What is the answer? A. B. C. D.

In triangle abc, the perimeter is 36, and ab=ac. line ad is perpendicular to bc at the point d, and triangle abd's perimeter is

Musya8 [376]

Let x=ab=ac, and y=bc, and z=ad.

Since the perimeter of the triangle abc is 36, you have:

Perimeter of abc = 36
ab + ac + bc = 36
x + x + y = 36
(eq. 1) 2x + y = 36

The triangle is isosceles (it has two sides with equal length: ab and ac). The line perpendicular to the third side (bc) from the opposite vertex (a), divides that third side into two equal halves: the point d is the middle point of bc. This is a property of isosceles triangles, which is easily shown by similarity.

Hence, we have that bd = dc = bc/2 = y/2 (remember we called bc = y).

The perimeter of the triangle abd is 30:

Permiter of abd = 30
ab + bd + ad = 30
x + y/2 + z =30
(eq. 2) 2x + y + 2z = 60

So, we have two equations on x, y and z:

(eq.1) 2x + y = 36
(eq.2) 2x + y + 2z = 60

Substitute 2x + y by 36 from (eq.1) in (eq.2):

(eq.2') 36 + 2z = 60

And solve for z:

36 + 2z = 60 => 2z = 60 - 36 => 2z = 24 => z = 12

The measure of ad is 12.

If you prefer a less algebraic reasoning:

- The perimeter of abd is half the perimeter of abc plus the length of ad (since you have "cut" the triangle abc in two halves to obtain the triangle abd).

- Then, ad is the difference between the perimeter of abd and half the perimeter of abc:

ad = 30 - (36/2) = 30 - 18 = 12

4 0

4 years ago

Read 2 more answers

Half a number plus 5 is 11.What is the number?

SOVA2 [1]

<h3>Solution :</h3>

Let x be the number

$\small\bold\red{→}\small\bold{(\frac{1}{2} )x + 5 = 11}$

$\small\bold\red{→}\small\bold{(\frac{1}{2})x + 5 - 5 = 11 - 5}$

$\small\bold\red{→}\small\bold{(\frac{1}{2})x = 6}$

$\small\bold\red{→}\small\bold{2 × (\frac{1}{2})x = 6 × 2 }$

$\small\bold\red{→}\small\bold{x = 12}$

6 0

3 years ago

Read 2 more answers

Explain how you would solve for the value of x when you are given the solution to a function.

Svetlanka [38]

Answer:

Substitute

Step-by-step explanation:

Substitute the values given in the function

and you will get the answer.

P.s. It depends on the question

3 0

3 years ago

Tim has an after-school delivery service that he provides for several small retailers in town. He uses his bicycle and charges $

nlexa [21]

Answer:

$4.84

Step-by-step explanation:

Given that

For delivery within $1\frac{1}2$ mi, charges = $1.25

For delivery within $1\frac{1}2$ mi - $1\frac{3}4$ mi, charges = $1.70

For delivery within $1\frac{3}4$ mi - 2 mi, charges = $2.15

and

so on.

i.e.

For delivery within 2 mi - 2 $\frac{1}4$ mi, charges = $2.60

For delivery within 2 $\frac{1}4$ mi - 2 $\frac{1}2$ mi, charges = $3.05

For delivery within 2 $\frac{1}2$ mi - 2 $\frac{3}4$ mi, charges = $3.50

For delivery within 2 $\frac{3}4$ mi - 3 mi, charges = $3.95

For delivery within 3 mi - 3 $\frac{1}4$ mi, charges = $4.40

So, every 0.25 mi or $\frac{1}4$ mi increase in distance, there is an increase of $0.45 in the charges.

It is given that there is increase of 10% in the rates.

i.e. for every 0.25 mi increase in distance, there is an increase of 0.45*1.10 = $0.495 in the charges.

The distance of $3\frac{1}8$ miles lies within the range 3 mi - 3 $\frac{1}4$ mi.

So actual charges after increase of 10%

$\Rightarrow \$4.40 \times \dfrac{110}{100}\\\Rightarrow \$4.40 \times 1.10\\\Rightarrow \bold{\$4.84}$

6 0

4 years ago

The Baltimore Marathon features a relay race.

Kazeer [188]

Answer:

$S = 149\ min$

or

$S = 2\ hr\ 29\ min$

Step-by-step explanation:

Let S be the sum of the times for all winning team.

Given:

leg 1. 32 minutes 56 seconds.

leg 2. 42 minutes 28 seconds.

leg 3. 34 minutes 34 seconds.

leg 4. 39 minutes 2 seconds

We need to find the total time to run all four legs of the marathon.

Solution:

Sum of the times for all winning team.

$Sum\ of\ the\ times = leg\ 1 + leg\ 2 + leg\ 3 + leg\ 4$

Substitute running times for all legs.

$S = 32\ min\ 56\ sec+ 42\ min\ 28\ sec + 34\ min\ 34\ sec + 39\ min\ 2\ sec$

Now, we write the minutes and seconds separately.

$S = (32+42+34+39)min+(56+28+34+2)sec$

$S = (147)min+(120)sec$

$120\ sec =\frac{120}{60} = 2\ min$

$S = (147)min+(2)min$

$S = 149\ min$

Therefore, Total time taken by all four legs $S = 149\ min$ or $S = 2\ hr\ 29\ min$ .

8 0

3 years ago