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2 years ago

Y= x + 6y= -x+2solve each system of equations by substitution

Mathematics

1 answer:

ser-zykov [4K]2 years ago

7 0

Answer:

x= -2
y=4

Step-by-step explanation:

Since we have an equation set equal to y, we can plug it in for either value of y.

I will be using y= x+6 in this case.

Plug in x+6 for the other equation, so instead of y=-x+2 it will now be that x+6 = -x+2

Now add x to both sides, and that will remove the x on the left side leaving us with 2x+6 = 2

Now, subtract 6 from both sides to get 2x isolated, and you will get 2x= -4

Divide both sides by 2 to get x= -2

Not plug x= -2 in back for the top (or bottom) equation and get that y=4

Hope this helps and isn't too complicated!

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The height of a can of coke is in 11 cm and the radius is 6 cm calculate the total surface area of the can in cm^3 assuming that

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The total surface area of the can of coke is 641.143 cm².

<h3>What is the total surface area of the can?</h3>

A can of coke has the shape of a cylinder. A cylinder is a three-dimensional object that is made up of a prism and two circular bases. The total surface area of a closed cylinder can be determined by adding the area of all its faces.

Total surface area of the closed cylinder = 2πr(r + h)

Where:

r = radius = 6cm
h = height = 11 cm
r = pi = 22 / 7

Total surface area of the closed cylinder = (2 x 22/7 x 6) x (6 + 11)

(264 / 7) x (17)

37.714 x 17 = 641.143 cm²

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2 years ago

A chef plans to mix 100% vinegar with Italian dressing. The Italian dressing contains 12%

Hitman42 [59]

Answer:

Amount of vinegar. 100% : 20 milliliters

Amount of Italian dressing: 140 milliliters

Step-by-step explanation:

Let's call A the amount of vinegar. 100%

Let's call B the amount of Italian dressing . 12% vinegar

The resulting mixture should have 23% vinegar, and 160 milliliters.

Then we know that the total amount of mixture will be:

$A + B = 160$

Then the total amount of pure antifreeze in the mixture will be:

$A + 0.12B = 0.23 * 160$

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Then we have two equations and two unknowns so we solve the system of equations. Multiply the first equation by -1 and add it to the second equation:

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$A + 0.12B = 36.8$

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$B = \frac{-123.2}{-0.88}$

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3 years ago

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Trava [24]

Answer:

use mathwsy

Step-by-step explanation:

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3 years ago

The numbers 1, 2, 3, 4, and 5 are written on slips of paper, and 2 slips are drawn at random one at a time without replacemen

mamaluj [8]

<h2>Answer:</h2>

(a)

The probability is : 1/2

(b)

The probability is : 1/2

<h2>Step-by-step explanation:</h2>

The numbers 1, 2, 3, 4, and 5 are written on slips of paper, and 2 slips are drawn at random one at a time without replacement.

The total combinations that are possible are:

(1,2) (1,3) (1,4) (1,5)

(2,1) (2,3) (2,4) (2,5)

(3,1) (3,2) (3,4) (3,5)

(4,1) (4,2) (4,3) (4,5)

(5,1) (5,2) (5,3) (5,4)

i.e. the total outcomes are : 20

(a)

Let A denote the event that the first number is 4.

and B denote the event that the sum is: 9.

Let P denote the probability of an event.

We are asked to find:

P(A|B)

We know that it could be calculated by using the formula:

$P(A|B)=\dfrac{P(A\bigcap B)}{P(B)}$

Hence, based on the data we have:

$P(A\bigcap B)=\dfrac{1}{20}$

( Since, out of a total of 20 outcomes there is just one outcome which comes in A∩B and it is: (4,5) )

and

$P(B)=\dfrac{2}{20}$

( since, there are just two outcomes such that the sum is: 9

(4,5) and (5,4) )

Hence, we have:

$P(A|B)=\dfrac{\dfrac{1}{20}}{\dfrac{2}{20}}\\\\i.e.\\\\P(A|B)=\dfrac{1}{2}$

(b)

Let A denote the event that the first number is 3.

and B denote the event that the sum is: 8.

Let P denote the probability of an event.

We are asked to find:

P(A|B)

Hence, based on the data we have:

$P(A\bigcap B)=\dfrac{1}{20}$

( since, the only outcome out of 20 outcomes is: (3,5) )

and

$P(B)=\dfrac{2}{20}$

( since, there are just two outcomes such that the sum is: 8

(3,5) and (5,3) )

Hence, we have:

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3 years ago

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Gekata [30.6K]

Answer: B. Square

Step-by-step explanation:

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3 years ago

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