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andre [41]
3 years ago
13

In the figure, polygon ABCD is dilated by a factor of 2 to produce A′B′C′D′ with the origin as the center of dilation. Point A′

is at , and point D′ is at . NextReset

Mathematics
1 answer:
emmasim [6.3K]3 years ago
3 0

You did not attach any picture to solve this problem. We cannot calculate for the value of A’ and D’ without the correct graph. However, I think I found the correct graph (see attached), please attach it next time.

So we are given that the figure is dilated by a factor of, meaning that all of its end points are multiplied by 2. By this rule, all we have to do is to simply multiply the initial coordinates of A and D by 2 to get A’ and D’, that is:

A’ = (-1 * 2, -1 * 2) = (-2, -2)

<span>D’ = (2 * 2, -1 * 2) = (4, -2)</span>

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Use the formula to determine the area of squares with side lengths of 3 cm, 10.5 cm, and π cm.
Nataliya [291]

Answer:

For length of side = 3 cm

Area of the square = 9 cm²

For length of side = 10.5 cm

Area of the square =  110.25 cm²

For length of side = π cm

Area of the square = 9.869 cm²

Step-by-step explanation:

The area of a square is given as :

Area = Side²

therefore,

For length of side = 3 cm

Area of the square = ( 3 cm )² = ( 3 × 3 ) cm² = 9 cm²

For length of side = 10.5 cm

Area of the square = ( 10.5 cm )² = ( 10.5 × 10.5 ) cm² = 110.25 cm²

For length of side = π cm

Area of the square = ( π cm )²  

= ( π × π ) cm²                

= 3.14² cm²                                [π = 3.14]

= 9.869 cm²

8 0
3 years ago
Adjust the equation so the line passes through the points. Y=x+1
lapo4ka [179]

Answer:

Slope=  

2.000

2.000

​  

=1.000

x−intercept=  

−1

1

​  

=−1.00000

y−intercept=  

1

1

​  

=1.00000

Step-by-step explanation:

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    y-(x+1)=0  

STEP

1

:

Equation of a Straight Line

1.1     Solve   y-x-1  = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  y-x-1  = 0 and calculate its properties

Graph of a Straight Line :

 

 

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 1/1 so this line "cuts" the y axis at y= 1.00000

 y-intercept = 1/1  =  1.00000  

Calculate the X-Intercept :

When y = 0 the value of x is 1/-1 Our line therefore "cuts" the x axis at x=-1.00000

 x-intercept = 1/-1  = -1.00000  

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 1.000 and for x=2.000, the value of y is 3.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 3.000 - 1.000 = 2.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

   Slope     =  2.000/2.000 =  1.000  

Geometric figure: Straight Line

1.  Slope = 2.000/2.000 = 1.000

2. x-intercept = 1/-1 = -1.00000

3.  y-intercept = 1/1 = 1.00000

3 0
3 years ago
Given g(x)=5x+4, solve for x when g(x)=9
Alex

Answer:

The value of <em>x</em> is equal to 1, written as <em>x</em> = 1.

General Formulas and Concepts:
<u>Algebra I</u>

Equality Properties

  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
  • Subtraction Property of Equality

Terms/Coefficients

Functions

  • Function Notation

Step-by-step explanation:

<u>Step 1: Define</u>

g(x) = 5x + 4

g(x) = 9

<u>Step 2: Solve for </u><u><em>x</em></u>

  1. Substitute in function value:                                                                           9 = 5x + 4
  2. [Subtraction Property of Equality] Subtract 4 on both sides:                       5 = 5x
  3. [Division Property of Equality] Divide 5 on both sides:                                1 = x
  4. Rewrite:                                                                                                            x = 1

∴ when the function g(x) equals 9, the value of <em>x</em> that makes the function true would be <em>x</em> = 1.

---

Topic: Algebra I

8 0
2 years ago
If the exchange rate of 1 dollar is rs 72.45, how many dollar can be exchanged for rs 1449?
Shalnov [3]

Answer:

20

Step-by-step explanation:

1449÷72.45=20

4 0
2 years ago
A ball of mass 0.4 kg flies through the air at low speed, so that air resistance is negligible. What is the net force acting on
arsen [322]

Answer:

-3.92 N

Step-by-step explanation:

We are given that

Mass of ball=0.4 kg

Acceleration due to gravity=-9.8m/s^2

Because the ball flies against to gravity

We have to find the net force acting on the ball while it is in motion.

We know that when there is no air resistance then the net  force acts on the ball is equal to weight of ball.

Net force,F =mg

Substitute the values then we get

F=0.4(-9.8)

F=-3.92N

Hence, the net force acting on the ball while it is on motion=-3.92 N

6 0
2 years ago
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