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jekas [21]
3 years ago
15

Are the lines described by the equations y=x+2 and x+y=6 intersecting, coinciding, or parallel? Explain

Mathematics
1 answer:
Novosadov [1.4K]3 years ago
7 0
<span>y = slope*x + y-intercept;
</span>We can rewrite our equation in a shorter form : y = mx + b;
y = x + 2 ; m1 = 2 and b1 = 2;
y = -x + 6; m2 = -1 and b2 = 6;
<span>Set the two equations for y equal to each other:
</span>x + 2 = -x + 6 ;
<span>Solve for x. This will be the x-coordinate for the point of intersection:
</span>2x = 4;
x = 2;
<span>Use this x-coordinate and plug it into either of the original equations for the lines and solve for y. This will be the y-coordinate of the point of intersection:
</span>y = 2 + 2 ;
y = 4;
<span>The point of intersection for these two lines is (2 , 4).</span>

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40% of x is 35 Write an equation that shows the relationship of 40%, X, and 35.
zhenek [66]

Answer:

87.5

Step-by-step explanation:

7 0
3 years ago
Which system of inequalities does the graph represent? Which test point satisfies both of the inequalities in that system?
AveGali [126]

Answer:

1) The inequality for the given system are

y ≥ 4x - 4

y ≥ x - 1.5

2)  The test point (0,0)  satisfies both of the inequalities in the system represented by the graph.

Step-by-step explanation:

Given : A graph showing  a system of inequalities.

We have to find the system of inequality.

For line 1)

The points that cut the x and y axis are (1,0) and (0,-4)

Thus, we can find the equation of line using two given point.

Since the general equation of line is y = mx + c

Where m is slope and c is y intercept

Slope is find as m=\frac{y_2-y_1}{x_2-x_1}

Substitute, we get,

m=\frac{-4-0}{0-1}=4

Slope is 4.

Thus, equation becomes y = 4x + c

For c put (0,-4)  in the above equation , we have,

-4 = 4(0) + c ⇒ c = -4

Thus, equation becomes y = 4x - 4

For inequality take a test point (0,0) and we check for which inequality it satisfies the graph region

For (0,0)

y = 4x - 4 becomes 0 = - 4  is satisfied when 0 > -4

thus, the inequality becomes y ≥ 4x - 4

Since, the line is a solid so it will take up equality sign too.

For line 2)

The points that cut the x and y axis are (1.5,0) and (0,-1.5)

Thus, we can find the equation of line using two given point.

Since the general equation of line is y = mx + c

Where m is slope and c is y intercept

Slope is find as m=\frac{y_2-y_1}{x_2-x_1}

Substitute, we get,

m=\frac{-1.5-0}{0-1.5}=1

Slope is 1.

Thus, equation becomes y = x + c

For c put (0,-1.5)  in the above equation , we have,

-1.5 = (0) + c ⇒ c = - 1.5

Thus, equation becomes y = x - 1.5

For inequality take a test point (0,0) and we check for which inequality it satisfies the graph region

For (0,0)

y = x - 1.5 becomes 0 = -1.5  is satisfied when 0 > - 1.5

thus, the inequality becomes y ≥ x - 1.5

Since, the line is a solid so it will take up equality sign too.

Thus, the inequality for the given system are

y ≥ 4x - 4

y ≥ x - 1.5

Also,  The test point (0,0)  satisfies both of the inequalities in the system represented by the graph.

6 0
3 years ago
A laptop computer consumes about 20 watts of electricity per hour when operating. At 10 cents per kilowatt-hour, how much does a
Flura [38]

Step 1:

Convert the electricity per hour in kilowatts,

Electricity per hour = 20 watts

=20/1000 kilo,watts

Step 2:

The electricity consumes in 5 hour is ,

Electricity in 5 hour = 5x 20/1000 kilo watts.

Obtain the cost as,

=5x20/1000x10

=1 Cent

Answer: =1 Cent

Please mark brainliest

<em><u>Hope this helps.</u></em>

6 0
3 years ago
Do the results support or contradict the common belief that the mean body temperature is 98.6degrees​F? A. The results contradic
nata0808 [166]

Answer:

A. The results contradict the belief that the mean body temperature is 98.6 °F because both the mean and the median are less than 98.6 °F.  

Step-by-step explanation:

Assume the temperature data were those in the table below.

You would have calculated that

  Mean = 97.9 °F

Median = 97.9 °F

These observations contradict the belief that the mean body temperature is 98.6 °F.

A 2017 study found the mean oral temperature of more than 35 000 British patients was 97.9 °F.

 

7 0
3 years ago
The data shows the weights of 2 groups of house cats in pounds.
lesantik [10]
I would say the answer is C
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3 years ago
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