prove that -

[tex] \sin {}^{2} (\theta) + \cos {}^{2} (\theta) = 1[/tex]


thankyou ~​

Answer:

The radical that is equal to ∛54 is 3∛2.

Step-by-step explanation:

Given

∛54

We need to find the radical that is similar to ∛54, we need to break down the radicand 54, into smaller numbers, therefore, take the LCM of the number,

54 = 2 x 3 x 3 x 3

As we are taking the cube root, therefore, we need numbers that are repeating thrice.

Thus, the radical can be written as,

[tex]\sqrt[3]{54} =\sqrt[3]{2x 3x 3x 3} \\\\\sqrt[3]{54} =3\sqrt[3]{2}[/tex]

Hence, the radical that is equal to ∛54 is 3∛2

Answer:

[tex]3\sqrt[3]{2}[/tex]

Step-by-step explanation:

Original expression:

[tex]\implies \sqrt[3]{54}[/tex]

Factorize 54 using prime factorization:

[tex]\implies \sqrt[3]{2 \cdot 3^3}[/tex]

Apply radical rule: [tex]\sqrt[n]{ab} =\sqrt[n]{a} \cdot \sqrt[n]{b}[/tex]

[tex]\implies \sqrt[3]{2} \cdot \sqrt[3]{3^3}[/tex]

Apply radical rule: [tex]\sqrt[n]{a^n} =a[/tex]

[tex]\implies \sqrt[3]{2} \cdot 3[/tex]

[tex]\implies 3\sqrt[3]{2}[/tex]

Find 2% of what she sold by multiplying the amount she sold by 2%:

5250 x 2% = 5250 x 0.02 = $105

Now add that to her monthly salary:

3462 + 105 = $3,567

Answer:

Answer:

[tex]2(3) {}^{x} [/tex]

Step-by-step explanation:

[tex]y = ab {}^{x} [/tex]

We know that when x=1, y=6

[tex]6 = a {b}^{1} [/tex]

x=2, y=18

[tex]18 = a {b}^{2} [/tex]

Notice that if we divide

[tex] \frac{ {ab}^{2} }{ab} = b[/tex]

So if we divide 18 and 6, that will give us our common ratio.

[tex] \frac{18}{6} = 3[/tex]

So our common ratio is 3.

So know we have

[tex]a(3) {}^{x} [/tex]

Plug in one of the points to find a.

[tex]6 = a(3)[/tex]

[tex]a = 2[/tex]

So the equation. we have

[tex]2 \times ({3}^{x} )[/tex]

Answer:

113.04

Step-by-step explanation:

The area of the square is 144 which means the length of each side of the square is 12. When the length on one side is 12 the radius of the circle will be half of the whole length. In this case, it means the radius is going to be 6. When we find the radius, we can use the formula r^2pie to find the area for the circle.

6 * 6 * 3.14

= 113.04

Answer:

Area = 113.04 in²

Step-by-step explanation:

Given:

Area of a square

[tex]\sf A=s^2\quad \textsf{(where s is the side length)}[/tex]

Substitute the given area of the square into the formula and solve for s:

[tex]\begin{aligned}\sf A & = \sf s^2\\\implies \sf 144 & = \sf s^2\\\sf \sqrt{144} & = \sf \sqrt{s^2}\\\sf 12 & = \sf s\\\implies \sf s & = \sf 12\:\:inches\end{aligned}[/tex]

From inspection of the given diagram, the side length of the square is equal to the diameter of the circle.  Therefore, the diameter is 12 inches.

Radius of a circle

[tex]\sf r = \dfrac{1}{2}\:d\quad \textsf{(where d is the diameter)}[/tex]

Substitute the found diameter into the formula and solve for r:

[tex]\begin{aligned}\sf r & = \sf \dfrac{1}{2}\:d\\\implies \sf r & = \sf \dfrac{1}{2}(12)\\\sf r & = \sf 6\:\:inches\end{aligned}[/tex]

Area of a circle

[tex]\sf A= \pi r^2 \quad \textsf{(where r is the radius)}[/tex]

Substitute the found radius into the formula and solve for A:

[tex]\begin{aligned}\sf A & = \sf \pi r^2\\\implies \sf A & = \sf 3.14 \cdot 6^2\\& = \sf 3.14 \cdot 36\\& = \sf 113.04\:\: in^2\end{aligned}[/tex]

Therefore, the approximate area of the paper circle is 113.04 in².

Answer:

I think it is 7.3.  Cos35=6/MN.

Step-by-step explanation:

Cosine of 35 degrees= adjacent side /hypotenuse.

Answer:

22:15

Step-by-step explanation:

1 hour = 60 mins

20:30 + 45 mins

= 21:15

Plus another hour

21:15+ 1 hour= 22:15

a + z + l = 720

l = 2z = 2a - 80

4z + 40 = 720

4z = 680

z = 170

l = 340

a = 210

The fact family like equations are 2 × 9 = 18 and 18 ÷ 9 = 2.

A fact family is a group of math equations that shows the relationship between the numbers involved. There are addition and subtraction fact family as well as division and multiplication fact family.

Hence:

2 × 9 = 18 and 18 ÷ 9 = 2 shows a fact family.

Find out more on fact family at: https://brainly.com/question/1250189

Answer:$15, 75%

$35-$20=$15

$15/$20*100=

Step-by-step explanation:

Answer:

i put it below

Step-by-step explanation:

but if you want to do it without a graphing calculator all you have to do is substitute random points then draw them on a graph

Answer:

The answer is 4.94, rounded.

Step-by-step explanation:

The pythagorean theorem is : a^2+b^2=c^2

Inserting our numbers:

3.4^2+b^2=6^2

We can find 'B' by finding the other two numbers and subtracting 'A', from 'C'.

3.4*3.4= 11.56

6*6= 36

36-11.56= 24.44

Then, find the root of the difference

√24.44

4.94368283772...

Then round, and you have your answer!

4.94

Answer:

Its solving equations with variable on both sides

Step-by-step explanation:

Example: 8a = 3a+25

You have to make a variable on the both side

So.....

8a-3a = 3a+25-3a

And then solve it. So the last thing you will have is

5a = 25

If you want to the simplest form...divide 25 with 5

a = 25/5

a = 5

Hope this help you.

Based on the inflation rate in the United States in 1949, the cost of the car at the end of the year would be $1,470.

The cost can be found by the formula:

= Cost x (1 + inflation rate)

The inflation rate is negative so solving gives:

= 1,500 x (1 - 2%)

= $1,470

Find out more on inflation at https://brainly.com/question/777738.

Answer:

$ 3.75

Step-by-step explanation:

divide 10.50 by 2.8 which gives us 3.75

Answer:

B $ 3.75

Step-by-step explanation:

hope it helps you

Move everything to one side and factorize by grouping.

x⁴ - 4 = x³ + 2x

x⁴ - x³ - 2x - 4 = 0

(x⁴ - 4) - (x³ + 2x) = 0

(x² - 2) (x² + 2) - x (x² + 2) = 0

(x² - x - 2) (x² + 2) = 0

(x - 2) (x + 1) (x² + 2) = 0

Then

x - 2 = 0   or   x + 1 = 0   or   x² + 2 = 0

x = 2   or   x = -1   or   x² = -2

If x is real, then the third case has no solution. Then x = 2 or x = -1. Otherwise, we can solve over the complexes and include x = ± √2 i where i = √(-1).

Answer:

226,080 cm³

Step-by-step explanation:

volume of cylinder : πr²h

Here given:

using volume formula:

π(15)²(320)

72000π

72000(3.14)          [ take π as 3.14 ]

226,080 cm³

Answer:

Step-by-step explanation:

Given:

Radius = 30/2 = 15cm

Height = 320cm

=> The volume of cylinder = πr²h

=> π×15×15×320

=> 3.14×225×320

=> 226,080cm³

Step-by-step explanation:

L : J

2:3

so Lara has 2 shares

2 shares = 8

what is one share

type in comments

and then I will explain the rest

The amount of the Joan's share will be $12.

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

Algebra is the study of graphic formulas, while logic is the interpretation among those signs.

A sum of money is divided between Laura and Joan in the ratio 2:3.

Laura’s share is $8.

Let J be the amount of Joan's share and L be the amount of Laura's share.

Then the amount of Joan's share will be

L / J = 2 / 3

8 / J = 2 / 3

By the cross multiplication, then the equation will be

2J = 8 x 3

2J = 24

 J = 24 / 2

 J = $12

The amount of the Joan's share will be $12.

More about the ratio and the proportion link is given below.

https://brainly.com/question/14335762

#SPJ5

The sum of -5a and 3 is greater than 1

Answer:

411

Step-by-step explanation:

Because it has a 4 , 1 , and a 1

meaning the first number can't be 1 so it is automatically a 4.

and then the only 2 numbers left is 2 one's so you have to put them in their also automatically and 4 is asking 1 to round up can it.

411 can't round up,it would round down because 1 is 4 and below so it can't go up and goes down.

so 4 1 1 can't go up the number would have to be 450 to go to 500 but because it is 411 it goes down to 400 because it is rounded to 400.

Hope this helps have a awesome day:)

Answer: 120

Step-by-step explanation: 10 [tex]10\int\limits^a_b {x} \, dx 3[/tex]

Answer:

26 x 26 x 26 x 26 x 26 x 26 x 26 x 26 x 26

Step-by-step explanation:

26 to the eighth power is like multiplying 26 times itself eight times. So since it started off as 26 times 26 eight times, you would times 26 by itself 9 times.

Answer:

Hope this helped you

Step-by-step explanation:

5/6 ÷ 3/6 = 5/6 × 6/3 = 5/3

5/3 × 3/5 = 1

5/6÷3/6x3/5

0.83÷0.50x0.60

0.83÷0.30

ANSWER: 2.767

I tried to make it as easy as possible!

pls mark brainliest!

Answer:

Step-by-step explanation:

The best estimate for the volume of a coffee mug would be the volume of a cylinder. The volume of a cylinder is:

[tex]V=\pi r^2h[/tex]

The volume can be thought of as the area of a circle, being scaled by the height. The area of the circular base of the mug, multiplied by the height of the mug.

Answer:

Step-by-step explanation:

4x + y = - 1 -------------(I)

-5x - 2y = -4 -----------(II)

Multiply the equation (I) by 2 and then add the equations.

(I)*2        8x + 2y = -2

(II)          -5x - 2y = -4  {Now add and y will be eliminated}

             3x         = -6

                       x = -6/3

x = -2

Substitute x = -2 in equation (I)

4*(-2) + y = -1

-8     + y = -1

          y  = - 1 + 8

           y = 7

Answer:

(-2, 7)

Step-by-step explanation:

4x + y = -1

-5x - 2y = -4

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

2(4x + y = -1) = 8x + 2y = -2

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

8x + 2y = -2

-5x - 2y = -4

3x = -6

÷3   ÷3

x = -2

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

4(-2) + y = -1

-8 + y = -1

+8          +8

y = 7

I hope this helps!

Answer:

B

Step-by-step explanation:

All angles are the same, all sides are of same length.

Answer:

[tex]u\cdot v=32[/tex]

Step-by-step explanation:

Assuming [tex]u[/tex] and [tex]v[/tex] are vectors, their dot product is [tex]u\cdot v[/tex] where [tex]u_1v_1 + u_2v_2[/tex]:

[tex]u\cdot v=u_1v_1+u_2v_2=(2)(8)+(-8)(-2)=16+16=32[/tex]

Therefore, [tex]u\cdot v=32[/tex]