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3 years ago

Proportions in similar triangles

Mathematics

1 answer:

Svetradugi [14.3K]3 years ago

4 0

Answer:

x = 4

Step-by-step explanation:

Given that DE is parallel to AC then DE divides the sides proportionally, so

$\frac{BD}{DA}$ = $\frac{BE}{EC}$ , substitute values

$\frac{x+2}{x}$ = $\frac{3}{2}$ ( cross- multiply )

3x = 2(x + 2) ← distribute

3x = 2x + 4 ( subtract 2x from both sides )

x = 4

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Answer: C- 480

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3 years ago

If a plant manufacturing carpet backing has a cylindrical tank that is 3 meters high and is 6 meters in diameter, what is the vo

Alik [6]

The formula for the volume of a cylinder is $\pi r^{2} h$

We know the diameter, so we can easily find the radius. The diameter is twice as long as the radius, so we divide the diameter by 2 to find the radius. This is equal to 6/2 = 3. Now, we plug our numbers into the formula.

$\pi * 3^{2} *3= \pi *9*3=27 \pi m^{3}$

This could also be written: $84.82 m^{3}$

Both 27 pi cubic meters and 84.82 cubic meters are correct answers, so choose whichever one you think your teacher would prefer.

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4 years ago

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The expression c- 0.25c can be used to find the cost of an item on sale for 25% off. Which expression below is equivalent to c-

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3 years ago

A marine biologist monitors the population of sunfish in a small lake. He records 800 sunfish in his first year, 600 sunfish in

Colt1911 [192]

Answer:

Let's use the variable y to represent the number of years passed since the first year.

The population on the first year (y = 0) was 800

The population in the second year (y = 1) was 600.

The ratio in which the population decreased can be calculated as:

R = 600/800 = 0.75

This means that 600 is the 75% of 800, this also means that between the first year and the second year, the population decreased by the 25%

Now let's look at the ratio between the second and third year (y = 2), the population the third year was 450

Now the ratio is:

R = 450/600 = 0.75

Same as before, then we already can see that the population will decrease by 25% each year.

The generic exponential decay equation is:

f(y) = A*(1 - r)^y

where:

A = initial population, in this case, is 800

y = our variable, in this case, represents the number of years

r = the amount that decreases per each unit of our variable, this must be written in decimal form. In this case, we know that the population decreases by 25% each year, and 25% written in decimal form is 0.25

Also, (1 - r) = R, where R is the ratio we found earlier.

To do this, we just divide 25% by 100% to get (25%/100% = 0.25)

Then our equation will be:

f(y) = 800*(1 - 0.25)^y

f(y) = 800*( 0.75)^y

1) We want to predict when the population will be 200.

to do this, we set:

f(y) = 200 = 800*( 0.75)^y

and solve it for y.

(200/800) = 0.75^y

(1/4) = 0.75^y

Now we can use the relationship:

Ln(a^x) = x*ln(a)

Then let's apply Ln( ) in both sides to get

ln(1/4) = y*ln(0.75)

ln(1/4)/ln(0.75) = y = 4.8 years.

This means that 4.8 years after the first year, the population will be around 200.

2) The population in the 25 th year (this is 24 years after the first one, so we take y = 24) is:

f(24) = 800*(0.75)^(24) = 0.80

Around this point, we will have no more sunfish in the lake.

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3 years ago

What is the negative root of 2x^2 + x − 6 = 0

max2010maxim [7]

Hello!

Here we can use the quad formula to solve for the x values or roots.
$x=(-2+or - \sqrt{2^2-4*2*-6})/2*2$ = -2 and 3/2
The negative root for this equation is x=-2

We find the roots of an equation by solving for x by different ways, most common ones being the quadratic formula of x= [-b +/-sqrt(b^2-4ac)]/2a or factoring and setting equal to zero and solving for x value(s) that way. Also the roots are where the graph of the equation crosses the x-axis.

Hope this helps. Any questions please just ask. Thank you kindly

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3 years ago