20. Which of the following is not an identity?
a) sin2 a+cos2 a = 1
b) sin a = tan a * cos a
c) 1 + cot2 a = csc2 a
d) 1 - sec2 a = tan2 a

[tex] \LARGE{ \underline{ \boxed{ \orange{ \rm{Solution:)}}}}}[/tex]

☃️ Refer to the trigonometric table....

Then, proceeding

⇛ tan 60 ° = √3

⇛ tan 60° = tan (a + b)

⇛ 60° = a + b

Flipping it,

⇛ a + b = 60° --------(1)

And,

⇛ tan 30° = 1 / √3

⇛ tan 30° = tan (a - b)

⇛ 30° = a - b

Flipping it,

⇛ a - b = 30° ---------(2)

Now adding eq.(1) and eq.(2),

⇛ a + b + a - b = 60° + 30°

⇛ 2a = 90°

⇛ a = 90° / 2

⇛ a = 45°

Putting value of a in eq.(1),

⇛ 45° + b = 60°

⇛ b = 15°

☄ So, Our Required answers:

━━━━━━━━━━━━━━━━━━━━

Answer:

[tex]x^\frac{9}{5}[/tex]

Step-by-step explanation:

[tex]\sqrt[5]{x}[/tex] is the same thing as [tex]x^{\frac{1}{5}}[/tex].

Now if we have [tex]x^{\frac{1}{5}}[/tex] to the power of 9, the exponents are multiplied.

[tex]x^{\frac{1}{5} \cdot9} = x^{\frac{9}{5} }[/tex].

Hope this helped!

Answer:

intersection of the lines drawn to bisect each vertex of the triangle

Step-by-step explanation:

trust

━━━━━━━☆☆━━━━━━━

▹ Answer

A ≈ 201.06 mm²

▹ Step-by-Step Explanation

A = πr²

Radius = 1/2d

Radius = 1/2(16)

Radius = 8

Substitute:

A = π8²

A ≈ 201.06 mm²

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

Answer:

Step-by-step explanation:

Area of a circle is given by πr²

where r is the radius

To find the radius we use the formula

radius = diameter / 2

From the question

diameter = 16mm

radius = 16 / 2 = 8mm

So the area of the circle is

π(8)²

= 64π

= 201.061

= 201 mm² to the nearest whole number

Hope this helps you

Answer:

13/48

Step-by-step explanation:

1 7/16 - 1 1/6

Make improper fraction

23/16 - 7/6

Common Denominator

69/48 - 56/48

Subtract

13/48

Hope that helped!!! k

Answer:

13/48

Step-by-step explanation:

1 7/16=1+7/16

1 1/6=1+1/6

So: 1 7/16 - 1 1/6=

1+7/16-(1+1/6)=

1+7/16-1-1/6=

7/16-1/6= (48 common denominator)

(7×3-8)/48=

(21-8)/48=

13/48

Step-by-step explanation:

hope this helps

pls mark me brainliest

Hello!

Answer:

[tex]\huge\boxed{x = 27}[/tex]

Given:

3x - 4y = 65 where y = 4;

Substitute in 4 for "y":

3x - 4(4) = 65

Simplify:

3x - 16 = 65

Add 16 to both sides:

3x - 16 + 16 = 65 + 16

3x = 81

Divide both sides by 3:

3x/3 = 81/3

x = 27.

Hope this helped you! :)

Answer:

x=27

Step-by-step explanation:

3x-4y=65

Let y=4

3x - 4(4) = 54

3x -16 = 65

Add 16 to each side

3x -16+16 = 65+16

3x = 81

Divide each side by 3

3x/3 =81/3

x =27

Answer: Answers are in the steps.

Step-by-step explanation:

The coefficients are 3, -5, and 1  

The terms are, 3m, -2,-5n and p

Answer:it’s the top right box

Step-by-step explanation: what I did was I added 24+24 and 19+19 which gives you 86ft

Answer:It is left side 21ft and top 22ft Step-by-step explanation:

Answer:

a) true

Step-by-step explanation:

$4.65. >$7.45.

Answer:

14

Step-by-step explanation:

I just got it correct on a.p.e.x :)

The solution to the equation [tex]\log_5(2x - 3) = 2[/tex] is x = 14

The equation is given as:

[tex]\log_5(2x - 3) = 2[/tex]

Convert the equation to an exponential equation

2x - 3 = 5^2

Evaluate the exponent

2x - 3 = 25

Add 3 to both sides

2x = 28

Divide both sides by 2

x = 14

Hence, the solution to the equation [tex]\log_5(2x - 3) = 2[/tex] is x = 14

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Answer:

A = 8%, B = 5%

Step-by-step explanation:

Let

a=concentration of solution A (in percent)

b=concentration of solution B (in percent)

Given

2a+4b = 0.06*(2+4)  ...........(1)

4a+2b = 0.07*(4+2)  ...........(2)

2(1) - (2)

4a-4a +8b-2b = 6 (2*0.06-0.07)

6b = 6(0.05)

b = 0.05  .............(3)

Substitute (3) into (1) and solve for a

2a+4(0.05) = 0.36

2a = 0.16

a = 0.08

Answer:

500

Step-by-step explanation:

A = the unknown number that we need to find

A x 13/100 = 65

=> A x 13 = 6500

=> A = 6500 / 13

=> A = 500

13% of 500 is 65.

Let's check whether the answer is correct or not.

=> 500 x 13/100

=> 5 x 13

=> 65.

So, the number whose 13% is 65 is 500

Answer:

Step-by-step explanation:

Let the number be x,

Then,

13% of x =65

Or, 13/100 of x =65

Or,x=6500/13

:.x=500

Answer:

91.125

Step-by-step explanation:

Each term is multiplied by 1.5 to get the next term.

12,18,27,40.5, 60.75, 91.125

Hope that helped!!! k

Answer:

91.125

Step-by-step explanation:

We know that this is a geometric sequence. By definition, this means that each subsequent term divided by the previous one is a common ratio r.

Here, divide 18 by 12 to get:

18/12 = 3/2 = 1.5

Divide 27 by 18 to check if it's also 1.5:

27/18 = 3/2 = 1.5

Indeed, the common ratio is 1.5. Now, we simply multiply 27 by 1.5 to get the 4th term:

27 * 1.5 = 40.5

Multiply 40.5 by 1.5 to get the 5th term:

40.5 * 1.5 = 60.75

Finally, multiply 60.75 by 1.5 to get the 6th term:

60.75 * 1.5 = 91.125

Our answer is thus 91.125.

~ an aesthetics lover

Answer:

[tex]Speed = 159.4\ km/hr[/tex]

[tex]Speed = 2.6\ km/m[/tex]

Step-by-step explanation:

The question has missing details; However, the given parameters are

[tex]Speed = 99\ miles/hour[/tex]

Required

Determine the speed in

- kilometre per hour

- kilometre per minute

From the question; we have that

[tex]1\ mile = 1.61\ kilometers[/tex]

[tex]1\ hour = 60\ minutes[/tex]

[tex]Speed = 99\ miles/hour[/tex] can be rewritten as

[tex]Speed = \frac{99\ miles}{hour}[/tex]

It can be further expressed as

[tex]Speed = \frac{99\ *\ 1\ mile}{hour}[/tex]

Recall that [tex]1\ mile = 1.61\ kilometers[/tex]'

So;

[tex]Speed = \frac{99\ *\ 1.61\ kilometre}{hour}[/tex]

[tex]Speed = \frac{159.39\ kilometres}{hour}[/tex]

[tex]Speed = 159.39\ kilometres/hour[/tex]

[tex]Speed = 159.4\ km/hr[/tex] -- Approximated

Solving further to get kilometre per minute equivalent

[tex]Speed = \frac{159.39\ kilometres}{hour}[/tex]

This can be rewritten as

[tex]Speed = \frac{159.39\ kilometres}{1\ hour}[/tex]

Recall that [tex]1\ hour = 60\ minutes[/tex]; So,

[tex]Speed = \frac{159.39\ kilometres}{60\ minutes}[/tex]

[tex]Speed = \frac{2.5565\ kilometres}{minute}[/tex]

[tex]Speed = 2.5565\ kilometres/minute[/tex]

[tex]Speed = 2.6\ km/m[/tex] --- Approximated

Answer:

Speed of the car is equivalent to 159.39 KM/hour or 2.6565 Km/min.

-Step by Step-:

-The speed of the car is given as  99 mi/hour.

Now, WE know that 1 Mile = 1.61 KM

Hence, in order to calculate the speed of the car in KM/hour we will multiply the speed of the car in miles with 1.61.

⇒The speed of the car in KM/hour = 99 × 1.61 KM = 159.39 KM/hour

Also, 1 hour = 60 minutes

⇒ Speed of the car in KM/min = (159.39) ÷ 60 = 2.6565 K/min

Answer:

y = -10.375x + 126.125

Step-by-step explanation:

(12-95)/(11-3) = -83/8 = -10.375

y = mx + b

12 = -10.375(11) + b

12 = -114.125 + b

b = 126.125

y = -10.375x + 126.125

The solution is, y = -10.375x + 126.125,  is the equation of a trend line that passes through the points (3, 95) and (11, 12).

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

here, we have,

given that,

a trend line that passes through the points (3, 95) and (11, 12).

so, the slope is,

(12-95)/(11-3) = -83/8 = -10.375

now, we have,

y = mx + b

12 = -10.375(11) + b

12 = -114.125 + b

b = 126.125

so, we get,

y = -10.375x + 126.125

Hence, The solution is, y = -10.375x + 126.125,  is the equation of a trend line that passes through the points (3, 95) and (11, 12).

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Answer:

2(x-4) (x+9)

Step-by-step explanation:

Answer:

Can you solve #18 from practice test 5 calculator section? ... years old and a pin oak tree with a diameter of 12 inches is ... because on the test you would have figured these mechanics out on ... Now, note that the concept of a “growth factor” as provided in the table ... That's a difference of about 1.3 inches.

Step-by-step explanation:

Answer:

[tex]\large \boxed{1296}[/tex]

Step-by-step explanation:

6 raised to 4 indicates that the base 6 has an exponent or power of 4.

[tex]6^4[/tex]

6 is multiplied by itself 4 times.

[tex]6 \times 6 \times 6 \times 6[/tex]

[tex]=1296[/tex]

Answer:

The triangles are not similar

Step-by-step explanation:

We can see that TU and EU are equal in length but SU and DU are not hence they are not similar

Answer:

Smaller coin = s = $0.25 = 25cent.

larger coin = l = $0.5 = 50 cent

Step-by-step explanation:

Given the following :

Let the two coins be s and l

Where s = smaller denomination and l = larger denomination coins

Two of the smaller denomination coins and three of the larger denomination coins have a value of $2

2s + 3l = 2 - - - - (1)

Two of the smaller denomination coins and seven of the larger denomination coins have a value of $4

2s + 7l = 4 - - - (2)

2s + 3l = 2 - - - (1)

2s + 7l = 4 - - - (2)

Subtracting both equations

3l - 7l = 2 - 4

-4l = - 2

l = 2/4

l = 0.5

Put l = 0.5 into (1)

2s + 3l = 2

2s + 3(0.5) = 2

2s + 1.5 = 2

2s = 2 - 1.5

2s = 0.5

s = 0.5 / 2

s = 0.25

Smaller coin = s = $0.25 = 25cent.

larger coin = l = $0.5 = 50 cent

Answer:

x=-1

Step-by-step explanation:

0.5 ( 5 - 7x ) = 8 - ( 4x + 6 )

- Distribute 0.5 by 5 and -7x

2.5 - 3.5x = 8 - ( 4x + 6 )

Second- Distribute the invisible one into 4x and 6

2.5 - 3.5x = 8 - 4x - 6

- Combine like terms: Subtract 6 from 8

2.5-3.5x= - 4x + 2

-Add 4x from both sides of the equation

2.5 + 0.5x = 2

-Subtract 2.5 from both sides of the equation

0.5x = 2- 2.5

0.5x = -0.5

-Then divide each side by 0.5x

0.5x  = -0.5

0.5      0.5

-Cancel the common factor of 0.5

x = - 0.5

      0.5

-Divide -0.5 by 0.5

X = -1

Answer:

4 and 34/63

Step-by-step explanation:

we know that he has to walk 8 and 2 thirds of an kilometer to school. so far he has ran 1 10/11 of a kilo.

To solve this you would have to divide 8 2/3 by 1 10/11.

you would have to make them into improper fractions so 26/3 divided by 21/11

your answer will be 4 34/63

Alan covers he distance by walking is   6+25/33 km.

distance is a scaler quantity which means it only have magnitude and no direction if any person or any thing moves from place A to B then it will show the distance between A and B

Given that Alan's school a distance is 8+2/3 km which is 26/3 km,

and he ran one and ten elevenths kilometers

means 1+10/11 = 21/11 km

and walks rest

let distance covered by walking be x

total distance for Alan school = distance covered by running + distance covered by walking

26/3 = 21/11 +x

x = 26/3 - 21/11

x = 223/33 = 6+25/33

Hence rest walking distance for Alan is 6+25/33

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Answer:

Step-by-step explanation:

Hello, please consider the following.

[tex]h(x)=5/2x+4 \\\\x=(h^{-1}o})(x)=(hoh^{-1})(x)=h(h^{-1}(x))=\dfrac{5}{2h^{-1}(x)+4}\\\\<=> 2h^{-1}(x)+4=\dfrac{5}{x}\\\\<=> h^{-1}=\dfrac{\dfrac{5}{x}-4}{2}\\\\<=>h^{-1}=\dfrac{5-4x}{2x}[/tex]

Thank you.

Answer:

18

Step-by-step explanation:

30-60-90 triangles have a set of x values that you can plug your numbers into.

we know that the side length opposite to 30 is x

the side length opposite to 60 is xsqrt3

the side length opposite to 90 is 2x

from this we can gather that y=2x where x=9 therefore y=18

Part (a)

BC = opposite side (furthest leg from the reference angle)

AB = adjacent side (closest leg from the reference angle)

AC = hypotenuse (always opposite the 90 degree angle)

=============================================

Part (b)

i. False. Angle B is 90 degrees as shown by the square angle marker.

ii. False. Side AB is opposite angle C. Note how "C" is part of "BC", so that means we cannot have BC be opposite C.

iii. True. Leg AB is the closer leg to angle A. We have "A" in "AB" to see this without having to draw the diagram. Refer to part (a) above.

iv. False. The longest side of any right triangle is always the hypotenuse. The longest side of any triangle is always opposite the largest angle.

==============================================

Part (c)

cos(theta) = adjacent/hypotenuse = AB/AC

tan(theta) = opposite/adjacent = BC/AB

Refer back to part (a) to determine the opposite,adjacent and hypotenuse side lengths.

==============================================

Part (d)

The reference angle has changed, so the opposite and adjacent sides swap. The hypotenuse remains the same regardless of what reference angle you pick.

sin(C) = opposite/hypotenuse = AB/AC

cos(C) = adjacent/hypotenuse = BC/AC

tan(C) = opposite/adjacent = AB/BC

Note the tangent ratio is the reciprocal of what we found back in part (c).

Answer & Step-by-step explanation:

(a)

The hypotenuse is on line CA (the hypotenuse is always opposite the 90° angle (marked by a little square))

The adjacent is on the line BA (adjacent is next to the given angle, but NOT the hypotenuse)

The opposite is on the line CB (this is opposite the given angle)

(b)

i.   false (b is a right angle)

ii.  false (the side opposite C is BA)

iii. true

iv. false (the side opposite B is the hypotenuse, and the hypotenuse is always the longest side in a triangle)

(c)

cosine ratio: [tex]cos=\frac{adjacent}{hypotenuse}[/tex]

tangent ratio: [tex]tan=\frac{opposite}{adjacent}[/tex]

The cosine and tangent ratios of the given angle:

[tex]cos0=\frac{AB}{CA} \\\\tan0=\frac{CB}{AB}[/tex]

(d)

Remember SOH-CAH-TOA:

Sine=Opposite/Hypotenuse

Cosine=Adjacent/Hypotenuse

Tangent=Opposite/Adjacent

Using the angle C, plug in the appropriate sides:

[tex]sinC=\frac{BA}{CA}\\\\ cosC=\frac{CB}{CA}\\\\ tanC=\frac{BA}{CB}[/tex]

:Done

Answer:

A) 0.875, 87.5%

B) 0.12, 12%

C) 1.6, 160%

Step-by-step explanation:

Answer:

A) 0.875, 87.5%

B) 0.001, 0.1%

C) 1.6, 160%

Step-by-step explanation:

I honestly just used a calculator, but it could also be solved using the butterfly technique. For percentages just move the decimal to the left two places.

Answer:

$18

Step-by-step explanation:

$18.02 rounds to $18

Answer:

  $17

Step-by-step explanation:

Rounded, the listed numbers are ...

  12 + 5 -1 +3 -2 = 17

The estimate of total cost is $17.

Answer:

[tex]D=-5y^2[/tex]

Step-by-step explanation:

We have the equation:

[tex]\displaystyle -15y^4=D(3y^2)[/tex]

And we want to find D such that the equation is true.

So, we can divide both sides by 3y². This will yield:

[tex]\displaystyle D=\frac{-15y^4}{3y^2}[/tex]

We can split this into:

[tex]\displaystyle D=\frac{-15}{3}\cdot\frac{y^4}{y^2}[/tex]

Simplify. Hence:

[tex]D=-5y^2[/tex]

Answer: 49 cm^2

Step-by-step explanation:

The length of the small pink square box will be:

L^2 = 9

L = sqrt( 9 )

L = 3

The length of the big pink square box will be:

L^2 = 16

L = sqrt( 16 )

L = 4

The length of the yellow square box will be:

4 + 3 = 7

The area of the third square box will be

A = 7^2

A = 49 cm^2