Solve the system of equations:
v=2x-4
y=x2 - 4

Recall the triple angle identity for cosine:

cos(3x) = cos³(x) - 3 sin²(x) cos(x)

… = cos³(x) - 3 (1 - cos²(x)) cos(x)

… = 4 cos³(x) - 3 cos(x)

and the definition of secant,

sec(x) = 1/cos(x)

So we have

sec(x) cos(3x) = 0

(4 cos³(x) - 3 cos(x))/cos(x) = 0

cos(x) (4 cos²(x) - 3)/cos(x) = 0

If cos(x) ≠ 0 (this happens at the endpoints of the interval [-π/2, π/2]), we can simplify this to

4 cos²(x) - 3 = 0

cos²(x) = 3/4

cos(x) = ±√3/2

But since -π/2 < x < π/2, we know cos(x) > 0, so we ignore the negative case:

cos(x) = √3/2

==>   x = π/6 and x = -π/6

The solution of the given trigonometric equation by using trigonometric identities is [tex]\frac{\pi }{6} \ and \frac{-\pi }{6}[/tex].

Trigonometric Identities are the equalities that involve trigonometry functions and holds true for all the values of variables given in the equation.

[tex]cos(3x) = 4cos^{3}(x) -3cos(x)[/tex]

According to the given question.

We have an equation

[tex]sec(x)cos(3x) = 0[/tex]

Since, the above equation can be written as by using trigonometric identities

[tex]sec(x)cos(3x) = 0\\\implies \frac{1}{cos(x)} (4cos^{3} x-3cos(x))=0[/tex]

Solve the above equation for x.

[tex]\implies 4cos^{2} x -3= 0[/tex]

[tex]\implies 4cos^{2}x = 3\\ \implies cos^{2} x = \frac{3}{4} \\\implies cos x = \sqrt{\frac{3}{4} } \\\implies cos x = \pm\frac{\sqrt{3} }{2}[/tex]

In the given domain [tex][\frac{-\pi }{2}, \frac{\pi }{2} ][/tex] we know that cosx > 0. Therefore, we take only positive part

[tex]\implies cosx = \frac{\sqrt{3} }{2} \\\implies x = cos^{-1} \frac{\sqrt{3} }{2} \\\implies x = \frac{\pi }{6}, and \frac{-\pi }{6}[/tex]

Hence, the solution of the given trigonometric equation by using trigonometric identities is [tex]\frac{\pi }{6} \ and \frac{-\pi }{6}[/tex].

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Answer:

trure correct

ok must of luck

Answer:

4x^4 + 6x^3 + 5x + 4 poly means many ....polynomial

x^2 + 1 ... two parts bi-nomial

ax^2 + bx + c ... three parts tri-nomial

3x^2y^3 ... one part  monomial

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

f(x) = 16x+12

g(x) = 4x+3

f(x) / g(x) =

Factoring f(x) =4(4x+3)

f(x) /g(x) = 4(4x+3) / (4x+3) = 4

Answer:

-i

Step-by-step explanation:

i =i

i^2=-1

i^3= -i

i^4=1

i^5=1

Answer:

1. x=72, y=, 108

2.x=30, y=72

Step-by-step explanation:

Brainliest please~

Answer:

69

Step-by-step explanation:

cuz

Answer:

3 3/4 tins of food

Step-by-step explanation:

Number of cats = 3

Quantity of food for each cat per day = 1/4 of a tin

Total tins of cat food sue bought = 4 tins

Has Sue bought enough cat food to feed her cats for 5 days?

Quantity of food 3 cats eat per day = Quantity of food for each cat per day × Number of cats

= 1/4 × 3

= 3/4 of a tin

Total Quantity of food 3 cats eat for 5 days = Quantity of food 3 cats eat per day × 5 days

= 3/4 × 5

= (3 * 5) / 4

= 15/4

= 3 3/4 tins of food

Total Quantity of food 3 cats eat for 5 days = 3 3/4 tins of food

Recall,

Total tins of cat food sue bought = 4 tins

Therefore, Sue bought enough cat food to feed her cats for 5 days

Answer:

13 - x

(18 + x) /2

Step-by-step explanation:

Given :

See = 18 sweets

Tony = 18 sweets

See gives Tony x sweets :

See = 18 - x

Tony = 18 + x

See eats 5 of her sweets:

See's sweets becomes :

18 - x - 5 = 13 - x

Tony eats half of his sweets;

Tony's sweets becomes ;

(18 + x) /2

Answer:

Let the cost of banana per dozen be Rs. x.

Amount for which bananas are bought = Rs. 840

No. of dozens of bananas for Rs 840  = 840/x

New cost of banana per dozen = Rs. (x + 1)

New No. of dozens of bananas for Rs 840 = 840/x+1

According to given condition,

840/x – 840 / x + 1 = 2

∴ 840[1/x – 1/x+1] = 2

∴ 840 [x+1- x / x(x+1)] = 2

∴ 840 [1/ (x² + x)] = 2

∴ 840 = 2(x² + x)

∴ 2x2 + 2x – 840 = 0

Dividing by 2, we get

x² + x – 420 = 0

x² – 20x + 21x – 420 = 0

∴  x (x – 20) + 21 (x – 20) = 0

∴  x – 20 = 0 or x + 21 = 0

∴  x = 20 or x = –21

∴  The cost of bananas cannot be negative.

∴  x = 20

The original cost of one dozen banana is Rs. 20

hope it helps you

Step-by-step explanation:

Step-by-step explanation:

x²+3x+x+3+x²+4x+2x+8

2x²+10x+11....then solve quadratically

Answer:

Step-by-step explanation:

Hello!

(x + 1)(x + 3) + (x + 2)(x + 4)

x*x = x²

x*3 = 3x

1*x = x

1*3=3

x*x=x²

x*4 = 4x

2*x= 2x

2*4 = 8

x²+3x+x+3+ x² + 4x+ 2x+  8=

2x² + 10x+ 11

Answer: 2.54647909 or 2.55

Step-by-step explanation:

radius=C/2π

r=16/2π

r=16/6.2831853071796

r=2.54647909

Answer:

t = -0.22secs and 0.85secs

Step-by-step explanation:

Given the expression

h = –16t² + vt + c.

If a child tosses a ball upward with a starting velocity of 10 ft/s from a height of 3 ft, then;

v = 10, c = 3

Since we are to let h = 0, then the equation becomes:

0 = –16t² + 10t + 3

Multiply through by a minus sign

16t² - 10t - 3 = 0

Factorize the reulting expression:

t = -(-10)±√(-10)²-4(16)(-3)/2(16)

t = 10±√100+192/32

t = 10±√292/32

t = 10±17.09/32

t = 10-17.09/32 and 10+17.09/32

t = -7.09/32 and 27.09/32

t = -0.22secs and 0.85secs

Answer:

0.8 s

Step-by-step explanation:

I got it right in grandpoint.

Answer:

x is any number

y depends on x value

Answer:

35

Step-by-step explanation:

Make equations, l = w+5 and 2l + 2w = 150

Substitute w+5 into 2l + 2w = 150

Simplify to get 4w + 10 = 150

Subtract 10 from both sides to get 4w = 140

Divide both sides by 4 and you get 35 as width

Answer:

The width of the field is 35 meters.

Step-by-step explanation:

Recall that the perimeter of a rectangle is given by:

[tex]\displaystyle P = 2(w+\ell)[/tex]

Where w is the width and l is the length of the rectangle.

We know that the perimeter is 150 meters. Thus:

[tex]150=2(w+\ell)[/tex]

Divide both sides by two:

[tex]75=w+\ell[/tex]

We are given that the length is five meters longer than the width. So:

[tex]\ell = w+5[/tex]

Substitute:

[tex]75=w+(w+5)[/tex]

Combine like terms:

[tex]75=2w+5[/tex]

Subtract five from both sides:

[tex]70=2w[/tex]

And divide both sides by two. Hence:

[tex]w=35[/tex]

Thus, the width of the rectangular field is 35 meters.

Answer:

In addition, from the response shown, using a graphical calculator brings the following benefits:

1) You can write the system of linear equations as big as you want. This is: systems 3 * 3, 4 * 4, 5 * 5.

2) The response to systems of equations greater than 2 * 2 can be complicated when you graph the solution, therefore, the graphing calculator can be much more efficient in these cases.

3) You can write the linear equations in any way. Resolving by hand you should probably rewrite the system of equations to find the solution.

Step-by-step explanation:

Answer:

Step-by-step explanation:

It is much simpler to graph and find the intersection points between the equations, which would be the solutions to the system, than graphing it by hand which would lead to some errors.

Given:

The number is 3.023.

To find:

The given number in the form of [tex]\dfrac{p}{q}[/tex], where [tex]q\neq 0[/tex].

Solution:

The given number is 3.023. It can be written as:

[tex]3.023=3.023\times \dfrac{1000}{1000}[/tex]

[tex]3.023=\dfrac{3023}{1000}[/tex]

It cannot be simplified further because 3023 and 1000  have no common factors.

Therefore, the given number 3.023 can be written as [tex]\dfrac{3023}{1000}[/tex].

Answer:

Commutative property of addition

Step-by-step explanation:

The points are ( 1,0) (0,1) .

a.) We seek the coordinates on the unit circle that represent an angle of 0 degrees.

The points on the unit circle are often provided by,

( cosθ, sinθ )

In order to do so,

θ= 0

to acquire,

(cos(0),sin(0))

(1,0)

b. With regard to the location on the unit circle where the angle is 90 degrees,

We swap out

θ = 90

to acquire,

(cos(90),sin(90))

This is condensed to, (0,1)

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Answer: 1,0

is the actual answer

Answer:

325

Step-by-step explanation:

Total Tickets = 585

Let the adult tickets be = x

If 65 fewer student tickets were sold than adult tickets then Student tickets = x-65

Student Tickets + Adult Tickets = 585

x + (x-65) = 585

x + x - 65 = 585

2x - 65 = 585

2x = 585 + 65

2x = 650

2x/2 = 650/2

x = 325

Answered by Gauthmath

Answer:

[tex]\sqrt{84^{2} } -37^{2} /47[/tex]=257 9/47

Step-by-step explanation:

Answer:

[tex]choice \: c. \: - 77 < f(x) < - 2[/tex]

Step-by-step explanation:

[tex]f( - 4) = - 5 ({ - 4}^{2}) + 3 = - 77[/tex]

[tex]f( - 1) = - 5( { - 1}^{2}) + 3 = - 2[/tex]

Thus finding the range of F(x).

The range of the given function is - 77 < f(x) < - 2.

"The range of a function is a set of all the images of elements in the domain."

The given function is:

f(x) = - 5x² + 3

It is defined over the domain - 4 < x < - 1.

For x = - 4, f(x) = - 5(- 4)² + 3 = - 80 + 3 = - 77

For x = - 1, f(x) = - 5(- 1)² + 3 = - 5 + 3 = - 2

Therefore, the range of the given function f(x) is:

- 77 < f(x) < - 2.

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5.

1m = 0.001 km

So, 1m² = 10^-6

Area = 5027 m² = 5027 × 10 ^-6 km²

6.

1mm = 0.1 cm

1mm² = 10^-2

Area = 210× 297 mm² =62370 mm² = 62370 ×10^-2 cm²

9514 1404 393

Answer:

  1/12

Step-by-step explanation:

The probability of any given outcome is the ratio of the number of ways that outcome can happen to the total number of outcomes.

  P(4) = 1/6 . . . . . roll = 4 is one of 6 possible outcomes

  P(odd) = 3/6 = 1/2 . . . . . of the 6 possible outcomes, 3 are odd

__

The two rolls of the die are presumed to be independent, so the probability of the two outcomes is the product of their individual probabilities.

  P(4 & odd) = (1/6)(1/2) = 1/12

Answer:

The number of sedans before any vehicle was sold is 168

Step-by-step explanation:

Let's define the variables:

x = number of sedans

y = number of SUVs

We know that:

"If 36 sedans are sold and 36  SUVs are added, there will be an equal number  of sedans and SUVs"

If 36 sedans are sold, the new number of sedans is:

x - 36

if 36 SUVs are added, the new number of SUVs is

y + 36

And these numbers are equal, then:

x - 36 = y + 36

We also know that:

" If 8 SUVs are sold and 8  sedans are added, there will be twice as many

sedans as SUVs. "

If 8 SUVs are sold, the new number of SUVs will be:

y - 8

If 8 sedans are added, the new number of sedans wil be:

x + 8

From this we can write the equation:

(x + 8) = 2*(y - 8)

x + 8 = 2*y - 16

Then we have two equations:

x - 36 = y + 36

x + 8 = 2*y - 16

We want to find the number of sedans, x, then we need to isolate the other variable in one of the equations, let's isolate y in the first one:

Let's isolate x in the first one:

x - 36 - 36 = y

x - 72 = y

Now we can replace it in the other equation:

x + 8 = 2*y - 16

x + 8 = 2*(x - 72) - 16

Now we can solve this for x.

x + 8 = 2*x - 144 - 16

8 + 144 + 16 = 2x - x

168  = x

The number of sedans before any vehicle was sold is 168

Answer:

the left side of the histogram is the mirror image of the right side.

Answer:

2048

Step-by-step explanation:

Formula for volume of a sphere is given:

V = 4/3πr^3

Where r = radius

The sphere shown has a given radius of 8

All we have to do to find the volume of the sphere is simply plug in the given value of the radius (8) into the volume of a sphere formula

(Note it says use 3 for π )

V = 4/3(3)r^3

Substitute 8 for r

V = 4/3(3)(8)^3

Plug this into a calculator and you get that the volume is 2048

Answer:

2,048in³

Step-by-step explanation:

The formula to find the volume of the sphere is already given to you in the problem. All we need to do is substitute and solve.

V = 4/3π(8)³

V = 4/3π(512)

V ≈ 682.67(3)

V ≈ 2,048

Best of Luck!

Answer:

n=8

Step-by-step explanation:

57=8n-7

add 7 on both sides

64=8n

divide 8

n=8

Answer:

8

Step-by-step explanation:

57=8n-7

add 7 to both sides

64=8n

divide by 8 on both sides

n=8

Answer:

19.3

Step-by-step explanation:

The base of the top triangle is 24.158 (approximately) found from the bottom triangle using the sine rule

from that,

sin(53) = r/24.158

or, r = 24.158×sin(53)

or, r = 19.3 (rounded to the nearest tenth)

Answer:

For the question below, you will need to find the GCF of 45 and 60. In this instance it is 5, so it will be outside the box. The GCF answers will be inside the parenthesis, which is 7 and 12.

45x + 60 = 5(7x + 12)

In this question you have to multiply 2 with every number inside the parenthesis. So 2 × 10x and 2 × 4.

2(10x+4) = 20x + 8

Hope this helped.