If you were 10 years old on
Earth, you would be 41.494 years old
on Mercury. Write the age on Mercury
as a mixed number in simplest form.

Answer:

Taking LHS

=1 by cos theta- cos theta

= (1- cos²0)/ cos0

= sin²0/ cos0 ( because 1-cos²0 is also equals to sin²0)

=RHS hence proved

Answer:

Step-by-step explanation:

Let theta be β.

So,

[tex]sec\beta - cos\beta = \frac{sin^2\beta }{cos\beta } \\=>\frac{1}{cos\beta } - cos\beta = \frac{1 - cos^2\beta }{cos\beta } \\=>\frac{1 - cos^2}{cos\beta } = \frac{1 - cos^2\beta }{cos\beta }[/tex]

Here , identity used = [tex]sin^2\beta + cos^2\beta = 1[/tex]

Answer:

x = 3*cos(t) - 2  

y = 3*sin(t) + 2  

Step-by-step explanation:

The equation for a circle of radius 3 and centered at the point ( h , k )           (  -2 , 2 ) is:

( x - h )²  +  (  y  - k )²  = r²

In this particular case

h = - 2   k = 2    and  r = 3

Then to parametrizace the equation

x  = r* cos(t) +  h

y = r*sin(t)  + k

x =  3*cos(t) + (- 2)       ⇒   x = 3*cos(t) - 2    

y = 3 *sin(t) + (2)          ⇒   y = 3*sin(t) + 2

Now :

when t = 0   x should be  1

Then   x = 3 cos(0) - 2      x  = 3 - 2        x  = 1

and t = 0   y should be 2

Then   y = 3*sin(t) + 2    ⇒  y =  3*sin(0) + 2       y  =  2

Answer:

111100 base 2

Step-by-step explanation:

The conversion of 60 base 10 to base 2

When converting a number from base 10 to base 2, the following steps are taken:

a) The number in base 10 is divided by 2 and the remainder is recorded, this continues until the remainder is less than 2.

b) The remainder from the bottom to the top are arranged so as to get the representation of the number in base 2.

60 base 10 to base 2

60 ÷ 2       =       30  remainder  0

30 ÷ 2       =        15 remainder   0

15 ÷ 2       =         7   remainder   1

7 ÷ 2        =          3  remainder   1

3 ÷ 2        =          1   remainder   1

1 ÷ 2         =          0  remainder   1

The remainder from bottom to top is 111100 base 2.

(60)₁₀ = (111100)₂

Answer:

8x²-2x-5

Step-by-step explanation:

2x²-(5+2x)+6x²

2x²-5-2x+6x²

2x²+6x²-2x-5

8x²-2x-5

Hope this helps ;) ❤❤❤

Answer:

[tex]8 {x}^{2} - 2x - 5[/tex]

Step-by-step explanation:

[tex]2 {x}^{2} - (5 + 2x) + 6 {x}^{2} [/tex]

[tex]2 {x}^{2} - 5 - 2x + 6 {x}^{2} [/tex]

[tex]8 {x}^{2} - 2x - 5[/tex]

Answer:

50

Step-by-step explanation:

Answer:

[tex]2\sqrt7,-2\sqrt7[/tex]

Step-by-step explanation:

So we have the function:

[tex]f(x)=4x^2-6[/tex]

And we want to find all x such that f(x) is 106. So, substitute 106 for f(x):

[tex]106=4x^2-6[/tex]

Add 6 to both sides:

[tex]112=4x^2[/tex]

Divide both sides by 4:

[tex]x^2=28[/tex]

Take the square root of both sides:

[tex]x=\pm\sqrt{28}[/tex]

Simplify the square root:

[tex]x=\pm\sqrt{28}=\pm\sqrt{4\cdot 7}=\pm2\sqrt7[/tex]

So, those are the two values that will satisfy our requirement.

And we're done!

Answer: The length is 88 yards  and the width is 10 yards. Look into the steps for more information.

Step-by-step explanation:

The length is 12 yards less than 10 times the width so we can represent that by the equation  L = 10w - 12  

And the area is 880  so the width times the length has to equal 880. the width is w and the length is 10w -12

w( 10w -12 ) = 880   solve for w

10w^2 - 12w  = 880    subtract 880 from both sides

              -880   -880

10w^2 - 12w - 880 = 0     They share the same factors so dive each side by 2

5w^2 - 6w^2 - 440 = 0  

a= 5     b = -6  and c=-440

The quadratic formula says that x= -b ± [tex]\sqrt{b^2- 4ac} / 2a[/tex]  

   x= 6 ±[tex]\sqrt{8836} / 5[/tex]  

x= 6 ± 94  /10

x= 100 /10

x = 10  

In this case the width is 10 yards.

The length is 12 less than 10 times the width .

So   L  = 10(10) - 12

   L =  100- 12

  l = 88  

So the length is 88

The required length and width are 229 and 27 yards.

It is required to find the dimension of rectangle.

A rectangle is a type of quadrilateral, whose opposite sides are equal and parallel. It is a four-sided polygon that has four angles, equal to 90 degrees. A rectangle is a two-dimensional shape.

Given:

A=l*w

w=width

10w-12=length

According to given question we have,

6183=(10w-12)(w)

6183=10[tex]w^{2}[/tex]-14w

9[tex]w^{2}[/tex]-14w-6183=0

By simplify we get,

(9w+229)(w-27)=0

w-27=0

w=27 yards

l=9*27-14=229 yards

Therefore, the required length and width are 229 and 27 yards.

Learn more details about rectangle here:

https://brainly.com/question/15019502

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Answer:

k = -9

Step-by-step explanation:

Answer:

t+8+3t

8+4t

Step-by-step explanation:

I guess the question is incomplete

Answer:

40r^6t^9

Step-by-step explanation:

Answer:

5+a/a-1

Step-by-step explanation:

3+a+2/a+2-3=5+a/a-1

Hey there! I'm happy to help!

Let's call our number n. Here is the information we have.

n×12=84

We want to figure out what n equals. To do this, we have to get it by itself in the equation. What we will do is cancel out the 12 by dividing both sides by 12.

n×12/12=84/12

n=7

Therefore, our number is 7.

Have a wonderful day! :D

Answer:

2f(x); g(x) = 10/x

Step-by-step explanation:

The second option on edge

The new equation is, g(x) =2f(x), g(x) =10/x. Option B is correct.

A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.

Given data in problem is;

a = F/M

f(x) = 5/x

We have to examine each option given and observe the graph for the function we got;

g(x) = 2f(x)

Substitute the values we get;

g(x) =  2×(5/x)

g(x)=10/x

The new equation is, g(x) =2f(x), g(x) =10/x.

Hence, option B is correct.

The complete question and graph are attached below.

To learn more about the graph, refer to the link;

https://brainly.com/question/14375099

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Answer:

It is a negative 1.75. (-1.75)

Answer: 123$

Step-by-step explanation:

I dont even know but this gives me free five points

Answer:

about $57.42

Step-by-step explanation:

we know how many miles they drove in all (510) and how many miles they can drive per gallon (23)

we need to find out how many gallons of gas they used by dividing the total number of miles they drove (510) by the number of miles per gallon (23) which is about 22.17

510 ÷ 23 = 22.17

we then need to find out how much money they spent on the total number of gallons of gas they purchased by multiplying 22.17 by the amount of money for one gallon of gas ($2.59)

22.17 × 2.59 = $57.42

Answer:

5 + 3a

Step-by-step explanation:

The expression is:

5 + 3a

Answer:

-4

Step-by-step explanation:

Hello,

x-y=4 <=> x=y+4

so, xy=y(y+4)

[tex]y(y+4)=y^2+4y=(y+2)^2-4[/tex]

so this is minimum for y = -2 and the minimum value is -4

thanks

Answer:

[See Below]

Step-by-step explanation:

✦ The pattern is y ÷ 8. (So just divided by 8 each time.)

  ✧ 512 ÷ 8 = 64

  ✧ 64 ÷ 8 = 8

  ✧ 8 ÷ 8 = 1

  ✧ 1 ÷ 8 = 0.125

  ✧ 0.125 ÷ 8 = 0.015625

✦ So then the next values would be:  

  ✧ 8⁰ = 1

  ✧ 8⁻¹ = 0.125

  ✧ 8⁻² = 0.015625

~Hope this helps Mate. If you need anything feel free to message me.

Answer:

B

Step-by-step explanation:

B is true because 0.2 x 10 = 2

y(6)+310=y

equals is =

product of is ×

add to is +

Answer: G.

Step-by-step explanation: you should divide both sides by 3. 3 divided by 3 is 0, and -12 divided by 3 is -4. therefore, your answer is (0,-4)

Answer: G (0,-4)

Step-by-step explanation:

You can use this website called "Desmos Graphing Calculator." The answer is G.(0,-4). It helps me a lot with graphing and graphing linear equations.

Answer:

4,1

Step-by-step explanation:

Answer:

$12750

Step-by-step explanation:

Initial price = $8500

Markup = 150%

Markup amount:

Selling price would be:

Answer: y = 7/3 - (4/3)*x

Step-by-step explanation:

First, let's write our line in the notation:

y = f(x)

So we must isolate y in the equation:

4x + 3y = 12

3y = 12 - 4x

y = 12/3 - (4/3)*x = 4 - (4/3)*x

Now, we have two translations, one horizontal and one vertical.

Let's define them in general cases:

Horizontal translation.

When we have y = f(x) and we want to do a horizontal translation of A units to the right (A positive) we have:

y = g(x) = f(x - A)

So we replace our variable x by x - A.

Vertical translation.

When we have y = f(x) and we want to do a horizontal translation of A units up (A positive) we have:

y = g(x) = f(x) + A.

Then in this case we have:

y = f(x) = 4 - (4/3)*x

then, the horizontal translation of 1 unit to the right is:

y = f(x - 1) = 4 - (4/3)*(x - 1)

And the translation of 3 units down (a vertical translation) is:

y = f(x - 1) - 3 = 4 - (4/3)*(x - 1) - 3  = 1 + 4/3 - (4/3)*x

y = 7/3 - (4/3)*x

This equation represents the new line.

Answer:

5u-25

Step-by-step explanation:

We have to simplify by distributing 5 to the variable and the number.

5(u-5)

5(u)5(-5)

5u-25

Answer:

y=50

Step-by-step explanation:

look at photo attached

Answer:

y=50

Step-by-step explanation:

on edge2021

Answer:

-21.5

Step-by-step explanation:

-8x+23-22+9=182

-8x+1+9=182

-8x+10=182

     -10   -10

-8x=172

x=172÷-8

x=-21.5

-21.5 IS THE ANSWER