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Anika [276]
3 years ago
15

An architect is sketching a blueprint of a patio for a new fence. On the blueprint, C is the midpoint of segment AD. Point B is

the midpoint of segment AC. If BC = 8 feet, what is the length of AD?
Mathematics
1 answer:
Gre4nikov [31]3 years ago
4 0

Answer:

<u><em>The length of AD is 32 feet</em></u>

Step-by-step explanation:

<u>Proportional distances </u>

When distances are proportions of others, we can express all of them as relative fractions until we reach some known distance and solve for the desired length

Let's call x the length of AD. Given C is the midpoint of AD, then

\displaystyle AC=CD=\frac{x}{2}

Given B is the midpoint of AC, then

\displaystyle AB=BC=\frac{AC}{2}=\frac{x}{4}

If we know BC=8 feet

\displaystyle \frac{x}{4}=8\ feet

\displaystyle x=32\ feet

The length of AD is 32 feet

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Answer:

C. 4

Step-by-step explanation:

         Since this one is already graphed and we can see it clearely we can just count, but you can also do change in y over change in x (aka "rise over run") to find the slope.

         So, we count and find it is four up and one over. 4/1 = 4 = c

Hope this helps, have a nice day! :)

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The coordinate plane below shows the graph of a linear function of x. Which of the following equations best describes the functi
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1 year ago
Let a line l be given in the coordinate plane. What linear equation is the graph of line l?
LUCKY_DIMON [66]

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y=2/7x+2.5

Step-by-step explanation:

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2 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
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The positive integer is 6.
The consecutive integers are 6 and 7.
8 0
3 years ago
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