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2 years ago

Why is the answer C? Plz explain

Mathematics

1 answer:

Dafna11 [192]2 years ago

5 0

Set the equations each to each other and solve for x
f(x) = g(x)
x^2 - 3x = 2x+14
x^2-3x-2x-14 = 0
x^2-5x-14 = 0 .... see note below
(x-7)(x+2) = 0
x-7 = 0 or x+2 = 0
x = 7 or x = -2
The two solutions are x = 7 or x = -2

note: we technically could stop at this line and divert to another path. Instead of finding the actual solutions, we can use the discriminant formula
d = b^2 - 4ac
to find the value of d. It turns out that
d = (-5)^2 - 4(1)(-14)
d = 81
which is a positive number. So that shows we have two solutions.

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Need help with inscribed angles If M

Bogdan [553]

Given:

In the given circle O, BC is diameter, OA is radius, DC is a chord parallel to chord BA and $m\angle BCD=30^\circ$ .

To find:

The $m\angle AOB$ .

Solution:

If a transversal line intersect two parallel lines, then the alternate interior angles are congruent.

We have, DC is parallel to BA and BC is the transversal line.

$\angle OBA\cong \angle BCD$ [Alternate interior angles]

$m\angle OBA=m\angle BCD$

$m\angle OBA=30^\circ$

In triangle AOB, OA and OB are radii of the circle O. It means OA=OB and triangle AOB is an isosceles triangle.

We know that base angles of an isosceles triangle are congruent.

$\angle OAB\cong \angle OBA$ [Base angles of an isosceles triangle]

$m\angle OAB=m\angle OBA$

$m\angle OAB=30^\circ$

In triangle AOB,

$m\angle OAB+m\angle OBA+m\angle AOB=180^\circ$

$30^\circ+30^\circ+m\angle AOB=180^\circ$

$60^\circ+m\angle AOB=180^\circ$

$m\angle AOB=180^\circ-60^\circ$

$m\angle AOB=120^\circ$

Therefore, the measure of angle AOB is 120 degrees.

6 0

2 years ago

Find the solutions of the system y = –2x – 1 and y = 3–x–1.

sweet [91]

There are two intersection points (-1, 1) and (-2, 3), and the x coordinates are -1 and -2.

<h3>What is an exponential function?</h3>

It is defined as the function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent y = a^x

where a is a constant and a>1

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have two equations:

y = –2x – 1 and

$\rm y = 3^{-x-1}$