All categories

4 years ago

Triangle Similarity What is the value of x?

Mathematics

1 answer:

Ksenya-84 [330]4 years ago

7 0

To solve this you can make a proportion where the matching sides will correspond to each other. It should look something like this:

$\frac{AC}{PD} =\frac{CR}{DR}$

$\frac{10}{15} =\frac{x}{42}$

Now you must cross multiply

10*42 = 15*x

420= 15x

To isolate x divide 15 to both sides

420/15 = 15x/15

28 = x

Hope this helped!

~Just a girl in love with Shawn Mendes

You might be interested in

A principal amount of $4,700 is deposited into an account paying interest at a rate of 3%, continuously compounded. What will be

kogti [31]

A = Pe^(rt)

A = Final Amount = ?
P = Principal = 4,700
e = <span>euler's number = 2.7183
r = rate = 3/100 = 0.03
t = time (in years) = 3

A = 4,700 * e^(0.03*3)

A = 4,700 * 1.094

A = 5142.62

Therefore, </span>the account balance after 3 years will be $5142.62

4 0

3 years ago

A city has a population of 280,000 people. suppose that each year the population grows by 4.5% . what will the population be aft

Anastasy [175]

Given that population of the city is 280000.

Rate of growth of the population = r = 4.5% = 0.045

We have to find population after 15 years so time

t = 15

We can use growth formula to find the required population which is given by :

$A=P(1+r)^t$

Where P= starting population = 280000

r= rate of growth = 0.45

t= time = 15

now plug these values into above formula.

$A=280000(1+0.45)^{15}$

$A=280000(1.45)^{15}$

$A=280000(263.34194176)$

$A=73735743.6928$

Hence population after 15 years will be approx 73735743.

8 0

3 years ago

The amount of money spent on textbooks per year for students is approximately normal.

Ostrovityanka [42]

Answer:a

$336.04 < \mu < 443.96$

The margin of error will increase

The margin of error will decreases

The 99% confidence interval is $0.4107 < p < 0.4293$

Step-by-step explanation:

From the question we are told that

The sample size $n = 19$

The sample mean is $\= x = \$\ 390$

The standard deviation is $\sigma = \$ \ 120$

Given that the confidence level is 95% then the level of significance is mathematically represented as

$\alpha = 100 - 95$

$\alpha = 5 \%$

$\alpha = 0.05$

Next we obtain the critical value of $\frac{\alpha }{2}$ from the normal distribution table

$Z_{\frac{\alpha }{2} } = 1.96$

The margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }$

=> $E = 1.96 * \frac{120}{\sqrt{19} }$

=> $E = 53.96$

The 95% confidence interval is

$\= x - E < \mu < \= x + E$

=> $390 - 53.96 < \mu < 390 - 53.96$

=> $336.04 < \mu < 443.96$

When the confidence level increases the $Z_{\frac{\alpha }{2} }$ also increases which increases the margin of error hence the confidence level becomes wider