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3 years ago

I don't understand the substitution method?

1 answer:

6 0

It depends on what variable you are tying to solve for first. Say you are trying to solve for x first and then y on the first problem you wrote.

In substitution you solve one of the equations for example with
6x+2y=-10
2x+2y=-10
you solve 2x+2y=-10 for x

2x+2y=-10
-2y = -2y (what you do to one side of the = you do to the other)
2x=-10-2y (to get the variable by its self you divide the # and the variable)
/2=/2 (-10/2=-5 and -2y/2= -y or -1y, they are the same either way)
x=-5-y

now you put that in your original equation that you didn't solve for:
6(-5-y)+2y=-10 solve for that
-30-6y+2y=-10 combine like terms
-30-4y=-10 get the y alone and to do this you first get the -30 away from it
+30=+30
-4y=20 divide the -4 from each side
/-4=/-4 (20/-4=-5)
y=-5

now the equation you previously solved for x can be solved for y.
x=-5-y
x=-5-(-5) a minus parenthesis negative -(- gives you a positive
-5+5=0
x=0

and now we have solved the problem. x=0 and y=-5

You might be interested in

Based on the pattern in the table what is the value of A

Arlecino [84]

Answer D, 1/64

The denominator has a pattern , if you look through it carefully each denominator is multiply by 2. There for you multiply 32 x 2 which gives you 64 so it’s 1/64. If you wanna confirm it , you could use a calculator to check your answer.

5 0

3 years ago

Read 2 more answers

Tom has a 500 gallon pool. He is able to drain it at a rate of 15 gallons per minute. if the pool still has 170 gallons of wa

Akimi4 [234]

Answer: 22 minutes

Step-by-step explanation: 500-170 means that he drained 330 gallons of water so 330 divided by 15 gallons a minute so you get 22 so it takes 22 minutes to have 170 gallons left in the pool

8 0

3 years ago

This is the pond in a shape of a prism, it is completely full of water. Colin uses a pump to empty the pond. The level goes down

AnnZ [28]

Answer:

150 minutes

Step-by-step explanation:

P.S - The exact question is -

Given - This is the pond in a shape of a prism, it is completely full of

water. Colin uses a pump to empty the pond. The level goes

down by 20 cm in the first 30 min.

To find - Work put how many minutes Colin has to wait for the pond

to completely empty.

Proof -

Given that,

Height of prism = 1 m

Also,

Base of the prism is trapezium and

Sides of the trapezium are 0.6 m and 1.4 m

Height of trapezium is 2 m

We know that,

Area of trapezium = $\frac{1}{2}$ × (sum of sides)× height

= $\frac{1}{2}$ × (0.6 + 1.4)× 2

= $\frac{1}{2}$ × (2)× 2

= 2 m²

⇒Area of trapezium = 2 m²

Now,

Volume of prism = Area of trapezium × height of prism

= 2 m² × 1 m

= 2 m³

⇒Volume of prism = 2 m³

Now,

Given that the level goes down by 20 cm in the first 30 min

We know

100 cm = 1 m

⇒1 cm = $\frac{1}{100} m$ = 0.01 m

⇒20 cm = 20×0.01 m = 0.2 m

⇒The level goes down by 0.2 m in the first 30 min.

Also,

we know that height of water = height of prism = 1 m

So, the remaining water left in the pond = 1 m - 0.2 m = 0.8 m

Also,

Volume of Remaining water = Area of trapezium × height

= 2 m² × 0.8 m

= 1.6 m³

⇒Volume of Remaining water = 1.6 m³

Now,

Volume of emptied water = Total Volume - Volume of Remaining water

= 2 m³ - 1.6 m³

= 0.4 m³

⇒Volume of emptied water = 0.4 m³

Now,

0.4 m³ water will be empty in 30 minutes

⇒ 1 m³ water will be empty in $\frac{30}{0.4}$ = 75 minutes

⇒1.6 m³ water will be empty in 1.6 × 75 = 120 minutes

∴ we get

The remaining water is empty in 120 minutes

So,

Total pond is empty in 120 + 30 minutes

⇒Total pond is empty in 150 minutes

5 0

3 years ago

Hey can you please help me!

melisa1 [442]

Answer:

Step-by-step explanation:

1) Tangent makes 90 degrees with the radius. Hence

a) Angle ABD = 90-angle BDC = 90-61.3 = 28.7

b) Triangle BCD is isosceles since tangents have equal length.

Hence angle BCD = 180-(61.3+61.3) = 57.4

c) Angle BDC = 57.4 (since triangle BCD is isosceles)

d) Angle BAC and Angle BCD are supplementary. Hence angle BAC = 122,6

-------------------------------------------

2) Arc length of minor arc BC = $\frac{79.3}{360} (24) = 5.287$

b) ARc length of minor arc = circumference -minor arc

= 18.713

---------------------------------------------

3) circumference = pi d = $3.14(9) = 28.26$

6 0

3 years ago

Please help! Brainliest

Mama L [17]

1.301

Explanation:

Given:

$\log_a5 \approx 0.699$ and $\log_a2 \approx 0.301$

Note that from the properties of logarithms,

$\log_a20 = \log_a(5×4)$

$\:\:\:\:\:\:\:\:\:\:= \log_a(5×2^2)$

$\:\:\:\:\:\:\:\:\:\:=\log_a5 + \log_a(2)^2$

$\:\:\:\:\:\:\:\:\:\:=\log_a5 + 2\log_a2$

$\:\:\:\:\:\:\:\:\:\:\approx 0.699 + 2(0.301)$

$\:\:\:\:\:\:\:\:\:\:= 1.301$

6 0

3 years ago