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Anestetic [448]
3 years ago
8

What is the length of ac?

Mathematics
2 answers:
Lelu [443]3 years ago
8 0

Answer:

The length of AC is 126 units.

Step-by-step explanation:

Given information: ED=9 units, AB=81 units, EC=x and AC=140-x.

In triangle ABC and EDC,

\angle A=\angle E                           (Given)

\angle ACD=\angle ECD                     (Given)

By AA property of similarity,

\triangle ABC\sim \angle EDC

Both triangles ABC and EDC are similar. The corresponding sides of two similar triangles are proportional.

\frac{AB}{ED}=\frac{AC}{EC}

\frac{81}{9}=\frac{140-x}{x}

9=\frac{140-x}{x}

9x=140-x

9x+x=140

10x=140

Divide both sides by 10.

x=14

The value of x is 14. So, the length of AC is

AC=140-14=126

Therefore the length of AC is 126 units.

leonid [27]3 years ago
7 0

Answer:

Step-by-step explanation:

Given triangles are similar, so we setup a proportion  

(140-x)/81 = x/9

solving gives x = 14

AC = 140-x = 140-14 = 126

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Daniel [21]

Answer:

here (edit I made a mistake)

Step-by-step explanation:

9) y=\frac{3}{5} x +5

10) y = x - 3

11)  y=-\frac{3}{5} x - 3

12) y=\frac{5}{4} x + 2

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3 0
2 years ago
Read 2 more answers
Jerry multiplied 3.04 x 7.091 and got the product 2.155664. Is his answer reasonable? Why or why not?
Readme [11.4K]

First we multiply the numbers ignoring the decimal and then place the decimal in the position

3.04 *7.091 = 2155664

Now the first number has two digits after the decimal and the second number has three digits after the decimal.

Therefore in the final result we have to move the decimal (2+3) =5 place from the left,

So the answer would be 21.55664

So, the correct answer is 21.55664

Jerry calculated the answer correctly , but made an error in the placement of the decimal point.  The answer is not reasonable because 2.155664 and 21.55664 mean two completely different answer far apart from each other


6 0
3 years ago
. Samantha is three times as old as Jason. The sum<br> of their ages is 56 years. How old is each?
8_murik_8 [283]

Step-by-step explanation:

let age of samantha be 3x and age of jason be x.(since samantha is three times as old as jason)

Now,

3x+x=56 (sum of their ages is 56)

or 4x=56

or x=56/4

or x=14

therefore age of samantha=3x=3×14=42

age of jason = x = 14

4 0
2 years ago
Complete parts a through f below to find nonnegative numbers x and y that satisfy the given requirements. Give the optimum value
MArishka [77]

Answer:

  • y = 81-x
  • the domain of P(x) is [0, 81]
  • P is maximized at (x, y) = (54, 27)

Step-by-step explanation:

<u>Given</u>

  • x plus y equals 81
  • x and y are non-negative

<u>Find</u>

  • P equals x squared y is maximized

<u>Solution</u>

a. Solve x plus y equals 81 for y.

  y equals 81 minus x

__

b. Substitute the result from part a into the equation P equals x squared y for the variable that is to be maximized.

  P equals x squared left parenthesis 81 minus x right parenthesis

__

c. Find the domain of the function P found in part b.

  left bracket 0 comma 81 right bracket

__

d. Find dP/dx. Solve the equation dP/dx = 0.

  P = 81x² -x³

  dP/dx = 162x -3x² = 3x(54 -x) = 0

The zero product rule tells us the solutions to this equation are x=0 and x=54, the values of x that make the factors be zero. x=0 is an extraneous solution for this problem so ...

  P is maximized at (x, y) = (54, 27).

7 0
3 years ago
Write the explicit formula for this geometric sequence.
Naily [24]

The explicit formula for this  geometric sequence 81, 27, 9, 3, … is aₙ = 81(1/3)ⁿ⁻¹. It has common ratio of 1/3 and first term of 81.

<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more variables and numbers.

A geometric sequence is in the form aₙ = ar⁽ⁿ⁻¹⁾, where a is the first term and r is the common ratio.

The geometric sequence 81, 27, 9, 3, … has common ratio:

r = 27/81 = 1/3

The explicit formula for this  geometric sequence 81, 27, 9, 3, … is aₙ = 81(1/3)ⁿ⁻¹. It has common ratio of 1/3 and first term of 81.

Find out more on equation at: brainly.com/question/2972832

#SPJ1

7 0
2 years ago
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