Use a half-angle identity to find the exact value of sin75

Answer:

sin 40/x =sin 60/12

Step-by-step explanation:

The question is on law of sines

Given a triangle with sides a, b, c and angles A, B, C respectively, the sine law states that; a/sin A = b/sin B = c/sin C

In the question x=a, b=12 feet, A=40° , B=60° and C=80°

Finding value of x;

x/sin 40° = 12/sin 60°

x sin 60° =12 sin 40°

x=12 sin 40 / sin 60

x=29.33 ft

Answer:

The length of the pole is 9.90 feet.

Step-by-step explanation:

From the figure, it is given that x is the length of the pole and the pole casts a shadow when the sun is at 40 degree angle.

Thus, using the sine law, we have

[tex]\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}[/tex]

Substituting the given values, we get

[tex]\frac{x}{sin40^{\circ}}=\frac{12}{sin60^{\circ}}=\frac{c}{sin80^{\circ}}[/tex]

Taking the first two equalities, we have

[tex]\frac{x}{sin40^{\circ}}=\frac{12}{sin60^{\circ}}[/tex]

[tex]x=\frac{12sin40^{\circ}}{sin60^{\circ}}[/tex]

[tex]x=\frac{12{\times}0.642}{0.866}[/tex]

[tex]x=8.90 feet[/tex]

Therefore, the length of the pole is 9.90 feet.

Answer:

10q

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

-2x+8=14

Subtract 8 from each side

-2x+8-8=14-8

-2x = 6

Divide by -2

-2x/-2 = 6/-2

x = -3

-2x + 8 = 14

Step 1: Bring 8 to the right side of the equation. To do this subtract 8 to both sides (this is the opposite of addition and will cancel 8 from the left side)

-2x + (8 - 8) = 14 - 8

-2x + 0 = 6

-2x = 6

Step 2: Isolate x by dividing -2 to both sides (division is the opposite of multiplication and will cancel -2 from the left side)

-2x/-2 = 6/-2

x = -3

Check:

Plug -3 where you see x and solve

-2(-3) + 8 = 14

6 + 8 = 14

14 = 14...............................Correct!

Hope this helped!

first off, let's recall that supplementary angles are just two sibling angles that add up to 180°.

so we have ∡T and ∡S, but we also know that ∡T = 3∡S, namely T = 3S.

[tex]\bf T+S=180\implies \stackrel{T}{3S}+S=180\implies 4S=180\implies S=\cfrac{180}{4}\implies S=45 \\\\\\ T=3S\implies T=3(45)\implies T=135[/tex]

Answer:

A. different probabilities

Answer:

tan e = -1

cot e = -1

sin e = √2/2

cosec e = √2

cos e = -√2/2

sec e = -√2.

Step-by-step explanation:

6/6-  is the tangent of e  so tan e = -1.

cot e = 1/tan e = -1.

The hypotenuse  of the triangle containing angle e = √(-6)^2 + (6)^2 ( By the pythagoras theorem) and = √72 =  6√2.

Therefore sin e =   6/6√2

= 1/√2

= √2/2

cosec e  = 1 ./ sin e = √2.

cos e = -6 / 6√2

= -√2/2.

sec e = 1/cos e = -√2.

C is the correct answer. Good luck!

Answer:

Object from Catapult B

Step-by-step explanation:

The question is on time of flight in falling objects

Given catapult A: h(x)= -16x^2+64x+17, find the height the object will reach at time 2.0

substitute value x=2 in h(x)= -16x^2+64x+17;

h(2)= -16 × (2)² +64 ×2 +17

h(2) = -16×4 + 145

h(2)= 81

However with catapult B at t=2.0 the height reached will be 60

Solution

Catapult A object will attain h=81, when t=2.0

Catapult B object will attain h=60, when t=2.0

Thus Object from Catapult B will hit the ground first because it covered a lesser distance compared to the object from catapult A

All you have to do is divide 150 by 18 and that will get you how many meters Pete drives per second

150 ÷ 18

8.3333333333333333333

so...

8.3 m/s (B)

Hope this helped!

~Just a girl in love with Shawn Mendes

Speed is defined as quotient of distance and time.

[tex]

s=\frac{d}{t}=\frac{150}{18}=8.33\dots

[/tex]

Speed is a scalar value therefore we cannot determine its vector. Speed with vector is known as velocity and that is where we specify its vector because velocity is a vector value.

So the answer is 8.3 m/s.

Hope this helps.

r3t40

Answer: The correct answer is 1/3x − 3 = −x + 1

Step-by-step explanation:

add 3 to both sides

simplify

add x to both sides

simplify

multiply both sides by 3

simplify

divide both sides by 2

simplify

The graph of the system of equations solves the equation -1/3x + 3 = x - 1.

The first step in solving a system of equations is to isolate one variable in one of the equations. We can begin by rearranging the first equation -1/3x + 3 = x - 1 to isolate x. First, multiply both sides of the equation by 3 to get rid of the fraction: -x + 9 = 3x - 3. Then, add x to both sides to bring all the x terms to one side: 9 = 4x - 3. Finally, add 3 to both sides to solve for x: 12 = 4x. Dividing both sides by 4 gives us x = 3.

Substitute this value of x into either of the original equations to solve for y. Let's use the second equation: (1/3)(3) - 3 = -3 + 1. Simplifying this equation, we get 1 - 3 = -2. This tells us that y = -2.

Therefore, the solution to the system of equations is x = 3 and y = -2, and it satisfies the equation -1/3x + 3 = x - 1.

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Answer:

Step-by-step explanation:

ΔQTR and ΔRTS are similar (AAA). Therefore the corresponding sides are in proportion:

[tex]\dfrac{RT}{TS}=\dfrac{TQ}{RT}[/tex]

We have

[tex]RT=x,\ TS=9,\ TQ=16[/tex]

Substitute:

[tex]\dfrac{x}{9}=\dfrac{16}{x}[/tex]              cross multiply

[tex]x^2=(9)(16)\\\\x^2=144\to x=\sqrt{144}\\\\x=12[/tex]

No. You cannot use the Pythagorean theorem to find the missing side, because you can only use The Pythagorean theorem when you are dealing with a right triangle.

Answer:

22

Step-by-step explanation:

We know that 1 miles = 5280 ft  and 1 hour = 3600 seconds

15 miles         5280 ft         1 hour

--------------- * ------------- *   --------------        =

1 hour               1 mile        3600 second

The units cancel leaving us ft/s

22 ft/s

the last one on the right

Answer:

I think it’s 28 but I’m not sure

(sorry if it’s wrong)

Step-by-step explanation:

For this case we have that by definition of trigonometric relations that, the sine of an angle is equal to the opposite leg to the angle on the hypotenuse. So:

[tex]Sin (36) = \frac {5} {x}[/tex]

Clearing x:

[tex]x = \frac {5} {sin (36)}\\x =\frac {5} {0.58778525}\\x = 8.517887564 [/tex]

Rounding off we have to:

[tex]x = 8.51[/tex]

Answer:

Option D

Answer:

b

Step-by-step explanation:

using pythagoras theorem:

d=(5^2+4^2)^1/2

=6.4 units

Answer:

The approximate length of the diagonal of the rectangle = 6.4 units ⇒ B

Step-by-step explanation:

* Lets revise the properties of the rectangle

- The rectangle has 4 sides

- Each two opposite sides are parallel and equal in length

- It has for right angles

- Its two diagonals are equal in length

- The diagonal divide the rectangle into two congruent right triangles

* Now lets solve the problem

∵ The length of the rectangle = 5 units

∵ The width of the rectangle = 4 units

∵ The diagonal of the rectangle with the length and the width formed

  right triangle, the length and the width are its two legs and the

  diagonal is its hypotenuse

- To find the length of the hypotenuse use Pythagoras theorem

∵ Hypotenuse = √[(leg1)² + (leg2)²]

∴ The length of the diagonal = √[5² + 4²] = √[25 + 16] = √41

∴ The approximate length of the diagonal of the rectangle = 6.4 units

Answer:

2 4/20, which you can simplify as 2 1/5

Hope this helps if u can (thanks and brainliest) please. Have a good day!! Ask any questions if u need to!!

Answer:

60cm^2

Step-by-step explanation:

5 * 12 = 60cm^2

Answer:

18

Step-by-step explanation:

The average rate of change of f(x) in the closed interval [ a, b ] is

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

here [ a, b ] = [ 1, 5 ]

f(b) = f(5) = 3 × 5² = 75

f(a) = f(1) = 3 × 1² = 3, hence

average rate of change = [tex]\frac{75-3}{5-1}[/tex] = [tex]\frac{72}{4}[/tex] = 18

Answer:18

Step-by-step explanation:

here [ a, b ] = [ 1, 5 ]

f(b) = f(5) = 3 × 5² = 75

f(a) = f(1) = 3 × 1² = 3, hence

average rate of change =  =  = 18

To find the slope, you should rearrange the equation into slope-intercept form, ie. y = mx + c, where m is the gradient.

y - 9 = 15(x - 5)

y = 15(x - 5) + 9 (Add 9 to each side)

y = 15x - 15*5 + 9 (Expand 15(x - 5))

y = 15x - 75 + 9

y = 15x - 66

Therefor, the slope of the equation is 15.

Answer:

Use the slope-intercept form  

y

=

m

x

+

b

 to find the slope  

m

.

m

=

15

Step-by-step explanation:

Cuz i know all that

Answer:  56 mph

Step-by-step explanation:

48 miles x 2 hours = 96 miles

60 miles x 4 hours =  240 miles

240 + 96 = 360 total miles

360 / 6 (hours) = 56 mph

Answer:

Transactional service

Step-by-step explanation:

If Allison pays all her bills using her bank's online bill pay, it will be considered as transactional service which is a type of electronic banking service.

A transaction involves paying a supplier for its services provided or any goods delivered.

Here the services used will include electricity, water, internet, gas, etc for which the bills are paid. Therefore, the correct answer is transactional service.

Answer:

Transaction service

Step-by-step explanation:

Answer:

If KE = OS then we can deduce that the trapezoid is constructed of 3 equilateral triangles and thus we can easily work out the angles.

OSK = 60

SKE = 120

KEP = 120

EPO  = 60

We can also easily work out the perimeter since we can deduce that PE = SK = KE and thus the perimeter is 5 * 8 = 40

The measure of ∠S, ∠K, ∠E, and ∠P is 60°, 120°, 120°, and 60°, respectively.  While the perimeter of EPSK is 40 units.

A trapezoid is a quadrilateral which is having a pair of opposite sides as parallel and the length of the parallel sides is not equal.

Given KE=OS=8, but OS is the radius of the circle, therefore, it can be written as,

OS = OP = KE = OK = OE = radius of the circle = 8 units.

Since in ΔOEK all sides are equal it is an equilateral triangle therefore, the measure of the angle ∠EOK is 60°.

As the measure of the angle, ∠EOK is 60°, the measure of the angle, ∠KOS and ∠EOP will be 60° each.

Also, in ΔSOK and ΔPOE, the sides OS = OP = KE = OK = OE are equal, they are equilateral triangles as well.

Therefore, the measure of ∠KSO and ∠EPO will be 60° each.

The angles at the end of the non-parallel sides of a trapezium are supplementary. Therefore, we can write,

∠KSO + ∠SKE= 180°

∠SKE = 120°

Similarly, the measure of the ∠PEK is 120°.

Further, it is known that the measure of the sides OS=OP=PE=EK=KS = 8 units, therefore, the perimeter of the trapezium is,

Perimeter = OS + OP + PE + EK + KS = 8+8+8+8+8 = 40 units.

Hence, the measure of ∠S, ∠K, ∠E, and ∠P is 60°, 120°, 120°, and 60°, respectively.  While the perimeter of EPSK is 40 units.

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Answer:

[tex]\large\boxed{Q1:\ x=2\ or\ x=5}\\\boxed{Q2:\ x=1-\sqrt{21}\ or\ x=1+\sqrt{21}}[/tex]

Step-by-step explanation:

[tex]\text{Use the quadratic formula:}\\\\ax^2+bx+c=0\\\\\text{If}\ b^2-4ac<0,\ \text{then the equation has}\ \bold{no\ solution}\\\\\text{If}\ b^2-4ac=0,\ \text{then the equation has one solution}\ x=\dfrac{-b}{2a}\\\\\text{If}\ b^2-4ac>0,\ \text{then the equation has two solutions}\ x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\==========================================[/tex]

[tex]\bold{Q1}\\\\x^2-7x+10=0\\\\a=1,\ b=-7,\ c=10\\\\b^2-4ac=(-7)^2-4(1)(10)=49-40=9>0\\\\\sqrt{b^2-4ac}=\sqrt9=3\\\\x_1=\dfrac{-(-7)-3}{2(1)}=\dfrac{7-3}{2}=\dfrac{4}{2}=2\\\\x_2=\dfrac{-(-7)+3}{2(1)}=\dfrac{7+3}{2}=\dfrac{10}{2}=5\\\\========================================[/tex]

[tex]\bold{Q2}\\x^2-2x=20\qquad\text{subtract 20 from both sides}\\\\x^2-2x-20=0\\\\a=1,\ b=-2,\ c=-20\\\\b^2-4ac=(-2)^2-4(1)(-20)=4+80=84>0\\\\\sqrt{b^2-4ac}=\sqrt{84}=\sqrt{4\cdot21}=\sqrt4\cdot\sqrt{21}=2\sqrt{21}\\\\x_1=\dfrac{-(-2)-2\sqrt{21}}{2(1)}=\dfrac{2-2\sqrt{21}}{2}=1-\sqrt{21}\\\\x_2=\dfrac{-(-2)+2\sqrt{21}}{2(1)}=\dfrac{2+2\sqrt{21}}{2}=1+\sqrt{21}[/tex]

Answer:

Step-by-step explanation:

x^2 - 7x + 10 = 0 can be factored as follows:  (x - 5)(x - 2).  Note that -5x -2x combine to -7x, the middle term of this quadratic, and that (-5)(-2) = +10, the constant term.  Setting each of these factors = to 0 separately, we get:

x = 5 and x = 2.

x^2 - 2x = 20 should be rewritten in standard form for a quadratic equation before you attempt to solve it:  x^2 - 2x - 20 = 0.  This quadratic is not so easily factored as was the previous one.  Let's use the quadratic formula:

      -b ± √(b²-4ac)

x = --------------------

             2a

Here, a = 1, b = -2 and c = -20, so the discriminant b²-4ac = (-2)^2 - 4(1)(-20), or 4 + 80, or 84.  84 has only one perfect square factor:  4·21.  Because the discriminant is +, we know that this equation has two real, unequal roots.

They are:

       -(-2) ± √(4·21)         2 ± 2√21

x = ----------------------  =  ----------------- =   1 ± √21

             2(1)                            2

Answer:

the answer is A.616.39

Step-by-step explanation:

Megan can withdraw $615.21 per month for 5 years from the new account.

Option B is the correct answer.

An equation contains one or more terms with variables connected by an equal sign.

Example:

2x + 4y = 9 is an equation.

2x = 8 is an equation.

We have,

To solve this problem, we need to use the formula for the future value of an annuity:

[tex]FV = P [(1 + r/n)^{n\times t} - 1]/(r/n)[/tex]

where:

P = payment per period

r = interest rate per period

n = number of compounding periods per year

t = number of years

FV = future value of the annuity

First, we can calculate the future value of Megan's semiannual payments after 10 years:

P = $1,624.13

r = 1.5%/2 = 0.0075 (semiannual interest rate)

n = 2 (semiannual compounding periods)

t = 10 years

So,

[tex]FV = 1,624.13 \times[(1 + 0.0075/2)^{2\times10} - 1]/(0.0075/2)[/tex]

= $21,070.58

Next, we need to calculate the future value of this amount when transferred to the new account:

r = 2.3% / 12 = 0.00191667 (monthly interest rate)

n = 12 (monthly compounding periods)

t = 5 years (60 months)

FV

[tex]= $21,070.58 \times (1 + 0.00191667)^{60}[/tex]

= $24,526.41

Finally, we need to calculate the monthly payment Megan can withdraw for 5 years from this account, assuming the balance is depleted at the end of the 5 years:

P = ?

r = 2.3% / 12 = 0.00191667 (monthly interest rate)

n = 12 (monthly compounding periods)

t = 5 years (60 months)

Using the formula for the present value of an annuity:

[tex]P = FV \times (r/n) / [(1 + r/n)^{n\timest} - 1][/tex]

[tex]= $24,526.41 \times (0.00191667) / [(1 + 0.00191667)^{60} - 1][/tex]

= $615.21

Therefore,

Megan can withdraw $615.21 per month for 5 years from the new account.

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Step-by-step explanation:

Shift to the right 5 units and down 2 units.

Answer:

Average = 1

Step-by-step explanation:

Let us define the average first:

Average is calculated by adding up all the values and then dividing the sum by total number of values.

The formula for average may be written as:

[tex]Average = \frac{Sum}{count}[/tex]

In the following case,

Sum of numbers = -3-2+2+2+6 = 5

Count = 5

So,

Average = 5/5

=> Average = 1

Answer:

the answer is 1

Step-by-step explanation:

Sum of numbers = -3-2+2+2+6 = 5

Count = 5

So,  

Average = 5/5

=> Average = 1

Answer:

A, B, D

Step-by-step explanation:

Use the LCM to help...