MATHEMATICS HIGH SCHOOL

2x + y = 5 , x + y = 4
Solve the system of linear equations.

Answers

Answer 1
Answer:

2x+y=5

x+y=4


We need to solve 2x+y=5 for y

let's start by adding -2x to both sides

2x+y-2x=5-2x

y=-2x+5

Now substitute -2x+5 for y in x+y=4

x+y=4

x-2x+5=4

-x+5 =4

Add -5 to both sides so we can find the value for x

-x+5-5=4-5

-x=-1

We know that x can not stay with the negative sign so to eliminate that we need to divide both sides by -1

-x/-1= -1/-1

x=1

Now we have the value for x :)

We need to find the value for y by substitute 1 for x in y=-2x+5

y=-2x+5

y= (-2)(1)+5

y= -2+5

y= 3

Final answer : x=1 and y=3

                          (1,3)


I hope that's help :)

Please let me know by rating my answer and a Thanks :0

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Peaches are being sold for $2 per pound. If x represents the number of pounds of peaches bought and y represents the total cost of the peaches, which best describes the values of x and y?
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Tram leaves Piccadilly to Eccles every 9 minutes and to didsbury every 12 minutes. A tram to Eccles and a tram to didsbury both leave Piccadilly at 9am. At what time will a tram to Eccles and a train to didsbury next leave picadilly at the same time?

Answers

See, the lowest common multiple of 9 and 12 is 36.
So the trams will leave together 36 minutes after they have left together the first time.
So it will be 36 minutes after 9 am.
So the time is 9:36 am. 
Hope I helped!!! You can contact me via messaging if you have any further doubts!

in 2004, 510,000 acres of farmland in region were devoted to growing nuts. by 2011, the number of acres used to grow nuts had increased to 830,000. find the avarage rate of change in the number of acres in a region used to grow nuts from 2004 to 2011

Answers

Consider the (x, y) coordinates to be:  (2004, 510000) and (2011, 830000).

Average rate of change is another name for slope, So, use the slope formula: m = (y2 - y1)/(x2 - x1)

m = (830,000 - 510,000)/(2011 - 2004)

m = (320,000)/(7)

Answer: 320,000 acres every 7 years

Answer: 45714 per year.

Step-by-step explanation:

Given : In 2004, 510,000 acres of farmland in region were devoted to growing nuts. by 2011, the number of acres used to grow nuts had increased to 830,000.

Change in acres of farmland from 2004 to 2011 = 830000-510000=320,000

Change in year = 2011-2004=7

The average rate of change is given by :-

\frac{\text{Change in acres of farmland}}{\text{Change in year}}\n\n=(320000)/(7)=45714.2857143\approx45714 \text{[Rounded to the nearest integer.]}

Hence, the average rate of change in the number of acres in a region used to grow nuts from 2004 to 2011 is 45714 per year.

A rectangular prism is 4 meters long, 5 meters wide, and has a height of 7 meters. What is its surface area?140 m 2
166 m 2
84 m 2
70 m 2

Answers

Answer:

The surface area of rectangular prism is 166 m².

Step-by-step explanation:

Given that,

length l= 4 m

Width b= 5 m

Height h=7 m

Using the formula of surface area of rectangular prism

A= 2(bh+lb+lh)

We substitute the value into formula

A= 2(5*7+4*5+4*7)

A= 2(35+20+28)

A=2*83

A= 166 m^2

Hence, The surface area of rectangular prism is 166 m².

Answer:

166 m^2

Step-by-step explanation:

In a bag of marbles, you have 4 green, 3 yellow, 5 blue, and 8 red marbles. What is the probability of picking a green marble from the bag?a) 3/20
b) 1/5
c) 1/10
d) 1/4

Answers

4 + 3 + 5 + 8 = 20

4 / 20 = 1/5
A) 3/20 
add up all of the marbles and whatever is asking you for possibilities is the number of marbles is given you already. for example. i have a ticket for a raffle. so i got only 1 and there is 25 people more with a ticket. what are my chances of winning? 1 out of 25 right?(1/25) because i got 1 ticket if i had 2 it would be 2 out of 25 or (2/25) hope this helps. :)

Which expression demonstrates the use of the commutative property of addition in the first step of simplifying the expression (–1 + i) + (21 + 5i)?

Answers

Answer:

The given expression is (–1 + i) + (21 + 5i) : It demonstrates the use of the commutative property of addition in the first step of simplifying the expression. The property of commutativity is that the bracket can change its position i.e. (i + 21 )+ (5i-1)

Step-by-step explanation:
The given expression is (–1 + i) + (21 + 5i) : It demonstrates the use of the commutative property of addition in the first step of simplifying the expression. The property of commutativity is that the bracket can change its position i.e. (i + 21 )+ (5i-1)

Find the equation of the line through the given point and perpendicular to the given line(0,0);-2x+4y=12

Answers

-2x+4y=12 <=> y = (-1/2)x + 3 => the slope of given line is -1/2;

the new line and the given line are perpendicular =>( the slope of new line )*(-1/2) = -1 =>

the slope of new line is 2;

the equation of the new line is y -0  =2( x -0) <=> y = 2x.
-2x+0 is perpendicular to -2x+4y=12, and go through (0,0).
So the answer is -2x+0
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