Solve −3.5 = x/4 for x using the multiplication property of equality.

The operation in the problem is
-Addition
-Subtraction
-Multiplication
-Divison

The inverse operation is
-Addition
-Subtraction
-Multiplication
-Divison

= x
0.5
-7.5
-12
-14

s = side length of square

4s = perimeter of square

L = length of rectangle

W = width of rectangle

P = 2L+2W = perimeter of rectangle

4s = 2L+2W .... since we want the perimeters the same

4s = 2(L+W)

s = 0.5(L+W)

s^2 = (0.5(L+W))^2 ... square both sides

s^2 = 0.25(L+W)^2

The last equation shows the area of the square, s^2, in terms of L and W. This way we can connect the square to the rectangle.

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

The area of the rectangle is LW

Let's subtract this from the area of the square and see what we get

A = area of square = s^2

B = area of rectangle = LW

C = difference in area

C = A - B

C = s^2 - LW

C = 0.25(L+W)^2 - LW

C = 0.25(L^2+2LW+W^2) - LW

C = 0.25L^2+0.5LW+0.25W^2-LW

C = 0.25L^2-0.5LW+0.25W^2

C = 0.25(L^2-2LW+W^2)

C = 0.25(L-W)^2

Regardless of what we pick for L and W, the expression (L-W)^2 is always positive. Squaring a negative number leads to a positive result.

So C is always positive as long as [tex]L \ne W[/tex]

If C > 0, and C = A - B, then

C > 0

A-B > 0 .... replace C with A-B

A > B .... add B to both sides

This shows the square area is always larger than the rectangle.

Again this only works if L and W are different values. If L = W, then the argument falls apart because the rectangle becomes the square.

We make [tex]L \ne W[/tex] to have a nonsquare rectangle.

Answer:

1.20 × 10^35

Step-by-step explanation:

There are 60 seconds in 1 min and there are 60 mins in 1 hour. So in an hour there are 60 × 60 = 3600 seconds. There are 24 hours in a day. In a day, there are 3600 × 24 = 86400 seconds. A year is 365 days. So in a year there are 86400 × 365 = 31536000 seconds.

[tex](3.8 \times {10}^{27}) \times 31536000 = 1.20 \times {10}^{35} [/tex]

Answer:

Kathy would take 7.56 seconds to run each of the 8-time segments of the 400-meter dash.

Step-by-step explanation:

Kathy ran the 400-meter dash in 60.48 seconds, so if she now divided that time into 8 equal time segments we have:

[tex] t = 60.48 s [/tex]

By dividing the above equation into 8:

[tex] t = \frac{60.48 s}{8} = 7.56 s [/tex]

Hence, she would take 7.56 seconds to run each of the 8-time segments of the 400-meter dash.

I hope it helps you!

9514 1404 393

Answer:

  3

Step-by-step explanation:

The radicals get in the way a bit, so we can define ...

  x = √p

  y = √q

Then the equation is ...

  (x +y)/(1-x) = (4x+y)/(1-x^2)

Multiplying by (1-x^2), we have ...

  (x +y)(1 +x) = 4x +y . . . . . . using 1-x^2 = (1-x)(1+x) the 1-x factor cancels

  x^2 +xy +x +y = 4x +y . . . eliminate parentheses

  x(x +y) = 3x . . . . . . . subtract (x+y)

  x +y = 3 . . . . . . . . . . divide by x

This is the sum we're looking for:

  √p +√q = 3

Answer: The answer is 3

Step-by-step explanation:

Answer:

Answers in step step-by-step explanation.

Step-by-step explanation:

1. 7

2. 0.3

3. 3

4. x = 50 degree

5. 15 (Sorry I accidentally made the answer to five the answer to six, 15 is the right answer)

6.  10.408125

7. 240

8. -29

9. I think 1/4 but double-check.

10. $5.4

Answer:

First one, Third one, Fifth one, and the last one too.

Step-by-step explanation:

Answer:

Step-by-step explanation:

First, make a ratio:

18 min/ 3mile = 6 min/mile

now multiply to finish the table:

1: 6

3: 18

5: 30

10: 60

25: 150

Answer:

[tex]y = - 4x - 3[/tex]

Step-by-step explanation:

[tex]y - 1 = - 4(x + 1) \\ y - 1 = - 4x - 4 \\ y = - 4x - 3[/tex]

Examine the operations above.

Answer:

Division property of equality

Step-by-step explanation:

Consider the equation and its solution. 8 (x minus 2) = 64.

8 x minus 16 = 64.

8 x = 80.

x = 10.

Which property is used in the last step to find that x = 10

The property used in the last step to find that x = 10 is called the DIVISION PROPERTY OF EQUALITY

The Division property of equality states that , when two sides of a quadratic equation are divide by the same integer that is greater than zero, both sides will be equal to one another

Let c be the integer greater than zero

ac = bc

Divide both sides by c

a = b

From the above question

8 x = 80

This is also written as:

8x = 8 × 10

Division property of equality

Divide both sides by 8

Hence,

x = 10

Answer:

division property of equality

Step-by-step explanation:

since the equation before our answer was a multiplication equation, you must counteract that with the division property of equality.

Answer:

x<6 should be the correct answer

Answer:

I believe it is

Step-by-step explanation:

None of the x and y values have the same number

Answer:

It is not the input 5 has 2 different output values, same as the input 3 it has more than one different output

Step-by-step explanation:

Hope this helps!

Answer:

6 feet

Step-by-step explanation:

240 feet : 10 inches

24 feet    : 1 inch

? feet       : 1/4 inch

to get from 1 to a 1/4 you divide by 4, so you do 24 ÷ 4

24 ÷ 4 = 6

Answer:

6 ft

Step-by-step explanation:

First, make this visually understandable using a ratio:

240 ft = x ft

10 in     [tex]\frac{1}{4}[/tex] in

To find the change between the inches,

1/4 ÷ 10 = 0.025

Use this same amount to find x ft:

240 (0.025) = 6

x = 6 ft

To double-check:

240/10 = 24

6/0.25 = 24

☺

Answer:

20 containers

Step-by-step explanation:

Given:

D = 0.07N

Where,

D = Amount of deposits

N = Number of containers

If D = $1.40 find N

D = 0.07N

1.40 = 0.07N

Divide both sides by 0.07

N = 1.40 / 0.07

= 20

N = 20 containers

if you deposit $1.40, you will buy a total of 20 containers.

Answer:

60.5 pounds

Step-by-step explanation:

The total amount of pound is 181.5

And there are three pandas.

So 181.5 divide by 3 is 60.5

Answer:

x would equal 23, so (x+92) would equal 115°, & (5x) would equal 115°.

Answer: 19 weeks.

Step-by-step explanation: 600 - 125 = 475. This means he needs to save $475 more. 475 divided by 25 is 19. So the answer is he must wait 19 more weeks.

Answer:

19 weeks

Step-by-step explanation:

600=25x+125  

x=19

Answer:

yes

Step-by-step explanation:

the diagnols are congruent meaning that the diagnol lines in the middle are the same length. So theoretically the left and right lengths are the same, and the top and bottom lengths are the same. The triagles named both have the same base and they're hieght is sbviouysly the same so they would be SSS each of the sides on one triangle coresspondes to the other.

Answer:

Option (A)

Step-by-step explanation:

Windmill is in the shape of a circle and each blade of the windmill is equally spaced.

There are 8 spaces in the windmill shown.

Therefore, angle between each blade = [tex]\frac{360}{n}[/tex]

Where n = number of blades

Angles between each blade = [tex]\frac{360}{8}[/tex]

                                               = 45°

To reach the position of blade U by blade P will cover 5 angles between the blades.

Therefore, angle of rotation covered by P to reach U = 5×45° = 225°

Option (A) will be the correct option.

Answer:

D

Step-by-step explanation:

from what I could tell, it sounds like D would be correct

Answer:

y = x + 2

Step-by-step explanation:

Answer:

1/125

Step-by-step explanation:

=1/5*5*5

=1/5^3

=1/125

Using exponent rules, when a number is raised to a negative exponent, change the exponent to positive and make a fraction with 1 as the numerator and the number as the denominator:

5^-3 = 1/(5^3)

Answer:

y = 0.5x + b, b ∈ ℜ - {12}

Step-by-step explanation:

==========================================================

Explanation:

The domain is the set of all possible x values. The range is the set of all possible y values.

Since we don't have any repeated x values, we have a function. Any given input x leads to exactly one y output value. Visually plotting the points leads to the graph passing the vertical line test, which shows the relation is a function.

Answer: 0ft < X ≤ 5.73ft

Step-by-step explanation:

In this case, we have a rectangle.

For a rectangle of length L and width W, the area is:

A = L*W.

And we have:

L = X

W = X  + 3ft.

Then the area will be:

A = X*(X + 3ft) = X^2 + 3ft*X.

And we want to have a maximum area of 50ft^2.

Then we can write:

A = X^2 + 3ft*X ≤ 50ft^2

Now let's solve this for X.

Now, the first thing we can see is that both coefficients in our quadratic equation are positive, so as the absolute value of X increases, also does the whole equation.

Then makes sense start for the upper limit of X, this is when:

X^2 + 3ft*X = 50ft^2.

Now we can solve the quadratic equation:

X^2 + 3ft*X - 50ft^2 = 0

Applying the Bhaskara formula, the solutions are:

[tex]X = \frac{-3ft +- \sqrt{(3ft)^2 - 4*1*(-50ft^2)} }{2} = \frac{-3ft +-14.46ft }{2}[/tex]

Then we have two solutions:

X = (-3ft - 14.46ft)/2 = -8.73 ft.

X = (-3ft + 14.46ft)/2 = 5.73 ft

Because X represents a distance, it can only be positive, then we must select the option X = 5.73ft.

This is the maximum value of X, and we will have:

0ft < X ≤ 5.73ft

Where the lower limit is there because we can not have X = 0ft, as this does not have physical meaning.

Answer:

You have no apples then loose 11 more

Step-by-step explanation:

Trust

Answer:

12⁴ × 9³ x 4 = 60,466,176

6³ × 8² × 27 = 373,248

Step-by-step explanation:

You could use the expanded form to calculate the answer

12⁴ = 20,736

9³ = 729

4 = 4

20,736 × 729 × 4 = 60,466,176

6³ x 8² x 27​

6³ = 216

8² = 64

27 = 27

216 × 64 × 27 = 373,248