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3 years ago

Factor the expression using the GCF 75m+85

Mathematics

2 answers:

Sloan [31]3 years ago

8 0

General Idea:

To find the Greatest Common Factor of binomial, we need to write each term as product of prime factors. GCF by definition means the product of common prime factors involved with its lowest terms. It is a number which will go in to both the terms in a binomial.

Given :

$75m + 85$

Applying the concept :

$75m=3 \; \times \; 5^2 \; \times m\\\\85=5 \; \times \; 17\\\\GCF\; of\; 75m + 85 \;is\; 5$

In order to get the expression inside the parenthesis after factoring GCF 5, we need to divide each term by what we factor out as shown below:

$75m+85=5( \frac{75m}{5} + \frac{85}{5} )=5(15m+17)$

jeka57 [31]3 years ago

4 0

75m + 85 = 5(15m + 17)

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3 years ago

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Which series of transformations will not map figure H onto itself

7nadin3 [17]

Answer:

Step-by-step explanation:

Given a square with vertices at points (2,1), (1,2), (2,3) and (3,2).

Consider option A.

1st transformation $(x+0,y-2)$ will map vertices of the square into points

$(2,1)\rightarrow (2,-1);$
$(1,2)\rightarrow (1,0);$
$(2,3)\rightarrow (2,1);$
$(3,2)\rightarrow (3,0).$

2nd transformation = reflection over y = 1 has the rule (x,2-y). So,

$(2,-1)\rightarrow (2,3);$
$(1,0)\rightarrow (1,2);$
$(2,1)\rightarrow (2,1);$
$(3,0)\rightarrow (3,2)$

These points are exactly the vertices of the initial square.

Consider option B.

1st transformation $(x+2,y-0)$ will map vertices of the square into points

$(2,1)\rightarrow (4,1);$
$(1,2)\rightarrow (3,2);$
$(2,3)\rightarrow (4,3);$
$(3,2)\rightarrow (5,2).$

2nd transformation = reflection over x = 3 has the rule (6-x,y). So,

$(4,1)\rightarrow (2,1);$
$(3,2)\rightarrow (3,2);$
$(4,3)\rightarrow (2,3);$
$(5,2)\rightarrow (1,2)$

These points are exactly the vertices of the initial square.

Consider option C.

1st transformation $(x+3,y+3)$ will map vertices of the square into points

$(2,1)\rightarrow (5,4);$
$(1,2)\rightarrow (4,5);$
$(2,3)\rightarrow (5,6);$
$(3,2)\rightarrow (6,5).$

2nd transformation = reflection over y = -x + 7 will map vertices into points

$(5,4)\rightarrow (3,2);$
$(4,5)\rightarrow (2,3);$
$(5,6)\rightarrow (1,2);$
$(6,5)\rightarrow (2,1)$

These points are exactly the vertices of the initial square.

Consider option D.

1st transformation $(x-3,y-3)$ will map vertices of the square into points

$(2,1)\rightarrow (-1,-2);$
$(1,2)\rightarrow (-2,-1);$
$(2,3)\rightarrow (-1,0);$
$(3,2)\rightarrow (0,-1).$

2nd transformation = reflection over y = -x + 2 will map vertices into points

$(-1,-2)\rightarrow (4,3);$
$(-2,-1)\rightarrow (3,4);$
$(-1,0)\rightarrow (2,3);$
$(0,-1)\rightarrow (3,2)$

These points are not the vertices of the initial square.

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3 years ago

Square root 7x+16 +4=x

gavmur [86]

1 Simplify 7x+16+47x+16+4 to 7x+207x+20 7x+20=x7x+20=x
2 Subtract 7x from both sides 20=x-7x20=x−7x
3 Simplify x-7xx−7x to -6x−6x
20=-6x20=−6x
4 Divide both sides by −6 -20/6=x
5 Simplify 20/6 to 10/3 -10/3=x
6 Switch sides
x=-10/3

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3 years ago

A certain group of women has a 0.86% rate of red/green color blindness. If a woman is randomly selected, what is the probabil

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Answer:

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Step-by-step explanation:

Given that the proportion of women having red/green color blindness is 0.86%

Represent that with p

$p= 0.86\%$