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pashok25 [27]
4 years ago
15

For the rectangle with given area of 10x^2+11x+3 determine the binomial factors that describes the dimensions.

Mathematics
1 answer:
rjkz [21]4 years ago
5 0
<h3>Answer: The two factors are 5x+3 and x+1</h3>

=========================================

Explanation:

We could use the AC factoring method here. Multiply the first coefficient (10) with the last term (3) to get 10*3 = 30.

We need to find factors of 30 that add to 11

1+30 = 31

2+15 = 17

3+10 = 13

5+6 = 11

we have found the pair of factors that add to 11. So we'll break the 11x into 5x+6x and then use factor by grouping method

10x^2 + 11x + 3

10x^2 + 5x + 6x + 3

(10x^2 + 5x) + (6x + 3)

5x(2x + 1) + 3(2x + 1)

(5x+3)(2x+1)

We see the two factors are 5x+3 and 2x+1.

To check the answer, use either the box method, distribution, or FOIL rule to expand out (5x+3)(2x+1) and you should get 10x^2+11x+3 again.

--------------------------------

As an alternative, you can solve 10x^2+11x+3 = 0 through any method you prefer (graphing, completing the square, quadratic formula). The quadratic formula is the best option as it works for any quadratic. The two solutions you should get are x = -3/5 and x = -1/2

Using x = -3/5 and x = -1/2, we can do the following

  • x = -3/5 becomes 5x = -3 after multiplying both sides by 5, then you add 3 to both sides to get 5x+3 = 0
  • x = -1/2 becomes 2x = -1 after multiplying both sides by 2, and then turns into 2x+1 = 0 after adding 1 to both sides

Note how we have the 5x+3 and 2x+1 as found in the section above. At this point we can stop as we found the factors needed. I'm using the zero product property which says that if A*B = 0, then either A = 0 or B = 0.

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Write the absolute value equation if it has the following solutions.
Alborosie

The absolute value equation is x^{2} +x-8.75=0, if the solutions are x=2.5 and x=-3.5.

Step-by-step explanation:

The given is,

                Two solutions: x = 2.5 and x = -3.5

Step:1

               In this question we use reverse method of quadratic equation solve method,

               From first solution, x = 2.5

                                       x - 2.5 = 0..........................(1)

               From the second solution, x = -3.5

                                               x + 3.5 = 0.................(2)

                From the equations (1) and (2),

                          ( x - 2,5 ) ( x + 3.5 )  = 0

               Multiply the equations,

                   (x^{2} +3.5x-2.5x-8.75)=0

                                     x^{2} +x -8.75=0

Step:2

            Check for solution,

                              x^{2} +x -8.75=0..........................(3)

            Substitute the value of x=2.5 in above equation,

                          2.5^{2} +2.5 -8.75=0

                         6.25 + 2.5 - 8.75 = 0

                                                 0 = 0          

Result:

           The absolute value equation is x^{2} +x-8.75=0, if the solutions are x=2.5 and x=-3.5.  

3 0
3 years ago
Suppose 60% of the graduating class in a certain high school goes on to college. If 126 students from this graduation class are
nikitadnepr [17]

Answer: 210

percent * base = amount

.6 * base = 126

base = 126/.6

x = 210

Step-by-step explanation:

5 0
3 years ago
What is the area of this trapezoid? Enter your answer in the box. ____ units2
Inga [223]
The Area of the trapezoid is 88 not 91
6 0
3 years ago
Read 2 more answers
1. The nominal rate on Sandra's loan is 7.125%. If the interest is compounded monthly, what rate of
Mrrafil [7]

Answer:

She is actually paying a rate of 7.36% of interest.

Step-by-step explanation:

The real interest rate, as a decimal, is given by:

I = (1 + \frac{r}{n})^{n}

In which r is the interest rate and n is the number of compoundings during an year.

The nominal rate on Sandra's loan is 7.125%, compounded monthly:

This means that r = 0.07125, n = 12

So

I = (1 + \frac{0.07125}{12})^{12} = 1.0736

As a percentage: 1.0736*100 = 107.36% - 100% = 7.36%

She is actually paying a rate of 7.36% of interest.

5 0
3 years ago
(The photo is too big to fit so don't mind that.)
mafiozo [28]

Answer:

82

Step-by-step explanation:

1'st step: a^{2} + b^{2}= c^{2} is the formula for the pythagorean theorem

2'nd step : 18^{2} + 80^{2} =  c^{2}

3'rd step:   324+6400 =  c^{2}

4'rd step: 6724=  c^{2}

5'th step: \sqrt{6724} =82

6'th step : therefore the value of c is 82 cm

8 0
3 years ago
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