Which Graph shows a system of equations with a solution at (2,-1)

Mathematics

2 answers:

zimovet [89]3 years ago

8 0

The one with the U shape going up, and the red line is tilting to the left that last picture

hjlf3 years ago

3 0

Answer:

its the 4 one with the parabola facing down and red line going through the y intercept -3

Step-by-step explanation:

a solution is the point of interception between 2 lines

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Consider each equation. is it the equation of the line that is parallel or perpendicular to y=3x+2? Select yes or no for a-c

Mkey [24]

Answer:

see explanation

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 3x + 2 is in this form with slope m = 3

• Parallel lines have equal slope

• The slopes of perpendicular lines are negative reciprocals of each other

y = - $\frac{1}{3}$ x - 8 has slope m = - $\frac{1}{3}$

3 and - $\frac{1}{3}$ are negative reciprocals

This line is perpendicular to y = 3x + 2

y = 3x - 10 has slope m = 3

This line is parallel to y = 3x + 2

y = 2x + 4 has slope m = 2

This line is neither parallel nor perpendicular to y = 3x + 2

5 0

3 years ago

What is the value of x?

Nikolay [14]

Answer: 7 centimeters

Explanation:

Let triangle ABC and triangle CDE form a bow tie such that
- triangle ABC is smaller than triangle CDE
- Segment AC and segment CD are the north sides
- Segment BC and segment CE are the bottom sides
- AC = 6, CD = 42, CE = 36, BC = x

Since angle ACB and angle ECD are formed by intersecting segment AE and segment BD at point C, they are vertical angles. (See the attached picture) So, angle ACB and angle ECD are congruent.

Moreover when we form our bowtie, point A is in the north side and point E is in the bottom sides and this implies that angle BAC and angle CED are alternate interior angles as shown in the attached figure.

Since it is given in the problem that alternating interior angle are congruent, angle BAC and angle CED are congruent.

Now, we have the following pairs of angles in triangle ABC and triangle CDE that are congruent:

- angle BAC and angle CED
- angle ACB and angle ECD

By AA Similarity theorem, when we have two pairs of congruent angles for two triangles, then the two triangles are similar. So, triangle ABC and triangle CDE are similar.

In similar triangles, the sides that are opposite to the congruent angles are proportional to each other. So,

$\frac{BC}{CD} = \frac{AC}{CE} 


$ (1)

Since $AC = 6, CD = 42, CE = 36, BC = x$ , we can substitute these values to equation (1). So, equation (1) becomes

$\frac{x}{42} = \frac{6}{36}$
$\frac{x}{42} = \frac{1}{6}$ (2)

SInce we are solving for x, we can multiply both sides of equation (2) by the denominator at the left side which is 42 so that

x = 42(1/6)
x = 7 centimeters