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4 years ago

Figure ABCD is a rectangle. The length of segment AE is (5x − 7) units and the length of segment EC is (2x − 1) units.

Mathematics

1 answer:

Anettt [7]4 years ago

3 0

Hello!

To find our answer, we will first want to find x. Our two line segments appear to be congruent. If we add them up, it will be equal to BD, so let's find x, plug it in, and add it up.

5x-7=2x-1

Let's subtract 2x from both sides.

3x-7=-1

We add 7 to both sides.

3x=6

We divide both sides by 3.

x=2

Now, let's plug it in to both equations.

5(2)-7

10-7

2(2)-1

4-3=3

3+3=6

Therefore, our answer is $\boxed {B) 6 units}$

I hope this helps!

You might be interested in

What are the solutions to the equation and check for extraneous solutions:<br><br> 16=(x-2)^2/3

GuDViN [60]

Answer:

we have x = -62 or x = 66

Step-by-step explanation:

16=(x-2)^2/3

I would take square root first

4 = (x - 2)^ (1/3)

or -4 = (x - 2)^(1/3)

.....

4^3 = x - 2

64 = x - 2

x = 66

or -4 ^3 = x - 2

-64 = x - 2

x = -62

we have x = -62 or x = 66

5 0

4 years ago

Find f(-5) and f(12) for each piecewise function f(x){-4x+3 if x<3

Law Incorporation [45]

<h3>Answers:</h3>

f(-5) = 23
f(12) = 433

==================================================

Explanation:

The given piecewise function is

$f(x) = \begin{cases}-4x+3 \ \text{ if } \ x < 3\\-x^3 \ \text{ if } \ 3 \le x \le 8\\3x^2+1 \ \text{ if } \ x > 8\end{cases}$

At first piecewise functions may be strange confusing things, but they aren't so bad. I like to think of it like this: f(x) is a function that changes its identity based on what the input x is. We have three situations

f(x) = -4x+3 when x < 3
f(x) = -x^3 when $3 \le x \le 8$
f(x) = 3x^2+1 when x > 8

In a sense, we have three different functions but they are combined somehow.

If x is smaller than 3, then we go for the first definition. Or if x is between 3 and 8, then we go for the second definition. Or if x is larger than 8, then we go for the third definition.

-----------------------

f(-5) means f(x) when x = -5. We see that -5 is smaller than 3, so x = -5 makes x < 3 true. We'll use the first definition

f(x) = -4x+3

f(-5) = -4(-5)+3

f(-5) = 20+3

f(-5) = 23

------------------------

Now the input is x = 12. This is larger than 8. In other words, x = 12 makes x > 8 true. We'll use the third definition

f(x) = 3x^2+1

f(12) = 3(12)^2+1

f(12) = 3(144)+1

f(12) = 432+1

f(12) = 433

------------------------

Side notes:

We won't use the second definition since we don't have any x inputs between 3 and 8
To say "less than or equal to" on a keyboard, you can write "<=" without quotes. For example, $x \le 5$ is the same as x<=5