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[tex]\\ \sf\longmapsto \dfrac{sin40.sin120}{sin110-sin340}[/tex]

[tex]\\ \sf\longmapsto \dfrac{sin(90-50).sin(90+30)}{sin(90+20).sin(360-20)}[/tex]

[tex]\\ \sf\longmapsto \dfrac{cos50.cos30}{cos20.(-sin20}[/tex]

[tex]\\ \sf\longmapsto \dfrac{cos50cos30}{-sin20cos20}[/tex]

[tex]\\ \sf\longmapsto -\dfrac{cos30cos50}{sin20cos20}[/tex]

Answer:

5

Step-by-step explanation:

Solution is 8 in

Let´s call dimensions of the box

According to the problem statement

y = x + 3     and    h = 4 in

The volume of the box is:

V = x×y×h       V = 360 in³

Then  V = x × ( x + 3 ) × 4     ( by substitution of y as a function of x )

360 = x × ( x + 3 ) × 4

Simplifying by 4

90 =  x × ( x + 3 )

90 = x² + 3x

We got a second degree equation, solving for x

x² + 3×x - 90 = 0

x₁,₂ = ( -3 ± √ (3)² + 4×90 )/2   ⇒   x₁,₂ = ( - 3 ± 19,21 )/2

x₁   ⇒  is a negative value    x = - 11,1  so we dismiss such solution

x₂  = 16.21/2

x₂  =  8.1 in

rounding to the nearest integer number we get the value for the length f the box

x₂ = 8 in        ⇒ x = 8 in

Note: In Brainly.com in search bar ask for cube dimensions

Answer:

245 boys

Step-by-step explanation:

54/100*750

=405 girls

so 750-405=245

Answer:

10kg and 60 kg.

Step-by-step explanation:

Let the kid's mass be x kg, then the goat's mass is 6x.

x + 6x = 70

7x = 70

x = 10.

Answer:

Equation: [tex]3x-5+2x=90[/tex]

Angle measures: 52 degrees and 38 degrees

Step-by-step explanation:

Hi there!

We're given that the two angles form a right angle, which means they add up to 90 degrees.

Knowing this, we can construct the following equation:

[tex]3x-5+2x=90[/tex]

Now, we must solve for x:

[tex]5x-5=90\\5x=95\\x=19[/tex]

Therefore, x=19. Plug this into the expression for each angle to find their measures:

[tex]3x-5\\= 3(19)-5\\= 57-5\\=52[/tex]

[tex]2x\\=2(19)\\=38[/tex]

Therefore, the two angles measure 52 degrees and 38 degrees.

I hope this helps!

Step-by-step explanation:

Here radical rule is that [tex]\sqrt[n]{x^{m} } = x^{m/n}[/tex]  ;  [tex]x\neq 0[/tex] so

[tex]\sqrt[4]{x^3} = x^{3/4}[/tex]

>>[tex](x^{3/4})/x^{1/12}[/tex]

>>[tex]x^{2/3}[/tex]

[tex]\\ \sf\longmapsto tan40=\dfrac{P}{430}[/tex]

[tex]\\ \sf\longmapsto 0.83=\dfrac{P}{430}[/tex]

[tex]\\ \sf\longmapsto P=430(0.83)[/tex]

[tex]\\ \sf\longmapsto P\approx361m[/tex]

Step-by-step explanation: Similar figures have the same shape, but not necessarily the size. If two figures are similar, then their corresponding angles are congruent so <E ≅ <O because these are the corresponding angles in the similarity statement.

Answer: <E ≅ <O

Step-by-step explanation:

Answer:

Step-by-step explanation:

When calculating x-intercept, always think: y=0.

Putting this into the formula creates:

3x+0 = -3

3x = -3

x = -1

Answer:

29.51%

Step-by-step explanation:

The change from 305 to 395 is the difference between the two numbers. So, it would be 395 - 305 or 90. Now, to find the percentage of change, we need to find what part of the original amount is the change. In other words, we would have to divide 90 by 305. By putting this in a calculator you get about 0.2951. To convert this decimal into a percent, we would multiply by 100 giving us 29.51%.

Answer:

r/2 = w

Step-by-step explanation:

r = 2w

Divide each side by 2

r/2 = 2w/2

r/2 = w

Answer:

8=3-5x

5x=3-8

5x=-5

x=-5/5

x=-1

is the required answer

[tex]\\ \sf\longmapsto \dfrac{2}{3}\:of\:180[/tex]

[tex]\\ \sf\longmapsto \dfrac{2}{3}\times 180[/tex]

[tex]\\ \sf\longmapsto 2(60)[/tex]

[tex]\\ \sf\longmapsto 120[/tex]

Convert to radians

[tex]\\ \sf\longmapsto 120\times \dfrac{\pi}{180}[/tex]

[tex]\\ \sf\longmapsto \dfrac{2\pi}{3}rad[/tex]

Answer:

g(6) = -1 -77

because the expression doesn't have r

Step-by-step explanation:

Answer:

B is in 4th quadrant.

Step-by-step explanation:

If mid point of AB is on x-axis then and A is in 3rd quadrant then B must be on the opposite side of A.Therefore it is in 4th

B is in fourth quadrant when AB is the midpoint on y axis

If the center of AB is on the x-axis

A is in the third quadrant,

let two points ( -2, -2 ) in third quadrant .

then B must be on the side of A that is opposite from A.

B thus comes in fourth.

then points ( 2,-2 ) are in fourth quadrant  .

Learn more about Quadrants here:

brainly.com/question/7196312

#SPJ2

Answer:

The numbers are --> x = -4 + √21 i and  x = -4 — √21 i

See the attachment for my step-by-step explanation

(solution is in red box)

The number that would have to be added in the given quadratic equation to complete the square is '-21' and this can be determined by using the factorization method.

Given :

Quadratic equation  --  [tex]x^2+8x+37 = 0[/tex]

The following steps can be used in order to determine the number that would have to be added to complete the square:

Step 1 - The factorization method can be used in order to determine the number that would have to be added to complete the square.

Step 2 - Write the given quadratic equation.

[tex]x^2+8x+37 = 0[/tex]

Step 3 - Now, if '-21' is added in the above quadratic equation then the above equation becomes the complete square.

[tex]x^2+8x+37+(-21) = 0[/tex]

[tex]x^2+8x+16 = 0[/tex]

[tex](x+4)^2 = 0[/tex]

For more information, refer to the link given below:

https://brainly.com/question/17177510

Answer:

5,000,000,000+200,000,000+40,000,000+8,000,000+600,000+60,000+3,000+700+10+1

Step-by-step explanation:

5,000,000,000 + 200,000,000+ 40,000,000+ 8,000,000+ 600,000+ 60,000+ 3,000

+ 700 + 10 + 1

Answer:

n = 12.546

Step-by-step explanation:

to find the value of n we need to transpose

n ÷ 102 = 0.123

n = 0.123 × 102

n = 12.546

Answer:

57.12 m

Step-by-step explanation:

velocity= distance/time

distance= velocity×time

=22.4×2.55

=57.12 m

Answer:

d = 28.6 m

Step-by-step explanation:

Given:

vi = 22.4 m/s

vf = 0 m/s

t = 2.55 s

Find:

d = ??

d = (vi + vf)/2 *t

d = (22.4 m/s + 0 m/s)/2 *2.55 s

d = (11.2 m/s)*2.55 s

d = 28.6 m

Answer:

B) x = 3

Step-by-step explanation:

This is the axis of symmetry because the graph is symmetric in this line

Answer:

a^2-ab+b^2

Step-by-step explanation:

factorize both of them.

Answer:

Step-by-step explanation:

Remember:

[tex]a^3+b^3=(a+b)(a^2-ab+b^2)\\[/tex]

[tex]a^3+b^3=(a+b)(a^2-ab+b^2)\\\\\\a^4+a^2b^2+b^4=a^4+2a^2b^2+b^4-a^2b^2\\\\=(a^2+b^2)^2-a^2b^2\\\\=(a^2+b^2-ab)(a^2+b^2+ab)\\\\HCF=a^2+b^2-ab\\[/tex]

Answer:

the least

Step-by-step explanation:

Answer:

-∞

Step-by-step explanation:

Negative numbers are the smallest on the number line. Since the number range is not specified -∞ would be a preferred answer.

Step-by-step explanation:

4-2x+8/3 = 6x+15/2

12-2x+8/3= 6x+15/2 ( taken LCM. of 1,3,3 in LHS)

20-2x/3=6x+15/2

Do cross multiplication

2(20-2x) = 3(6x+15)

40-4x=18x+45

-4x-18x=45+40

-22x= 85

-x= 85/22

x= - 3.86..

hope it helps

Answer:

3 × x³ - 10

Step-by-step explanation:

three times = 3×

difference = -

number cubed (unknown so we use x) = x³

10 = 10

Hope this helps!

I'm sorry if wrong :(

Answer:

Step-by-step explanation:

Horizontal translations changes the x-axis

Vertical translations changes the y-axis

Answer:

D

Step-by-step explanation:

Using the Altitude- on- hypotenuse theorem

DF² = CD × DE , substitute values

12² = 6 DE

144 = 6 DE ( divide both sides by 6 )

24 = DE → D