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Ipatiy [6.2K]
3 years ago
11

Lf a+b=10 ,ab=21 then a^3+b^3=​

Mathematics
2 answers:
Goshia [24]3 years ago
8 0

Answer:

370

Step-by-step explanation:

a=3 or 7

b=7 or 3

3³+7³=370

maksim [4K]3 years ago
6 0
Equations
a + b = 10 ... (1)
ab = 21 ...(2)

Answer: a³ + b³ = 370

• Form a new equation out of either eq. 1 or 2
b = 10 - a ... (3)

• Substitute b in second equation

-> a(10 - a) = 21

• Solve

-> 10a - a² = 21
-> 10a - a² - 21 = 0

• Simplify the quadratic expression

-> (a - 5)² - 4 = 0 (using completing the square method.
-> a - 5 = √4 or a - 5 = -√4
-> a - 5 = 2 or a - 5 = -2
-> a = 7 or a = 3

• Substitute values of a in second equation

When a = 7,

-> (7)b = 21
-> 7b = 21
-> b = 21/7
-> b = 3

When a = 3,

-> (3)b = 21
-> 3b = 21
-> b = 21/3
-> b = 7

(a, b) = (7, 3) or (3, 7)

• Substitute values for a and b into new equation

-> (7)³ + (3)³
-> 343 + 27
-> 370
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The library has thirteen
dybincka [34]

Answer:

If the shelves  are 4/5 full, then the total number of books in the library is 1,040 books

Step-by-step explanation:

13 roll of bookcases

All the bookcases have four shelves

Total number of shelves = 4 x 13

                                        = 52 shelves

Each shelve holds 25 books each

Total number of books that can be in the shelves altogether = 52 x 25

                                                                                                    = 1,300 books

If the shelves  are 4/5 full, then the total number of books in the library is,

 4/5 x 1300

= 1,040 books

5 0
3 years ago
Find the vertex: -4x² + 16x - 7​
guapka [62]

Find the vertex: -4x^2 + 16x - 7​

Vertex = ( x, f(x)).

x = -b/2a

x = -16/2(-4)

x = -16/-8

x = 2

f(x) = -4x^2 + 16x - 7

Let x = 2

f(2) = -4(2)^2 + 16(2) - 7

f(2) = -4(4) + 32 - 7

f(2) = -16 + 32 - 7

f(2) = 16 - 7

f(2) = 9

Vertex = (2, 9)

7 0
4 years ago
Find area round to nearest hundredth
LUCKY_DIMON [66]

Answer:

area = 693

Step-by-step explanation:

The area of a quadrilateral can be found using the formula; base * height

It is given that the height is 33, the base is 21;

Multiply the two

21 *33 = 693

6 0
3 years ago
Please explain how you got your answer (:
melisa1 [442]
I used math

anyway
remember you can do anything to an equation as long as you do it to both sides

so

4n+2 and 1/2=2n+5
minus 2n both sides
4n-2n+2 and 1/2=2n-2n+5
2n+2 and 1/2=0+5
2n+2 and 1/2=5
minus 2 and 1/2 both sides
2n=2 and 1/2
divide both sides by 2
I mean times both sides by 1/2
n=1 and 1/4

answer is C
6 0
4 years ago
Using the formula V = l × w × h, find the volume of a right rectangular prism when the length of the prism is 45 cm, the width i
user100 [1]

Answer:

The volume of the right rectangular prism is 5400 cubic centimeter.

Step-by-step explanation:

Given : The length of the prism is 45 cm, the width is 12 cm, and the height is 10 cm.

To find : The volume of a right rectangular prism ?

Solution :

The formula used is V=l\times w\times h

Where, l is the length of the prism l=45 cm

w is the width of the prism w=12 cm

h is the height of the prism h=10 cm

Substitute the value in the formula,

V=45\times 12\times 10

V=5400\ cm^3

Therefore, The volume of the right rectangular prism is 5400 cubic centimeter.

7 0
4 years ago
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