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FIND THE VOLUME OF THE SPHERE

svp [43]

Answer:

about 65.4 inches cubed

Step-by-step explanation:

The formula for the volume of a sphere is 4/3πr^3.

V = 4/3πr^3

= 4/3π(2.5^3)

= 20.83π = <u>about 65.4 inches cubed</u>

4 0

3 years ago

Given: mAngleEDF = 120°; mAngleADB = (3x)°; mAngleBDC = (2x)° Prove: x = 24 3 lines are shown. A line with points E, D, C inters

N76 [4]

Answer:

" Vertical angles are congruent " ⇒ 2nd answer

Step-by-step explanation:

* <em>Look to the attached figure </em>

- There are three lines intersected at point D

- We need to find the missing in step 3

∵ Line FA intersects line EC at point D

- The angles formed when two lines cross each other are called

vertical angles

- Vertical angles are congruent (vertical angles theorem)

∴ ∠ADC and ∠FDE are vertical angles

∵ Vertical angles are congruent

∴ ∠EDF ≅ ∠ADC

∴ m∠EDF ≅ m∠ADC

∵ m∠EDF = 120° ⇒ given

∵ m∠ADC = m∠ADB + m∠BDC

∴ m∠ADB + m∠BDC = 120°

∵ m∠ADB = (3x)° ⇒ given

∵ m∠BDC = (2x)° ⇒ given

∴ 3x + 2x = 120 ⇒ add like terms

∴ 5x = 120 ⇒ divide both sides by 5

∴ x = 24

Column (1) Column (2)

m∠EDF = 120° given

m∠ADB = 3 x given

m∠BDC = 2 x given

∠EDF and ∠ADC are vertical angles defin. of vert. ∠s

∠EDF is congruent to ∠ADC vertical angles are

congruent

m∠ADC = m∠ADB + m∠BDC angle add. post.

m∠EDF = m∠ADC defin. of cong.

m∠EDF = m∠ADB + m∠BDC substitution

120° = 3 x + 2 x substitution

120 = 5 x addition

x = 24 division

∴ The missing reason is " vertical angles are congruent "

- From the explanation above ∠ADC and ∠FDE are vertical

angles then they are congruent according to vertical angle

theorem

6 0

4 years ago

Read 2 more answers

Which represents the solution(s) of the graphed system of equations, y = x2 – 2x and y = –2x – 1? (1, –1) (0, 0) and (0, –1) (0,

olganol [36]

ANSWER

No solution

EXPLANATION

The first equation is

$y = {x}^{2} - 2x$

and the second equation is

$y = - 2x - 1$

We equate the two equations to obtain;

${x}^{2} - 2x = - 2x - 1$

This implies that

${x}^{2} = - 2x + 2x - 1$

${x}^{2} = - 1$

There is no real number whose square is -1.

Therefore, the equation has no solution.

6 0

3 years ago

Read 2 more answers

Sunday morning, the temperature in Bayfield, Wisconsin was -15.6 degrees Fahrenheit. If the temperature rose 3.8 degrees Fahrenh

Ostrovityanka [42]

Answer:

just add them and leave it as a positive

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

The cheetah is 7/6 the Perigen falcon is 10/3

Brilliant_brown [7]

The answer is $2 \frac{1}{6}$ .

Explanation:

In order to subtract the fractions, we must make them like fractions. To do this, the denominators must be the same by multiplying (only). Since the first fraction is $\frac{10}{3}$ , 3 can be multiplied by 2 to get 6, which is the other fraction, we can multiply it. Whatever you do to the denominator you must do to the numerator. Now multiply 2 by the numerator (10) to get $\frac{20}{6}$ . Now we can subtract the fractions $\frac{20}{6}$ and $\frac{7}{6}$ to get 13/6. Since this fraction is not in mixed fraction form yet, we must do that first. goes into 13 twice, so the whole number is 2 and there is still 1 left, making the fraction $\frac{1}{6}$ . Therefore, the difference is 2 $\frac{1}{6}$ .

8 0

3 years ago