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3 years ago

Find the value of x when 2(x - 3) + 1 = 3x + 4

1 answer:

7 0

Step 1. Expand

$2x-6+1=3x+4$

Step 2. Simplify $2x-6+1$ to $2x-5$

$2x-5=3x-4$

Step 3. Subtract $2x$ from both sides

 $-5=3x+4-2x$

Step 4. Simplify $3x+4-2x$ to $x+4$

$-5=x+4$

Step 5. Subtract 4 from both sides

$-5-4=x$

Step 6. Simplify $-5-4$ to $-9$

$-9=x$

Step 7. Switch sides

$x=-9$

Done! Your answer is $x=-9$

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Give reasons how graphing can help prove if a function is linear or not ?

icang [17]

If the line graphed is a straight line, then that function is linear. If the line curves in any way, then it is not linear. Hope this helps!

5 0

3 years ago

Using prime factorization what is the GCF 3y 2 squared, 24y 3 cubed

WINSTONCH [101]

Answer:

$3y^2$

Step-by-step explanation:

Given:

To find the GCF of $3y^2\ and\ 24y^3$ using prime factorization.

Writing each in prime factors:

3 = 1 $\times$ 3

24 = 1 $\times$ 2 $\times$ 2 $\times$ 2 $\times$ 3

Now, GCF of 3 and 24 is 3

$y^2=1\times y\times y$

$y^3=1\times y\times y\times y$

GCF of $y^2$ and $y^3$ is $y\times y=y^2$ .

Therefore, the overall GCF of the two terms is $3y^2$

8 0

3 years ago

Manny observed a Northern Gannet, a deep diving seabird, hovering at a height of 10 meters above the ocean surface. The bird the

mr Goodwill [35]

Answer:

9.2 seconds.

Step-by-step explanation:

We have been given an equation that represents dive of a bird as $y=x^2-10.3x+10$ , where x represents the time the dive lasted in seconds and y represents the height of the bird in meters.

We can see that our given equation is a parabola. The leading coefficient is positive, so our parabola will be an upward opening parabola.

Upon graphing our given equation, we will get our required graph as shown in the attachment.

As x represents the time the dive lasted in seconds and y represents the height of the bird in meters, so the bird will be at the surface when the graph will cross x-axis.

We can see that graph crosses x-axis at $x=1.085\text{ and }x=9.215$ .

Upon rounding to nearest tenth, we will get:

$x\approx 1.1\text{ and }x=9.2$ .

At $x\approx 1.1$ the bird dives in water and goes down the water surface and at $x=9.2$ the bird comes to the surface, therefore, the bird will be at surface after 9.2 seconds.