If the area of a circle measures 25 cm?, what is the circumference of the circle in terms of ?

Are the triangles Similar? (yes or no). If yes, by what

kakasveta [241]

Answer:

The triangles are not similar

Step-by-step explanation:

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

Triangle X.Y.Z

$\angle X=61^o$

$\angle Z=90^o$

$\angle Y=90^o-61^o=29^o$ ---> angle X and angle Y are complementary angles

Triangle H.G.J

$\angle H=90^o-34^o=56^o$ ---> angle H and angle J are complementary angles

$\angle G=90^o$

$\angle J=34^o$

so

X.Y.Z is a $61^o-90^o-39^o$ triangle

H.G.J is a $56^o-90^o-34^o$ triangle

The measure of its corresponding angles are not congruent

therefore

The triangles are not similar

8 0

3 years ago

You are designing a rectangular garden. the garden will be enclosed by fencing on three sides and by a house on the fourth side.

RUDIKE [14]

Suppose the dimensions of the rectangle is x by y and let the side enclosed by a house be one of the sides measuring x, then the sides that is to be enclosed are two sides measuring y and one side measuring x.

Thus, the length of fencing needed is given by

P = x + 2y

The area of the rectangle is given by xy,

i.e.

$xy = 288 \\ \\ \\ \\ \Rightarrow y= \frac{288}{x}$

Substituting for y into the equation for the length of fencing needed, we have

$P=x+2\left( \frac{288}{x} \right)=x+ \frac{576}{x}$

For the amount of fencing to be minimum, then

$\frac{dP}{dx} =0 \\ \\ \Rightarrow1- \frac{576}{x^2} =0 \\ \\ \Rightarrow \frac{576}{x^2} =1 \\ \\ \Rightarrow x^2=576 \\ \\ \Rightarrow x=\sqrt{576}=24$

Now, recall that

$y= \frac{288}{x} = \frac{288}{24} =12$

Thus, the length of fencing needed is given by

P = x + 2y = 24 + 2(12) = 24 + 24 = 48.

Therefore, 48 feets of fencing is needed to enclose the garden.

8 0

3 years ago

Mr. Fink's economy car can travel 420 miles on a 12-gallon tank of gas. Determine how many miles he can travel on 8 gallons.

Sphinxa [80]

Answer:

280 miles

Step-by-step explanation:

So, 420 miles=12 gallons

That means that for 1 gallon you would be able to go 35 miles.

Just multiply that by 8. 35*8=280

3 0

3 years ago

A researcher collated data on Americans’ leisure time activities. She found the mean number of hours spent watching television e

irakobra [83]

The answer is:

(null hypothesis) u=2.7; Ha(alt hypothesis): u<2.7

7 0

3 years ago

Read 2 more answers

After how many years are the salaries offered by Company A and Company B the same?

iren2701 [21]

Answer:

Step-by-step explanation:

24,000 = 24 thousands

30,000 = 30 thousands

3,000 = 3 thousands

2,4000 = 2.4 thousands

"x" years

24 + 3x = 30 + 2.4x

3x - 2.4x = 30 - 24

0.6x = 6

x = 10 years

4 0

2 years ago