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3 years ago

Select all of the equations that are equivalent to

Mathematics

1 answer:

Citrus2011 [14]3 years ago

8 0

Answer:

The options 2√20 and 4*5^(1/2) and 3*5^(1/2) + 5^(1/2) are the only expressions that are equivalent to 4√5

Step-by-step explanation:

We will factorise and simplify each term to get 4√5 in the end:

a) 2√20

2√5*4

2√5√4

2*2√5 Because √4 = 2

4√5

b)6^1/2 +5^1/2

√6 + √5

√2√3 + √5

c) 3*5^(1/2) + 5^(1/2)

3*√5 + √5

√5 (3*1 + 1)

√5 (3 + 1)

√5 (4)

4√5

d) 4*5^(1/2)

4√5 Because any integer with power 1/2 = √

e) 2√10

2√5*2

2√5√2

f) 3*5^(1/2)

3√5

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Which equation can be used to find the volume of a sphere that has a radius of 9 miles?

Licemer1 [7]

V=(4/3)pir^3

r=9
V=(4/3)pi9^3
V=12pi243
V=972pi

aprox pi=3.14
3052.08 mi^3

6 0

3 years ago

Ted and Jude are each saving money each month. After x months, the amount of money, in dollars, that Ted has saved is represente

Nadusha1986 [10]

Answer:

True Statements are -

B. In 3 months, Ted will have saved the same amount that Jude saved in 2 months.

D. The total amount of money Jude has saved is always $20 more than the total amount Ted has saved.

Step-by-step explanation:

Given - Ted and Jude are each saving money each month. After x months, the amount of money, in dollars, that Ted has saved is represented by the

equation T = 40x, and the amount of money that Jude has saved is represented by the equation J = 60x.

To find - Choose all of the statements that are true.

A. Each month, Jude saves two-thirds as much money as Ted saves.

B. In 3 months, Ted will have saved the same amount that Jude saved in 2 months.

C. The amount of money Jude saves each month is $20 more than the amount Ted saves each month.

D. The total amount of money Jude has saved is always $20 more than the total amount Ted has saved.

Proof -

Given that,

After x months,

Ted saved the amount of money, T(x) = 40x

Jude saved the amount of money, J(x) = 60x

Now,

In 1 month,

Ted saved money, T(1) = 40(1) = 40

Jude saved money, J(1) = 60(1) = 60

So,

In 1st month, Jude saved money 20 more than Ted saved.

Now,

In 2 month,

Ted saved money, T(2) = 40(2) = 80

Jude saved money, J(2) = 60(2) = 120

So,

In 2nd month, Jude saved money 40 more than Ted saved.

Now,

In 3 month,

Ted saved money, T(3) = 40(3) = 120

Jude saved money, J(3) = 60(3) = 180

So,

In 3rd month, Jude saved money 60 more than Ted saved.

So,

Option C is incorrect

Because

In 1st month, Jude saves is $20 more than the amount Ted saves

In 2nd month, Jude saves is $40 more than the amount Ted saves

Now,

In 1st month,

Ted saves = 40

and

$\frac{2}{3}(40)$ = 26.67

So, Jude will save = 40 + 26.67 = 66.67

But Jude saves 60

So,

Option A is incorrect.

i.e. A. Each month, Jude saves two-thirds as much money as Ted saves.

Now,

We can see that,

In 3 months, Ted will have saved the money = 120

In 2 months, Jude will have saved the money = 120

So,

Option B is correct.

i.e. B. In 3 months, Ted will have saved the same amount that Jude saved in 2 months.

Also,

We can see that

In 1st month, Jude saved money 20 more than Ted saved.

In 2nd month, Jude saved money 40 more than Ted saved.

In 3rd month, Jude saved money 60 more than Ted saved.

So,

Option D is correct.

i.e. D. The total amount of money Jude has saved is always $20 more than the total amount Ted has saved.

∴ we get

True Statements are -

B. In 3 months, Ted will have saved the same amount that Jude saved in 2 months.

D. The total amount of money Jude has saved is always $20 more than the total amount Ted has saved.

7 0

3 years ago

Work out the area of a circle with radius of 7.5cm

lidiya [134]

Answer:

Area of circle is equal A = πr²

Here r = 7.5 and π = 3.142

so,

A = 3.142(7.5)²

A = 176.17 after rounding off.

3 0

3 years ago

Help help i need help anyone ?

REY [17]

-9-6i/-3-2i
Factor -3 out of expression
-3(3+2i)/-3-2i
Then extract the negative sign out of the expression
-3(3+2i)/-(3+2i)
Reduce the fraction with -(3+2i)
-3/-1
-3*-1=3
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3 0

3 years ago

What is the definition of the cosine ratio of an acute angle of a triangle?

Liula [17]

Answer:

I think the answer is the last one

adjacent side / hypotenuse

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3 years ago