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spin [16.1K]
3 years ago
14

Find the length of side AB. Give your answer to 1 decimal place.

Mathematics
1 answer:
ehidna [41]3 years ago
7 0

Answer:

Length of side AB = 5.6 cm

Step-by-step explanation:

From the figure attached.

In right triangle ABC,

m∠ABC = 62°

m(BC) = 12 cm

By applying Cosine rule in this triangle,

Cos62° = \frac{\text{Adjacent side}}{\text{Hypotenuse}}

Cos62°= \frac{AB}{BC}

0.46947 = \frac{AB}{12}

AB = 12 × 0.46947

AB = 5.63

     ≈ 5.6 cm  

Therefore, length of side AB = 5.6 cm

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31-inch piece of steel is cut into three pieces so that the second piece is twice as long as the first piece and the third piece
pychu [463]

"31-inch piece of steel is cut into three pieces"

Call the pieces a,b,c

a + b + c = 31

"second piece is twice as long as the first piece"

b = 2a

"third piece is one inch more than seven times the length of the first piece"

c = 1 + 7a

Ok, we have our equations, let's substitute the second and third into the first.

a + 2a + 1 + 7a = 31

10a + 1 = 31

10a = 30

a = 30/10 = 3

b = 2a = 6

c = 1 + 7a = 22

Check: 3 + 6 + 22 = 31, good

Answer: 3 inches, 6 inches, 22 inches


4 0
3 years ago
Help with 6 a and b please
34kurt

Answer:

a) y=\frac{50}{x}

b) y=25 when x=2

Step-by-step explanation:

y=\frac{k}{x} since y varies inversely with x.

We need to find the constant, k.

Let's use a point (x,y) on the curve.

We are given an (x,y)=(5,10):

10=\frac{k}{5}

Multiply both sides by 5:

10(5)=k

50=k.

So the equation is:

y=\frac{50}{x}

What is y when x=2?

y=\frac{50}{2}

y=25

8 0
3 years ago
Look at the picture below please
Phantasy [73]

Answer:

  1. 1.73205080757
  2. 4.58257569496
  3. 7.87400787401

8 0
3 years ago
Tiana has already taken 1 page of notes on her own, and she will take 1 page during each hour of class. In all, how many hours w
Novosadov [1.4K]

Answer:

<u>42 Hours.</u>

Step-by-step explanation:

As an equation where y is the total pages and x is hours of class:

y=1+1x since she started with 1 page and does 1 page per hour.

Setting the total pages she needs as 43 (y=43) we get:

43=1+1x

Subtract one on both sides

42=1x

The 1 doesn't need to be written so

x=42

Therefore, it'll take her 42 hours to write all those notes.

4 0
3 years ago
A shop keeper has offered an item for sale. Its label price is Rs . It is not sold in one-month period and after one month its l
BigorU [14]

Answer:

x = Rs 20,833.33

the value of x is Rs 20,833.33

Step-by-step explanation:

Let x,y and z represent the price of the item initially, after one month and after two months respectively.

Given that;

after one month its label price is reduced by 20%

y = x - 20% of x

y = x - 0.20x

y = 0.80x ........1

after 2 months its reduced price is further reduced by 10% and then sold it for Rs 15000.

z = y - 10% of y

z = y - 0.10y

z = 0.90y ........2

Substituting equation 1 into 2;

z = 0.90(0.80x)

z = 0.72x

Also z = Rs 15000

So,

z = 0.72x = Rs 15000

0.72x = Rs 15000

x = Rs 15000/0.72

x = Rs 20833.33333333

x = Rs 20,833.33

the value of x is Rs 20,833.33

5 0
3 years ago
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