2 + 24x + 16\)

To find the x-intercepts, set the function to zero, factor and solve for x:

\(\implies f(x)=0\)

\(\implies -16x^2 + 24x + 16=0\)

\(\implies -8(2x^2-3x-2)=0\)

\(\implies 2x^2-3x-2=0\)

\(\implies 2x^2-4x+x-2=0\)

\(\implies 2x(x-2)+1(x-2)=0\)

\(\implies (2x+1)(x-2)=0\)

Therefore:

\(\implies 2x+1=0 \implies x=-\dfrac{1}{2}\)

\(\implies x-2=0 \implies x=2\)

Therefore, the x-intercepts of the graph of f(x) are

\(\left(-\dfrac{1}{2} , 0\right) \textsf{ and } (2, 0)\)

As the leading coefficient is negative, the parabola will open downwards. Therefore, the vertex of the graph of f(x) will be a maximum.

The x-coordinate of the vertex is the midpoint of the x-intercepts:

\(\implies \sf midpoint=\dfrac{2+\left(-\frac{1}{2}\right)}{2}=\dfrac{3}{4}\)

To find the y-coordinate of the vertex, substitute the x-value into the function:

\(\implies f\left(\dfrac{3}{4}\right)=-16\left(\dfrac{3}{4}\right)^2 + 24\left(\dfrac{3}{4}\right) + 16\)

\(\implies f\left(\dfrac{3}{4}\right)=-9+18+16\)

\(\implies f\left(\dfrac{3}{4}\right)=25\)

Therefore, the coordinates of the vertex are:

\(\left(\dfrac{3}{4},25 \right)\)

Find the y-intercept by substituting x = 0 into the function:

\(\implies f(0) =-16(0)^2 + 24(0) + 16=16\)

Therefore, the y-intercept is (0, 16)

To graph f(x)

The axis of symmetry is the x-value of the vertex. Use this to help ensure the curve is symmetrical.

#A

Take y =0

On solving we will get

#B

Find x co ordinate of vertex

Find y

As a is negative vertex is maximum as its facing downwards.

#C

Steps:-

Answer:1380

Step-by-step explanation: proportionality constant equals 1150/25=46. 46x30=1380

Answer:

8. y=2x+6

9. y=1/2x-5

Step-by-step explanation:

Use point slope form to figure out the y intercept. Because it needs to be parallel, the same slope will be used to solve for point slope form.

The expression's value is when x 0, and since |x| = -x when x 0, x + |x| simplifies to 0. In this case, x + |x| = x + (-x) = 0 for x 0.

When the variables and constants in a mathematical expression are given values, the outcome of the computation it describes is the expression's value. The value of a function, given the value(s) assigned to its argument, is the sum that the function assumes for these input values (s).

For x =7,x+|x| =7+|7| =14

For x =10,x+|x|= 10+|10| =20

For x = 0,x+|x| =0+|0| =0

For x = -3, x + |x| = -3 + |-3| = 0

For x = -8, x + |x| = -8 + |-8| = 0

The expression's value is when x 0, and since |x| = -x when x 0, x + |x| simplifies to 0. In this case, x + |x| = x + (-x) = 0 for x 0.

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2

−

4

−

1

1

7 there you go

Answer:

x^2 -4x-117

Step-by-step explanation:

(x+9) (x-13)

(x * x)+(-13x)+(9x)+(-117)

Answer:

The correct answers are the following:

A) P=12n-275

B) 124

C) Decrease by $100

Step-by-step explanation:

A) P=12n-275 - Each person (n) pays $12, then the cost/expense ($275) is subtracted from the income to get the profit.

B) 1,213=12n-275  - Plug in the value for P ($1,213).

1,488=12n  - Add $275 to both sides.

124=n  - Divide both sides by $12.

n=124 - This the number (n) of people that attended.

C) P=12n-375 - Change the value for expense to $375.

P=12(124)-375  - Plug in the value for n (124).

P=1488-375  - Simplify and find the difference.

P=1,113 - This is your profit.

1,113-1,213=-100 - $100 reduction/decrease of profit (or -$100 to profit)

Hope this helps!

The amount of each quarterly payment, rounded, for a $30,000 loan with a 6% annual interest rate to be paid off in 10 equal quarterly payments is $2,803 (option B).


To calculate the amount of each quarterly payment, we need to use the formula for calculating the equal payments on an installment loan. In this case, the loan amount is $30,000, the annual interest rate is 6%, and the loan term is 10 quarters.

Using the formula, we can determine that the amount of each quarterly payment is approximately $2,803. This amount is rounded to the nearest whole number, as specified in the question. Therefore, option B, $2,803, is the correct answer. The other options (A, C, and D) are not applicable to the calculation based on the given information.

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Answer:

The answer is C.

Answer:

45

Step-by-step explanation:

you can see that the time increases by 10.

ex: 5+10=15, 15+10=25.

So, 35 + 10 = 45

Step-by-step explanation:

To calculate the minimum number of days required to finish this project, we need to use the critical path method (CPM), which involves identifying the longest sequence of dependent tasks and their durations.

First, we need to draw the network diagram for the project:

```

|---(T1-8)---(T3-10)---|

(T2-6) (T5-12)

| / |

|---(T4-7)---(T6-15)---|

```

Next, we need to calculate the earliest start time (EST), earliest finish time (EFT), latest start time (LST), and latest finish time (LFT) for each task. For the starting task, EST = 0 and EFT = 0.

```

EST EFT LST LFT

T1 (8 days) 0 8 22 30

T2 (6 days) 0 6 6 12

T3 (10 days) 8 18 22 32

T4 (7 days) 18 25 25 32

T5 (12 days) 18 30 32 44

T6 (15 days) 32 47 32 47

```

The critical path is the longest sequence of dependent tasks that have no slack (i.e., the difference between LST and EST, or LFT and EFT, is zero). In this case, the critical path is T1-T3-T5-T6.

Therefore, the minimum number of days to finish this project is the sum of the durations of tasks on the critical path:

8 + 10 + 12 + 15 = 45 days

Therefore, the minimum number of days required to finish this project is 45 days.