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3 years ago

Evaluate and simplify (-2)^4/(3^2+2^2)^2

Mathematics

1 answer:

LenaWriter [7]3 years ago

4 0

Answer: 16/169

Step-by-step explanation:

1. Evaluate the power

16/(x^2+2^2)^2
16/(9+2^2)^2
16/(9+4)^2

2. Add the numbers

16/13^2

3. Evaluate the power

16/169

4. Solution, 16/169

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Find 93 • 87 using mental math.

bagirrra123 [75]

Okay so start with multiplying 93 * 7

So 3 x 7= 21

9 X 7 +63, carry the 2 = 651

Then 8 x 93
Remember that first is a zero.
8 X 3= 24
8 X 9= 72, carry the 2= 74
So that is 7440
Now
0651
+7440
8091
And that's the answer

7 0

3 years ago

Read 2 more answers

Add.

Maru [420]

Answer:

4x^2 +3x -7

Step-by-step explanation:

(4x^2 – 2x) + (5x - 7)

Combine like terms

4x^2 -2x+5x -7

4x^2 +3x -7

8 0

2 years ago

Read 2 more answers

Compare the two graphs and explain the transformation that was applied to f(x) in order to look exactly like the graph of g(x).

Neporo4naja [7]

The two graphs are represented below.

Answer and Step-by-step explanation: One graph can "transform" into another through changes in the function.

There are 3 ways to change a function:

Shifting: it adds or subtracts a constant to one of the coordinates, thus changing the graph's location. When the y-coordinate is added or subtract and the x-coordinate is unchanged, there is a vertical shift. If it is the x-coordinate which changes and y-coordinate is kept the same, the shift is a horizontal shift;
Scaling: it multiplies or divides one of the coordinates by a constant, thus changing position and appearance of the graph. If the y-coordinate is multiplied or divided by a constant but x-coordinate is the same, it is a vertical scaling. If the x-coordinate is changed by a constant and y-coordinate is not, it is a horizontal scaling;
Reflecting: it's a special case of scaling, where you can multiply a coordinate per its opposite one;

Now, the points for f(x) are:

(-5,0) (0,6) (5,-4) (8,0)

And the points for g(x) are:

(-5,-3) (0,-9) (5,1) (8,-3)

Comparing points:

(-5,0) → (-5,-3)

(0,6) → (0,-9)

(5,-4) → (5,1)

(8,0) → (8,-3)

It can be noted that x-coordinate is kept the same; only y-coordinate is changing so we have a vertical change. Observing the points:

(-5,0-3) → (-5,-3)

(0,6-15) → (0,-9)

(5,-4+5) → (5,1)

(8,0-3) → (8,-3)

Then, the vertical change is a Vertical Shift.

Another observation is that y-coordinate of f(x) is the opposite of g(x). for example: At the second point, y-coordinate of f(x) is 6, while of g(x) is -9. So, this transformation is also a Reflection.

Range of a function is all the values y can assume after substituting the x-values.

Domain of a function is all the values x can assume.

Reflection doesn't change range nor domain of a function. However, vertical or horizontal translations do.

Any vertical translation will change the range of a function and keep domain intact.

Then, for f(x) and g(x):

graph translation domain range

f(x) none [-5,8] [-4,6]

g(x) vertical shift [-5,8] [-9,1]

In conclusion, this transformation (or translation) will affect the range of g(x)

5 0

2 years ago

I need help solving unit rates

guapka [62]

It takes Selma 1/6 of a hour to run 3/4 miles.
Just multiply 3/4 by 6 to get 18/4 which is 4.5 miles or 4 1/2 mile

7 0

3 years ago

PLEASE HELP

irina [24]

Take the longer leg length as $x$

$(x-8)^2+x^2=(x+8)^2 \\ \\ x^2-16x+64+x^2=x^2+16x+64 \\ \\ x^2-32x=0$

Use the formular
$x={ \frac{-b+ \sqrt{ b^2-4ac}}{2a} } \\ \\ x={ \frac{32+32}{2} } \\ \\ x=32$

∴ shorter leg = 32 - 8 = 24ft
longer leg = 32ft
hypotenuse = 32 + 8 = 40ft

8 0

3 years ago