A recipe for sparkling water calls for 1 1/2 quarts of sparkling water and 3/4 quarts of grape juice how much sparkling water will you need to mix 9 quarts of grape juice

18 quarts

Step-by-step explanation:

Quantity of sparkling water and gape juice are used in proportion in  the recipe.

Let x=  quantity of sparkling water when 9 quarts of grape juice is used.

Then,

Hence, 18 quarts of sparkling water is required to mix with 9 quarts of grape juice.

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°