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velikii [3]
2 years ago
7

Determine if the solution set for the system of equations shown is the empty set, contains one point or is infinite.

Mathematics
1 answer:
PolarNik [594]2 years ago
8 0

Answer:

  one point

Step-by-step explanation:

A system of two linear equations will have one point in the solution set if the slopes of the lines are different.

__

When the equations are written in the same form, the ratio of x-coefficient to y-coefficient is related to the slope. It will be different if there is one solution.

  • ratio for first equation: 1/1 = 1
  • ratio for second equation: 1/-1 = -1

These lines have <em>different slopes</em>, so there is one solution to the system of equations.

_____

<em>Additional comment</em>

When the equations are in slope-intercept form with the y-coefficient equal to 1, the x-coefficient is the slope.

  y = mx +b . . . . . slope = m

When the equations are in standard form (as in this problem), the ratio of x- to y-coefficient is the opposite of the slope.

  ax +by = c . . . . . slope = -a/b

As long as the equations are in the same form, the slopes can be compared by comparing the ratios of coefficients.

__

If the slopes are the same, the lines may be either parallel (empty solution set) or coincident (infinite solution set). When the equations are in the same form with reduced coefficients, the lines will be coincident if they are the same equation.

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Merry early Christmas to you too,have a great night!

Step-by-step explanation:

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Use\ (a+b)^2=a^2+2ab+b^2\qquad(*)\\\\y=x^2+6x+10=x^2+2(x)(3)+10=\underbrace{x^2+2(x)(3)+3^2}_{(*)}-3^2+10\\\\=(x+3)^2-9+10=(x+3)^2+1\\\\Answer:\ \boxed{y=(x+3)^2+1}

3 0
3 years ago
Subtract (r - 3q + 5p) - (-4r - 3q - 8p)
Alex787 [66]

Answer: ok so Let's simplify step-by-step.

r−3q+5p−(−4r−3q−8p)

Distribute the Negative Sign:

=r−3q+5p+−1(−4r−3q−8p)

=r+−3q+5p+−1(−4r)+−1(−3q)+−1(−8p)

=r+−3q+5p+4r+3q+8p

Combine Like Terms:

=r+−3q+5p+4r+3q+8p

=(5p+8p)+(−3q+3q)+(r+4r)

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Step-by-step explanation:

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In 2000, the population of Massachusetts
Zepler [3.9K]

Answer:

The population reaches 7 million people in the year 2032.

Step-by-step explanation:

We have that

f(x) = 6.3*(1.0032)^{x}

Using this model, find the year when the population reaches 7 million people.

This is x years after 2000, in which x is found when f(x) = 7. So

f(x) = 6.3*(1.0032)^{x}

7 = 6.3*(1.0032)^{x}

(1.0032)^{x} = \frac{7}{6.3}

(1.0032)^{x} = 1.11

We have to following logarithm rule

\log{a^{x}} = x\log{a}

So we apply log to both sides of the equality

\log{(1.0032)^{x}} = \log{1.11}

x\log{1.0032} = \log{1.11}

x = \frac{\log{1.11}}{\log{1.0032}}

x = 32.66

2000 + 32.66 = 2032

The population reaches 7 million people in the year 2032.

3 0
3 years ago
The solids are similar. Find the surface area of the red solid.
alisha [4.7K]

Answer:

756

Step-by-step explanation:

The ratio of areas is the square of the scale factor.

First, we find the scale factor from the blue solid to the red solid.

scale factor = 6/4 = 3/2

The ratio of areas is the square of the scale factor:

ratio of areas = (3/2)^2 = 9/4

volume of red solid = volume of blue solid * ratio of areas

volume of red solid = 336 m^2 * 9/4 = 756 m^2

Answer: S = 756 m^2

8 0
3 years ago
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