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3 years ago

In this question, all lengths are in cm. ABC. 3x-4, 2x+12, 7x-2. Given that AB:AC = 1:2 Show that AC:BC = 2:3

Mathematics

1 answer:

tresset_1 [31]3 years ago

5 0

Answer: AC : BC = 22 : 33 = 2 : 3

Step-by-step explanation:

Since we have given that

AB = 3x-4

AC= 2x+12

BC = 7x-2

And AB: AC = 1 : 2

and To show : AC : BC = 2 : 3

So, it becomes ,

$\dfrac{AB}{AC}=\dfrac{3x-4}{2x+12}=\dfrac{1}{2}\\\\2(3x-4)=2x+12\\\\6x-8=2x+12\\\\6x-2x=12+8\\\\4x=20\\\\x=\dfrac{20}{4}\\\\x=5$

So, AC: BC becomes:

$\dfrac{AC}{BC}=\dfrac{3x-4}{7x-2}=\dfrac{2(5)+12}{7(5)-2}=\dfrac{22}{33}=\dfrac{2}{3}$

Hence, proved.

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<img src="https://tex.z-dn.net/?f=%20%5Cfrac%7Bx%20%2B%202%7D%7B%20%7Bx%7D%5E%7B2%7D%20-%209%20%7D%20%20%5Ctimes%20%20%5Cfrac%7B

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Answer:

$\frac{1}{(x-3)(x-2)}$

Step-by-step explanation:

Factorise the denominators of both fractions

x² - 9 and x² - 4 are both differences of squares and factor as

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$\frac{x+2}{(x-3)(x+3)}$ × $\frac{x+3}{(x-2)(x+2)}$

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$\frac{1}{(x-3)(x-2)}$

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3 years ago

A company that makes cartons finds that the probability of producing a carton with a puncture is 0.03, the probability that a c

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(a) Having a smashed corner need to now not depend on whether or not the carton had a puncture or not,

so these occasions have to be independent.

One manner to check it the usage of the given probabilities:

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Here we have : (0.05)(0.08) which is 0.004, that is P(A and B), so the events are independent.

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Step-by-step explanation:

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3 years ago

In Lucille’s class, 35% of the students have blond hair. There are 20 students in the class. How many students have blond hair.

MrRissso [65]

Answer:

7 the answer is 7

Step-by-step explanation:

1. We assume, that the number 20 is 100% - because it's the output value of the task.

2. We assume, that x is the value we are looking for.

3. If 20 is 100%, so we can write it down as 20=100%.

4. We know, that x is 35% of the output value, so we can write it down as x=35%.

5. Now we have two simple equations:

1) 20=100%

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6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

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20/x=100/35

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