All categories

3 years ago

Identify the scale factor if the length of a model train engine is 3 feet and the length of the engine itself is 24 feet

Mathematics

2 answers:

Whitepunk [10]3 years ago

3 0

Answer:

jHshshshhzysjshhddbhxsbsshshsgshy
skins
disbanded
s

zloy xaker [14]3 years ago

3 0

Answer:

it should be 1 over 8

Step-by-step explanation:

You might be interested in

What is the rule of 72 used to determine? A. the approximate time it takes an investment to triple in value B. the approximate t

ValentinkaMS [17]

Answer:

Step-by-step explanation:

This can be derived using the formula to calculate future value of an amount which is given as:

FV=PV(1+i)^{n}

Where

FV is the future value

PV is the present value

i is the compound interest rate

n is the time period

To calculate how much time it takes to triple an amount, let's substitute $1 in place of PV and $3 in place of FV in the above equation.

3=(1+i)^{n}

Taking natural log on both sides, we get

log_{e} 3= n log_{e}(1+i)

n={\log_{e}3}/{log_{e}(1+i)}....................(1)

Using some log magic, this formula can also be written as

n=log_{(1+i)}3................(2)

Both equations (1) and (2) work fine.

(b)

In order to derive a rule 72 style formula start from equation (1) above. In that formula, we can say that for small values of interest rate,

log_{e}(1+i) ~ i ( This is a property of log)

Substituting this is equation (1), we get

n=log_{e}3/{i}

n={1.098}/{i}

Since, we want to use i as an integer and not as a percentage (so, 3% will be used as 3 and not 0.03), we multiply the RHS by 100

n={109.8}/{i}

and then to make it cleaner, we round off 109.8 to 110.

n={110}/{i}

Now, many times, people round this 109.8 off to 114. This is to make the calculations a little bit easier as 114 is number that has a lot of factors. So, if the numerator is rounded off to 114, the formula becomes

n={114}/{i}

6 0

3 years ago

Read 2 more answers

The polynomial p(x)=3x^3-20x^2+37x-20 has a known factor of (x-4). Rewrite p(x) as a product of linear factors. p(x) =

vesna_86 [32]

Answer:

$p(x) = (3x^{2} - 8x + 5)(x - 4)$

Step-by-step explanation:

p(x) has degree 3

(x - 4) has degree 1

So p(x) can be rewritten as a polynomial of degree 2 multiplying (x-4)

$p(x) = (ax^{2} + bx + c)(x - 4)$

To find a, b and c, we have to divide p(x) by x - 4.

Finding a:

Dividing the first term of p(x) by x - 4.

$\frac{3x^{3}}{x - 4} = 3x^{2}$

So a = 3.

Now multiplying 3x² by, x - 4, we have:

$3x^{2}(x - 4) = 3x^{3} - 12x^{2}$

Subtracting p(x) from this:

$3x^{3} - 20x^{2} + 37x - 20 - (3x^{3} - 12x^{2}) = 3x^{3} - 20x^{2} + 37x - 20 - 3x^{3} + 12x^{2} = -8x^{2} + 37x - 20$

Finding b:

Dividing the first term, after the subtraction, by x - 4.

$\frac{-8x^{2}}{x - 4} = -8x$

So b = -8.

Multiplying -8x by x - 4, we have:

$-8x(x-4) = -8x^{2} + 32x$

Then

$-8x^{2} + 37x - 20 - (-8x^{2} + 32x) = -8x^{2} + 37x - 20 + 8x^{2} - 32x = 5x - 20$

Finding c:

$\frac{5x}{x - 4} = 5$

So c = 5.

Just to verify if the remainder is 0.

$5(x - 4) = 5x - 20$

$5x - 20 - (5x - 20) = 0$

Then:

$p(x) = (ax^{2} + bx + c)(x - 4)$

$p(x) = (3x^{2} - 8x + 5)(x - 4)$

7 0

3 years ago

The price of the box of 10 markers is $7. The price of the box of 24 markers is $14. All prices without tax, and the price of th

stepladder [879]

Answer:

see below

Step-by-step explanation:

10 markers =7 dollars

Divide each side by 10

10/10 = 7 /10

1 marker = 7/10

y =7/10 x where y is the cost and x is the number of markers

24 markers =14 dollars

Divide each side by 24

24/24 = 14 /24

1 marker = 7/12

y = 7/12 x where y is the cost and x is the number of markers

6 0

3 years ago

Solve by the method of your choice 6x-2y= 16, 5x+y=24

Soloha48 [4]

6x-2y=16
(5x+y=24)*2
__________

6x-2y=16
10+2y=48 Add the equations”+”
—-
16x=64
X=4
So y=1

6 0

3 years ago

Factor the expression -18+42x

Brums [2.3K]

Answer:

6(-3+7x)

Step-by-step explanation:

Factor out 6 from each term

- 6*3 + 6*7x

6(-3+7x)

3 0

3 years ago