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Ivahew [28]
4 years ago
8

What do the following two equations represent? -4x-4y = -5 12x+12y = 112x

Mathematics
1 answer:
7nadin3 [17]4 years ago
4 0

Answer:

These two lines are parallel and system of these equations have no solution

Step-by-step explanation:

Parallel Lines: Lines having same slope and different x and y intercept are parallel lines. System of such equations does not have any solution as these lines does not intersect at any finite points.

Standard form of line is y=mx+c where m is slope and c is y-intercept.

First Line:

-4x-4y=-5\\\\-4y=-5+4x\\\\Divide\ both\ sides\ by\ -4\\\\y=-x+\frac{5}{4}\\\\compare\ with\ y=mx+c\\\\slope=-1,\ c=\frac{5}{4}

Second Line:

12x+12y=112\\\\12y=112+-12x\\\\Divide\ both\ sides\ by\ 12\\\\y=-x+\frac{12}{112}\\\\compare\ with\ y=mx+c\\\\slope=-1,\ c=\frac{12}{112}

Hence these two lines are parallel and system of these equations have no solution

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Help me please!!!!!!
lara [203]

Answer:

a. b=2

b. b = 2a

c. a = \frac{1}{2}b\\

d. b = 10

Step-by-step explanation:

Gradient is just another similar term for slope l, m, and it can be calculated by m = \frac{y_2 -y_1}{x_2 -x_1}\\ where x_n and 1y_n is the xy-coordinates of point n

We let (0,0) be point 1 and (a,b) be point 2, we can then write the equation:

m = \frac{b -0}{a -0}\\ m = \frac{b}{a}.

It also says that the points are with a gradient of 2 so m = 2. We can then write the equation:

2 = \frac{b}{a}\\

Finding bIf a = 1:

2 = \frac{b}{a} \\ 2 = \frac{b}{1} \\ 2 = b \\ b = 2

Writing an expression for b in terms of a.

2 = \frac{b}{a} \\ \frac{b}{a} = 2 \\ \frac{b}{a} \times a = 2 \times a \\ b = 2a

Writing an expression for a in terms of b

2 = \frac{b}{a} \\ \frac{b}{a} = 2 \\ \frac{a}{b} = \frac{1}{2} \\ \frac{a}{b} \times b = \frac{1}{2} \times b \\ a = \frac{1}{2}b

Finding b if a = 5

2 = \frac{b}{a} \\ 2 = \frac{b}{5} \\ \frac{b}{5} = 2 \\ \frac{b}{5} \times 5 = 2 \times 5 \\ b = 10

4 0
3 years ago
A triangle has the following measurements: B=79 degrees a=5ft
Ganezh [65]
<span>the Law of Cosines </span>b^2=a^2+c^2-2accosB


6 0
4 years ago
8. Noah rides his motorcycle 90 miles in 2 hours 30 minutes. What is his average speed in
Nookie1986 [14]

Hey there! I'm happy to help!

We see that Noah rides his motorcycle 90 miles is 2 hours and 30 minutes, which is 150 minutes. We want to find his mph. To find this his mph, we want to find how far he has gone in one hour.

How much bigger is 150 than 60?

150/60=2.5

150 is 2.5 times bigger than 60. This means that we need to divide 90 by 2.5 to figure out how far Noah rode in 1 hour.

90/2.5=36

Therefore, Noah's average speed is 36 mph.

Have a wonderful day! :D

6 0
3 years ago
In a sample of 800 U.S. adults, 218 dine out at a restaurant more than once a week. If two U.S adults are selected at random fro
andre [41]

Answer: 0.074

Step-by-step explanation:

Given : The total number of U.S. adults in the sample = 800

The number of U.S. adults dine out at a restaurant more than once a week = 216

The probability for an adult dine out more than once per week :-

\dfrac{218}{800}

If another person is selected without replacement ,then

Total adults left = 799

Total adults left who dine out at a restaurant more than once a week = 217

The probability for the second person dine out more than once per week :-

\dfrac{217}{799}  

Now, the probability that both adults dine out more than once per week :-

\dfrac{218}{800}\times\dfrac{217}{799}=0.074

3 0
3 years ago
What is the sum? Complete the equation.<br> -5 + (20)
Stella [2.4K]

Answer: The answer is 15

HOPE THIS HELPS AND HAVE A VERY GOOD DAY

4 0
3 years ago
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