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3 years ago

11

Given that the triangles are similar, find the value of x. Find the length of NR. S T 40 60 R 2x-2 8

N
M
X=
NR =

1 answer:

andrew-mc [135]3 years ago

6 0

Answer:

NR = 12

Step-by-step explanation:

Given that both trjangles are similar, therefore, it follows that their corresponding side lengths would be proportional to each other. Thus:

$\frac{40}{8} = \frac{60}{2x - 2}$

$5 = \frac{60}{2x - 2}$

Cross multiply

$5(2x - 2) = 60$

$10x - 10 = 60$

$10x = 60 + 10$ (addition property of equality)

$10x = 70$

Divide both sides by 10

x = 7

✔️NR = 2x - 2

Plug in the value of x

NR = 2(7) - 2 = 14 - 2

NR = 12

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37 is ____ % of 148; 148 is ____ % of 37 fill in the blanks

soldier1979 [14.2K]

37 is 25% of 148; 148 is 400% of 37

Step-by-step explanation:

Let us solve the questions one by one

"37 is ____ % of 148"

Let x be the percentage

Then

$37 = x\%\ of\ 148\\37 = 148x\\x = \frac{37}{148}\\x = 0.25$

to convert in percentage, multiplying by 100

= 25%

"148 is ____ % of 37"

Let y be the percentage

then

$148 = y\%\ of\ 37\\148 = 37y\\y = \frac{148}{37}\\y = 4$

To convert into percentage, multiplying by 100

= 400%

Hence,

37 is 25% of 148; 148 is 400% of 37

Keywords: Percentage, percent

Learn more about percentage at:

#LearnwithBrainly

4 0

3 years ago

How long will it take for an investment to triple if it is compounded continuously at 12%

myrzilka [38]

Answer:

9.694 years

Step-by-step explanation:

Let the investment is $P.

So, we are asked to determine the time it will grow to triple with the compound interest rate of 12%.

Let the time is y years.

So, from the formula of compound interest we can write

$3P = P(1 + \frac{12}{100} )^{y}$

⇒ $(1 + \frac{12}{100} )^{y} = 3$

⇒ $(1.12)^{y} = 3$

Now, taking log both sides we get,

y log 1.12 = log 3 {Since, $\log a^{b} = b \log a$ }

⇒ 0.04922y = 0.477712

⇒ y = 9.694 years (Answer)

3 0

3 years ago

The parallel line of the AC line intersects the sides AB and BC of the triangle ABC, respectively, at the points M and N, AM: MB

amid [387]

Answer:

it equals 125

Step-by-step explanation:

8 0

3 years ago

Find the area of each figure. round to the hundredths place when necessary

notsponge [240]

Answer:

115.48 $m^{2}$

Step-by-step explanation:

This shape can be split into two distinct shapes

Two halves of a semi circle, and a rectangle in between

Circle:

Putting both halves of the semi circle together will give you a full circle. The diameter of the circle is given (7m).

The area of a circle is A = π $r^{2}$

The radius, r, is half of the diameter, so 7 / 2 = 3.5m

A = π $r^{2}$

A = π * $3.5^{2}$

A = 38.38 $m^{2}$

Rectangle:

The area of a rectangle is A = h b

The height, h, is known at 7m

The base, b, can be found by removing the length from the dot to the end of the semi circles. This length is the radius of the semi circles, 3.5m

Removing the radius from the total length given

18 - 3.5 - 3.5 = 11m

The base is 11m

A = h b

A = 7 * 11 = 77 $m^{2}$

Total Area = Circle area + Rectangle area

Total Area = 38.38 + 77 = 115.48 $m^{2}$

6 0

3 years ago

A private and a public university are located in the same city. For the private university, 1038 alumni were surveyed and 647 sa

Snezhnost [94]

Answer:

The difference in the sample proportions is not statistically significant at 0.05 significance level.

Step-by-step explanation:

Significance level is missing, it is α=0.05

Let p(public) be the proportion of alumni of the public university who attended at least one class reunion

p(private) be the proportion of alumni of the private university who attended at least one class reunion

Hypotheses are:

$H_{0}$ : p(public) = p(private)

$H_{a}$ : p(public) ≠ p(private)

The formula for the test statistic is given as:

z= $\frac{p1-p2}{\sqrt{{p*(1-p)*(\frac{1}{n1} +\frac{1}{n2}) }}}$ where

p1 is the sample proportion of public university students who attended at least one class reunion ( $\frac{808}{1311}=0.616$ )

p2 is the sample proportion of private university students who attended at least one class reunion ( $\frac{647}{1038}=0.623$ )

p is the pool proportion of p1 and p2 ( $\frac{808+647}{1311+1038}=0.619$ )

n1 is the sample size of the alumni from public university (1311)

n2 is the sample size of the students from private university (1038)

Then z= $\frac{0.616-0.623}{\sqrt{{0.619*0.381*(\frac{1}{1311} +\frac{1}{1038}) }}}$ =-0.207

Since p-value of the test statistic is 0.836>0.05 we fail to reject the null hypothesis.

6 0

3 years ago