Trigonometric identities: Performance task

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:

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:

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

I hope I helped you^_^

Answer:

All math operation

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

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

the equal is correctly

3x + 1 = 2x + 4

what was done now :

2 x-blocks (2x) subtracted from the right side, and 1 numbered block subtracted from the left side.

to reestablish balance and equality of both sides, we need to do more the exact same things - just in the other sides.

2 x-blocks subtracted from the LEFT side, and 1 numbered block subtracted from the RIGHT side.

and that is answer B.

bathroom

Step-by-step explanation:

Answer:

In ft - 0.52493432098, in cm - 15.9999981034704

Step-by-step explanation:

2/3 x 2/3 x 2/3 x 2/3 x (2.65748ft) -> 81 cm in ft

= 0.52493432098ft -> converted to cm = 15.9999981034704cm

Answer:

7 to the power of 3/2

Step-by-step explanation:

7 is the same as 7¹ and [tex]\sqrt{7}[/tex] is the same as 7 to the power of 1/2

since the bases are both 7, we keep the base and add the exponents when we multiply with exponents, giving us:

7 to the power of 3/2

Step-by-step explanation:

72 tan gloves and 13 black

Answer:

85/10 = 8.5

11/6 = 1.83333333

Step-by-step explanation:

Step-by-step explanation:

change the ÷ into × flip the number too.

[tex] \frac{85}{10} \div \frac{11}{6} = \frac{85}{10} \times \frac{6}{11} [/tex]

Reduce the fraction with 5

[tex] \frac{85}{10} \times \frac{6}{11} = \frac{17}{2} \times \frac{6}{11} [/tex]

Reduce the numbers with the greatest common factor 2

[tex] \frac{17}{2} \times \frac{6}{11} = \frac{17}{1} \times \frac{3}{11} [/tex]

Just multiply now, To multiply the fractions , multiply the numerators and denominators separately

[tex] \frac{17 \times 3}{1 \times 11} = \frac{51}{11} [/tex]

Solution :

[tex] \frac{51}{11} [/tex]

Alternative form:

[tex]4 \frac{7}{11}[/tex]

[tex]4.63[/tex]

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The perpendicular bisector of the of the hypotenuse side forms a right

triangle with the hypotenuse and the longer leg of the of the triangle.

The ratio, of the length of the segment cut from the perpendicular bisector by the hypotenuse and the longer leg to the length of the longer leg, is 1 : 3

Reason:

The given parameters are;

An acute angle of the right triangle = 30°

Let R represent the length of the hypotenuse side, we have;

The length of the longer leg, [tex]L_{ll}[/tex] = R × cos(30°) = [tex]\dfrac{\sqrt{3} }{2} \cdot R[/tex]

The perpendicular bisector forms a right triangle with a leg length = R/2

The length of the hypotenuse formed by the bisector is therefore;[tex]R_{bisector} = \dfrac{\dfrac{R}{2} }{cos(30^{\circ})} = \dfrac{\dfrac{R}{2} }{\dfrac{\sqrt{3} }{2} } = \dfrac{R}{\sqrt{3} }[/tex]

The length, L, of the segment cut by the hypotenuse and the longer leg is therefore;

[tex]L= R_{bisector} \times sin(30^{\circ}) = \dfrac{1}{2} \times \dfrac{R}{\sqrt{3} } = \dfrac{R}{2 \cdot \sqrt{3} }[/tex]

The ratio, of the length of the segment cut from this perpendicular bisector by the hypotenuse and the longer leg to the length of the longer leg, r, is therefore;

[tex]r = \dfrac{L}{L_{ll}} = \dfrac{ \dfrac{R}{2 \cdot \sqrt{3} }}{\dfrac{\sqrt{3} }{2} \cdot R} = \dfrac{2 \cdot R}{2 \cdot \sqrt{3} \times \sqrt{3} \times R } = \dfrac{1}{3}[/tex]

The ratio, of the lengths, r = [tex]\dfrac{1}{3}[/tex], therefore, r = 1:3

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Answer:

1:3

Step-by-step explanation:

If the shorter leg is equal to x, AB is 2x and AC is x root 3.

AE is half of AB which is x.

Angle ADE is 90-30=60 degrees.

DE is x/root 3.

[tex]\frac{\frac{x}{\sqrt{3}} }{x\sqrt{3}} = 1:3[/tex]

Answer:

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

Step-by-step explanation:

Answer:

the answer is B i think

Step-by-step explanation:

Consider ABCD is a rhombus

We know that

All sides are equal in rhombus

=> AB=BC=CD=DA

and AC and BD are digonals

Given that

Diagonal and the side of the rhombus are equal.

=> AB = BC = CD = DA = AC

Diagonal AC divides the rhombus into two triangles .

They are ∆ BAC and ∆ DAC

In triangle BAC

BA=BC=AC,(Given)

=> < BAC=<ABC= < ACB =60°………(1)

Similarly in ∆DAC ,

DA=DC=AC

=><DAC=<ACD=<ADC=60°……….(2)

From (1) and (2)

<A=<BAC+< DAC=60°+60°=120°

and

< B= < ABC = 60°.

and

<C=<ACB+<ACD=60°+60°=120°

and

< D =<ADC=60°

Therefore, <A = 120° , <B = 60° ,<C = 120° ,<D = 60°

Answer:-

The measures of the all angles in the rhombus are 120° , 60° ,120° and 60°

Used formulae:-

all sides in a rhombus are equal

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.

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:

Its 50

Step-by-step explanation:

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:

all real numbers greater than or equal to 0

Step-by-step explanation:

All real numbers greater than or equal to 0.

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:

[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:  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:

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

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

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:

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:

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

Step-by-step explanation: