Simplify this numerical expression. (-12)(-13)

Answer:

[tex]18 + ( - 30) = 18 - 30 = - 12[/tex]

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Answer:

[tex]y = e^{3x}.cos4x.sin2x[/tex]

[tex]=> y' =- 3e^{3x}.4sin4x.2cos2x=-24.e^{3x}.sin4x.cos2x[/tex]

[tex]dy=y'.dx => dy = -24e^{3x}.sin4x.cos2x.dx[/tex]

Step-by-step explanation:

The function [tex]e^3^x[/tex].cos4x.sin2x on differentiating gives the solution as 2[tex]e^3^x[/tex]cos2x.cos4x - 4[tex]e^3^x[/tex]sin2x.sin4x + 3[tex]e^3^x[/tex]cos4x.sin2x.

Product rule in differentiation states that, for two functions f(x) and g(x),

[tex]\frac{d}{dx}[/tex] [f(x).g(x)] = f(x) . [tex]\frac{d}{dx}[/tex][g(x)] + g(x) . [tex]\frac{d}{dx}[/tex][f(x)]

The question is to differentiate y = [tex]e^3^x[/tex].cos4x.sin2x

We have three functions here.

Let u = [tex]e^3^x[/tex] and v = cos4x.sin2x

[tex]\frac{d}{dx}[/tex] [u . v] = u [tex]\frac{d}{dx}[/tex][v] + v [tex]\frac{d}{dx}[/tex][u]

             = [tex]e^3^x[/tex] [tex]\frac{d}{dx}[/tex] [cos4x.sin2x] + cos4x.sin2x [tex]\frac{d}{dx}[/tex] [[tex]e^3^x[/tex] ]

             = [tex]e^3^x[/tex] [tex]\frac{d}{dx}[/tex] [cos4x.sin2x] + cos4x.sin2x (3[tex]e^3^x[/tex])

[tex]\frac{d}{dx}[/tex] [u . v] =  [tex]e^3^x[/tex] [tex]\frac{d}{dx}[/tex] [cos4x.sin2x] + 3[tex]e^3^x[/tex]cos4x.sin2x

Let the above equation be equation E.

Again apply the product rule for [tex]\frac{d}{dx}[/tex] [cos4x.sin2x].

Let u' = cos4x and v' = sin2x

[tex]\frac{d}{dx}[/tex] [u'. v'] = u' [tex]\frac{d}{dx}[/tex][v'] + v' [tex]\frac{d}{dx}[/tex][u']

            = cos4x [tex]\frac{d}{dx}[/tex][sin2x] + sin2x [tex]\frac{d}{dx}[/tex][cos4x]

            = cos4x [2cos2x] + sin2x [-4sin4x]

            = 2cos2x.cos4x - 4sin2x.sin4x

Substituting this is equation E, we get,

[tex]\frac{d}{dx}[/tex] [u . v] =  [tex]e^3^x[/tex] [2cos2x.cos4x - 4sin2x.sin4x] + 3[tex]e^3^x[/tex]cos4x.sin2x

             =  2[tex]e^3^x[/tex]cos2x.cos4x - 4[tex]e^3^x[/tex]sin2x.sin4x + 3[tex]e^3^x[/tex]cos4x.sin2x

Hence the function [tex]e^3^x[/tex].cos4x.sin2x on differentiating gives 2[tex]e^3^x[/tex]cos2x.cos4x - 4[tex]e^3^x[/tex]sin2x.sin4x + 3[tex]e^3^x[/tex]cos4x.sin2x.

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Answer:

32 square units

Step-by-step explanation:

You can split this shape into four different shapes:

2 unit by 2 unit triangle

2 unit by 2 unit square

2 unit by 6 unit triangle

To find the length of the big triangle, add the lengths of the small triangle,the square,and the bigger leg of the other triangle:

2 + 2 + 6 = 10

10 unit by 4 unit triangle

Then solve all these areas:

( 2 x 2 ) / 2 = 4 / 2 = 2

2 x 2 = 4

( 2 x 6 ) / 2 = 12 / 2 = 6

( 10 x 4 ) / 2 = 40 / 2 = 20

Then add all these areas together to get the total area of the composite shape:

2 + 4 + 6 + 20 = 32

Answer:

2 3/4

Step-by-step explanation:

You need to find the greatest common factor of 4 and 2 then you multiply the 2 by 2 to get a 4 and multiply the 1, then you add those together to get 2 3/4.

Answer:

b answer

Step-by-step explanation:

hope helpful

if wrong sorry

Answer:

slope = -4

Step-by-step explanation:

3y = 9 - 12x

Rearrange the right-hand side:

3y = - 12x + 9

Next, Divide both sides by 3 to isolate y:

[tex]\frac{3y}{3} = \frac{-12x + 9}{3}[/tex]

y = -4x +3 this is the slope-intercept form where the slope, m = -4, and the y-intercept, b = 3.

Therefore, the slope = -4.

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Answer:

use desmos to graph it

.....

Answer:

Equally likely

Step-by-step explanation:

Hope this is right!

Answer:

Its 50

Step-by-step explanation:

Answer:

All math operation

Basic Operations. The basic arithmetic operations for real numbers are addition, subtraction, multiplication, and division.

Step-by-step explanation:

Answer:

Yes, B is correct, the horizontal line test is used to test if an INVERSE is a function.

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

18/2-3/.75=15/1.25

The average speed of Even between two checkpoints is 9 miles per hour.

The distance covered by the particle or the body in an hour is called the average speed. It is a scalar quantity. It is the ratio of the total distance to the total time.

We know that the average speed formula is given as,

Average speed = Total distance / Total time

Running a marathon is Evan. Between two checkpoints, he wants to compute his average speed. He takes 0.75 hours to go to the 3-mile checkpoint and 2 hours to get to the 18-mile milestone.

The average speed is given as,

Average speed = 18 / 2

Average speed = 9 miles per hour

The average speed of Even between two checkpoints is 9 miles per hour.

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Answer:

Step-by-step explanation:

Find the number of cups in 80 gallons:

Now multiply the number of cups by 4 since each cup of ice cream  is equivalent of 4 cookies:

Answer:

The slope-intercept form of the given line is: y = -1/3x+1

Step-by-step explanation:

Answer:  65 degrees

Explanation:

The adjacent angle directly above angle 8 is congruent to the 115 degree angle (due to the corresponding angles theorem). This only works because p || q and q || r, so by the transitive property of parallel lines, we know that p || r.

Since the 115 degree angle and angle 8 pair up to form a straight line, we know that the two angles must add to 180 degrees

115+(angle 8) = 180

angle 8 = 180 - 115

angle 8 = 65 degrees

Answer:

[tex]m[/tex]∠8 = 65°

Step-by-step explanation:

The other side (angle) of 115 is [tex]n[/tex] and [tex]n =[/tex] ∠8

To find [tex]n[/tex] you need to subtract 180 - 115 giving you 65, and since n is angle 8, angle 8 is also 65 since the angles have a state of congruence...

Answer:

15

Step-by-step explanation:

if he walks 6 kilometres per hour multiply 6 times 2 and you get 12 and he walked for half an hour and half of 6 is 3 so 12 plus 3 equals 15

Answer:

15 km

Step-by-step explanation:

given:

1 hour=6 km

9:30--12:00=2.5 hours

•°•2.5×6=15 km

Answer:

I think that Maya is right because the question doesn't state that they had to split it equally, you could split it infinite ways.

Step-by-step explanation:

You could give one person 8$ and the other7$. you could do it infinitely.

Answer: 14720 dollars, or $14720

Step-by-step explanation:

128 red tomato plants plus 102 yellow tomato plants = 230 tomato plants in total.

230 plants with 32 tomatoes each = 7360 tomatoes in all

7360 x 2 dollars = 14720 dollars

Answer:the anwser is 4

Step-by-step explanation:

Step-by-step explanation:

I am not sure who made the dots on the charts, but they are wrong.

y = 1/2 x + 3

domain means all valid values for x.

range means all valid values for y (the functional results).

x = 0

y = 1/2 × 0 + 3 = 3

x = 1

y = 1/2 × 1 + 3 = 3.5

x = 2

y = 1/2 × 2 + 3 = 4

x = 3

y = 1/2 × 3 + 3 = 4.5

x = 4

y = 1/2 × 4 + 3 = 5

so, the range is 3, 3.5, 4, 4.5, 5

y = x - 6

x = 10

y = 10 - 6 = 4

x = 12

y = 12 - 6 = 6

x = 14

y = 14 - 6 = 8

x = 16

y = 16 - 6 = 10

x = 18

y = 18 - 6 = 12

so, the range is 4, 6, 8, 10, 12

Step-by-step explanation:

72 tan gloves and 13 black

Answer:

n-315=1245

Step-by-step explanation:

n stands for the original amount of the loan. Margo has paid $315, so the original number minus what Margo has paid, and the equality is the amount that Margo still owes.

bathroom

Step-by-step explanation:

Answer:

all real numbers greater than or equal to 0

Step-by-step explanation:

All real numbers greater than or equal to 0.

Step-by-step explanation:

we need to find the slope of each line.

the slope is the ratio y/x indicating how many units y changes, when x changes a certain amount of units.

parallel lines have the same slope.

for a perpendicular line x and y in the slope ratio are put upside down, and the sign is flipped (+ to - and vice versa).

a.

2x - 8y = -24

2x + 24 = 8y

y = 2/8 x + 24/8 = 1/4 x + 3

the slope is 1/4 (always the factor of x).

4x + y = -2

y = -4x - 2

the slope is -4 = -4/1.

this line is therefore perpendicular to the first line.

x - 4y = 4

x - 4 = 4y

y = 1/4 x - 4/4 = 1/4 x - 1

the slope is 1/4.

this line is therefore parallel to the first line.

b.

3x - 9y = 9

9y = 3x - 9

y = 3/9 x - 9/9 = 1/3 x - 1

the slope is 1/3

3y = x + 12

y = 1/3 x + 4

the slope is 1/3.

this line is therefore parallel to the first line.

2x - 6y = 12

6y = 2x - 12

y = 2/6 x - 12/6 = 1/3 x - 2

the slope is 1/3.

this line is therefore parallel to the first line.

1000

Step-by-step explanation:

Find the height of the triangle using the Pythagoras theorem

Then, use it to calculate the area of the triangle

Answer:

s=8r/9

Step-by-step explanation:

2r=5s/2-s/4 multiply both sides by 4

8r=10s-s (5s times 4 = 20s and 20s/2=10s) combine like terms

8r=9s divide by 9 to isolate s

8r/9=s