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2 years ago

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Felicia is solving the expression -5(3x+2)+10x. Gregory is solving the expression -12-4x+?+?x. Both students simplified their an

swers to get the same expression. What are the values missing from Gregory's expression?

1 answer:

densk [106]2 years ago

7 0

Answer:

see the explanation

Step-by-step explanation:

we have

<em>Felicia</em>

$-5(3x+2)+10x$

Apply distributive property

$-5(3x)-5(2)+10x$

$-15x-10+10x$

Combine like terms

$-5x-10$

Let

a ----> the missing term with coefficient x in Gregory's expression

b ----> the missing constant term in Gregory's expression

so

$-12-4x+ax+b$

equate Gregory's expression to Felicia's expression

$-12-4x+ax+b=-5x-10$

so

$-12+b=-10$ -----> $b=2$

$-4x+ax=-5x$ ------> $a=-1$

so

Gregory's expression is

$-12-4x+2-x$

therefore

The missing terms are 2 and -x

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Sauron [17]

I think the answer is C.... I’m not sure tho.

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2 years ago

Number 36 please for geometry

Mumz [18]

Answer:

(x - 1)² + (y + 1/2)² = 65/4

Step-by-step explanation:

Given: the endpoints of the diameter are (3, 3) and (-1, -4). a( To determine the center of this circle, find the midpoint of the line segment connecting these two points:

3 - 1

x = -----------

2

and

-1

y = ----------

2

The center is at x = 1 and y = -1/2: (1, -1/2).

b) The radius is half the diameter. The diameter is the distance between the two endpoints given, that is, the distance between (-1, -4) and (3, 3):

diameter = √(4² + 7²) = √(16 + 49) = √65; therefore,

radius = (1/2)√65.

square of the radius = r² = 65/4

The general equation of a circle with center at (h, k) and radius r is

(x - h)² + (y - k)² = r². In this case, the equation is:

(x - 1)² + (y + 1/2)² = 65/4

8 0

2 years ago

y′′ −y = 0, x0 = 0 Seek power series solutions of the given differential equation about the given point x 0; find the recurrence

sukhopar [10]

Let

$\displaystyle y(x) = \sum_{n=0}^\infty a_nx^n = a_0 + a_1x + a_2x^2 + \cdots$

Differentiating twice gives

$\displaystyle y'(x) = \sum_{n=1}^\infty na_nx^{n-1} = \sum_{n=0}^\infty (n+1) a_{n+1} x^n = a_1 + 2a_2x + 3a_3x^2 + \cdots$

$\displaystyle y''(x) = \sum_{n=2}^\infty n (n-1) a_nx^{n-2} = \sum_{n=0}^\infty (n+2) (n+1) a_{n+2} x^n$

When x = 0, we observe that y(0) = a₀ and y'(0) = a₁ can act as initial conditions.

Substitute these into the given differential equation:

$\displaystyle \sum_{n=0}^\infty (n+2)(n+1) a_{n+2} x^n - \sum_{n=0}^\infty a_nx^n = 0$

$\displaystyle \sum_{n=0}^\infty \bigg((n+2)(n+1) a_{n+2} - a_n\bigg) x^n = 0$

Then the coefficients in the power series solution are governed by the recurrence relation,

$\begin{cases}a_0 = y(0) \\ a_1 = y'(0) \\\\ a_{n+2} = \dfrac{a_n}{(n+2)(n+1)} & \text{for }n\ge0\end{cases}$

Since the n-th coefficient depends on the (n - 2)-th coefficient, we split n into two cases.

• If n is even, then n = 2k for some integer k ≥ 0. Then

$k=0 \implies n=0 \implies a_0 = a_0$

$k=1 \implies n=2 \implies a_2 = \dfrac{a_0}{2\cdot1}$

$k=2 \implies n=4 \implies a_4 = \dfrac{a_2}{4\cdot3} = \dfrac{a_0}{4\cdot3\cdot2\cdot1}$

$k=3 \implies n=6 \implies a_6 = \dfrac{a_4}{6\cdot5} = \dfrac{a_0}{6\cdot5\cdot4\cdot3\cdot2\cdot1}$

It should be easy enough to see that

$a_{n=2k} = \dfrac{a_0}{(2k)!}$

• If n is odd, then n = 2k + 1 for some k ≥ 0. Then

$k = 0 \implies n=1 \implies a_1 = a_1$

$k = 1 \implies n=3 \implies a_3 = \dfrac{a_1}{3\cdot2}$

$k = 2 \implies n=5 \implies a_5 = \dfrac{a_3}{5\cdot4} = \dfrac{a_1}{5\cdot4\cdot3\cdot2}$

$k=3 \implies n=7 \implies a_7=\dfrac{a_5}{7\cdot6} = \dfrac{a_1}{7\cdot6\cdot5\cdot4\cdot3\cdot2}$

so that

$a_{n=2k+1} = \dfrac{a_1}{(2k+1)!}$

So, the overall series solution is

$\displaystyle y(x) = \sum_{n=0}^\infty a_nx^n = \sum_{k=0}^\infty \left(a_{2k}x^{2k} + a_{2k+1}x^{2k+1}\right)$

$\boxed{\displaystyle y(x) = a_0 \sum_{k=0}^\infty \frac{x^{2k}}{(2k)!} + a_1 \sum_{k=0}^\infty \frac{x^{2k+1}}{(2k+1)!}}$

4 0

2 years ago

11. Shrimp are often found in tropical climates and can be raised on farms or caught in the wild.

seropon [69]

Answer:

3/83

Step-by-step explanation:

Probability: the ways to get the desired result / all of the possible results.

To solve, plug in the values they give.

There are 6 packages of wild-caught shrimp from Honduras. (The desired result)

Now, to find all of the possible results, add the total number of packages together.

27 + 40 + 52 + 13 + 6 + 28 = 166

6/166 = 3/83

Thus, the answer is a 3/83 chance of getting a package of wild-caught shrimp came from Honduras.

7 0

2 years ago

What is an explicit formula for the geometric sequence 64,16,4,1,... where the first term

olya-2409 [2.1K]

Answer:

A

Step-by-step explanation:

The explicit formula for a geometric sequence is

f(n) = f(1) $(r)^{n-1}$

where f(1) is the first term and r the common ratio

Here f(1) = 64 and r = $\frac{f(2)}{f(1)}$ = $\frac{16}{64}$ = $\frac{1}{4}$ , then

f(n) = 64 $(\frac{1}{4}) ^{n-1}$ → A

7 0

2 years ago