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3 years ago

If bcd~gef find value of x

Mathematics

1 answer:

ddd [48]3 years ago

3 0

Answer:

$x = 13$

Step-by-step explanation:

Given

See attachment

Required

Find x

From the attachment, we have:

$BC = x + 4$

$BD = 2x - 7$

$GE = 51$

$GF = 57$

Because both triangles are similar, we use the following equivalent ratios:

$BC : BD = GE : GF$

Substitute values for each parameter

$x + 4 : 2x- 7 = 51 : 57$

Convert to fractions

$\frac{x + 4}{2x- 7} = \frac{51 }{ 57}$

Simplify the right-hand side

$\frac{x + 4}{2x- 7} = \frac{17}{19}$

Cross Multiply

$19(x + 4) = 17(2x - 7)$

$19x + 76 = 34x - 119$

Collect Like Terms

$19x - 34x = -76 - 119$

$-15x = -195$

Solve for x

$x = \frac{-195}{-15}$

$x = 13$

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at a particular high school, 42% of the students participate in sports and 25% of the students participate in drama. if 53% of t

baherus [9]

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<h3>What is the formula for P(AUB), where A and B are any two events?</h3>

If $A$ and $B$ are any two events, then the probability of the joint event $(A\cup B)$ is given by the following formula: $P(A\cup B)=P(A)+P(B)-P(A\cap B)$

Given that 42% of the students participate in sports and 25% of the students participate in drama and 53% of the students participate in either sports or drama.

Suppose $S$ denotes that "a student participates in sports" and $D$ denotes that "a student participates in drama".
So, we have $P(S)=\frac{42}{100}=0.42$ , $P(D)=\frac{25}{100}=0.25$ , $P(S\cup D)=\frac{53}{100}=0.53$ .

We want to find the probability that a student participates in both sports and drama i.e., we want to find $P(S\cap D)$ .

By the above formula, we obtain:

$P(S\cup D)=P(S)+P(D)-P(S\cap D)\\\Longrightarrow P(S\cap D)=P(S)+P(D)-P(S\cup D)\\\Longrightarrow P(S\cap D)=0.42+0.25-0.53\\\therefore P(S\cap D)=0.14=\frac{14}{100}$