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zavuch27 [327]
2 years ago
12

30 POINTS!!! Louie is trying to find a rectangular canvas for his art project. Its diagonal must measure 23.3 inches and form a

31° angle with the bottom of the canvas. What is the height of the canvas? Round your answer to the nearest inch. 12 inches 14 inches 24 inches 27 inches
Mathematics
2 answers:
Lisa [10]2 years ago
7 0

Answer:

12 inches

Step-by-step explanation:

Given

\theta = 31^{\circ}

diagonal = 23.3\ in

Required

Determine the height of the canvas

The question is illustrated using the attached image.

Using the attachment as a point of reference, the height is calculated from

sin \theta = \frac{opp}{hyp}

This gives:

sin 31^{\circ}= \frac{h}{23.3}

Make h the subject

h = 23.3 * sin(31^{\circ)

h = 23.3 * 0.5150\\

h = 11.9995

h = 12\ inches

zysi [14]2 years ago
5 0

Answer:

A 12 Inches

Step-by-step explanation:

I got it right on the test

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5x-23=87
add 23 to both sides
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To check your answer...
5(22)-23=87
110-23=87
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3 years ago
Solve the following quadratics. State the FACTORS AND SOLUTIONS. 1. 2x^2 - 7x + 3 2. 3x^2 + 7x +2
tekilochka [14]

Answer:

1. x = 3, 1/2 (solutions); (x - 3)(2x - 1) (factors)

2. x = -1/3, -2 (solutions); (3x + 1)(x + 2) (factors)

Step-by-step explanation:

<u>1. 2x^2 - 7x + 3</u>

To solve problem 1, you will need to identify your a, b, and c values in this quadratic function.

Since this problem is in standard form, it will be easy to identify these values. The standard form of a quadratic function is ax^2 + bx + c.

The a value is 2, the b value is -7, and the c value is 3 if we use our standard form and see which numbers are plugged into it.

Since we know that

  • a = 2
  • b = -7
  • c = 3

we can use the quadratic formula: x = \frac{-b~\pm~\sqrt{b^2~-~4ac} }{2a}

Substitute the a, b, and c values into the quadratic formula: x=\frac{-(-7)\pm\sqrt{(-7)^2-4(2)(3)} }{2(2)}

Now simplify using the laws of pemdas: x=\frac{7\pm\sqrt{(49)-(24)} }{4}

Simplify even further: x=\frac{7\pm\sqrt{(25)} }{4} \rightarrow x=\frac{7\pm (5) }{4}

Now split this equation into two equations to solve for x: x=\frac{12 }{4} ~~and~~ x=\frac{2 }{4}

12/4 can be simplified to 3, and 2/4 can be simplified to 1/2.

This means your solutions to problem 1 is 3, 1/2.

\boxed {x=3,\frac{1}{2} }

There is also another way to solve for the quadratic functions, and this was by factoring.

If you factor 2x^2 - 7x + 3 using the bottoms-up method, you will get (x - 3)(2x - 1).

After factoring, solving for the solutions is simple because all you have to do is set each factor to 0.

  • x - 3 = 0
  • 2x - 1 = 0

After solving for x by adding 3 to both sides, or by adding 1 to both sides then dividing by 2, you will end up with the same solutions: x = 3 and x = 1/2.

<u>2. 3x^2 + 7x + 2</u>

To save time I'll be using the bottoms-up factoring method, but remember to refer back to problem 1 (quadratic formula) if you prefer that method.

Factor this quadratic function using the bottoms-up method. After factoring you will have (3x + 1)(x + 2). These are your factors.

Now to solve for x and find the solutions of the quadratic function, you will set both factors equal to 0.

  • 3x + 1 = 0
  • x + 2 = 0

Solve.

<u>First factor:</u> 3x + 1 = 0

Subtract 1 from both sides.

3x = -1

Divide both sides by 3.

x = -1/3

<u>Second factor:</u> x + 2 = 0

Subtract 2 from both sides.

x = -2

Your solutions are x = -1/3 and x = -2.

\boxed {x = -\frac{1}{3} , -2}

7 0
3 years ago
I will give Branliest
Yuliya22 [10]
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Paraphin [41]

Answer:

1,000

Step-by-step explanation:

10*10*10= 1,000

next step

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5 0
2 years ago
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