Vertical line through the point (9,6)

What is the length of BC , rounded to the nearest tenth?

Arte-miy333 [17]

Step $1$

In the right triangle ADB

Find the length of the segment AB

Applying the Pythagorean Theorem

$AB^{2} =AD^{2}+BD^{2}$

we have

$AD=5\ units\\BD=12\ units$

substitute the values

$AB^{2}=5^{2}+12^{2}$

$AB^{2}=169$

$AB=13\ units$

Step $2$

In the right triangle ADB

Find the cosine of the angle BAD

we know that

$cos(BAD)=\frac{adjacent\ side }{hypotenuse}=\frac{AD}{AB}=\frac{5}{13}$

Step $3$

In the right triangle ABC

Find the length of the segment AC

we know that

$cos(BAC)=cos (BAD)=\frac{5}{13}$

$cos(BAC)=\frac{adjacent\ side }{hypotenuse}=\frac{AB}{AC}$

$\frac{5}{13}=\frac{AB}{AC}$

$\frac{5}{13}=\frac{13}{AC}$

solve for AC

$AC=(13*13)/5=33.8\ units$

Step $4$

Find the length of the segment DC

we know that

$DC=AC-AD$

we have

$AC=33.8\ units$

$AD=5\ units$

substitute the values

$DC=33.8\ units-5\ units$

$DC=28.8\ units$

Step $5$

Find the length of the segment BC

In the right triangle BDC

Applying the Pythagorean Theorem

$BC^{2} =BD^{2}+DC^{2}$

we have

$BD=12\ units\\DC=28.8\ units$

substitute the values

$BC^{2}=12^{2}+28.8^{2}$

$BC^{2}=973.44$

$BC=31.2\ units$

therefore

the answer is

$BC=31.2\ units$

8 0

3 years ago

Read 2 more answers

The circumstances of Z is 84cm. What is the length of XY (the mirror arc)

Serga [27]

Answer:

B

Step-by-step explanation:

arc length = circumference × fraction of circle

= 84 × $\frac{90}{360}$ = 21 cm

8 0

3 years ago

What is the product of (5^-1)(5^-3) A. 1/625 B.1/25 C.25 D.125

Mice21 [21]

The correct answer is A

6 0

3 years ago

Read 2 more answers

Which ordered pairs cause this relation NOT to be a function? Why?

dangina [55]

Answer:

(3,1) and (3,2)

Step-by-step explanation:

We are given that a relation

{(0,0.5),(0.5,1),(3,1),(1,6),(3,2)}

We have to find that ordered pair which causes this relation not to be a function.

We know that

Function: It is a mapping between two non- empty set A and B.

Every element of set A has unique image in set B.

One element of set A can not have two or more images in set B.

Two or more elements of set A have same images in set B.

In given relation images of 3 are 1 and 2 which is not possible if a relation is function because one element can not have two or more images.

The ordered pair (3,2) and (3,1) cause this relation not to be a function because image of 3 are 1 and 2 which is not possible .

Answer: (3,1) and (3,2)

3 0

3 years ago

Lucas is borrowing money to purchase a vehicle. A car dealership will loan Lucas $18,000 with a simple interest rate of 14.5% ap

ASHA 777 [7]

Answer:

Difference in total payback = $5734.64

Step-by-step explanation:

Formula for the simple interest payout,

Interest = $\frac{P\times r\times t}{100}$

P = Principal amount of loan

r = rate of interest (Annually)

t = Duration for the payment

Interest = $\frac{18000\times 14.5\times 5}{100}$

= $13050

Total payable amount = 18000 + 13050

= $31050

Formula for the amount payable with compound interest,

Final amount = $\text{Initial amount}(1+\frac{r}{n})^t$

Here, t = Duration of investment

r = rate of interest (Annual)

n = Number of compounding per year

Payable amount = $18000(1+\frac{0.089}{1})^4$

= 18000(1.089)⁴

= $25315.36

Difference in total payback = $31050 - $25315.36

= $5734.64

7 0

2 years ago