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3 years ago

I WILL GIVE BRAINLIES!!!

Mathematics

2 answers:

White raven [17]3 years ago

6 0

Answer:

y=-5x+9

m=-5

b=9

y=5x-4

m=5

b= -4

y=8

m=0

b=8

Step-by-step explanation:

ivanzaharov [21]3 years ago

4 0

Answer:

1) 15x + 3y = 27 in slope-intercept form.

→y=-5x+9

→m =-5

→b =(0,9)

2) 15x − 3y = 12 in slope-intercept form.

→y =5x-4

→m =5

→b =(0,-4)

3) 2y = 16 in slope-intercept form.

→y =8

→m =0

→b =(0,8)

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ACBM is a segment of a circle such

tatiyna

Answer:

a. 8.94 cm b. 127° c. 12.37 cm²

Step-by-step explanation:

a. Since CM = 4 cm is the perpendicular bisector of AB = 16 cm and r is the radius off the circle. From Pythagoras' theorem,

r² = (AB/2)² + CM²

r = √[(AB/2)² + CM²]

Substituting the values of the variables into r, we have

r = √[(16/2)² + 4²]

r = √[8² + 4²]

r = 4√[2² + 1²]

r = 4√[4 + 1]

r = 4√5 cm

r = 8.94 cm

b. We know that the length of a chord L = 2rsin(θ/2) where r is the radius of the circle, and θ is the angle subtended by the chord AB.

Since L = 2rsin(θ/2) and L = AB = 16 cm,

L/2r = sin(θ/2)

taking sine inverse of both sides, we have

θ/2 = sin⁻¹(L/2r)

multiplying both sides by 2, we have

θ = 2sin⁻¹(L/2r)

substituting the values of the variables, we have

θ = 2sin⁻¹[16/(2 × 8.94)]

θ = 2sin⁻¹[16/17.88]

θ = 2sin⁻¹[0.8949]

θ = 2 × 63.49°

θ = 126.98°

θ ≅ 127°

c. The area of a segment A is given by

A = (θπ/360 - sinθ)r²/2 where θ is the angle subtended by the segment and r = radius of the circle

since θ ≅ 127° and r = 4√5 cm, substituting these values into A, we have

A = (127°π/360 - sin127°)(4√5)²/2

A = (398.93/360 - 0.7988)40

A = (1.1081 - 0.7988)40

A = 0.3093 × 40

A = 12.372 cm²

A ≅ 12.37 cm²

5 0

3 years ago

Which ordered pair is a solution of this equation? -7x - 5y = 42

andreyandreev [35.5K]

(-6,0) is the ordered pair for this solution, you might want to double check though

7 0

4 years ago

Read 2 more answers

In New York City at the spring equinox there are 12 hours 8 minutes of daylight. The longest and the shortes days of the year va

gayaneshka [121]

Question:

In New York City at the spring equinox there are 12 hours 8 minutes of daylight. The longest and the shortest days of the year vary by 2 hours 53 minutes from the equinox. In this year, the equinox falls on March 21. In this task, you'll use a trigonometric function to model the hours of daylight hours on certain days of the year in New York City.

- Find amplitude and the period of the function

- Create a trigonometric function that describes the hours of sunlight for each day of the year

- Then use the function you built to find how fewer daylight hours February 10 will have then March 21

Answer:

(a)

$A = 2.883$ --- Amplitude

$T = 365$ ---- Period

(b) Trigonometry function

$f(x) = 12.133 + 2.883sin(\frac{2\pi}{365}[x - 80])$

(c) $Hours= 1.794$

Step-by-step explanation:

Given

$Average\ Sunlight = 12hr\ 8 min$

$Variance = 2hr\ 53min$

Solving (a): Amplitude (P) and Period (T)

The amplitude is the amount of time the longest and the shortest day vary.

$A = 2\ hr\ 53\ min$

Convert to hours

$A = 2\ + \frac{53}{60}$

$A = 2+0.883$

$A = 2.883$

The period (T) is the duration i.e 1 year

$T = 1\ year$

Assume no leap year

$T = 365$

Solving (b): Trigonometry function

The function follows a sinusoidal pattern and the general form is:

$f(x) = \mu+ Asin(\frac{2\pi}{T}(x -n))$

Where

$\mu = Average\ Value$

$\mu = 12\ hr 8\ min$

Convert to hours

$\mu = 12 + \frac{8}{60}$

$\mu = 12 + 0.133$

$\mu = 12.133$

$A = 2.883$ --- Amplitude

$T = 365$ ---- Period

$n = Equinox$

$n = March\ 21$

$March\ 21st = 80th\ day$

So:

$n= 80$

The function becomes:

$f(x) = \mu+ Asin(\frac{2\pi}{T}(x -n))$

$f(x) = 12.133 + 2.883sin(\frac{2\pi}{365}[x - 80])$

Solving (c): Fewer daylight hours will Feb. 10 have.

$Feb\ 10 = 41st\ day$

So:

$f(x) = 12.133 + 2.883sin(\frac{2\pi}{365}[x - 80])$

$f(41) = 12.133 + 2.883sin(\frac{2\pi}{365}[41 - 80])$

$f(41) = 12.133 + 2.883sin(\frac{2\pi}{365}[-39])$

$2\pi = 360^\circ$

So:

$f(41) = 12.133 + 2.883sin(\frac{360}{365}[-39])$

$f(41) = 12.133 + 2.883sin(-38.466)$

$f(41) = 12.133 - 2.883*0.6221$

$f(41) = 10.339$

The fewer daylight hours is the calculated as:

$Hours= Average - f(41)$

$Hours= \mu - f(41)$

$Hours= 12.133 - 10.339$

$Hours= 1.794$

4 0

3 years ago

You spent half of your money at the theater and 1/4 at the arcade. You have $17.50 left. How much money did you have originally?

valentina_108 [34]

If you spent 1/2 at the theater, and 1/4 at the arcade then you spent 3/4 of your money leaving you with 1/4 left. multiply the amount of money you have left ($17.50), by 4. You originally had $70. hope this helps!

7 0

4 years ago

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3x + 4y + 4 > 0<br><br> how would i solve this?

klasskru [66]

Y > -3x/4 - 1 (this is the answer)

6 0

3 years ago

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