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3 years ago

Compare. Write <, >, or =. Write the strategy you used. 2/3 or 7/8

Mathematics

1 answer:

Firlakuza [10]3 years ago

5 0

Answer:

2/3<7/8.

Step-by-step explanation:

Well the easiest and most simple way is to get a common denominator.The lcm of 3 and 8 is 24.so 2*8=16.So 2/3=16/24.Also 7*3 = 21.So 21/24=2/3.so 2/3<7/8.

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The quotient of 49 and d increased by the product of k and f?

stich3 [128]

"d increased by the product of k and f" is d+kf

49/(d+kf)

The final answer is 49/(d+kf)~

6 0

3 years ago

Please help with the question in the picture!

Stella [2.4K]

Answer:

Tan C = 3/4

Step-by-step explanation:

Given-

∠ A = 90°, sin C = 3 / 5

METHOD - I

Sin² C + Cos² C = 1

Cos² C = 1 - Sin² C

Cos² C = $1 - \frac{9}{25}$

Cos² C = $\frac{25 - 9}{25}$

Cos² C = $\frac{16}{25}$

Cos C = $\sqrt{\frac{16}{25} }$

Cos C = $\frac{4}{5}$

As we know that

Tan C = $\frac{Sin C}{Cos C }$

Tan C = $\frac{\frac{3}{5} }{\frac{4}{5} }$

Tan C = $\frac{3}{4}$ 

METHOD - II

Given Sin C = $\frac{3}{5} = \frac{Height}{Hypotenuse}$

therefore,

AB ( Height ) = 3; BC ( Hypotenuse) = 5

∵ ΔABC is Right triangle.

∴ By Pythagorean Theorem-

AB² + AC² = BC²

AC² = BC² - AB²

AC² = 5² - 3²

AC² = 25 - 9

AC² = 16

AC ( Base) = 4

Since,

Tan C = $\frac{Height}{Base}$ 

Tan C = $\frac{AB}{AC}$

Hence Tan C = $\frac{3}{4}$ 

4 0

3 years ago

A $20 shirt was 30% off and you had a coupon for another 10% off. What is the new price?

laila [671]

Answer:

$12.60 is the new price!

Step-by-step explanation:

20 x 0.7 = 14

14 x 0.9 = 12.6

Hope this helped!

4 0

3 years ago

Read 2 more answers

Look at the picture of a scaffold used to support construction workers. The height of the scaffold can be changed by adjusting t

timama [110]

Step-by-step explanation:

Using Pythagorus theorem :

(A)

$PR = \sqrt{ {PQ}^{2} + {QR}^{2} }$

$PR = \sqrt{196 + 81} = \sqrt{277} = 16.64 \: cm$

(B)

$QR = \sqrt{ {PQ}^{2} + {PR}^{2} } = \sqrt{196 +324 } = 22.8 \: cm$

5 0

4 years ago

You purchased a rare painting for $150 that is increasing in value by 3% annually. How many years will it take until it is doubl

Ahat [919]

Answer:

23 years.

Step-by-step explanation:

It is given that the initial price of painting is $150 and its values increasing by 3% annually.

We need to find how many years will it take until it is doubled in value.

The value of painting after t years is given by

$y=150(1+0.03)^t$

$y=150(1.03)^t$

The value of painting after double is 300. Substitute y=300.

$300=150(1.03)^t$

Divide both sides by 150.

$2=(1.03)^t$

Taking log both sides.

$\log 2=\log (1.03)^t$

$\log 2=t\log (1.03)$

$t=\dfrac{\log 2}{\log (1.03)}$

$t=23.44977$

$t\approx 23$

Therefore, the required number of years is 23.

6 0

3 years ago