Preston reads for 20 minutes each night and practices his math facts for 5 minutes each night. after several days, he had practiced maths facts for 45 minutes. how many minutes did preston read in the same time period? using tape diagram

For every 20 minutes read each night , maths fact practiced by Preston each night=5 Minutes

Now, Maths facts practiced by Preston =45 Minutes

⇒45 minutes=5 Minutes × 9

Number of Minute read by Preston is Directly proportional to Number of minutes he practices his maths facts.

Number of Minutes read by Preston in same time period=20 minutes ×9

 =180 minutes

=3 Hours

You can solve it by concept of Proportion.

a reflection across the x-axis , followed by the by a reflection across the y-axis , and then a scale dilation of 0.5 .

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°