What is the greatest common divisor of x and y

Mathematics

1 answer:

Helen [10]3 years ago

8 0

What is the greatest common factor of x and y ?

(1) x and y are both divisible by 4 --> clearly insufficient: of course 4 itself could be the GCD but it's also possible that x and y share some other common factor more than 4, for example 5 (in this case both will be divisible by 20), or 8, or 4,000,000 ... so GCD could be more than 4 as well. Though from this statement we know that GCD cannot possibly be less than 4.

(2) x - y = 4 --> according to the property #2: GCD(x,y)≤4

GCD(x,y)≤4, but still insufficient.

(1)+(2) From (1) GCD≥4

GCD≥4 and from (2) GCD≤4

GCD≤4 --> GCD=4

GCD=4 Sufficient.

Answer: C.

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6 0

3 years ago

WILL MARK AS BRAINLIEST IF YOU ANSWER THESE CORRECTLY*** Can someone please help me with these math questions? I would really ap

igor_vitrenko [27]

ANSWER:

Question a):

$\dfrac{5}{3}*x= \dfrac{5}{6}\\ \\ \\ \dfrac{5}{3}x= \dfrac{5}{6}\\ \\6(5x)=3(5)\\ \\30x=15\\ \\x= \dfrac{15}{30}\\ \\ \\x= \dfrac{\not{15}}{\not{30}}\\ \\ \\x= \dfrac{1}{2}\quad\Longrightarrow\boxed{\mathbb{ANSWER\ \checkmark}}$

Question b):

$\dfrac{5}{3}\div{x}= \dfrac{10}{9}\\ \\ \\ \dfrac{5}{3}\div{ \dfrac{x}{1} }= \dfrac{10}{9}\\ \\ \\ \dfrac{5*1}{3*x}= \dfrac{10}{9}\\ \\ \\ \dfrac{5}{3x}= \dfrac{10}{9}\\ \\9(5)=10(3x)\\ \\45=30x\\ \\ \dfrac{45}{30}=x\\ \\ \\ \dfrac{\not{45}}{\not{30}}=x\\ \\ \\ \dfrac{3}{2}=x\quad\Longrightarrow\boxed{\mathbb{ANSWER\ \checkmark}}$

Question c):

$12\%*x= \dfrac{3}{4}\\ \\ \\ \dfrac{12}{100}*x= \dfrac{3}{4}\\ \\ \\ \dfrac{\not{12}}{\not{100}}x= \dfrac{3}{4}\\ \\ \\ \dfrac{3}{25}x= \dfrac{3}{4}\\ \\4(3x)=3(25)\\ \\12x=75\\ \\x= \dfrac{75}{12}\\ \\ \\x= \dfrac{\not{75}}{\not{12}}\\ \\ \\x= \dfrac{25}{4}\quad\Longrightarrow\boxed{\mathbb{ANSWER\ \checkmark}}$

Question d):

$\dfrac{12}{7}*x= \dfrac{18}{35}\\ \\ \\ \dfrac{12}{7}x= \dfrac{18}{35}\\ \\35(12x)=7(18)\\ \\420x=126\\ \\x= \dfrac{126}{420}\\ \\ \\x= \dfrac{\not{126}}{\not{420}}\\ \\ \\x= \dfrac{3}{10}\quad\Longrightarrow\boxed{\mathbb{ANSWER\ \checkmark}}$

Question e):

$x\div{ \dfrac{8}{11} }= \dfrac{22}{7}\\ \\ \\ \dfrac{x}{1}\div{ \dfrac{8}{11} }= \dfrac{22}{7}\\ \\ \\ \dfrac{11*x}{8*1}= \dfrac{22}{7}\\ \\ \\ \dfrac{11x}{8}= \dfrac{22}{7}\\ \\7(11x)=8(22)\\ \\77x=176\\ \\x= \dfrac{176}{77}\\ \\ \\x= \dfrac{\not{176}}{\not{77}}\\ \\ \\x= \dfrac{16}{7}\quad\Longrightarrow\boxed{\mathbb{ANSWER\ \checkmark}}$

Question f):

$120\%\div{x}= \dfrac{14}{15}\\ \\ \\ \dfrac{120}{100}\div{x}= \dfrac{14}{15}\\ \\ \\ \dfrac{\not{120}}{\not{100}}\div{}x= \dfrac{14}{15}\\ \\ \\ \dfrac{6}{5}\div{x}= \dfrac{14}{15}\\ \\ \\ \dfrac{6}{5}\div{ \dfrac{x}{1} }= \dfrac{14}{15}\\ \\ \\ \dfrac{1*6}{5*x}= \dfrac{14}{15}\\ \\ \\ \dfrac{6}{5x}= \dfrac{14}{15}\\ \\6(15)=14(5x)\\ \\90=70x\\ \\ \dfrac{90}{70}=x\\ \\ \\ \dfrac{\not{90}}{\not{70}}=x\\ \\ \\ \dfrac{9}{7}=x\quad\Longrightarrow\boxed{\mathbb{ANSWER\ \checkmark}}$

$\textbf{HOPE\ THIS\ HELPS...!!}$

3 0

3 years ago

Please help ill give you 20 points :c

posledela

Answer: D+Q= 30

0.10 d+ 0.25 q= 4.80

Step-by-step explanation:

A dime is worth 10 cents and a quarter is worth 25 cents.

7 0

3 years ago

Read 2 more answers

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