Given: PKHE - inscribed, m∠E=120°,

Emma's square patio below has been area=31 sq ft. She decides to decrease one dimension by 1 foot and decreases the other dimens

Andreas93 [3]

Answer:

4.57ft by 1.57 ft

Step-by-step explanation:

We are given that

Emma's square patio has been area=31 sq.ft

One dimension decrease by 1 foot and other dimension decrease by 4 feet.

We have to find the new dimensions of Emma's patio.

Let x be the side of Emma's square patio

We know that

Area of square= $x^2$

$x^2=31$

$x=\sqrt{31}=5.57$ ft

One dimension= $5.57-1=4.57$ ft

other dimension= $5.57-4=1.57 ft$

Hence, the new dimension of Emma's patio is given by

4.57ft by 1.57 ft

5 0

2 years ago

A trampoline salesman makes $25,000 annually plus 6% commission on his total sales. If he sold $40,000 worth of trampolines this

Katarina [22]

Multiply sales by 6%

40,000 x 0.06 = 2,400

Add that to his base pay:

2400 + 25000 = $27,400 total pay.

5 0

1 year ago

A wall in Maria’s bedroom is in the shape of a trapezoid. The wall can be divided into a rectangle and a triangle. Using the 45°

Radda [10]

A wall is in the shape of a trapezoid and it can be divided into a rectangle and a triangle. A triangle is with angles 45°- 45° - 90°. The hypotenuse of that triangle is 13√2 ft.Using the 45° - 45° - 90° theorem, sides of that triangle are in the proportion:x : x : x√2, and since that x√2 = 13√2 ( hypotenuse ), x = 13.Therefore h = 13 ft.We can check it: c² = 13² + 13²,c² = 169 + 169c² = 338c = √ 338 = 13√2Answer: h = 13 ft

8 0

2 years ago

Read 2 more answers

The height of a cylinder is twice the radius of its base. A cylinder has a height of 2 x and a radius of x. What expression repr

cluponka [151]

<h2>Answer:</h2><h2>volume of the cylinder = 2π $x^{3}$ </h2>

Step-by-step explanation:

The height of a cylinder is twice the radius of its base.

Let the height of the cylinder = 2x

Let the radius of the cylinder = x

By formula, volume of the cylinder = π $r^{2}$ h

here r = x, h = 2x

substituting the values in the equation, we get

volume of the cylinder = π $r^{2}$ h = π $x^{2}$ (2x)

volume of the cylinder = 2π $x^{3}$

5 0

2 years ago

Read 2 more answers

On her first day in a hospital, Kiri receives u1 milligrams (mg) of a therapeutic drug. The amount of the drug Kiri receives inc

Valentin [98]

Answer:

a. 21 = u1 + 6·d

b. 29 = u1 + 10·d

c. d = 2, u1 = 9

Step-by-step explanation:

a. The given parameters are;

The amount of therapeutic drug Kiri receives on her first at the hospital = u1 milligrams

The amount of drug increase received by Kiri each day = d

The amount of drug Kiri received on the seventh day = 21 mg

The amount of drug she received on the eleventh day = 29 mg

Therefore, we have an arithmetic progression with the formula for the nth term given as follows;

aₙ = a₁ + (n - 1)·d

Where;

a₁ = u1

n = The number of terms

Therefore, for the 7th day, the amount of drugs she receives, which is 21 milligrams, is given as follows;

a₇ = u1 + (7 - 1)·d = u1 + 6·d = 21

The equation for the amount of drugs she receives in terms of u1 and d on the seventh day is given as follows;

21 = u1 + 6·d

b. For the eleventh day, the amount of drugs she receives, which is 29 milligrams, is given as follows;

a₁₁ = u1 + (11 - 1)·d = u1 + 10·d = 29

Therefore, the equation for the amount of drugs she receives in terms of u1 and d on the eleventh day is given as follows;

29 = u1 + 10·d

c. Therefore, we have two equations which are given as follows;

21 = u1 + 6·d................(1)

29 = u1 + 10·d..............(2)

Subtracting equation (1) from equation (2) gives;

29 - 21 = (u1 + 10·d) - (u1 + 6·d)

8 = 4·d

d = 8/4 = 2

d = 2

From equation (1), we have;

21 = u1 + 6·d = u1 + 6×2 = u1 + 12

21 = u1 + 12

21 - 12 = u1

∴ u1 = 9

d = 2, u1 = 9.

4 0

1 year ago