MATHEMATICS MIDDLE SCHOOL

The coordinates below represent two linear equations. How many solutions does this system of equations have?

Line 1
x y
–4 5
0 2
Line 2
x y
0 5
4 2


A.
0

B.
exactly 1

C.
exactly 2

D.
infinitely many

Answers

Answer 1
Answer: so solve for the equations of the lines
y=mx+b
m=slope
b=y intercept

line 1=
(-4,5)
(0,2)
(x,y)
slope=(y1-y2)/(x1-x2)
x1=-4
y1=5
x2=0
y2=2
subsitute
(5-2)/(-4-0)=3/-4=-3/4
slope=-3/4
subsitute
y=-3/4x+b
subsitute one of the points
(0,2)
x=0 and y=2 is one solution
2=-3/4(0)+b
2=0+b
2=b
the equation is y=-3/4x+2



other line
(0,5)
(4,2)
x1=0
y1=5
x2=4
y2=2
sybsitute
(5-2)/(0-4)=3/-4=-3/4
slope=-3/4
subsitute
y=-3/4x+b
now subsitute one of the points to solve for b
(0,5)
x=0 and y=5 is one solution
5=-3/4(0)+b
5=0+b
5=b
y=-3/4x+5

so we have the lines/equations
y=-3/4x+2 and y=-3/4x+5
(at this point we can see that since slopes are the same and the y intercepts are different, they are paralell and therefor have 0 solutions, but for those who don't know paralellline thingie read on)

solve for  common (x,y)
y=-3/4x+2
y=-3/4x+5
subsitute
-3/4x+2=y=-3/4x+5
-3/4x+2=-3/4x+5
subtract 2 from both sides
-3/4x=-3/4x+5
add 3/4x to both sides
0=5
fasle
there are no solutions

the answer is A: 0 solutions
Answer 2
Answer:

Answer:

i just want the point because i dont have any go sit on a

Step-by-step explanation:

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The expression 4x/5 - 2x/5 is equivalent to...a.) x/2
b.) x/5
c.) x/15
d.) 2x/15

Answers

If you would like to know the equality of the expression 4 * x/5 - 2 * x/5, you can calculate this using the following steps:

4 * x/5 - 2 * x/5 = (4 - 2) * x/5 = 2 * x/5

The correct result is 2 * x/5, which is none of the results written above.

How would I write these problems?

Answers

21) Total number of cups: 26

6) Solution of the equation: x = -12

7) Father's age: 40

4) Distance driven: 400 miles

Step-by-step explanation:

21)

Let's call:

h=10 cm the height of each cup

H=30 cm the total height available in the dispenser

We are told that each cup added to the stack add a height of

\Delta h = 0.8 cm

We can therefore solve the problem by writing the following equation:

H=h+N\Delta h

which means that the total height available (H) is filled by the height of one cup (h) + the number of additional cup multiplied by 0.8.

Solving for N:

N=(H-h)/(\Delta h)=(30-10)/(0.8)=25

And including the first cup, the total number of cups is

N+1=25+1=26

6)

The equation that we have to solve is

(5)/(2)x-1=-31

We proceed as follows:

First of all, we add +1 on both sides of the equation,

(5)/(2)x-1+1=-31+1\n(5)/(2)x=-30

Now we multiply by 2 on both sides:

(5)/(2)x\cdot 2=-30\cdot 2\n5x=-60

And now we divide both sides by 5:

(5x)/(5)=(-60)/(5)\nx=-12

7)

Let's call:

k = Karma's age

f = father's age

We are told that Karma is 13 years old, so

k = 13

Also, Karma's age is 2 years less than 3/8 of the father's age, so we can write

k=(3)/(8)f-2

By combining the two equations,

13=(3)/(8)f-2

And solving for f, we find:

(3)/(8)f=13+2\n(3)/(8)f=15\n3f=15\cdot 8 =120\nf=(120)/(3)=40

So, the father's age is 40.

4)

Let's call:

T = 16 the total volume of the tank (16 gallons)

We also know that the car burns 0.03 gallons per mile, so the amount of fuel consumed after x miles is

0.03 x

This means that the amount of fuel left after x miles is

16-0.03x

We also know that the amount of fuel left is 4 gallons, therefore:

16-0.03x=4\n0.03x=16-4\n0.03x=12\nx=(12)/(0.03)=400

So, 400 miles.

Learn more about equations:

brainly.com/question/13168205

brainly.com/question/3739260

#LearnwithBrainly

Jorge wants the ratio of tulips to daisies in his garden to be 2 to 5. He does not want to take any flowers out of his garden. How many of what type of flower should he plant in order to get the desired ratio?

Answers

Dont know because it doesnt say how many flowers are in the garden

How would you replace 27/50 with the nearest half or whole number without using a number line?

Answers

25/50 = 1/2 soooooooooooooooooooooooooooooooooo

Pedro bought lb of red sand and lb of brown sand to refill his sand box. Both types of sand cost $4.60 a pound. How much did Pedro spend on the sand? A. $29.85 B. $31.05 C. $33.05 D. $33.75

Answers

If we know that Pedro bought 1 (1)/(4) pounds of red sand, and 5 (1)/(2) pounds of brown sand, and they both cost $4.60, then we just have to add the individual amounts of sand, since they cost the same.

1 (1)/(4) + 5 (1)/(2) = 6 (3)/(4)

So Pedro bought 6 (3)/(4) lbs of sand overall. Now, we just need to multiply the cost per pound by the total amount of sand he bought.

6 (3)/(4) * 4.6 = 31.05

Pedro spent $31.05 on sand, which is answer choice B.
Hope that helped =)
b. $31.05
5.5 + 1.25 = 6.75
6.75 * $4.60 = $31.05

500 people fill up 4/9 of the hall. What is the seating capacity of the hall?

Answers

the answer would be 1125 because you have to divide 500 by 4 then multiply it by 9
If 4/9 of the hall hold 500 people, then 1/9 of the hall holds 125 people.
Times that by 9 and you have your answer which is 1125 people.
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