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Rudik [331]
3 years ago
13

Solve the system by graphing. Where necessary, indicate when the system has no solution or infinitely many solutions.

Mathematics
2 answers:
anzhelika [568]3 years ago
6 0

Answer:

D. No Solution

Step-by-step explanation:

Both lines have a slope of 2x so that means they are parallel and will never cross

Shalnov [3]3 years ago
4 0

Answer:

(D)

Step-by-step explanation:

When graphed, the lines do not cross at any point.  There is a picture of this below.

The system has no solution.

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The line through (1,6) and (0,3) passes through every quadrant expect one. Which one?​
KATRIN_1 [288]

4 quadrant

plot the graph of the line

6 0
3 years ago
write an equation of the line that passes through the given point and has the given slope slope is -3 (-5, 4)
Paraphin [41]

point slope form of a line

y-y1 = m(x-x1)

y-4 = -3(x--5)

y-4 =-3(x+5)

to change to slope intercept form

dstribute

y-4 = -3x-15

add 4 to each side

y = -3x-15+4

y = -3x-11

3 0
3 years ago
Solve the problem algebraically. Clearly define all variables, write an appropriate equation, and solve.
hichkok12 [17]

Answer:

Y=8 and X=21

Step-by-step explanation:

The key to solving word (story) problems is to learn how to translate words and phrases into concise, precise math expressions (variables and operations).  Make a table and add to it as you do problems:

      is              means           =

    more than                        +

      twice                              2*x

      sum                               +

      of                            usually means multiply

     ...

Assign variables.  Try to assign variables to the values the problem asks you to find.

In this problem, there are two variables.   Let x = one number;   y = other numbers

Translate:

 "One number is 5 more than twice the other number"    means

            x          =    5    +        2     *      y

 "sum of the two numbers is 29"     means

      x   +   y                    = 29

Now, the easy math.

Use the value for x from the first equation and substitute that into the second equation:

    (5 + 2y)      +     y       =  29

     5 + 3y = 29                    (collect terms)

           3y = 24                (subtract 5 from both sides)

             y = 8

Now, put that value of y into either equation to solve for x  (Which equation is easier??)

     x + 8 = 29

       x  = 21                 (subtract 8 from both sides)

Checking (very important):

 Is 21 really 5 more than 2(8)?

      21 = 5+16     ?

      21  =  21? yes

 Is  21 + 8 = 29  ?

        29 = 29? yes

p.s., learn the process, don't just get the right answer;  there will be lots of problems that are solved the same way!

3 0
1 year ago
List the integers that satisfy both these inequalities, 2x+9 -12
Flura [38]

Answer:

x < -10.5

Step-by-step explanation:

list the integers that satisfy both these inequalities, 2x+9 <-12

Subtract 9 from  both sides;

2x +9 - 9 < -12-9

2x < -21

x < -21/2

x < -10.5

<em>Hence all the integers are values of x less than 10.5</em>

<em></em>

4 0
3 years ago
HELP 40 POINTS
Tom [10]
Answer: the function g(x) has the smallest minimum y-value.


Explanation:


1) The function f(x) = 3x² + 12x + 16 is a parabola.


The vertex of the parabola is the minimum or maximum on the parabola.


If the parabola open down then the vertex is a maximum, and if the parabola open upward the vertex is a minimum.


The sign of the coefficient of the quadratic term tells whether the parabola opens upward or downward.


When such coefficient is positive, the parabola opens upward (so it has a minimum); when the coefficient is negative the parabola opens downward (so it has a maximum).


Here the coefficient is positive (3), which tells that the vertex of the parabola is a miimum.


Then, finding the minimum value of the function is done by finding the vertex.

I will change the form of the function to the vertex form by completing squares:

Given: 3x² + 12x + 16

Group: (3x² + 12x) + 16
Common factor: 3 [x² + 4x ] + 16
Complete squares: 3[ ( x² + 4x + 4) - 4] + 16
Factor the trinomial: 3 [(x + 2)² - 4] + 16
Distributive property: 3 (x + 2)² - 12 + 16
Combine like terms: 3 (x + 2)² + 4

That is the vertex form: A(x - h)² + k, whch means that the vertex is (h,k) = (-2, 4).


Then the minimum value is 4 (when x = - 2).


2) The othe function is <span>g(x)= 2 *sin(x-pi)
</span>

The sine function goes from -1 to + 1, so the minimum value of sin(x - pi) is - 1.


When you multiply by 2, you just increased the amplitude of the function and obtain the new minimum value is 2 (-1) = - 2


Comparing the two minima, you have 4 vs - 2, and so the function g(x) has the smallest minimum y-value.

7 0
3 years ago
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