From chapter Lines and angles

After school Philippe spent 1 3/4 hours at baseball practice, 2 1/4 hours on homework, and 1/4 hour getting ready for bed. About

marshall27 [118]

Answer:

4 hours. 1 3/4 is about 2, and 2 1/4 rounds to 2. 1/4 would round to 0, but it would not affect the estimate's accuracy much because we rounded up by 1/4 on 1 3/4 already. Philipe spent about 4 hours on activities.

Step-by-step explanation:

4 0

3 years ago

8-35. Use your knowledge of polygons to answer the questions below, if possible.

Nataliya [291]

Answer:

(a)I. 13 Sides II. 7 Sides

(b) 4 Sides, Square

(c)x=52 degrees

(d)x=107 degrees

(e)1620 degrees

Step-by-step explanation:

(a)The Sum of the Interior angle of polygon with n sides is derived using the formula: (n-2)180.

I. If the Interior angle is $1980^0$

Then:

$(n-2)180^0=1980^0\\$Divide both sides by 180^0 $ to isolate n$\\n-2=11\\$Add 2 to both sides of the equation\\n-2+2=11+2\\n=13$

The polygon has 13 sides.

II. If the Interior angle is $900^0$

Then:

$(n-2)180^0=900^0\\$Divide both sides by 180^0 $ to isolate n$\\n-2=5\\$Add 2 to both sides of the equation\\n-2+2=5+2\\n=7$

The polygon has 7 sides.

(b)The sum of the exterior angle of a polygon is 360 degrees,

Each exterior angle of a n-sided regular polygon is: $\frac{360^0}{n}$

If the exterior angle of a regular polygon is 90°

Then:

$90\°=\frac{360^0}{n}\\ 90n=360\\n=4$

The regular polygon has 4 sides and it is called a Square.

(c)The Sum of the Interior angle of polygon with n sides is derived using the formula: (n-2)180.

Each Interior angle of a regular n-sided polygon is: $\frac{(n-2)180^0}{n}$

For a pentagon, n=5

Then:

$\frac{(5-2)180^0}{5}=2x+4\\108=2x+4\\108-4=2x\\104=2x\\x=52^0$

(d)The sum of the exterior angle of a polygon is 360 degrees.

If four of the exterior angles of a pentagon are 57, 74, 56, and 66.

Let the fifth angle=x

Then:

$57+74+56+66+x=360^0\\253+x=360\\x=107^0$

(e)The Sum of the Interior angle of polygon with n sides is derived using the formula: (n-2)180.

In an 11-gon., n=11

Therefore, the sum of the interior angle=(11-2)180= $1620^0$

The sum of the interior angle does not change either in a regular or irregular polygon.

3 0

3 years ago

Use logarithmic differentiation to find dy/dx

liq [111]

Answer:

dy/dx = (x^2 - 3)^sin x [2x sin x/ (x^2 - 3) + cos x ln(x^2 - 3)]

Step-by-step explanation:

y = (x^2 - 3)^sinx

ln y = ln (x^2 - 3)^sinx

ln y = sin x * ln (x^2 - 3)

1/y * dy/dx = sin x * {1 / (x^2 - 3)} * 2x + ln(x^2 - 3) * cos x

1/y dy/dx = 2x sin x/ (x^2 - 3) + cos x ln(x^2 - 3)

dy/dx = [2x sin x/ (x^2 - 3) + cos x ln(x^2 - 3)] * y

dy/dx = (x^2 - 3)^sin x [2x sin x/ (x^2 - 3) + cos x ln(x^2 - 3)]

7 0

3 years ago

Several years ago, 39% of parents who had children in grades K-12 were satisfied with the quality of education the students r

Mkey [24]

Answer:

let p be the population proportion of parents who had children in grades k-12 were satisfied with the quality of education the students receive.

Step-by-step explanation:

6 0

3 years ago

Barry read for 15 more minutes than Robert.

Greeley [361]

Hi!

C. v + 15

Barry read for 15 MORE minutes than Robert.

6 0

4 years ago