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2 years ago

Find the solution to the system of equations. 1 + 3y = 4 2r + 5y = 12

Mathematics

1 answer:

ivann1987 [24]2 years ago

5 0

Answer: {x,y}={-1,2}

step-by-step explanation:

// Solve equation [2] for the variable x

[2] 2x = 5y - 12

[2] x = 5y/2 - 6

// Plug this in for variable x in equation [1]

[1] 2•(5y/2-6) + 3y = 4

[1] 8y = 16

// Solve equation [1] for the variable y

[1] 8y = 16

[1] y = 2

// By now we know this much :

x = 5y/2-6

y = 2

// Use the y value to solve for x

x = (5/2)(2)-6 = -1

Solution :

{x,y} = {-1,2}

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aksik [14]

Kaitlin bought 4 pounds of coffee.

70-39.24=30.76
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3 years ago

The length of each side of an equilateral triangle is increased by 20%, resulting in triangle ABC. If the length of each side of

kompoz [17]

Answer: Area of ΔABC is 2.25x the area of ΔDEF.

Step-by-step explanation: Because equilateral triangle has 3 equal sides, area is calculated as

$A=\frac{\sqrt{3} }{4} a^{2}$

with a as side of the triangle.

Triangle ABC is 20% bigger than the original, which means its side (a₁) measures, compared to the original:

a₁ = 1.2a

Then, its area is

$A_{1}=\frac{\sqrt{3} }{4}(1.2a)^{2}$

$A_{1}=\frac{\sqrt{3} }{4}1.44a^{2}$

Triangle DEF is 20% smaller than the original, which means its side is:

a₂ = 0.8a

So, area is

$A_{2}=\frac{\sqrt{3} }{4} (0.8a)^{2}$

$A_{2}=\frac{\sqrt{3} }{4} 0.64a^{2}$

Now, comparing areas:

$\frac{A_{1}}{A_{2}}= (\frac{\sqrt{3}.1.44a^{2} }{4})(\frac{4}{\sqrt{3}.0.64a^{2} } )$

$\frac{A_{1}}{A_{2}} =$ 2.25

The area of ΔABC is 2.25x greater than the area of ΔDEF.

7 0

3 years ago

PLEASE HELP ME I DO NOT UNDERSTAND WHAT TO DO COULD SOMEONE HELP ME PLEASE THANK YOU I REALLY APPRECIATE IT

mamaluj [8]

a.) A flat pattern that could be folded to make a 3-dimensional figure is called a "net." You can draw one for Tyler's bench by picking any surface of that rectangular prism and making a drawing of it. At any edge you choose, you can add the adjacent surface to your drawing. Keep doing this until all 6 surfaces are shown in their correct relationship to adjacent surfaces. An example is attached. (This is not the only way the net can be drawn.)

Interior lines of the net can be solid or dashed as you wish. I have shown some of them dashed so as to better illustrate how the area can be computed.

b.) The area of this figure represents the surface area of the rectangular prism. The dimensions of each surface will be 1×1.5, 1×5, or 1.5×5. There are two surfaces with each pair of dimensions. (Perhaps you can find each of these rectangles on the net diagram. Ones with the same dimensions are opposite faces of the rectangular prism.) We can add up the areas of the smaller rectangles to find the total, or we can take advantage of the drawing and divide the area into a smaller number of larger chunks that may make the computation easier.

For example, the rectangle AI that is shaded red is 5×4 in size, for a total of 20 ft². The rectangle KN that is shaded green is 8×1 in size, for a total of 8 ft². Then the total amount of cloth Tyler needs to reupholster his bench is

... 20 ft² + 8 ft² = 28 ft²

8 0

3 years ago

Please help me , at least do one and explain it please .

Len [333]

9514 1404 393

Answer:

113.0 cm²
2464.0 in²
95.0 ft²

Step-by-step explanation:

1. The area of a circle is given by the formula ...

A = πr² . . . . . where r is the radius

The radius is shown as 6 cm, so the area is ...

A = (3.14)(6 cm)² = 113.0 cm²

2. The radius is shown as 28 in. We note that this is a number divisible by 7, so we choose 22/7 for π.

A = (22/7)(28 in)² = 2464 in² . . . . see comment

3. The radius is half the diameter, so is 11/2 = 5.5 ft. Then the area is ...

A = (3.14)(5.5 ft)² = 95.0 ft²

_____

Additional comment

If you use a more exact value of π for problem 2, the area is 2463.0 in². If you use 3.14 as the value of π, the area rounds to 2461.8 in². For these values of pi (3.14 or 22/7), the answer is only good to about 3 significant digits. 2464 has more significant digits, so digits beyond the first 3 may be in error.

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2 years ago

The cafe sells Beetle Juice and Potion Punch. A cup of Beetle Juice costs $2.50 and a cup of Potion Punch costs $3. Owen ordered

nexus9112 [7]

Answer:

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Step-by-step explanation:

j = Beetle Juice cost $2.50

p = Potion Punch Cost $3

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- .50j = -1

j = 2 Beetle Juice

Substitute into the fist equation and solve for y j + p = 5

2 + p = 5

p = 3 Potion Punch

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2 years ago