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Stells [14]
3 years ago
14

If one side of a rectangle is increased by 12 and an adjacent side is decreased by 3 a rectangle is formed whose perimeter is 64

. What is the length of the side of the original square
Mathematics
1 answer:
Dima020 [189]3 years ago
8 0
The length of the side of the original square is 7cm

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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
A. A farmer irrigates her fields with 120,000 cubic yards of water. She has a 1,000-acre farm. How
horsena [70]

Answer:

120 cc yards of water

Step-by-step explanation:

A farmer has 1,000-acre farm. And she irrigates her fields with 120,000 cubic yards of water. We are asked to find how many cubic feet of water does she apply per acre?

1000 acre is irrigated by = 120000 cc yard of water

Hence 1 Acre is irrigated by

= \frac{120000}{1000} cc yards of water

Hence 1 Acre is irrigated by 120 cc yards of water .

8 0
3 years ago
No<br> please no please whyyyyyyy
mestny [16]

Answer:?

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
The number of books read by a mathematician 2 years after he turned 25 is given by the polynomial
stich3 [128]

Evaluating a function means to plug the required value, substituting every x occurrence with that value.

So, you have

f(x)=3x^2+80x \implies f(2) = 3\cdot 2^2+80\cdot 2 = 3\cdot 4 + 160 = 12+160=172

5 0
3 years ago
Consider the following: A medical researcher wants to determine the effects of pH (a measure of alkalinity or acidity, with pure
natita [175]

Answer:

See below

Step-by-step explanation:

<h3>Continuation of the question</h3>

<u>Data in the table:</u>

<u>PH             4       5     6     7     8    9     10     11 </u>

<u>Bacteria    116   120  131  136  141  151  148   163</u>

  • <em>Create a scatter plot to represent the data: Based on the data and your scatter plot, what do you think a good linear function would be to represent the data?</em>
<h3>Solution</h3>

<em>See attached for scatter plot</em>

We can see the chart is close to linear function. Let's build one based on data in the table

<u>The line will be in the form of:</u>

  • y = mx + b

<u>If we use two points and get the equation</u>

  • (4, 116) and (8, 141)

<u>Finding the slope:</u>

  • m = (141-116)/(8-4) = 25/4 = 6.25

<u>Then, finding y-intercept:</u>

  • 116 = 6.25*4 + b
  • b = 116 - 25 = 91

<u>So the line is:</u>

  • y = 6.25x + 91

<em>Note: This is approximate best fit graph and it is attached as well. Exact formula for the line is built by using different method and is very close to the one above</em>

4 0
3 years ago
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