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2 years ago

Sophia determined that the expression Negative (4 x minus 5) + 2 (x minus 3) is equivalent to –2x – 5 by using the steps below.

Mathematics

1 answer:

LenaWriter [7]2 years ago

6 0

The correct statement is:

"She is not correct because she did not substitute the same number in both expressions in Step 1."

<h3>Is Sophia correct?</h3>

First, let's see if Sophia is correct.

She starts with the expression:

-(4x - 5) + 2*(x - 3) = -2x - 5

Expanding the left side:

-4x + 5 + 2x - 6 = -2x - 5

-2x -1 = -2x - 5

So the constant term is different.

Now, what Sophia does is evaluating in x = 1 and x = -1. You can't do that when finding equivalent expressions. (never evaluate in different numbers).

"She is not correct because she did not substitute the same number in both expressions in Step 1."

If you want to learn more about equivalent expressions:

brainly.com/question/2972832

#SPJ1

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

Law Incorporation [45]

Answer:

According to the rule of 72, the doubling time for this interest rate is 8 years.

The exact doubling time of this amount is 8.04 years.

Step-by-step explanation:

Sometimes, the compound interest formula is quite complex to be solved, so the result can be estimated by the rule of 72.

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 9%. So, by the rule of 72:

$D = \frac{72}{9} = 8$ .

According to the rule of 72, the doubling time for this interest rate is 8 years.

Exact answer:

The exact answer is going to be found using the compound interest formula.

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

In which 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.

is double the initial amount, double the principal.

$A = 2P$

$r = 0.09$

The interest is compounded anually, so $n = 1$

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

$2P = P(1 + \frac{0.09}{1})^{t}$

$2 = (1.09)^{t}$

Now, we apply the following log propriety:

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

So:

$\log_{1.09}(1.09)^{t} = \log_{1.09} 2$

$t = 8.04$

The exact doubling time of this amount is 8.04 years.

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4 years ago

Peter is making an "X marks the spot" flag for a treasure hunt. The flag is made of a square white flag with sides of 121212 inc

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He will need 17 inches of ribbon.

The diagonal splits the square into two right triangles. We can then use the Pythagorean theorem to find the length of the diagonal (the hypotenuse of the triangle):

12² + 12² = x²
144 + 144 = x²
288 = x²

Take the square root of both sides:
√288 = √x²
16.97 = x
17≈x

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4 years ago

2:14 = 1:<br> What is the equivalent ratio?

Vlad [161]

The answer would be 1:7

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4 years ago

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The midpoint of a segment is at (1, 1) and one

Nikolay [14]

Answer:

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Step-by-step explanation:

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3 years ago

Given that one root is twice the other for the quadratic equation px-3x^2=24 . Find the values of p

Dvinal [7]

Alright, so we can write this as -3x^2+px-24=0 (by subtracting 24 from both sides)

3*-24=-72, so 2 numbers have to add to 72 but multiply to a number p. If a number is y and the other is 2y, that means that y*2y=-72 and 2y^2=72. Therefore, y^2=36 by dividing both sides by 2 and y is either 6 or -6. If y is 6, then 2y is 12 and 6+12=18=p
If y is -6, then 2y=-12 and -6-12=-18=p

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3 years ago