Describe a sequence of transformations that maps triangle ABC onto triangle A"B"C"<br> Help please?

2/3g + 1/2g = 14<br><br>what is g?

miskamm [114]

2/3 g + 1/2 g = 14

4/6 g + 3/6 g = 14

7/6 g = 14

7g = 84

g = 12

5 0

3 years ago

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(a) Jane pumped 54 gallons of water out of her pool. This was done over a period of 9 minutes at

STALIN [3.7K]

Answer: -6
Step-by-step explanation:
From the question, Elsa pumped 18 gallons of water out of her pool and this was done over a period of 3 minutes at a constant rate. Since it is done at a content rate, to get the change in the amount of water in the pool each minute, we divide 18 gallons by 3. This can be written mathematically as:
= 18 gallons ÷ 3
= 6 gallons
Change = -6
The change in the amount of water in the pool each minute will be -6gallons hope this helps

6 0

3 years ago

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Find the value of X in that isosceles triangle shown below

ipn [44]

Answer:

sqrt(13) =x

Step-by-step explanation:

We have 2 right triangles, one on the right and one on the left

The base is 1/2 of 4 or 2 and the height is 3

We can use the Pythagorean theorem to find the hypotenuse

a^2 + b^2 = c^2

2^2 + 3^2 = x^2

4+9 = x^2

13 = x^2

Take the square root of each side

sqrt(13) =x

5 0

3 years ago

Use the "rule of 72" to estimate the doubling time (in years) for the interest rate, and then calculate it exactly. (Round your

bonufazy [111]

Answer:

Using the rule of 72, the doubling time is 9.35 years.

The exact answer is that the doubling time is 8.89 years.

Step-by-step explanation:

By the rule of 72, we have that the doubling time D is given by:

$D = \frac{72}{Interest Rate}$

The interest rate is in %.

In our exercise, the interest rate is 7.7%. So, by the rule of 72:

$D = \frac{72}{7.7} = 9.35$ .

Exact answer:

The exact answer is going to be found using the compound interest formula(since the rule of 72 is a simplification of this formula).

The compound interest formula is given by:

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

Where A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the time the money is invested or borrowed for.

So, for this exercise, we have:

We want to find the doubling time, that is, the time in which the amount is double the initial amount, double the principal.

$A = 2P$

$r = 0.077$

There are 52 weeks in a year, so $n = 52$

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

$2P = P(1 + \frac{0.077}{52})^{52t}$

$2 = (1.0015)^{52t}$

Now, we apply the following log propriety:

$\log_{a} a^{n} = n$

So:

$\log_{1.0015}(1.0015)^{52t} = \log_{1.0015} 2$

$52t = 462.44$

$t = \frac{462.44}{52}$

$t = 8.89$

The exact answer is that the doubling time is 8.89 years.

6 0

3 years ago

What is this percent of change 40;72

salantis [7]

Given:
Original or base : 40
New amount : 72

We need to find the difference of the new amount and the original amount

72 - 40 = 32

We then divide the difference by the original amount

32/40 = 0.80

We multiply the quotient by 100%

0.80 x 100% = 80%

The percentage of change is 80%

6 0

3 years ago

Describe a sequence of transformations that maps triangle ABC onto triangle A"B"C" Help please?