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jonny [76]
3 years ago
9

Tamara says she used the GCF to factor the expression 21x + 56xy as 7(3x + 8xy). Is she correct? Explain.

Mathematics
1 answer:
cestrela7 [59]3 years ago
6 0

Answer:

Tamara  incorrectly factored the whole expression.

Step-by-step explanation:

Note that

  • 21x=3·7·x;
  • 56xy=2·2·2·7·x·y.

Mark in bold all common factors, then GCF(21x,56xy)=7·x=7x.

Thus,

21x+56xy=7x(3+8y).

Hence, Tamara correctly found the GCF of numbers 21 and 56, but incorrectly factored the whole expression.

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PLEASE HELP!!!
vovikov84 [41]

Answer:

Both the parts of this question require the use of the "Intersecting Secant-Tangent Theorem".

Part A

The definition of the Intersecting Secant-Tangent Theorem is:

"If a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment."

This, when applied to our case becomes, "The length of the secant RT, times its external segment, ST, equals the square of the tangent segment TU".

Mathematically, it can be written as:

Part B

It is given that RT = 9 in. and ST = 4 in. Thus, it is definitely possible to find the value of the length TU and it can be found using the Intersecting Secant-Tangent Theorem as:

Thus,  

Thus the length of TU=6 inches

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Read 2 more answers
Find the inverse of f(x) = x2 - 5:
Volgvan

Answer:

g(f(x))=x g ( f ( x ) ) = x , f−1(x)=√x+5,−√x+5 f - 1 ( x ) = x + 5 , - x + 5 is the inverse of f(x)=x2−5 f ( x ) = x 2 - 5 .

Step-by-step explanation:

( f ( x ) ) = x , f−1(x)=√x+5,−√x+5 f - 1 ( x ) = x + 5 , - x + 5 is the inverse of f(x)=x2−5 f ( x ) = x 2 - 5 .

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