What is the rate of change y= 29/5x. HELP ME PLS!!

etermine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. 3 2 x

nata0808 [166]

Answer:

(32/15, -2/5)

Step-by-step explanation:

(1) ³/₂x - 2y = 4

(2) x + ⅓y = 2

(3) 3x - 4y = 8 Multiplied (1) by 2

(4) 3x + y = 6 Multiplied (2) by 3

5y = -2 Subtracted (3) from (4)

(5) y = -⅖ Divided each side by 5

x + ⅓(-⅖) = 2 Substituted (5) into (2)

x - ²/₁₅ = 2

x = 2 + ²/₁₅ Added ²/₁₅ to each side

x = 32/15

The system of equations has only one solution: (32/15, -2/5).

3 0

2 years ago

In engineering, equilateral triangles can support the most weight and so are commonly found in the design of bridges and buildin

Dafna1 [17]

Answer:

60°

Step-by-step explanation:

Am equilateral triangle is a triangle that has all its sides and angles equal. Note that an equilateral triangle has 3 sides and angles.

Let the angles be a, b and c

The sum of angle in a triangle is 180°, hence;

a+b+c = 180°

Since a = b = c

The equation becomes;

a+a+a = 180°

3a = 180

a = 180/3

a = 60°

Hence the measure of the angles of an equilateral triangle is 60° for the three angles.

4 0

2 years ago

Which equation has the solutions x = -3 ± √3i/2 ?

Maurinko [17]

Answer:Answer is option C : [ $x^{2}$ + 3x + 3 ] =0

Note: None of options matches with given question.

instead of "-3" , there should be "- $\frac{3}{2}$ ".

Step-by-step explanation:

Note: None of options matches with given question.

instead of "-3" , there should be " $\frac{3}{2}$ ".

Here, First thing you have to observe the nature of roots.

∴ x = - $\frac{3}{2}$ + $\frac{\sqrt{3}}{2}$ i and x = - $\frac{3}{2}$ - $\frac{\sqrt{3}}{2}$

∴ [ x+( $\frac{3}{2}$ - $\frac{\sqrt{3}}{2}$ i) ][ x+( $\frac{3}{2}$ + $\frac{\sqrt{3}}{2}$ i) ]=0

∴ [ $x^{2}$ + x( $\frac{3}{2}$ + $\frac{\sqrt{3}}{2}$ i)+ x( $\frac{3}{2}$ - $\frac{\sqrt{3}}{2}$ i) + ( $\frac{3}{2}$ - $\frac{\sqrt{3}}{2}$ i)( $\frac{3}{2}$ + $\frac{\sqrt{3}}{2}$ i) ]=0

∴ [ $x^{2}$ + $\frac{3}{2}$ x + $\frac{\sqrt{3}}{2}$ ix + $\frac{3}{2}$ x - $\frac{\sqrt{3}}{2}$ ix + (3- $\frac{\sqrt{3}}{2}$ i)(3+ $\frac{\sqrt{3}}{2}$ i) ] =0

∴ [ $x^{2}$ + 3x + ( $\frac{3}{2}$ - $\frac{\sqrt{3}}{2}$ i)( $\frac{3}{2}$ + $\frac{\sqrt{3}}{2}$ i) ] =0

∴ [ $x^{2}$ + 3x + $\frac{9}{4}$ - ( $\frac{\sqrt{3}}{2}$ i)( $\frac{\sqrt{3}}{2}$ i) ] =0