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3 years ago

In the figure, ΔABC~ΔADE. Find the length of line segment DE.

Mathematics

1 answer:

jeka943 years ago

5 0

Answer:

Step-by-step explanation:

$\triangle ABC \sim \triangle ADE => \frac{x}{x+10}=\frac{x+3}{x+16}=>x^{2}+16x=x^{2}+13x+30=>3x=30=>x=10\\DE=x+3=>DE=13$

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Two sides and the non-included right angle of one right triangle are congruent to the corresponding parts of another

fgiga [73]

Answer:

hypotenuse leg theorem or OHL

Step-by-step explanation:

Since the congruent angle is a right angle and it is not included, the two congruent sides of the triangles must include their hypotenuses and one of their legs.

The triangles would be congruent by the hypotenuse leg theorem, which states that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and a leg of another right triangle, the triangles are congruent.

7 0

3 years ago

Read 2 more answers

A recent national survey found that high school students watched an average (mean) of 7.8 movies per month with a population sta

notka56 [123]

Answer:

Step-by-step explanation:

Given that :

Mean = 7.8

Standard deviation = 0.5

sample size = 30

Sample mean = 7.3 5.4772

The null and the alternative hypothesis is as follows;

$\mathbf{ H_o: \mu \geq 7.8}$

$\mathbf{ H_1: \mu < 7.8}$

The test statistics can be computed as :

$z = \dfrac{X- \mu}{\dfrac{\sigma}{\sqrt{n}}}$

$z = \dfrac{7.3- 7.8}{\dfrac{0.5}{\sqrt{30}}}$

$z = \dfrac{-0.5}{\dfrac{0.5}{5.4772}}$

$z = - 5.4772$

The p-value at 0.05 significance level is:

p-value = 1- P( Z < -5.4772)

p value = 0.00001

Decision Rule:

The decision rule is to reject the null hypothesis if p value is less than 0.05

Conclusion:

At the 0.05 significance level, there is sufficient information to reject the null hypothesis. Therefore ,we conclude that college students watch fewer movies a month than high school students.

8 0

4 years ago

A community had a population of 12,000 in 1985, which is increased to 20,000 in 2010. The saturation population is 80,000. Estim

ivann1987 [24]

Answer:

The right answer is :

(a) 23,200

(b) 24,514

(c) 22,926

Step-by-step explanation:

According to the question,

$P_1 = 12000$

$P_2 = 20000$

$P_{sat}=80000$

(a)

We know that the arithmetic growth formula will be:

⇒ $P=Pi+K\times t$ ...(1)

here,

⇒ $K=\frac{P_2-P_1}{\Delta t}$

$=\frac{20000-12000}{25}$

$=\frac{80000}{25}$

$=320$

On putting the values in equation (1), we get

⇒ $P_{2020}=20000+320\times 10$

$=23,200$

(b)

The geometric growth formula will be:

⇒ $P=ln(Pi)+K\times t$

here,

⇒ $K=\frac{lnP_2-lnP_1}{\Delta t}$

$=\frac{ln(20000)-ln(12000)}{25}$

By putting the values of general log, we get

hence,

⇒ $P_f=ln(20000)+0.0204\times 10$

$=10.107$

$P_{2020}=e^{10.107}$

$=24,514$

(c)

⇒ $P_f=P_{sat}-(P_{sat}-P_i)e^{-K\times t}$

or,

⇒ $K=-\frac{1}{\Delta t}ln(\frac{P_{sat}-P_2}{P_{sat}-P_1} )$

from here, we get

$=0.005$

hence,

⇒ $P_{2020}=80000-(80000-20000)e^{-0.005\times 10}$

$=80000-(60000)e^{-0.005\times 10}$

$=22,926$

5 0

3 years ago

I really need this for a test <br><br> How do I get the width and area

Zigmanuir [339]

Area is length times width but if u do not have the width u have to multiply the length times 2 and subtract the result from the perimeter when u have the total length for both sides divide by 2 and ur answer for that is the width. gl

7 0

3 years ago

IM DIEING PLEASE HELP ME FOR BRAINLIEST

Helga [31]

Answer:

Step-by-step explanation:

y= 9,800 x 2 ^x = 1,254,400

Just substitute x for 7

y= 9800 x 2 ^7 = 1,254,400

8 0

3 years ago