I need alot of help plz

4. Which property of operations is used to write 15x + 9 as 9 + 15x?

suter [353]

Solution: The commutative property of addition states that when two numbers are being added, their order can be changed without affecting the sum.

8 0

2 years ago

HELP PLEASE!!!!!!!!!!!!

Bogdan [553]

Answer:

See the explanation.

Step-by-step explanation:

We are given the function f(x) = x² + 2x - 5

Zeros :

If f(x) = 0 i.e. x² + 2x - 5 = 0

The left hand side can not be factorized. Hence, use Sridhar Acharya formula and

$x= \frac{-2+\sqrt{2^{2}-4\times(-5)\times1 } }{2}$ and

$x= \frac{-2-\sqrt{2^{2}-4\times(-5)\times1 } }{2}$

⇒ x = -3.45 and 1.45

Y- intercept :

Putting x = 0, we get, f(x) = - 5, Hence, y-intercept is -5.

Maximum point :

Not defined

Minimum point:

The equation can be expressed as (x + 1)² = (y + 5)

This is an equation of parabola having the vertex at (-1,-5) and axis parallel to + y-axis

Therefore, the minimum point is (-1,-5)

Domain :

x can be any real number

Range:

f(x) ≥ - 6

Interval of increase:

Since this is a parabola having the vertex at (-1,-5) and axis parallel to + y-axis.

Therefore, interval of increase is +∞ > x > -1

Interval of decrease:

-∞ < x < -1

End behavior :

$f(x) = x^{2} +2x-5 =x^{2} (1+\frac{2}{x} -\frac{5}{x^{2} } )$

So, as x tends to +∞ , then f(x) tends to +∞

And as x tends to -∞, then f(x) tends to +∞. (Answer)

7 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 $(x,y) \to (0.5x,2y)$ .