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3 years ago

How does scale factor change the area?

1 answer:

5 0

Answer: in summary, a scale factor is simply a number that multiplies the dimensions of a shape. ... If the scale factor is three, then the perimeter of the new object will be three times the original perimeter. The area of a scaled object will be equal to the scale factor squared.

Step-by-step explanation:

For example, if you had a triangle with a base measuring 6 units, and a height measuring 3 units, the area would be 9 square units. If we scale it by 1/3, the triangle's base is 2 units, the height is 1 unit, and the area is 1 square unit. The dimensions were scaled by 1/3, but the area was scaled by 1/9 (1/3 * 1/3).

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A square with side x is changing with time where x(t)=3t+1. What is rate of change of the area of the square when t=2 seconds.

GuDViN [60]

Answer:

Rate of change of the area of the square is 42 units at t = 2.

Step-by-step explanation:

We note that the area of the square is given by: $A(x) = x^2$ but we aim to find $\frac{dA}{dt}$ . But we can use the chain rule to pull out that dA/dt. Doing so gives us:

$\frac{dA}{dt} = \frac{dA}{dx} \times \frac{dx}{dt}.$

Now, $\frac{dA}{dx} = 2x$ (by the power rule and $\frac{dx}{dt} = 3.$

But since we have "x" and not "t", we want to find what x is when t = 2. Substituting t = 2 gives us x(2) = 3(2) + 1 = 7.

So, finally, we see that:

$\frac{dA}{dt} = 2(7) \times 3 = 14 \times 3 = 42.$

7 0

3 years ago

Using the equation x+3, write one equation that has one solution, one equation that has no solution, and one equation that has i

neonofarm [45]

9514 1404 393

Answer:

one: x+3 = 2x
none: x+3 = x
infinite: x+3 = x+3

Step-by-step explanation:

A linear equation with variable terms on opposite sides of the equal sign will have one solution when the coefficients of those variables are different.

x+3 = 2x . . . . has one solution (x=3)

There will be no solution if the variable terms on opposite sides of the equal sign have the same coefficient, but the constants are different. Such an equation can be reduced to 0 = 1, which cannot be made true by any value of the variable.

x +3 = x . . . . has no solutions

There will be an infinite number of solutions if the left side of the equal sign is the same as the right side. Every value of the variable will satisfy the equation.

x +3 = x +3 . . . . has infinite solutions

8 0

2 years ago

A bag contains 4 tan socks and 7 grey socks. emily reaches into the bag and randomly selects two socks without replacement. what

Y_Kistochka [10]

Tan socks = 4
Grey socks = 7
Total number of socks = 4+7 = 11 socks
Probability of picking a tan sock then grey sock:
P(T)*P(G) = (4/11)*(7/10) = 14/54

Probability of picking a Grey sock then Tan sock
P(G)*P(T) = (7/11)*(4/10) = 14/55

Probability of two different colored socks
P(T&G)+P(G&T) = (14/55)+(14/55) = 28/55

8 0

2 years ago

What is 1/3 of 57 current size?

ludmilkaskok [199]

Answer:

Step-by-step explanation:

one third of 57 is the same as saying 57 divided by 3 and if you do that then you get the answer above

3 0

3 years ago

Solve the system of equations. 4x+2y+5z=8 5x+3y+4z=9 6x+3y+3z=3

Alchen [17]

Answer:

x = -4, y = 7, z = 2.

Step-by-step explanation:

4x + 2y + 5z = 8......(1)

5x + 3y + 4z = 9......(2)

6x + 3y + 3z = 3......(3)

Subtract: equation (2) - equation (3):

-x + z = 6 ........(4)

Multiply (1) by 3 and (2) by 2:

12x + 6y + 15z = 24 .........(5)

10x + 6y + 8z = 18 ...........(6)

Subtract: (5) - (6):

2x + 7z = 6..............(7)

Multiply equation (4) by 2:

- 2x + 2z = 12.........(8)

Add (7) + (8):

9z = 18 , so z = 2.

Substitute for z in equation (4)

-x + 2 = 6

-x = 4 so x = -4.

Now find y by substituting in equation (1):

4(-4) + 2y + 5(2) = 8

2y = 8 + 16 - 10 = 14

y = 7.

3 0

3 years ago