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alisha [4.7K]
3 years ago
11

The graph shows the solution to which system of inequalities?

Mathematics
1 answer:
Westkost [7]3 years ago
8 0

Answer:

The graph shows the solution to the system inequalities

y ≥ -3x + 3 and y ≥ 2x ⇒ answer D

Step-by-step explanation:

* Lets study the graph to solve the question

- There are two solid lines, that means the sign of the inequalities

  are ≤ or ≥

- One of the two line passes through the origin and the other

  intersect the y-axis

- The shaded region is over the two lines, then the signs of the

  inequalities are ≥ (greater than or equal)

* Lets make the equations of the two lines

∵ The form of the equation is y = mx + c, where m is the slope of the

   line and c is the y-intercept

- The rule of the slope of the line wich passes through points (x1 , y1)

  and (x2 , y2) is m = (y2 - y1)/(x2 - x1)

- Y-intercept means the line intersect the y-axis at point (0 , c)

* Now lets find from the graph two points on each line to make the

 equations of the lines

# The line which passes through the origin

∵ Points (0 , 0) and (5 , 10) are on the line

- Let (0 , 0) is (x1 , y1) and (5 , 10) is (x2 , y2)

∴ m = (10 - 0)/(5 - 0) = 10/5 = 2

∴ The equation of the line is y = 2x + c

∵ The line passes through the origin

∴ c = 0

∴ The equation of the line is y = 2x

- The shaded is over the line

∴ The inequality is y ≥ 2x

# The line which intersect the y-axis at point (0 , 3)

∵ Points (0 , 3) and (1 , 0) are on the line

- Let (0 , 3) is (x1 , y1) and (1 , 0) is (x2 , y2)

∴ m = (0 - 3)/(1 - 0) = -3/1 = -3

∴ The equation of the line is y = -3x + c

∵ The line passes through the point (0 , 3)

∴ c = 3

∴ The equation of the line is y = -3x + 3

- The shaded is over the line

∴ The inequality is y ≥ -3x + 3

∴ The graph shows the solution to the system inequalities :

   y ≥ -3x + 3 and y ≥ 2x

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Answer:

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Step-by-step explanation:

The exact question is as follows :

Given - The dot plots compare the number of raffle tickets sold by boys and girls during a school fund-raiser.

To find - Which plot has an outlier?

Proof -

The correct answer is - Girls

Reason -

Girls plot has an outlier because values way outside the majority of the data.

Definition of outlier -

A value that "lies outside" (is much smaller or larger than) most of the other values in a set of data.

Here in the Girl's plot we can see that, all the dots are close but there is one dot that is lies outside

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So,

The correct option is -

Girl's plot has an outlier.

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My brain is lagging:<​
Lubov Fominskaja [6]

Distance between two points (-3, 4) and (5, -2) is 10 units.

Mid-point of the line segment joining (-1, -5) and (7, 1) is  (3, -2).

Degree of the given polynomial is 7.

6) Distance between two points (x_1, y_1) and (x_2, y_2) is:

\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

So, distance between two points (-3, 4) and (5, -2) is:

=\sqrt{(5-(-3))^2+(-2-4)^2}

=\sqrt{(8)^2+(-6)^2}

=\sqrt{64+36}

=\sqrt{100}

=10

So, option D is correct.

7) Mid-point of the line segment joining (x_1, y_1) and (x_2, y_2) is:

(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})

Mid-point of the line segment joining (-1, -5) and (7, 1) is:

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= (\frac{6}{2}, \frac{-4}{2})

= (3, -2)

So, option A is correct.

8) Degree of a polynomial is the highest power of the variable in the polynomial.

f(x)=3x^2-7x^4+9x^7+2x^3

Here, the highest power of the variable is 7.

So, option B is correct.

Learn more about distance formula, mid point formula, and degree of polynomial.

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swat32
272 / 8 = 34

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