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Westkost [7]
3 years ago
8

Simplify (x - square root 7)^2

Mathematics
1 answer:
svetoff [14.1K]3 years ago
3 0

Answer:

x^2 + -2 sqrt(7) x + 7

Step-by-step explanation:

Expand the following:

(x - sqrt(7))^2

(x - sqrt(7)) (x - sqrt(7)) = (x) (x) + (x) (-sqrt(7)) + (-sqrt(7)) (x) + (-sqrt(7)) (-sqrt(7)):

x x - sqrt(7) x - sqrt(7) x - (-sqrt(7) sqrt(7))

(-1)^2 = 1:

x x - sqrt(7) x - sqrt(7) x + (sqrt(7))^2

x x = x^2:

x^2 - sqrt(7) x - sqrt(7) x + sqrt(7)^2

Cancel exponents. (sqrt(7))^2 = 7:

x^2 - sqrt(7) x - sqrt(7) x + 7

Combining like terms, sqrt(7) x (-1) + sqrt(7) x (-1) = -2 sqrt(7) x:

Answer:  x^2 + -2 sqrt(7) x + 7

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In the adjoining equilateral triangle PQR , X , Y and Z are the middle points of the sides PQ , QR and RP respectively. Prove th
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Answer:

See Below

Step-by-step explanation:

<u>Statements:</u>                                                        <u>Reasons:</u>

<u />1)\text{ } \Delta PQR\text{ is equilateral}                                        Given

2)\text{ }PQ=QR=RP                                               Definition of Equilateral

3)\text{ } X, Y, Z\text{ are the midpoints of } PQ, QR, RP       Given

4)\text{ } PX=XQ                                                        Definition of Midpoint

5)PQ=PX+XQ                                               Segment Addition

6)\text{ } PQ=2XQ                                                      Substitution

7)\text{ } QY=YR                                                        Definition of Midpoint

8)\text{ }QR=QY+YR                                               Segment Addition

9)\text{ } QR=2QY                                                       Substitution

10)\text{ } 2XQ=2QY                                                  Substitution

11)\text{ } XQ=QY                                                      Division Property of Equality

12)\text{ }  XQ=PX=QY=YR                                Transitive Property

13)\text{ } RZ=ZP                                                       Definition of Midpoint

14)\text{ } RP=RZ+ZP                                             Segment Addition

15)\text{ } RP=2RZ                                                     Substitution

16)\text{ } 2XQ=2RZ                                                   Substitution

17)\text{ } XQ=RZ                                                       Substitution

18)\text{ } XQ=PX=QY=YR=RZ=ZP            Transitive Property

19)\text{ } \angle Q\cong \angle R\cong \angle P                                             Definition of Equilateral

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there are 46 2-digit numbers in which the tens digit is greater than the ones digit.

<h3>How many 2-digit numbers are there in which the tens digit is larger than the ones digit?</h3>

A 2-digit number is written as:

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Where a and b are single-digit numbers.

Tens digit and ones digit refers to place values:

a is the tens digit, and b is the ones digit. The numbers with a larger tens digit than the ones digit are:

98, 97, 96, 95, 94, 93, 92, 91, 90, 87, 86, 85, 84, 83, 82, 81, 80, 76, 75, 75, 74, 73, 72, 71, 70, 65, 64, 63, 62, 61, 60, 54, 53, 52, 51, 50, 43, 42, 41, 40, 32, 31, 30, 21, 20, 10.

We can see that there are 46 numbers in that list, so we conclude that there are 46 2-digit numbers in which the tens digit is greater than the ones digit.

If you want to learn more about place values:

brainly.com/question/12386995

#SPJ1

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