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valina [46]
2 years ago
14

How do I solve qudratic equations with factions, like this one:

0" id="TexFormula1" title=" \frac{5}{3} " alt=" \frac{5}{3} " align="absmiddle" class="latex-formula">x²-5= 0
Mathematics
1 answer:
IceJOKER [234]2 years ago
8 0
There are several approaches.

(5/3)x^2 - 5 = 0 has the coefficients a=5/3, b=0 and c = -5.

Thus, the quadratic formula would be appropriate here:

         -0 plus or minus sqrt(0^2 - 4(5/3)(-5) )
x  = -------------------------------------------------------
                                 2(5/3)
         plus or minus sqrt(100/3)
    = ------------------------------------
                         10/3
            3      10
     = ------* ----------- = sqrt(3)    (answer)
          10     sqrt(3)
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The perimeter of a triangular field is 120m. Two of the sides are 21m and 40m.Calculate the largest angle of the field.
Mama L [17]

Answer:

the largest angle of the field is 149⁰

Step-by-step explanation:

Given;

perimeter of the triangular filed, P = 120 m

length of two known sides, a and b = 21 m and 40 m respectively

The length of the third side is calculated as follows;

a + b + c = P

21 m  + 40 m  + c = 120 m

61 m +  c = 120 m

c = 120 m - 61 m

c = 59 m

                         B

                     ↓            ↓  

                  ↓                          ↓

                ↓                                       ↓

            A →  →  → →  →  → →  → →    →    →  C

Consider ABC as the triangular field;

Angle A is calculated by applying cosine rule;

a^2 = b^2 + c^2 - 2bc \ Cos A\\\\Cos \ A = \frac{b^2 + c^2 - a^2}{2bc} \\\\Cos \ A = \frac{40^2 + 59^2 - 21^2}{2 \times 40 \times 59} \\\\Cos \ A = 0.983\\\\A = Cos ^{-1} (0.983)\\\\A = 10.6 \ ^0

Angle B is calculated as follows;

Cos \ B = \frac{a^2 + c^2 - b^2}{2ac} \\\\Cos \ B = \frac{21^2 + 59^2 - 40^2}{2 \times 21 \times 59} \\\\Cos \ B = 0.937\\\\B= Cos ^{-1} (0.937)\\\\B = 20.5 \ ^0

Angle C is calculated as follows;

Cos \ C = \frac{a^2 + b^2 - c^2}{2ab} \\\\Cos \ C = \frac{21^2 + 40^2 - 59^2}{2 \times 21 \times 40} \\\\Cos \ C = -0.857\\\\C = Cos ^{-1} (-0.857)\\\\C = 149\ ^0

Therefore, the largest angle of the field is 149⁰.

       

8 0
3 years ago
Find the solution to the following system using substitution or elimination: y = 3x + 2 y = -2x - 8 O A. (-5,-) OB. (-2,-4) O C.
mr Goodwill [35]

Answer:

B. (-2,-4)

Explanation

Given equations:

   y = 3x + 2

   y = -2x - 8

Solving both equations will yield the values of x and y;

Solution:

   y = 3x + 2    ----- (i)

   y = -2x - 8   ------ (ii)

Using substitution method, input equation i, into ii

    3x + 2 = -2x - 8

Collect like terms and solve;

     3x + 2x = -8 -2

         5x  = -10

            x  = -2

Then put x = -2 into i, to find y

      y = (-2 x 3) + 2

       y = -6 + 2 = -4

So, the solution of the equation is B. (-2,-4)

6 0
2 years ago
The blue figure is a translation of the black image. Write a rule to describe the translation.
vivado [14]

Answer:

The point at the Origin was moved down 4 and right 2

Step-by-step explanation:

5 0
2 years ago
Help this question question
Step2247 [10]

Answer:

-65 i suppose

Step-by-step explanation:

7 0
2 years ago
In the following exercises, multiply the binomials. Use any method.<br> 241. (x + 8)(x + 3)
Lelu [443]

Answer:

Hence the expression $(x+8)(x+3)=x^{2}+11 x+24$.

Step-by-step explanation:

- The given expression is (x+8)(x+3).

- We have to multiply the given expression.

- Multiply the (x+8) by 3 , multiply the (x+8) by x then add like terms.

$$\begin{array}{r}x+8 \\\underline {\times \quad x+3} \\3 x+24 \\\underline {x^{2}+8 x+24} \\x^{2}+11 x+24\end{array}$$

5 0
1 year ago
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