One of the roots of the equation 5x^2-36x+t=0 is five times as big as the other root. Find the value of t.

t = 36

Step-by-step explanation:

If you divide the equation by 5, you have ...

 x^2 -7.2x +t/5 = 0

The opposite of the sum of the roots is the coefficient of the linear term, so is 7.2. If the roots are "r" and "5r", then their sum is r+5r = 6r, so the value of r is.

 7.2/6 = 1.2

The roots are 1.2 and 5·1.2 = 6.

The constant term t/5 is the product of the roots, so ...

 t/5 = 1.2 · 6

 t = 6·6 = 36 . . . . . multiply by 5

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°