In the following expression, both A and B are variables that can take positive values.

Solve the system of equations using substitution or elimination. Show all work for credit.

Tomtit [17]

Using substitution:
first you have to express one variable in terms of the other, in this we can express y in terms of x:
$y = \frac{ - \frac{1}{2} x + 2}{3} \\ y = - x + 9$

Since both expressions are equal to y, you have to equal both expressions like this:
$\frac{ - \frac{ 1}{2}x + 2 }{3} = - x + 9$
Now you can solve the equation:
$- \frac{1}{2} x + 2 = 3( - x + 9) \\ - \frac{ 1}{2}x + 2 = - 3x + 27 \\ \\ - \frac{1}{2} x + 3x = 27 - 2 \\ \frac{5}{2} x = 25 \\ x = \frac{(25)(2)}{5} \\ x = 10$
Knowing x=10, you can use any of the expressions we found before to find y. In this case I'm going to use y= -x+9 because it's simpler but boy should give you the same result

$y = - (10) + 9 \\ y = - 1$
So, the answer is x=10 and y=-1

4 0

3 years ago

A bracelet is exactly 6.97 cm across from one side to the other, through the center. What is the approximate area of the bracele

Vadim26 [7]

Answer:

≈ 38.14 cm²

Step-by-step explanation:

Diameter of circle= 6.97 cm

Area of circle = ?

Area = πr² = πd²/4 =
3.14*(6.97)²/4 ≈ 38.14 cm²

3 0

3 years ago

Mary’s mother invested in an internet stock the price went up and down over the next few months: +32, -10 +13 -25 at the end of

babunello [35]

Answer:

higher

Step-by-step explanation:

add all of these numbers, if the sum is positive it is higher, if the sum is negative it is lower

32-10+13-25=10, this is positive so it is higher

8 0

3 years ago

3x to the x power plus 1 equals 9

Pani-rosa [81]

Do you want the answer or it written out? The written out would be down below and the answer is also down below in the x to the power of x equals 8/3 and its written out.

5 0

3 years ago

1. Write a rule that will take the triangle to a congruent triangle. Write your rule as (x,y)

olga nikolaevna [1]

Transforming a shape involves changing the size and/or the location of the shape.

The rule that will take the triangle to a congruent triangle is $(x,y) \to (x,-y)$
The rule that will take the triangle to a figure that is similar is $(x,y) \to (0.5x,0.5y)$ .
The rule that will take the triangle to a figure that is not similar or congruent is $(x,y) \to (0.5x,2y)$ .

<h3>Rigid transformation</h3>

When a shape is transformed by a rigid transformation, then the image of the shape will be congruent to the original shape.

An example of a rigid transformation is a reflection over the x-axis; and the rule is:

$(x,y) \to (x,-y)$

So, a rule that will take the triangle to a congruent triangle is $(x,y) \to (x,-y)$

<h3>Nonrigid transformation</h3>

When a shape is transformed by a nonrigid transformation, then the image of the shape will not be congruent to the original shape, however the original shape and the transformed shape would be similar

An example of a nonrigid transformation is a dilation by a scale factor od 0.5; and the rule is:

$(x,y) \to (0.5x,0.5y)$

So, a rule that will take the triangle to a figure that is similar is $(x,y) \to (0.5x,0.5y)$

However, if the x and y coordinates of the shape are dilated by different scale factors, then the resulting shape would neither be similar nor be congruent to the original shape.

A rule that will take the triangle to a figure that is not similar or congruent is $(x,y) \to (0.5x,2y)$ .