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Vlada [557]
2 years ago
10

Solve the following system: 3x + 2y = 7 -4.5x - 3y = -10.5

Mathematics
1 answer:
valentina_108 [34]2 years ago
4 0

Answer:

<u>infinitely many solutions</u>

Step-by-step explanation:

The system of equations :

  1. 3x + 2y = 7
  2. -4.5x - 3y = -10.5

Multiplying Equation 1 times 3 and Equation 2 times 2 :

  • 9x + 6y = 21
  • -9x - 6y = -21

Putting the equations in standard form after simplifying :

  1. 6y = -9x + 21 ⇒ <u>y = -1.5x + 3.5</u>
  2. -6y = 9x - 21 ⇒ <u>y = -1.5x + 3.5</u>

<u />

As both equations are the same, the system will have <u>infinitely many solutions</u>.

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Cant figure out the improper and mixed
Ymorist [56]
The mixed number for this diagram would be: 4 5/6
The improper fraction would be: 29/6
That’s going off of the whole diagram.
6 0
3 years ago
You have 42 ft. of fencing (1 ft. segments) to make a rectangular garden. How much should each side be to maximize your total ar
Verizon [17]

Answer:

Length=10.5\ ft

Width=10.5\ ft

Area=110.25\ ft^{2}

Step-by-step explanation:

Let

x----> the length of the rectangular garden

y---> the width of the rectangular garden

we know that

The perimeter of the rectangle is equal to

P=2(x+y)

we have

P=42\ ft

so

42=2(x+y)

simplify

21=(x+y)

y=21-x------> equation A

Remember that the area of rectangle is equal to

A=xy ----> equation B

substitute equation A in equation B

A=x(21-x)

A=21x-x^{2}----> this is a vertical parabola open downward

The vertex is a maximum

The y-coordinate of the vertex is the maximum area

The x-coordinate of the vertex is the length side of the rectangle that maximize the area

using a graphing tool

The vertex is the point (10.5,110.25)

see the attached figure

so

x=10.5\ ft

Find the value of y

y=21-10.5=10.5\ ft

The garden is a square

the area is equal to

A=(10.5)(10.5)=110.25\ ft^{2} ----> is equal to the y-coordinate of the vertex is correct

6 0
3 years ago
a right triangle is rotated a round a line that includes one of the legs of the triangle. What figure is located?
Crank

Answer: Its a cone

Explanation:

When a right angle triangle is rotated about any of its leg a cone is formed.

5 0
3 years ago
With reference to the figure, sin X equals?<br> 1.) 0.250<br> 2.)0.447<br> 3.)0.894<br> 4.)1
Flura [38]

Answer:

3.) 0.894

Step-by-step explanation:

✔️First, find BD using Pythagorean Theorem:

BD² = BC² - DC²

BC = 17.89

DC = 16

Plug in the values

BD² = 17.89² - 16²

BD² = 64.0521

BD = √64.0521

BD = 8.0 (nearest tenth)

✔️Next, find AD using the right triangle altitude theorem:

BD = √(AD*DC)

Plug in the values into the equation

8 = √(AD*16)

Square both sides

8² = AD*16

64 = AD*16

Divide both sides by 16

4 = AD

AD = 4

✔️Find AB using Pythagorean Theorem:

AB = √(BD² + AD²)

AB = √(8² + 4²)

AB = √(64 + 16)

AB = √(80)

AB = 8.9 (nearest tenth)

✔️Find sin x using trigonometric ratio formula:

Reference angle = x

Opposite side = BD = 8

Hypotenuse = AB = 8.944

Thus:

sin(x) = \frac{opp}{hyp} = \frac{8}{8.944} = 0.894 (nearest thousandth)

6 0
3 years ago
What is 90 divided by 9 + 72 divided by 12
grandymaker [24]

Answer: That's 16 i hope this helps

4 0
3 years ago
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