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3 years ago

PLEASE HELP ME OUT...

Mathematics

1 answer:

katrin2010 [14]3 years ago

7 0

Answer:

$area = 144\pi$

Step-by-step explanation:

$volume = \frac{4}{3} \pi {r}^{3} \\ \\ 288\pi = \frac{4}{3} \pi {r}^{3} \\ \\ 3(288\pi) = 4\pi {r}^{3} \\ \\ \frac{3(288\pi)}{4\pi} = {r}^{3} \\ \\ 216 = {r}^{3} \\ \\ r = \sqrt[3]{216} \\ r = 6$

$area = 4\pi {r}^{2} \\ area = 4\pi ({6}^{2}) \\ area = 144\pi$

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Solve equation by using the quadratic formula.

Sati [7]

Answer: 1: x=3, x=1

2: x= -5

3: There are 2 real solutions.

4: There are 2 real solutions.

5: There are no real solutions.

6. There is 1 real solution.

8. x= -6, x = -2

9. x = -1/6, x=1

10.

Explanation:

1. The quadratic formula is

Substituting our known information we have:

2. Rewriting the quadratic in standard form we have x²+10x-25=0. Substituting this into the quadratic formula gives us:

3. The discriminant is b²-4ac. For this problem, that is 20²-4(-4)(25)=400--400=800. Since this is greater than 0, there are 2 real solutions.

4. The discriminant in this problem is 7²-4(2)(-15)=49--120=49+120=169. This is greater than 0, so there are 2 real solutions.

5. The discriminant in this problem is 1²-4(-2)(-28)=1-224=-223. Since this is less than 0, there are no real solutions.

6. If the discriminant of a quadratic is 0, then by definition there is 1 real solution.

7. Rewriting the quadratic we have 3x²-4x-2=0. Using the quadratic formula we have:

8. Factoring this trinomial we want factors of 12 that sum to 8. 6*2 = 12 and 6+2=8, so those are our factors. This gives us:

(x+6)(x+2)=0

Using the zero product property we know that either x+6=0 or x+2=0. Solving these equations we get x= -6 or x= -2.

9. Factoring this trinomial we want factors of 6(-1)=-6 that sum to -5. (-6)(1)=-6 and -6+1=-5, so this is how we "split up" the x term:

6x²-6x+1x-1=0

We group together the first two and the last two terms:

(6x²-6x)+(1x-1)=0

Factor the GCF out of each group. In the first group, that is 6x:

6x(x-1)+(1x-1)=0

In the second group, the GCF is 1:

6x(x-1)+1(x-1)=0

Both terms have a factor of (x-1), so we can factor it out:

(x-1)(6x+1)=0

Using the zero product property, we know either x-1=0 or 6x+1=0. Solving these equations we get x=1 or x=-1/6.

10. Substituting our information into the quadratic formula we get:

Step-by-step explanation:

5 0

2 years ago

Given a+b=7 and a–b=3, find: 2a·2b

nekit [7.7K]

I believe the answer is 40

5 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

3 years ago

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What is the range of the cluster in the scatter plot?

mestny [16]

I think that it is C

3 0

3 years ago

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Can anyone help me in this whole math question? Especially Number b and c. <br>Thanks.

Bogdan [553]

Answer:

Irregular polygons are polygons that do not have equal sides or equal angles. When finding the area of an irregular polygon, partition the polygon into smaller regular polygon shapes. You can then plug those measurements into their respective area formulas and multiply to find the area of one part of the shape.

This is 16cm.

5 0

3 years ago