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3 years ago

What is the greatest common factor of 48 and 64?

Mathematics

1 answer:

aleksklad [387]3 years ago

8 0

Answer:

The GCF of 48 and 64 is 16

Step-by-step explanation:

To figure out GCF, you make a list of all the prime factors, pick out the numbers they have in common, and multiply them together. In this case:

48: 2 x 2 x 2 x 2 x 3

64: 2 x 2 x 2 x 2 x 2 x 2

They have four 2's in common, so you multiply 2 x 2 x 2 x 2 =16

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Using the geometric mean and Pythagorean theorem, calculate the values of the missing sides. Round your answers to the thousandt

Pachacha [2.7K]

Answer:

a = 9.849

b = 20.25

c = 491.03

Step-by-step explanation:

By using Pythagoras theorem in the right triangle BDC,

(Hypotenuse)² = (Leg 1)² + (Leg 2)²

BC² = BD² + DC²

a² = 9² + 4²

a = $\sqrt{(81+16)}$

a = $\sqrt{97}$

a = 9.8489

a ≈ 9.849 units

By mean proportional theorem,

$\frac{\text{DC}}{\text{BD}}=\frac{\text{BD}}{\text{AD}}$

AD × DC = BD²

b × 4 = 9²

b = $\frac{81}{4}$

b = 20.25 units

BY Pythagoras theorem in ΔADB,

AB² = AD² + BD²

c² = b² + 9²

c² = (20.25)² + 9²

c² = 410.0625 + 81

c = 491.0625

c = 491. 063 units

6 0

3 years ago

In the triangle below, ∠Q is a right angle. Which ratio would be equivalent to the ratio of sin∠R?

MrMuchimi

Answer:

b) cos∠S

Step-by-step explanation:

sin ∠R = SQ/SR

cos S

Correct option is b)

4 0

3 years ago

The cost of a postage is determined by the following step function: How much would a package that weighs 3 ounces cost, in cents

bija089 [108]

Answer:

I think its C) 43. Let me know what you get

4 0

3 years ago

Mr. Abaya goy P700,000 loan for the expansion of his business payable monthly in 4years. How much os the monthly amortization if

Vaselesa [24]

The monthly amortization is P23,511.63

<h2>Compound interest</h2>

The formula for calculating the compound interest is expressed as:

$A = P(1+r/n)^t$

whrere:

P is the principal = P700,000
r is the rate = 12% = 0.12
t is the time = 4 years
n = 12

Substitute the parameters

$A = 700000(1+0.12/12)^{4(12)}\\
A = 700,000(1.01)^{48}\\
A =1,128,558.25$

Calculate the monthly payment:

Monthly payment = $\frac{1,128,558.25}{48} =23,511.63$

Hence the monthly amortization is P23,511.63

Learn more on compound interest here: brainly.com/question/24924853

8 0

2 years ago

You find an interest rate of 10% compounded quarterly. Calculate how much more money you would have in your pocket if you had us

Elena-2011 [213]

Answer:

see the explanation

Step-by-step explanation:

we know that

step 1

The compound interest formula is equal to

$A=P(1+\frac{r}{n})^{nt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

$r=10\%=10/100=0.10\\n=4$

substitute in the formula above

$A=P(1+\frac{0.10}{4})^{4t}$

$A=P(1.025)^{4t}$

Applying property of exponents

$A=P[(1.025)^{4}]^{t}$

$A=P(1.1038)^{t}$

step 2

The formula to calculate continuously compounded interest is equal to

$A=P(e)^{rt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

e is the mathematical constant number

we have

$r=10\%=10/100=0.10$

substitute in the formula above

$A=P(e)^{0.10t}$

Applying property of exponents

$A=P[(e)^{0.10}]^{t}$

$A=P(1.1052)^{t}$

step 3

Compare the final amount

$P(1.1052)^{t} > P(1.1038)^{t}$

therefore

Find the difference

$P(1.1052)^{t} - P(1.1038)^{t}$ ----> Additional amount of money you would have in your pocket if you had used a continuously compounded account with the same interest rate and the same principal.

3 0

3 years ago