Solve: [tex]cos^2(2x)-sin^2(2x)=0[/tex] Thanks

Answer:

The quotient is 4x-20/x+5

Step-by-step explanation:

The quotient is simply the result of the division

Through factorization, can express x^2 -25 as (x-5)(x+5)

Also x^2 + 10x + 25 as (x+5)(x+5)

and lastly 4x-44 as 4(x-11)

Now when we divide, the numerator of the second fraction will come down while the denominator goes up;

So we have ;

x^-25/x-11 * 4x-44/x^2 + 10x + 25

Now, making use of the factorizations, we have ;

(x-5)(x+5)/(x-11) * 4(x-11)/(x+5)(x+5)

Canceling out like factors, we have

= 4(x-5)/(x+5)

Answer:

Step-by-step explanation:

The length is 3 × width.

l = 3w

The perimeter is 24 centimeters.

P = 2l + 2w

24 = 2(3w) + 2w

24 = 6w + 2w

24 = 8w

3 = w

The width is 3 centimeters.

l = 3(3)

l = 9

The length is 9 centimeters.

Area is l × w.

A = l × w

A = 9 × 3

A = 27

The area is 27 squared centimeters.

Answer:

27

Width= x

Length= x × 3 =3x

so, 3x+3x+x+x=24

8x=24

x=24/8

x=3

so, length=3(3)=9

width=3

therefore,

Area=9×3

=27

Answer:

Hello! The answer to your question will be below.

Step-by-step explanation:

Attached below....

Number form:820,245

Word form: eight hundred twenty thousand two hundred forty-five

Expanded form: 800,000+20,000+0+200+40+ 5

Place value chart below!!

Hope this helps! :)

⭐️Have a wonderful day!⭐️

Answer:

Copy this onto a piece of graph paper

Step-by-step explanation:

when graphing you want to make sure  that the slope is correct and the y-intercept is the same

1st 2nd and last

Step-by-step explanation:

simplify your inequality

6x >= 3 + 4(2x -1)

6x >= 3 + 8x - 4

2x >= 1

x >= 1/2

so indeed the

1st one , the 2nd and the last one

first, second, last

Hope it helps

Answer:

Expanded expression of the area of the rectangle = 10x² - 4x + 6 square units

Step-by-step explanation:

Area of a rectangle = Length × Width

Area of the rectangle = 2 × (5x² - 2x + 3)

= 2 × 5x² - 2× 2x + 2×3

= 10x² - 4x + 6 square units

Answer:

(Choice C) C Infinitely many solutions.

Step-by-step explanation:

First of all, let us learn about solutions of linear equations in one variable.

The linear equations in one variable usually have one solution.

For example:

[tex]2x =x+3[/tex]

When we solve this:

[tex]2x-x=3\\\Rightarrow x=3[/tex]

One solution is [tex]x = 3[/tex]

But there can be situations when there are

1. No solutions:

For example:

[tex]x =x+9[/tex]

It means that value x is equal to value of x+9 which can never be true.

Truth is the term on Right Hand Side is always 9 greater than the value of Left Hand Side.

Such situations are called Contradictions.

Here, no solution exists.

2. Infinitely many solutions:

For example:

[tex]x+2x+8=3x+8[/tex]

The Right hand Side is just the simplification of the LHS.

And LHS is always equal to RHS no matter what is the value of variable [tex]x[/tex].

It means there are infinitely many solutions for this equation.

-----------------------------------------------------

Now, let us have a look at the given equation in the question:

[tex]-4x-7+10x=-7+6x[/tex]

Taking LHS: [tex]-4x-7+10x[/tex]

Taking the terms with [tex]x[/tex] on one side:

[tex]-7+10x-4x\\\Rightarrow -7+6x[/tex]

which is equal to Right Hand Side.

Hence, as we discussed in case 2 above.

For every value of [tex]x[/tex] the equation holds true.

[tex]\therefore[/tex] There exists infinitely many solutions to the given equation.

Correct answer is:

(Choice C) C Infinitely many solutions

Answer:

C Infinitiy solutions

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

x=2.5&.5

Step-by-step explanation:

The quadratic formula is (-b+or-sqrt(b^2-4ac)/2a

12+or-sqrt((-12^2)-4(4)(5))

12+or-sqrt(144-80)

12+or-sqrt(64)

(12+8)/8 and (12-8)/8

x=2.5 and x=.5

Answer: [tex]x=\frac{5}{2},\:x=\frac{1}{2}[/tex] or [tex]x=2.5,\:x=0.5[/tex]

Step-by-step explanation:

[tex]4x^2-12x=-5[/tex]

[tex]\mathrm{Add\:}5\mathrm{\:to\:both\:sides}[/tex]

[tex]4x^2-12x+5=-5+5[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]4x^2-12x+5=0[/tex]

Solve with Quadratic Formula

[tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

[tex]a=4,\:b=-12,\:c=5:\quad x_{1,\:2}=\frac{-\left(-12\right)\pm \sqrt{\left(-12\right)^2-4\cdot \:4\cdot \:5}}{2\cdot \:4}[/tex]

[tex]\frac{-\left(-12\right)+\sqrt{\left(-12\right)^2-4\cdot \:4\cdot \:5}}{2\cdot \:4}[/tex]

[tex]\mathrm{Apply\:rule}\:-\left(-a\right)=a[/tex]

[tex]\frac{12+\sqrt{\left(-12\right)^2-4\cdot \:4\cdot \:5}}{2\cdot \:4}[/tex]

[tex]12+\sqrt{\left(-12\right)^2-4\cdot \:4\cdot \:5}=12+\sqrt{64}[/tex]

[tex]\sqrt{\left(-12\right)^2-4\cdot \:4\cdot \:5}=\sqrt{64}[/tex]

[tex]\sqrt{64}=8[/tex]

[tex]=\frac{12+8}{8}[/tex]

[tex]=\frac{20}{8}[/tex]

[tex]=\frac{5}{2}[/tex]

[tex]x=\frac{5}{2},\:x=\frac{1}{2}[/tex]

The correct answer is Maxine

Explanation:

One of the easiest ways for knowing if a fraction is greater than another is by converting fractions to decimal numbers. This implies dividing the numerator (top number) by the denominator (bottom number). In the case of fraction, [tex]\frac{1}{2}[/tex] the decimal number is 0.5 considering 1 divided into 2 is equal to 0.5. Now to know if other fractions are greater or smaller, this process needs to be repeated.

Gina: [tex]\frac{3}{8} = 0.375[/tex]  

Maxine: [tex]\frac{2}{3} = 0.666[/tex]

Shari: [tex]\frac{2}{4} = 0.5[/tex]

Vanessa: [tex]\frac{3}{12} = 0.25[/tex]

According to this, the girl with a heigh increased greater than 1/2 inch is Maxine because 0.666 (Maxine heigh increase) is greater than 0.5 (1/2 inch).

Answer:

11 and 2/3.

Step-by-step explanation:

6 and 3/12 = 72/12 + 3/12 = 75/12.

5 and 5/12 = 60/12 + 5/12 = 65/12.

75/12 + 65/12 = 140 / 12 = 70 / 6 = 35 / 3 = 11 and 2/3.

Hope this helps!

Answer: 11 2/3

Step-by-step explanation:

[tex]6\frac{3}{12}+5\frac{5}{12}[/tex]

[tex]Add\:whole\:numbers[/tex]

[tex]6+5=11[/tex]

[tex]Combine\:fractions[/tex]

[tex]\frac{3}{12}+\frac{5}{12}=\frac{8}{12}[/tex]

[tex]Simplify[/tex]

[tex]\frac{8}{12} =\frac{2}{3}[/tex]

[tex]11+\frac{2}{3}[/tex]

[tex]=11\frac{2}{3}[/tex]

Answer:

D

Step-by-step explanation:

Solution:-

- The given question pertains to the translation of a function f ( x ) over the cartesian coordinate system.

- There are certain guidelines that must be followed when performing any translations of any function f ( x ).

Translation Guideline

  Vertical shifts

  Horizontal shifts

Where, " a " and " b " are constants for respective horizontal and vertical shifts.

- We can make a generalized form of the translated function f ( x ) to f* ( x ) as follows:

 Generalized shift: f ( x ) - > f ( x ± a ) ± b

Where,   a: Unit of horizontal shift

               b: Unit of vertical shift

- We are given a function f ( x ) defined. We are to replace the variable ( x ) with ( x + 7 ).

                          [tex]f ( x ) = x^2\\\\f^*(x) = f ( x + 7 ) = (x + 7 )^2[/tex]

- Use the above given guidelines to determine the type of shift. Take a look at the Left shift in the horizontal shift section.

- Left shift : f ( x ) -> f ( x + a ) = f ( x + 7 )

Answer: The function f ( x ) is slided a = 7 units to the left!              

Answer:

It's 144 square units

Step-by-step explanation:

The pyramid has a square base with 8 sides and a slant height of 5

a=8

l=5

The total are of the square base pyramid is

A= [tex]a^{2}[/tex]+2al

a is side length of square and l is slant height

A= [tex](8)^{2}+2[/tex] x 8 x 5

A=64+80

A=144

Answer:

Not a triangle

Step-by-step explanation:

Side lengths do not adhere to the triangle inequality theorem. Which states that the sum of the side lengths of any 2 sides of a triangle must exceed the length of the third side.

Answer:

66.63

Step-by-step explanation:

To find the diagonal length, use Pythagorean’s theorem.

Diagonal = √45^2 + 45^2 = √2025+2025 = √4050 = 63.63.

Hope this helps

Step-by-step explanation:

your answer is C

HOPE IT HELPS YOU MATE

Answer:

Both have the same period which is 2π

Step-by-step explanation:

Answer:

see attached diagram

Step-by-step explanation:

1.  1 and 70 are angles on a line (supplementary)

2. vertical angles with 70

3. angles on a line are supplementary

4. 2 and 4 are supplementary interior angles between parallel lines m & n

5. corresponding angle with 70

[tex]\bold{\text{Answer:}\quad \dfrac{-48x^4-42x^3-15x^2-5x}{(8x+7)(3x+1)}}[/tex]

Step-by-step explanation:

[tex].\quad \dfrac{-5x}{8x+7}-\dfrac{6x^3}{3x+1}\\\\\\=\dfrac{-5x}{8x+7}+\dfrac{-6x^3}{3x+1}\\\\\\=\dfrac{-5x}{8x+7}\bigg(\dfrac{3x+1}{3x+1}\bigg)+\dfrac{-6x^3}{3x+1}\bigg(\dfrac{8x+7}{8x+7}\bigg)\\\\\\=\dfrac{-15x^2-5x}{(8x+7)(3x+1)}+\dfrac{-48x^4-42x^3}{(8x+7)(3x+1)}\\\\\\=\large\boxed{\dfrac{-48x^4-42x^3-15x^2-5x}{(8x+7)(3x+1)}}[/tex]

Answer:

-4

Step-by-step explanation:

When looking at the graph look at the y axis and look to see where the line passes through

Answer:

-4 is the y intercept.

Step-by-step explanation:

Brainliest? Have a great day!

Answer:

Step-by-step explanation:

[tex]5(y - 3.8) = 4.7(y - 4)[/tex]

Distribute 5 through the parentheses

[tex]5y - 19 = 4.7(y - 4)[/tex]

Distribute 4.7 through the parentheses

[tex]5y - 19 = 4.7y - 18.8[/tex]

Move ' 4.7 y ' to L.H.S and change it's sign

[tex]5y - 4.7y - 19 = - 18.8[/tex]

Move constant to R.H.S and change it's sign

[tex]5y - 4.7y = - 18.8 + 19[/tex]

Collect like terms

[tex]0.3y = - 18.8 + 19[/tex]

Calculate

[tex]0.3y = 0.2[/tex]

Divide both sides of the equation by 0.3

[tex] \frac{0.3y}{0.3} = \frac{0.2}{0.3} [/tex]

Calculate

[tex]y = 0.67[/tex]

Hope this helps...

Best regards!!

Answer:

[tex]y = 0.67[/tex]   (To 2 dps)

y = 0.7 (To 1 dps)

y = 1 (To nearest whole no.)

Step-by-step explanation:

[tex]5(y-3.8) = 4.7 (y-4)[/tex]

Distribute the terms

[tex]5y - 19 = 4.7y-18.8[/tex]

Combining like terms

[tex]5y - 4.7y = -18.8+19[/tex]

Adding and subtracting

[tex]0.3y = 0.2[/tex]

Dividing both sides by 0.3

[tex]y = 0.2/0.3[/tex]

[tex]y = 0.67[/tex]

Answer:

10a²b²6ab²

Step-by-step explanation:

Distribute the 2ab the other values

Answer:  39) 1              40) 2

                41) 1              42) 0

Step-by-step explanation:

39)     ∠A = ?        ∠B = ?       ∠C = 129°

            a = ?          b = 15         c = 45

Use Law of Sines to find ∠B:

[tex]\dfrac{\sin B}{b}=\dfrac{\sin C}{c} \rightarrow\quad \dfrac{\sin B}{15}=\dfrac{\sin 129}{45}\rightarrow \quad \angle B=15^o\quad or \quad \angle B=165^o[/tex]

If ∠B = 15°, then ∠A = 180° - (15° + 129°) = 36°

If ∠B = 165°, then ∠A = 180° - (165° + 129°) = -114°

Since ∠A cannot be negative then ∠B ≠ 165°

∠A = 36°        ∠B = 15°       ∠C = 129°       is the only valid solution.

40)      ∠A = 16°        ∠B = ?       ∠C = ?

             a = 15           b = ?         c = 19

Use Law of Sines to find ∠C:

[tex]\dfrac{\sin A}{a}=\dfrac{\sin C}{c} \rightarrow\quad \dfrac{\sin 16}{15}=\dfrac{\sin C}{19}\rightarrow \quad \angle C=20^o\quad or \quad \angle C=160^o[/tex]

If ∠C = 20°, then ∠B = 180° - (16° + 20°) = 144°

If ∠C = 160°, then ∠B = 180° - (16° + 160°) = 4°

Both result with ∠B as a positive number so both are valid solutions.

Solution 1:  ∠A = 16°        ∠B = 144°       ∠C = 20°    

Solution 2:  ∠A = 16°        ∠B = 4°       ∠C = 160°    

41)       ∠A = ?        ∠B = 75°       ∠C = ?

             a = 7           b = 30         c = ?

Use Law of Sines to find ∠A:

[tex]\dfrac{\sin A}{a}=\dfrac{\sin B}{b} \rightarrow\quad \dfrac{\sin A}{7}=\dfrac{\sin 75}{30}\rightarrow \quad \angle A=13^o\quad or \quad \angle A=167^o[/tex]

If ∠A = 13°, then ∠C = 180° - (13° + 75°) = 92°

If ∠A = 167°, then ∠C = 180° - (167° + 75°) = -62°

Since ∠C cannot be negative then ∠A ≠ 167°

∠A = 13°        ∠B = 75°       ∠C = 92°       is the only valid solution.

42)      ∠A = ?         ∠B = 119°       ∠C = ?

             a = 34         b = 34           c = ?

Use Law of Sines to find ∠A:

[tex]\dfrac{\sin A}{a}=\dfrac{\sin B}{b} \rightarrow\quad \dfrac{\sin A}{34}=\dfrac{\sin 119}{34}\rightarrow \quad \angle A=61^o\quad or \quad \angle A=119^o[/tex]

If ∠A = 61°, then ∠C = 180° - (61° + 119°) = 0°

If ∠A = 119°, then ∠C = 180° - (119° + 119°) = -58°

Since ∠C cannot be zero or negative then ∠A ≠ 61° and ∠A ≠ 119°

There are no valid solutions.

Answer:

[tex]\frac{x^2}{16}-\frac{b^2}{4}=1[/tex]

Step-by-step explanation:

A hyperbola is the locus of a point such that its distance from a point to two points (known as foci) is a positive constant.

The standard equation of a hyperbola centered at the origin with transverse on the x axis is given as:

[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1[/tex]

The coordinates of the foci is at (±c, 0), where c² = a² + b²

Given that  a hyperbola centered at the origin with x-intercepts +/- 4 and foci of +/-2√5. Since the x intercept is ±4, this means that at y = 0, x = 4. Substituting in the standard equation:

[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\\\frac{4^2}{a^2}-\frac{0}{b^2} =1\\\frac{4^2}{a^2}=1\\ a^2=16\\a=\sqrt{16}=4\\ a=4[/tex]

The foci c is at +/-2√5, using c² = a² + b²:

[tex]c^2=a^2+b^2\\(2\sqrt{5} )^2=4^2+b^2\\20 = 16 + b^2\\b^2=20-16\\b^2=4\\b=\sqrt{4}=2\\ b=2[/tex]

Substituting the value of a and b to get the equation of the hyperbola:

[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\\\\\frac{x^2}{16}-\frac{b^2}{4}=1[/tex]

Answer:

I won't give you the answer straight away so you take the time to read my answer and understand

Step-by-step explanation:

We knoe that 2 to the third is 8. when you square to a negative power, you do squaring normally, and then take the reciprocal of that number. so 8 to the second power is 64, and we flip it over, sp the answer is 1/64

Answer:

x = 1

Step-by-step explanation:

Given

8 - 5(x - 3) = 18 ( subtract 8 from both sides )

- 5(x - 3) = 10 ( divide both sides by - 5 )

x - 3 = - 2 ( add 3 to both sides )

x = 1

Answer:

k = - 3

Step-by-step explanation:

Given that (x - 1) is a factor of the polynomial then x = 1 is a root

Substitute x = 1 into the polynomial and equate to zero, that is

4(1)³ + 3(1)² - 4(1) + k = 0, that is

4 + 3 - 4 + k = 0

3 + k = 0 ( subtract 3 from both sides )

k = - 3

CHECK THE COMPLETE QUESTION BELOW;

Lindy works at a pizza restaurant and gets a 10% employee discount. She knows that if she orders d drinks and a medium pizza with t toppings, her total cost can be found using this expression: 0.90(2.25d + 1.40t + 6). What is the total cost for Lindy and her friends to order 4 drinks and a medium pizza with 3 toppings? A. $17.28 B. $16.52 C. $15.69 D. $28.40

Answer:

OPTION A. is correct

A)$17.28

Step-by-step explanation:

From the question we were giventhis expression as the total cost for all.

0.90(2.25d + 1.40t + 6).

We know that Lindy and her friends to order 4 drinks and a medium pizza with 3 topping

Then we can say d= 4 and t= 3 ,

Then we can substitute into below expresion

0.90(2.25d + 1.40t + 6).

0.90[2.25(4)+1.40(3)+6]

= 0.90[9+4.2+6]

= 17.8

Hence the total cost for Lindy = $ 17.28

Answer:

k=180-23-90=67...................

Answer:

< k = 67°

Step-by-step explanation:

HJ tangent to HG => < H = 90°

< K = 180° - (<J + <H)

= 180° - (90° + 23°)

= 180° - 113°

= 67°