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4 years ago

Which graph represents x≤7 ?

Mathematics

2 answers:

Alexus [3.1K]4 years ago

6 0

Answer:

Answer D

Step-by-step explanation:

there needs to be a filled circle since the symbol says "or equal to".

then the arrow needs to point to the left indicating that the answer to x is less that 7, so the answer is D

Sav [38]4 years ago

4 0

Answer: D

Step-by-step explanation: To graph x ≤ 7 on a number line, we start with a closed dot at 7. The reason we use a closed dot in this problem is that not only is <em>x</em> less than 7 but it's also equal to 7.

We then draw an arrow going to the left to

represents all numbers less than -7.

The line underneath the sign means that you are including

that number as a solution to the inequality.

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4 years ago

What are the coordinates of point B on \overline{AC} such that AB = 1/2 BC

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Answer:

C. $B(x,y) = \left(3,-\frac{16}{3} \right)$

Step-by-step explanation:

Let $A(x,y) = (6,-7)$ , $B(x,y) = (x,y)$ and $C(x,y) = (-3,-2)$ . From statement we know that $AB = \frac{1}{2}\cdot BC$ , which is equivalent to the following linear algebraic formula:

$B(x,y) -A(x,y) = \frac{1}{2}\cdot [C(x,y)-B(x,y)]$ (1)

$B(x,y)-A(x,y) = \frac{1}{2}\cdot C(x,y)-\frac{1}{2}\cdot B(x,y)$

$\frac{3}{2}\cdot B(x,y) = \frac{1}{2}\cdot C(x,y)+A(x,y)$

$B(x,y) = \frac{1}{3}\cdot C(x,y) +\frac{2}{3}\cdot A(x,y)$ (2)

Then, the coordinates of point B on AC are:

$B(x,y) = \frac{1}{3}\cdot (-3,-2)+\frac{2}{3}\cdot (6,-7)$

$B(x,y) = \left(-1, -\frac{2}{3}\right)+\left(4, -\frac{14}{3} \right)$

$B(x,y) = \left(3,-\frac{16}{3} \right)$

Which means that correct answer is C.

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